Commit e549ccfec53fc3e7aafd37eff590897bce340a6a
2004-10-29T22:07:18
added libtommath-0.32
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diff --git a/bn.ind b/bn.ind
index ae1dcde..e5f7d4a 100644
--- a/bn.ind
+++ b/bn.ind
@@ -1,82 +1,82 @@
\begin{theindex}
- \item mp\_add, \hyperpage{25}
- \item mp\_add\_d, \hyperpage{48}
- \item mp\_and, \hyperpage{25}
- \item mp\_clear, \hyperpage{7}
- \item mp\_clear\_multi, \hyperpage{8}
- \item mp\_cmp, \hyperpage{20}
- \item mp\_cmp\_d, \hyperpage{21}
- \item mp\_cmp\_mag, \hyperpage{19}
- \item mp\_div, \hyperpage{26}
- \item mp\_div\_2, \hyperpage{22}
- \item mp\_div\_2d, \hyperpage{24}
- \item mp\_div\_d, \hyperpage{48}
- \item mp\_dr\_reduce, \hyperpage{36}
- \item mp\_dr\_setup, \hyperpage{36}
- \item MP\_EQ, \hyperpage{18}
- \item mp\_error\_to\_string, \hyperpage{6}
- \item mp\_expt\_d, \hyperpage{39}
- \item mp\_exptmod, \hyperpage{39}
- \item mp\_exteuclid, \hyperpage{47}
- \item mp\_gcd, \hyperpage{47}
- \item mp\_get\_int, \hyperpage{16}
- \item mp\_grow, \hyperpage{12}
- \item MP\_GT, \hyperpage{18}
- \item mp\_init, \hyperpage{7}
- \item mp\_init\_copy, \hyperpage{9}
- \item mp\_init\_multi, \hyperpage{8}
- \item mp\_init\_set, \hyperpage{17}
- \item mp\_init\_set\_int, \hyperpage{17}
- \item mp\_init\_size, \hyperpage{10}
- \item mp\_int, \hyperpage{6}
- \item mp\_invmod, \hyperpage{48}
- \item mp\_jacobi, \hyperpage{48}
- \item mp\_lcm, \hyperpage{47}
- \item mp\_lshd, \hyperpage{24}
- \item MP\_LT, \hyperpage{18}
- \item MP\_MEM, \hyperpage{5}
- \item mp\_mod, \hyperpage{31}
- \item mp\_mod\_d, \hyperpage{48}
- \item mp\_montgomery\_calc\_normalization, \hyperpage{34}
- \item mp\_montgomery\_reduce, \hyperpage{33}
- \item mp\_montgomery\_setup, \hyperpage{33}
- \item mp\_mul, \hyperpage{27}
- \item mp\_mul\_2, \hyperpage{22}
- \item mp\_mul\_2d, \hyperpage{24}
- \item mp\_mul\_d, \hyperpage{48}
- \item mp\_n\_root, \hyperpage{40}
- \item mp\_neg, \hyperpage{25}
- \item MP\_NO, \hyperpage{5}
- \item MP\_OKAY, \hyperpage{5}
- \item mp\_or, \hyperpage{25}
- \item mp\_prime\_fermat, \hyperpage{41}
- \item mp\_prime\_is\_divisible, \hyperpage{41}
- \item mp\_prime\_is\_prime, \hyperpage{42}
- \item mp\_prime\_miller\_rabin, \hyperpage{41}
- \item mp\_prime\_next\_prime, \hyperpage{42}
- \item mp\_prime\_rabin\_miller\_trials, \hyperpage{42}
- \item mp\_prime\_random, \hyperpage{43}
- \item mp\_prime\_random\_ex, \hyperpage{43}
- \item mp\_radix\_size, \hyperpage{45}
- \item mp\_read\_radix, \hyperpage{45}
- \item mp\_read\_unsigned\_bin, \hyperpage{46}
- \item mp\_reduce, \hyperpage{32}
- \item mp\_reduce\_2k, \hyperpage{37}
- \item mp\_reduce\_2k\_setup, \hyperpage{37}
- \item mp\_reduce\_setup, \hyperpage{32}
- \item mp\_rshd, \hyperpage{24}
- \item mp\_set, \hyperpage{15}
- \item mp\_set\_int, \hyperpage{16}
- \item mp\_shrink, \hyperpage{11}
- \item mp\_sqr, \hyperpage{29}
- \item mp\_sub, \hyperpage{25}
- \item mp\_sub\_d, \hyperpage{48}
- \item mp\_to\_unsigned\_bin, \hyperpage{46}
- \item mp\_toradix, \hyperpage{45}
- \item mp\_unsigned\_bin\_size, \hyperpage{46}
- \item MP\_VAL, \hyperpage{5}
- \item mp\_xor, \hyperpage{25}
- \item MP\_YES, \hyperpage{5}
+ \item mp\_add, \hyperpage{29}
+ \item mp\_add\_d, \hyperpage{52}
+ \item mp\_and, \hyperpage{29}
+ \item mp\_clear, \hyperpage{11}
+ \item mp\_clear\_multi, \hyperpage{12}
+ \item mp\_cmp, \hyperpage{24}
+ \item mp\_cmp\_d, \hyperpage{25}
+ \item mp\_cmp\_mag, \hyperpage{23}
+ \item mp\_div, \hyperpage{30}
+ \item mp\_div\_2, \hyperpage{26}
+ \item mp\_div\_2d, \hyperpage{28}
+ \item mp\_div\_d, \hyperpage{52}
+ \item mp\_dr\_reduce, \hyperpage{40}
+ \item mp\_dr\_setup, \hyperpage{40}
+ \item MP\_EQ, \hyperpage{22}
+ \item mp\_error\_to\_string, \hyperpage{10}
+ \item mp\_expt\_d, \hyperpage{43}
+ \item mp\_exptmod, \hyperpage{43}
+ \item mp\_exteuclid, \hyperpage{51}
+ \item mp\_gcd, \hyperpage{51}
+ \item mp\_get\_int, \hyperpage{20}
+ \item mp\_grow, \hyperpage{16}
+ \item MP\_GT, \hyperpage{22}
+ \item mp\_init, \hyperpage{11}
+ \item mp\_init\_copy, \hyperpage{13}
+ \item mp\_init\_multi, \hyperpage{12}
+ \item mp\_init\_set, \hyperpage{21}
+ \item mp\_init\_set\_int, \hyperpage{21}
+ \item mp\_init\_size, \hyperpage{14}
+ \item mp\_int, \hyperpage{10}
+ \item mp\_invmod, \hyperpage{52}
+ \item mp\_jacobi, \hyperpage{52}
+ \item mp\_lcm, \hyperpage{51}
+ \item mp\_lshd, \hyperpage{28}
+ \item MP\_LT, \hyperpage{22}
+ \item MP\_MEM, \hyperpage{9}
+ \item mp\_mod, \hyperpage{35}
+ \item mp\_mod\_d, \hyperpage{52}
+ \item mp\_montgomery\_calc\_normalization, \hyperpage{38}
+ \item mp\_montgomery\_reduce, \hyperpage{37}
+ \item mp\_montgomery\_setup, \hyperpage{37}
+ \item mp\_mul, \hyperpage{31}
+ \item mp\_mul\_2, \hyperpage{26}
+ \item mp\_mul\_2d, \hyperpage{28}
+ \item mp\_mul\_d, \hyperpage{52}
+ \item mp\_n\_root, \hyperpage{44}
+ \item mp\_neg, \hyperpage{29}
+ \item MP\_NO, \hyperpage{9}
+ \item MP\_OKAY, \hyperpage{9}
+ \item mp\_or, \hyperpage{29}
+ \item mp\_prime\_fermat, \hyperpage{45}
+ \item mp\_prime\_is\_divisible, \hyperpage{45}
+ \item mp\_prime\_is\_prime, \hyperpage{46}
+ \item mp\_prime\_miller\_rabin, \hyperpage{45}
+ \item mp\_prime\_next\_prime, \hyperpage{46}
+ \item mp\_prime\_rabin\_miller\_trials, \hyperpage{46}
+ \item mp\_prime\_random, \hyperpage{47}
+ \item mp\_prime\_random\_ex, \hyperpage{47}
+ \item mp\_radix\_size, \hyperpage{49}
+ \item mp\_read\_radix, \hyperpage{49}
+ \item mp\_read\_unsigned\_bin, \hyperpage{50}
+ \item mp\_reduce, \hyperpage{36}
+ \item mp\_reduce\_2k, \hyperpage{41}
+ \item mp\_reduce\_2k\_setup, \hyperpage{41}
+ \item mp\_reduce\_setup, \hyperpage{36}
+ \item mp\_rshd, \hyperpage{28}
+ \item mp\_set, \hyperpage{19}
+ \item mp\_set\_int, \hyperpage{20}
+ \item mp\_shrink, \hyperpage{15}
+ \item mp\_sqr, \hyperpage{33}
+ \item mp\_sub, \hyperpage{29}
+ \item mp\_sub\_d, \hyperpage{52}
+ \item mp\_to\_unsigned\_bin, \hyperpage{50}
+ \item mp\_toradix, \hyperpage{49}
+ \item mp\_unsigned\_bin\_size, \hyperpage{50}
+ \item MP\_VAL, \hyperpage{9}
+ \item mp\_xor, \hyperpage{29}
+ \item MP\_YES, \hyperpage{9}
\end{theindex}
diff --git a/bn.pdf b/bn.pdf
index bf80e6a..fbd5b2a 100644
Binary files a/bn.pdf and b/bn.pdf differ
diff --git a/bn.tex b/bn.tex
index 3d1d26d..74a4f01 100644
--- a/bn.tex
+++ b/bn.tex
@@ -49,7 +49,7 @@
\begin{document}
\frontmatter
\pagestyle{empty}
-\title{LibTomMath User Manual \\ v0.31}
+\title{LibTomMath User Manual \\ v0.32}
\author{Tom St Denis \\ tomstdenis@iahu.ca}
\maketitle
This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been
@@ -96,27 +96,34 @@ LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well
also build in MSVC, Borland C out of the box. For any other ISO C compiler a makefile will have to be made by the end
developer.
-To build the library for GCC simply issue the
-
+\subsection{Static Libraries}
+To build as a static library for GCC issue the following
\begin{alltt}
make
\end{alltt}
-command. This will build the library and archive the object files in ``libtommath.a''. Now you simply link against that
-and include ``tommath.h'' within your programs.
-
-Alternatively to build with MSVC type
-
+command. This will build the library and archive the object files in ``libtommath.a''. Now you link against
+that and include ``tommath.h'' within your programs. Alternatively to build with MSVC issue the following
\begin{alltt}
nmake -f makefile.msvc
\end{alltt}
-This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC version 6.00
-with service pack 5.
+This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC
+version 6.00 with service pack 5.
+
+\subsection{Shared Libraries}
+To build as a shared library for GCC issue the following
+\begin{alltt}
+make -f makefile.shared
+\end{alltt}
+This requires the ``libtool'' package (common on most Linux/BSD systems). It will build LibTomMath as both shared
+and static then install (by default) into /usr/lib as well as install the header files in /usr/include. The shared
+library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''. Generally
+you use libtool to link your application against the shared object.
-There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires Cygwin
-to work with since it requires the auto-export/import functionality. The resulting DLL and imprt library ``libtomcrypt.dll.a''
-can be used to link LibTomMath dynamically to any Windows program using Cygwin.
+There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires
+Cygwin to work with since it requires the auto-export/import functionality. The resulting DLL and import library
+``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.
\subsection{Testing}
To build the library and the test harness type
@@ -144,6 +151,96 @@ This will output a row of numbers that are increasing. Each column is a differe
that is being performed. The numbers represent how many times the test was invoked. If an error is detected the program
will exit with a dump of the relevent numbers it was working with.
+\section{Build Configuration}
+LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.
+Each phase changes how the library is built and they are applied one after another respectively.
+
+To make the system more powerful you can tweak the build process. Classes are defined in the file
+``tommath\_superclass.h''. By default, the symbol ``LTM\_ALL'' shall be defined which simply
+instructs the system to build all of the functions. This is how LibTomMath used to be packaged. This will give you
+access to every function LibTomMath offers.
+
+However, there are cases where such a build is not optional. For instance, you want to perform RSA operations. You
+don't need the vast majority of the library to perform these operations. Aside from LTM\_ALL there is
+another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt. Additional
+classes can be defined base on the need of the user.
+
+\subsection{Build Depends}
+In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
+which further define symbols. All of the symbols (technically they're macros $\ldots$) represent a given C source
+file. For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''. When a define has been enabled the
+function in the respective file will be compiled and linked into the library. Accordingly when the define
+is absent the file will not be compiled and not contribute any size to the library.
+
+You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).
+This is to help resolve as many dependencies as possible. In the last pass the symbol LTM\_LAST will be defined.
+This is useful for ``trims''.
+
+\subsection{Build Tweaks}
+A tweak is an algorithm ``alternative''. For example, to provide tradeoffs (usually between size and space).
+They can be enabled at any pass of the configuration phase.
+
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Define} & \textbf{Purpose} \\
+\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\
+ & functional mp\_div() function \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+\subsection{Build Trims}
+A trim is a manner of removing functionality from a function that is not required. For instance, to perform
+RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.
+Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
+only if LTM\_LAST has been defined.
+
+\subsubsection{Moduli Related}
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Restriction} & \textbf{Undefine} \\
+\hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\
+ & BN\_MP\_REDUCE\_C \\
+ & BN\_MP\_REDUCE\_SETUP\_C \\
+ & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+ & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+\hline Exponentiation with random odd moduli & (The above plus the following) \\
+ & BN\_MP\_REDUCE\_2K\_C \\
+ & BN\_MP\_REDUCE\_2K\_SETUP\_C \\
+ & BN\_MP\_REDUCE\_IS\_2K\_C \\
+ & BN\_MP\_DR\_IS\_MODULUS\_C \\
+ & BN\_MP\_DR\_REDUCE\_C \\
+ & BN\_MP\_DR\_SETUP\_C \\
+\hline Modular inverse odd moduli only & BN\_MP\_INVMOD\_SLOW\_C \\
+\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+\subsubsection{Operand Size Related}
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Restriction} & \textbf{Undefine} \\
+\hline Moduli $\le 2560$ bits & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
+ & BN\_S\_MP\_MUL\_DIGS\_C \\
+ & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+ & BN\_S\_MP\_SQR\_C \\
+\hline Polynomial Schmolynomial & BN\_MP\_KARATSUBA\_MUL\_C \\
+ & BN\_MP\_KARATSUBA\_SQR\_C \\
+ & BN\_MP\_TOOM\_MUL\_C \\
+ & BN\_MP\_TOOM\_SQR\_C \\
+
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+
\section{Purpose of LibTomMath}
Unlike GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with
bleeding edge performance in mind. First and foremost LibTomMath was written to be entirely open. Not only is the
diff --git a/bn_error.c b/bn_error.c
index 7cac649..1546784 100644
--- a/bn_error.c
+++ b/bn_error.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static const struct {
int code;
@@ -39,3 +40,4 @@ char *mp_error_to_string(int code)
return "Invalid error code";
}
+#endif
diff --git a/bn_fast_mp_invmod.c b/bn_fast_mp_invmod.c
index c9a9459..492a3f1 100644
--- a/bn_fast_mp_invmod.c
+++ b/bn_fast_mp_invmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
- * Based on mp_invmod except this is optimized for the case where b is
+ * Based on slow invmod except this is optimized for the case where b is
* odd as per HAC Note 14.64 on pp. 610
*/
int
@@ -141,3 +142,4 @@ top:
__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
+#endif
diff --git a/bn_fast_mp_montgomery_reduce.c b/bn_fast_mp_montgomery_reduce.c
index c7a3413..7373ae6 100644
--- a/bn_fast_mp_montgomery_reduce.c
+++ b/bn_fast_mp_montgomery_reduce.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,11 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction
*
- * This is an optimized implementation of mp_montgomery_reduce
+ * This is an optimized implementation of montgomery_reduce
* which uses the comba method to quickly calculate the columns of the
* reduction.
*
@@ -165,3 +166,4 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_fast_s_mp_mul_digs.c b/bn_fast_s_mp_mul_digs.c
index d268df3..92b50bb 100644
--- a/bn_fast_s_mp_mul_digs.c
+++ b/bn_fast_s_mp_mul_digs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Fast (comba) multiplier
*
@@ -33,8 +34,9 @@
int
fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int olduse, res, pa, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
/* grow the destination as required */
if (c->alloc < digs) {
@@ -43,48 +45,39 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
}
}
- /* clear temp buf (the columns) */
- memset (W, 0, sizeof (mp_word) * digs);
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
- /* calculate the columns */
- pa = a->used;
- for (ix = 0; ix < pa; ix++) {
- /* this multiplier has been modified to allow you to
- * control how many digits of output are produced.
- * So at most we want to make upto "digs" digits of output.
- *
- * this adds products to distinct columns (at ix+iy) of W
- * note that each step through the loop is not dependent on
- * the previous which means the compiler can easily unroll
- * the loop without scheduling problems
- */
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy, pb;
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix <= pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
- /* alias for the the word on the left e.g. A[ix] * A[iy] */
- tmpx = a->dp[ix];
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* alias for the right side */
- tmpy = b->dp;
-
- /* alias for the columns, each step through the loop adds a new
- term to each column
- */
- _W = W + ix;
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* the number of digits is limited by their placement. E.g.
- we avoid multiplying digits that will end up above the # of
- digits of precision requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- pb = MIN (b->used, digs - ix);
+ iy = MIN(a->used-tx, ty+1);
- for (iy = 0; iy < pb; iy++) {
- *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
@@ -93,32 +86,11 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
register mp_digit *tmpc;
-
- /* At this point W[] contains the sums of each column. To get the
- * correct result we must take the extra bits from each column and
- * carry them down
- *
- * Note that while this adds extra code to the multiplier it
- * saves time since the carry propagation is removed from the
- * above nested loop.This has the effect of reducing the work
- * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
- * cost of the shifting. On very small numbers this is slower
- * but on most cryptographic size numbers it is faster.
- *
- * In this particular implementation we feed the carries from
- * behind which means when the loop terminates we still have one
- * last digit to copy
- */
tmpc = c->dp;
- for (ix = 1; ix < digs; ix++) {
- /* forward the carry from the previous temp */
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-
+ for (ix = 0; ix < digs; ix++) {
/* now extract the previous digit [below the carry] */
- *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ *tmpc++ = W[ix];
}
- /* fetch the last digit */
- *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
@@ -128,3 +100,4 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_fast_s_mp_mul_high_digs.c b/bn_fast_s_mp_mul_high_digs.c
index 779aa14..9e0cf55 100644
--- a/bn_fast_s_mp_mul_high_digs.c
+++ b/bn_fast_s_mp_mul_high_digs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,10 +14,9 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
- #include <tommath.h>
-/* this is a modified version of fast_s_mp_mul_digs that only produces
- * output digits *above* digs. See the comments for fast_s_mp_mul_digs
+/* this is a modified version of fast_s_mul_digs that only produces
+ * output digits *above* digs. See the comments for fast_s_mul_digs
* to see how it works.
*
* This is used in the Barrett reduction since for one of the multiplications
@@ -26,73 +27,69 @@
int
fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int oldused, newused, res, pa, pb, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ mp_word _W;
- /* calculate size of product and allocate more space if required */
- newused = a->used + b->used + 1;
- if (c->alloc < newused) {
- if ((res = mp_grow (c, newused)) != MP_OKAY) {
+ /* grow the destination as required */
+ pa = a->used + b->used;
+ if (c->alloc < pa) {
+ if ((res = mp_grow (c, pa)) != MP_OKAY) {
return res;
}
}
- /* like the other comba method we compute the columns first */
- pa = a->used;
- pb = b->used;
- memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word));
- for (ix = 0; ix < pa; ix++) {
- {
- register mp_digit tmpx, *tmpy;
- register int iy;
- register mp_word *_W;
+ /* number of output digits to produce */
+ pa = a->used + b->used;
+ _W = 0;
+ for (ix = digs; ix <= pa; ix++) {
+ int tx, ty, iy;
+ mp_digit *tmpx, *tmpy;
- /* work todo, that is we only calculate digits that are at "digs" or above */
- iy = digs - ix;
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* copy of word on the left of A[ix] * B[iy] */
- tmpx = a->dp[ix];
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* alias for right side */
- tmpy = b->dp + iy;
-
- /* alias for the columns of output. Offset to be equal to or above the
- * smallest digit place requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- _W = W + digs;
-
- /* skip cases below zero where ix > digs */
- if (iy < 0) {
- iy = abs(iy);
- tmpy += iy;
- _W += iy;
- iy = 0;
- }
+ iy = MIN(a->used-tx, ty+1);
- /* compute column products for digits above the minimum */
- for (; iy < pb; iy++) {
- *_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
- oldused = c->used;
- c->used = newused;
+ olduse = c->used;
+ c->used = pa;
- /* now convert the array W downto what we need
- *
- * See comments in bn_fast_s_mp_mul_digs.c
- */
- for (ix = digs + 1; ix < newused; ix++) {
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
- c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
- }
- c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK));
+ {
+ register mp_digit *tmpc;
+
+ tmpc = c->dp + digs;
+ for (ix = digs; ix <= pa; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
- for (; ix < oldused; ix++) {
- c->dp[ix] = 0;
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
}
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_fast_s_mp_sqr.c b/bn_fast_s_mp_sqr.c
index f62ae54..9f6962d 100644
--- a/bn_fast_s_mp_sqr.c
+++ b/bn_fast_s_mp_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* fast squaring
*
@@ -31,109 +32,98 @@
* Based on Algorithm 14.16 on pp.597 of HAC.
*
*/
+/* the jist of squaring...
+
+you do like mult except the offset of the tmpx [one that starts closer to zero]
+can't equal the offset of tmpy. So basically you set up iy like before then you min it with
+(ty-tx) so that it never happens. You double all those you add in the inner loop
+
+After that loop you do the squares and add them in.
+
+Remove W2 and don't memset W
+
+*/
+
int fast_s_mp_sqr (mp_int * a, mp_int * b)
{
- int olduse, newused, res, ix, pa;
- mp_word W2[MP_WARRAY], W[MP_WARRAY];
-
- /* calculate size of product and allocate as required */
- pa = a->used;
- newused = pa + pa + 1;
- if (b->alloc < newused) {
- if ((res = mp_grow (b, newused)) != MP_OKAY) {
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
+
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
return res;
}
}
- /* zero temp buffer (columns)
- * Note that there are two buffers. Since squaring requires
- * a outer and inner product and the inner product requires
- * computing a product and doubling it (a relatively expensive
- * op to perform n**2 times if you don't have to) the inner and
- * outer products are computed in different buffers. This way
- * the inner product can be doubled using n doublings instead of
- * n**2
- */
- memset (W, 0, newused * sizeof (mp_word));
- memset (W2, 0, newused * sizeof (mp_word));
-
- /* This computes the inner product. To simplify the inner N**2 loop
- * the multiplication by two is done afterwards in the N loop.
- */
- for (ix = 0; ix < pa; ix++) {
- /* compute the outer product
- *
- * Note that every outer product is computed
- * for a particular column only once which means that
- * there is no need todo a double precision addition
- * into the W2[] array.
- */
- W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
-
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy;
-
- /* copy of left side */
- tmpx = a->dp[ix];
-
- /* alias for right side */
- tmpy = a->dp + (ix + 1);
-
- /* the column to store the result in */
- _W = W + (ix + ix + 1);
-
- /* inner products */
- for (iy = ix + 1; iy < pa; iy++) {
- *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix <= pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
+
+ /* clear counter */
+ _W = 0;
+
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
+
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+ }
+
+ /* store it */
+ W[ix] = _W;
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
olduse = b->used;
- b->used = newused;
-
- /* now compute digits
- *
- * We have to double the inner product sums, add in the
- * outer product sums, propagate carries and convert
- * to single precision.
- */
- {
- register mp_digit *tmpb;
-
- /* double first value, since the inner products are
- * half of what they should be
- */
- W[0] += W[0] + W2[0];
+ b->used = a->used+a->used;
+ {
+ mp_digit *tmpb;
tmpb = b->dp;
- for (ix = 1; ix < newused; ix++) {
- /* double/add next digit */
- W[ix] += W[ix] + W2[ix];
-
- /* propagate carry forwards [from the previous digit] */
- W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-
- /* store the current digit now that the carry isn't
- * needed
- */
- *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
}
- /* set the last value. Note even if the carry is zero
- * this is required since the next step will not zero
- * it if b originally had a value at b->dp[2*a.used]
- */
- *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
- /* clear high digits of b if there were any originally */
+ /* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
-
mp_clamp (b);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_2expt.c b/bn_mp_2expt.c
index 502e85b..45a6818 100644
--- a/bn_mp_2expt.c
+++ b/bn_mp_2expt.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes a = 2**b
*
@@ -40,3 +41,4 @@ mp_2expt (mp_int * a, int b)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_abs.c b/bn_mp_abs.c
index a5e9ab0..34f810f 100644
--- a/bn_mp_abs.c
+++ b/bn_mp_abs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = |a|
*
@@ -35,3 +36,4 @@ mp_abs (mp_int * a, mp_int * b)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_add.c b/bn_mp_add.c
index f625195..554b7f7 100644
--- a/bn_mp_add.c
+++ b/bn_mp_add.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
@@ -45,3 +46,4 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
return res;
}
+#endif
diff --git a/bn_mp_add_d.c b/bn_mp_add_d.c
index edc93c1..bdd0280 100644
--- a/bn_mp_add_d.c
+++ b/bn_mp_add_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit addition */
int
@@ -101,3 +102,4 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_addmod.c b/bn_mp_addmod.c
index 691dc50..13eb33f 100644
--- a/bn_mp_addmod.c
+++ b/bn_mp_addmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a + b (mod c) */
int
@@ -33,3 +34,4 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_and.c b/bn_mp_and.c
index 9abb618..61dc386 100644
--- a/bn_mp_and.c
+++ b/bn_mp_and.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* AND two ints together */
int
@@ -49,3 +50,4 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_clamp.c b/bn_mp_clamp.c
index c6285ce..c172611 100644
--- a/bn_mp_clamp.c
+++ b/bn_mp_clamp.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* trim unused digits
*
@@ -36,3 +37,4 @@ mp_clamp (mp_int * a)
a->sign = MP_ZPOS;
}
}
+#endif
diff --git a/bn_mp_clear.c b/bn_mp_clear.c
index cd439df..5342648 100644
--- a/bn_mp_clear.c
+++ b/bn_mp_clear.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* clear one (frees) */
void
@@ -36,3 +37,4 @@ mp_clear (mp_int * a)
a->sign = MP_ZPOS;
}
}
+#endif
diff --git a/bn_mp_clear_multi.c b/bn_mp_clear_multi.c
index d262b2f..24cbe73 100644
--- a/bn_mp_clear_multi.c
+++ b/bn_mp_clear_multi.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
@@ -26,3 +27,4 @@ void mp_clear_multi(mp_int *mp, ...)
}
va_end(args);
}
+#endif
diff --git a/bn_mp_cmp.c b/bn_mp_cmp.c
index ed27d21..583b5f8 100644
--- a/bn_mp_cmp.c
+++ b/bn_mp_cmp.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare two ints (signed)*/
int
@@ -35,3 +36,4 @@ mp_cmp (mp_int * a, mp_int * b)
return mp_cmp_mag(a, b);
}
}
+#endif
diff --git a/bn_mp_cmp_d.c b/bn_mp_cmp_d.c
index 6baa172..882b1c9 100644
--- a/bn_mp_cmp_d.c
+++ b/bn_mp_cmp_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare a digit */
int mp_cmp_d(mp_int * a, mp_digit b)
@@ -36,3 +37,4 @@ int mp_cmp_d(mp_int * a, mp_digit b)
return MP_EQ;
}
}
+#endif
diff --git a/bn_mp_cmp_mag.c b/bn_mp_cmp_mag.c
index b50f769..a0f351c 100644
--- a/bn_mp_cmp_mag.c
+++ b/bn_mp_cmp_mag.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (mp_int * a, mp_int * b)
@@ -47,3 +48,4 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
}
return MP_EQ;
}
+#endif
diff --git a/bn_mp_cnt_lsb.c b/bn_mp_cnt_lsb.c
index 07cb709..571f03f 100644
--- a/bn_mp_cnt_lsb.c
+++ b/bn_mp_cnt_lsb.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static const int lnz[16] = {
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
@@ -45,3 +46,4 @@ int mp_cnt_lsb(mp_int *a)
return x;
}
+#endif
diff --git a/bn_mp_copy.c b/bn_mp_copy.c
index 1c45f3e..183ec9b 100644
--- a/bn_mp_copy.c
+++ b/bn_mp_copy.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* copy, b = a */
int
@@ -60,3 +61,4 @@ mp_copy (mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_count_bits.c b/bn_mp_count_bits.c
index 33b971b..f3f85ac 100644
--- a/bn_mp_count_bits.c
+++ b/bn_mp_count_bits.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns the number of bits in an int */
int
@@ -37,3 +38,4 @@ mp_count_bits (mp_int * a)
}
return r;
}
+#endif
diff --git a/bn_mp_div.c b/bn_mp_div.c
index ea2d514..39d921a 100644
--- a/bn_mp_div.c
+++ b/bn_mp_div.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,78 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_copy(a, &ta)) != MP_OKAY) ||
+ ((res = mp_copy(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto __ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto __ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto __ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = n;
+ }
+__ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
/* integer signed division.
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
@@ -209,3 +282,7 @@ __T1:mp_clear (&t1);
__Q:mp_clear (&q);
return res;
}
+
+#endif
+
+#endif
diff --git a/bn_mp_div_2.c b/bn_mp_div_2.c
index ebad7ae..5777997 100644
--- a/bn_mp_div_2.c
+++ b/bn_mp_div_2.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
@@ -60,3 +61,4 @@ int mp_div_2(mp_int * a, mp_int * b)
mp_clamp (b);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_div_2d.c b/bn_mp_div_2d.c
index 75f090c..cf103f2 100644
--- a/bn_mp_div_2d.c
+++ b/bn_mp_div_2d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
@@ -89,3 +90,4 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_div_3.c b/bn_mp_div_3.c
index 3bc2bd2..7cbafc1 100644
--- a/bn_mp_div_3.c
+++ b/bn_mp_div_3.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* divide by three (based on routine from MPI and the GMP manual) */
int
@@ -71,3 +72,4 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
return res;
}
+#endif
diff --git a/bn_mp_div_d.c b/bn_mp_div_d.c
index f8caf83..9b58aa6 100644
--- a/bn_mp_div_d.c
+++ b/bn_mp_div_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static int s_is_power_of_two(mp_digit b, int *p)
{
@@ -54,7 +55,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
/* power of two ? */
if (s_is_power_of_two(b, &ix) == 1) {
if (d != NULL) {
- *d = a->dp[0] & ((1<<ix) - 1);
+ *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
}
if (c != NULL) {
return mp_div_2d(a, ix, c, NULL);
@@ -62,10 +63,12 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return MP_OKAY;
}
+#ifdef BN_MP_DIV_3_C
/* three? */
if (b == 3) {
return mp_div_3(a, c, d);
}
+#endif
/* no easy answer [c'est la vie]. Just division */
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
@@ -100,3 +103,4 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return res;
}
+#endif
diff --git a/bn_mp_dr_is_modulus.c b/bn_mp_dr_is_modulus.c
index 0206e0e..5ef78a3 100644
--- a/bn_mp_dr_is_modulus.c
+++ b/bn_mp_dr_is_modulus.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
@@ -35,3 +36,4 @@ int mp_dr_is_modulus(mp_int *a)
return 1;
}
+#endif
diff --git a/bn_mp_dr_reduce.c b/bn_mp_dr_reduce.c
index bad240a..308b80a 100644
--- a/bn_mp_dr_reduce.c
+++ b/bn_mp_dr_reduce.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
*
@@ -86,3 +87,4 @@ top:
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_dr_setup.c b/bn_mp_dr_setup.c
index f269436..029d310 100644
--- a/bn_mp_dr_setup.c
+++ b/bn_mp_dr_setup.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
@@ -24,3 +25,4 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
((mp_word)a->dp[0]));
}
+#endif
diff --git a/bn_mp_exch.c b/bn_mp_exch.c
index b0f1cd0..0ef485a 100644
--- a/bn_mp_exch.c
+++ b/bn_mp_exch.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* swap the elements of two integers, for cases where you can't simply swap the
* mp_int pointers around
@@ -26,3 +27,4 @@ mp_exch (mp_int * a, mp_int * b)
*a = *b;
*b = t;
}
+#endif
diff --git a/bn_mp_expt_d.c b/bn_mp_expt_d.c
index 6ec12a4..fdb8bd9 100644
--- a/bn_mp_expt_d.c
+++ b/bn_mp_expt_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calculate c = a**b using a square-multiply algorithm */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
@@ -49,3 +50,4 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
mp_clear (&g);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_exptmod.c b/bn_mp_exptmod.c
index 21d0cc5..da88fec 100644
--- a/bn_mp_exptmod.c
+++ b/bn_mp_exptmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this is a shell function that calls either the normal or Montgomery
@@ -31,6 +32,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
/* if exponent X is negative we have to recurse */
if (X->sign == MP_NEG) {
+#ifdef BN_MP_INVMOD_C
mp_int tmpG, tmpX;
int err;
@@ -57,22 +59,42 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
err = mp_exptmod(&tmpG, &tmpX, P, Y);
mp_clear_multi(&tmpG, &tmpX, NULL);
return err;
+#else
+ /* no invmod */
+ return MP_VAL
+#endif
}
+#ifdef BN_MP_DR_IS_MODULUS_C
/* is it a DR modulus? */
dr = mp_dr_is_modulus(P);
+#else
+ dr = 0;
+#endif
+#ifdef BN_MP_REDUCE_IS_2K_C
/* if not, is it a uDR modulus? */
if (dr == 0) {
dr = mp_reduce_is_2k(P) << 1;
}
+#endif
/* if the modulus is odd or dr != 0 use the fast method */
+#ifdef BN_MP_EXPTMOD_FAST_C
if (mp_isodd (P) == 1 || dr != 0) {
return mp_exptmod_fast (G, X, P, Y, dr);
} else {
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
/* otherwise use the generic Barrett reduction technique */
return s_mp_exptmod (G, X, P, Y);
+#else
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
}
+#endif
}
+#endif
diff --git a/bn_mp_exptmod_fast.c b/bn_mp_exptmod_fast.c
index c281733..4351e60 100644
--- a/bn_mp_exptmod_fast.c
+++ b/bn_mp_exptmod_fast.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
*
@@ -84,29 +85,52 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* determine and setup reduction code */
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* now setup montgomery */
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
goto __M;
}
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
if (((P->used * 2 + 1) < MP_WARRAY) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
- } else {
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
}
} else if (redmode == 1) {
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
/* setup DR reduction for moduli of the form B**k - b */
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
} else {
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
/* setup DR reduction for moduli of the form 2**k - b */
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
goto __M;
}
redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
}
/* setup result */
@@ -116,16 +140,21 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* create M table
*
- * The M table contains powers of the input base, e.g. M[x] = G^x mod P
+
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
goto __RES;
}
+#else
+ err = MP_VAL;
+ goto __RES;
+#endif
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
@@ -269,7 +298,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
* to reduce one more time to cancel out the factor
* of R.
*/
- if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
@@ -285,3 +314,5 @@ __M:
}
return err;
}
+#endif
+
diff --git a/bn_mp_exteuclid.c b/bn_mp_exteuclid.c
index cb3f787..545450b 100644
--- a/bn_mp_exteuclid.c
+++ b/bn_mp_exteuclid.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Extended euclidean algorithm of (a, b) produces
a*u1 + b*u2 = u3
@@ -67,3 +68,4 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
return err;
}
+#endif
diff --git a/bn_mp_fread.c b/bn_mp_fread.c
index ef665e5..293df3f 100644
--- a/bn_mp_fread.c
+++ b/bn_mp_fread.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
@@ -59,3 +60,4 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_fwrite.c b/bn_mp_fwrite.c
index 2853ec1..8fa3129 100644
--- a/bn_mp_fwrite.c
+++ b/bn_mp_fwrite.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
@@ -44,3 +45,4 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_gcd.c b/bn_mp_gcd.c
index 78ddda2..1cd21fc 100644
--- a/bn_mp_gcd.c
+++ b/bn_mp_gcd.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
@@ -105,3 +106,4 @@ __V:mp_clear (&u);
__U:mp_clear (&v);
return res;
}
+#endif
diff --git a/bn_mp_get_int.c b/bn_mp_get_int.c
index 41df6e1..034467b 100644
--- a/bn_mp_get_int.c
+++ b/bn_mp_get_int.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
@@ -37,3 +38,4 @@ unsigned long mp_get_int(mp_int * a)
/* force result to 32-bits always so it is consistent on non 32-bit platforms */
return res & 0xFFFFFFFFUL;
}
+#endif
diff --git a/bn_mp_grow.c b/bn_mp_grow.c
index 43a3028..12a78a8 100644
--- a/bn_mp_grow.c
+++ b/bn_mp_grow.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* grow as required */
int mp_grow (mp_int * a, int size)
@@ -49,3 +50,4 @@ int mp_grow (mp_int * a, int size)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_init.c b/bn_mp_init.c
index cac782a..9d70554 100644
--- a/bn_mp_init.c
+++ b/bn_mp_init.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* init a new mp_int */
int mp_init (mp_int * a)
@@ -38,3 +39,4 @@ int mp_init (mp_int * a)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_init_copy.c b/bn_mp_init_copy.c
index 1c5da4d..b1b0fa2 100644
--- a/bn_mp_init_copy.c
+++ b/bn_mp_init_copy.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
@@ -24,3 +25,4 @@ int mp_init_copy (mp_int * a, mp_int * b)
}
return mp_copy (b, a);
}
+#endif
diff --git a/bn_mp_init_multi.c b/bn_mp_init_multi.c
index 99ce331..8cb123a 100644
--- a/bn_mp_init_multi.c
+++ b/bn_mp_init_multi.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#include <stdarg.h>
int mp_init_multi(mp_int *mp, ...)
@@ -51,3 +52,4 @@ int mp_init_multi(mp_int *mp, ...)
return res; /* Assumed ok, if error flagged above. */
}
+#endif
diff --git a/bn_mp_init_set.c b/bn_mp_init_set.c
index c8d8bf8..0251e61 100644
--- a/bn_mp_init_set.c
+++ b/bn_mp_init_set.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
@@ -24,3 +25,4 @@ int mp_init_set (mp_int * a, mp_digit b)
mp_set(a, b);
return err;
}
+#endif
diff --git a/bn_mp_init_set_int.c b/bn_mp_init_set_int.c
index 2d6628d..f59fd19 100644
--- a/bn_mp_init_set_int.c
+++ b/bn_mp_init_set_int.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
@@ -23,3 +24,4 @@ int mp_init_set_int (mp_int * a, unsigned long b)
}
return mp_set_int(a, b);
}
+#endif
diff --git a/bn_mp_init_size.c b/bn_mp_init_size.c
index c763ee0..845ce2c 100644
--- a/bn_mp_init_size.c
+++ b/bn_mp_init_size.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,22 +14,31 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
+ int x;
+
/* pad size so there are always extra digits */
size += (MP_PREC * 2) - (size % MP_PREC);
/* alloc mem */
- a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size);
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
if (a->dp == NULL) {
return MP_MEM;
}
+
+ /* set the members */
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
+
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_invmod.c b/bn_mp_invmod.c
index 4ac5b2f..46118ad 100644
--- a/bn_mp_invmod.c
+++ b/bn_mp_invmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,163 +14,26 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
- mp_int x, y, u, v, A, B, C, D;
- int res;
-
/* b cannot be negative */
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
return MP_VAL;
}
+#ifdef BN_FAST_MP_INVMOD_C
/* if the modulus is odd we can use a faster routine instead */
if (mp_isodd (b) == 1) {
return fast_mp_invmod (a, b, c);
}
-
- /* init temps */
- if ((res = mp_init_multi(&x, &y, &u, &v,
- &A, &B, &C, &D, NULL)) != MP_OKAY) {
- return res;
- }
-
- /* x = a, y = b */
- if ((res = mp_copy (a, &x)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_copy (b, &y)) != MP_OKAY) {
- goto __ERR;
- }
+#endif
- /* 2. [modified] if x,y are both even then return an error! */
- if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
- res = MP_VAL;
- goto __ERR;
- }
-
- /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
- if ((res = mp_copy (&x, &u)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_copy (&y, &v)) != MP_OKAY) {
- goto __ERR;
- }
- mp_set (&A, 1);
- mp_set (&D, 1);
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
-top:
- /* 4. while u is even do */
- while (mp_iseven (&u) == 1) {
- /* 4.1 u = u/2 */
- if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
- goto __ERR;
- }
- /* 4.2 if A or B is odd then */
- if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
- /* A = (A+y)/2, B = (B-x)/2 */
- if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
- goto __ERR;
- }
- }
- /* A = A/2, B = B/2 */
- if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* 5. while v is even do */
- while (mp_iseven (&v) == 1) {
- /* 5.1 v = v/2 */
- if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
- goto __ERR;
- }
- /* 5.2 if C or D is odd then */
- if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
- /* C = (C+y)/2, D = (D-x)/2 */
- if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
- goto __ERR;
- }
- }
- /* C = C/2, D = D/2 */
- if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* 6. if u >= v then */
- if (mp_cmp (&u, &v) != MP_LT) {
- /* u = u - v, A = A - C, B = B - D */
- if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
- goto __ERR;
- }
- } else {
- /* v - v - u, C = C - A, D = D - B */
- if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* if not zero goto step 4 */
- if (mp_iszero (&u) == 0)
- goto top;
-
- /* now a = C, b = D, gcd == g*v */
-
- /* if v != 1 then there is no inverse */
- if (mp_cmp_d (&v, 1) != MP_EQ) {
- res = MP_VAL;
- goto __ERR;
- }
-
- /* if its too low */
- while (mp_cmp_d(&C, 0) == MP_LT) {
- if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* too big */
- while (mp_cmp_mag(&C, b) != MP_LT) {
- if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* C is now the inverse */
- mp_exch (&C, c);
- res = MP_OKAY;
-__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
- return res;
+ return MP_VAL;
}
+#endif
diff --git a/bn_mp_invmod_slow.c b/bn_mp_invmod_slow.c
new file mode 100644
index 0000000..8ecb009
--- /dev/null
+++ b/bn_mp_invmod_slow.c
@@ -0,0 +1,171 @@
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_SLOW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, A, B, C, D;
+ int res;
+
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v,
+ &A, &B, &C, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x = a, y = b */
+ if ((res = mp_copy (a, &x)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_copy (b, &y)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ /* 2. [modified] if x,y are both even then return an error! */
+ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
+ res = MP_VAL;
+ goto __ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto __ERR;
+ }
+ mp_set (&A, 1);
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto __ERR;
+ }
+ /* 4.2 if A or B is odd then */
+ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
+ /* A = (A+y)/2, B = (B-x)/2 */
+ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+ /* A = A/2, B = B/2 */
+ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto __ERR;
+ }
+ /* 5.2 if C or D is odd then */
+ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
+ /* C = (C+y)/2, D = (D-x)/2 */
+ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+ /* C = C/2, D = D/2 */
+ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, A = A - C, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto __ERR;
+ }
+ } else {
+ /* v - v - u, C = C - A, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0)
+ goto top;
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto __ERR;
+ }
+
+ /* if its too low */
+ while (mp_cmp_d(&C, 0) == MP_LT) {
+ if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* too big */
+ while (mp_cmp_mag(&C, b) != MP_LT) {
+ if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* C is now the inverse */
+ mp_exch (&C, c);
+ res = MP_OKAY;
+__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+ return res;
+}
+#endif
diff --git a/bn_mp_is_square.c b/bn_mp_is_square.c
index 1f01bca..969d237 100644
--- a/bn_mp_is_square.c
+++ b/bn_mp_is_square.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
@@ -69,7 +70,7 @@ int mp_is_square(mp_int *arg,int *ret)
return MP_OKAY;
}
- /* product of primes less than 2^31 */
+
if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
return res;
}
@@ -101,3 +102,4 @@ int mp_is_square(mp_int *arg,int *ret)
ERR:mp_clear(&t);
return res;
}
+#endif
diff --git a/bn_mp_jacobi.c b/bn_mp_jacobi.c
index 634370f..1c69cfd 100644
--- a/bn_mp_jacobi.c
+++ b/bn_mp_jacobi.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
@@ -97,3 +98,4 @@ __P1:mp_clear (&p1);
__A1:mp_clear (&a1);
return res;
}
+#endif
diff --git a/bn_mp_karatsuba_mul.c b/bn_mp_karatsuba_mul.c
index 105590e..daa78c7 100644
--- a/bn_mp_karatsuba_mul.c
+++ b/bn_mp_karatsuba_mul.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
@@ -159,3 +160,4 @@ X0:mp_clear (&x0);
ERR:
return err;
}
+#endif
diff --git a/bn_mp_karatsuba_sqr.c b/bn_mp_karatsuba_sqr.c
index c335613..315ceab 100644
--- a/bn_mp_karatsuba_sqr.c
+++ b/bn_mp_karatsuba_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Karatsuba squaring, computes b = a*a using three
* half size squarings
*
- * See comments of mp_karatsuba_mul for details. It
+ * See comments of karatsuba_mul for details. It
* is essentially the same algorithm but merely
* tuned to perform recursive squarings.
*/
@@ -113,3 +114,4 @@ X0:mp_clear (&x0);
ERR:
return err;
}
+#endif
diff --git a/bn_mp_lcm.c b/bn_mp_lcm.c
index 4aa5749..340d757 100644
--- a/bn_mp_lcm.c
+++ b/bn_mp_lcm.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
@@ -52,3 +53,4 @@ __T:
mp_clear_multi (&t1, &t2, NULL);
return res;
}
+#endif
diff --git a/bn_mp_lshd.c b/bn_mp_lshd.c
index f170237..398b648 100644
--- a/bn_mp_lshd.c
+++ b/bn_mp_lshd.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
@@ -59,3 +60,4 @@ int mp_lshd (mp_int * a, int b)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mod.c b/bn_mp_mod.c
index ad963a9..75779bb 100644
--- a/bn_mp_mod.c
+++ b/bn_mp_mod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a mod b, 0 <= c < b */
int
@@ -40,3 +41,4 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_mod_2d.c b/bn_mp_mod_2d.c
index 89e9081..f81a0d4 100644
--- a/bn_mp_mod_2d.c
+++ b/bn_mp_mod_2d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calc a value mod 2**b */
int
@@ -47,3 +48,4 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mod_d.c b/bn_mp_mod_d.c
index c5dbe46..8a2ad24 100644
--- a/bn_mp_mod_d.c
+++ b/bn_mp_mod_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,10 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
return mp_div_d(a, b, NULL, c);
}
+#endif
diff --git a/bn_mp_montgomery_calc_normalization.c b/bn_mp_montgomery_calc_normalization.c
index a38555c..0a760cf 100644
--- a/bn_mp_montgomery_calc_normalization.c
+++ b/bn_mp_montgomery_calc_normalization.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,31 +14,31 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* calculates a = B^n mod b for Montgomery reduction
- * Where B is the base [e.g. 2^DIGIT_BIT].
- * B^n mod b is computed by first computing
- * A = B^(n-1) which doesn't require a reduction but a simple OR.
- * then C = A * B = B^n is computed by performing upto DIGIT_BIT
+/*
* shifts with subtractions when the result is greater than b.
*
* The method is slightly modified to shift B unconditionally upto just under
* the leading bit of b. This saves alot of multiple precision shifting.
*/
-int
-mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
{
int x, bits, res;
/* how many bits of last digit does b use */
bits = mp_count_bits (b) % DIGIT_BIT;
- /* compute A = B^(n-1) * 2^(bits-1) */
- if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
- return res;
+
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
}
+
/* now compute C = A * B mod b */
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
@@ -51,3 +53,4 @@ mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_montgomery_reduce.c b/bn_mp_montgomery_reduce.c
index 52b98cd..3095fa7 100644
--- a/bn_mp_montgomery_reduce.c
+++ b/bn_mp_montgomery_reduce.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
@@ -23,7 +24,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* can the fast reduction [comba] method be used?
*
- * Note that unlike in mp_mul you're safely allowed *less*
+ * Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
@@ -46,7 +47,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* mu = ai * rho mod b
*
* The value of rho must be precalculated via
- * bn_mp_montgomery_setup() such that
+ * montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
@@ -110,3 +111,4 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_montgomery_setup.c b/bn_mp_montgomery_setup.c
index 36253af..9dfc087 100644
--- a/bn_mp_montgomery_setup.c
+++ b/bn_mp_montgomery_setup.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* setups the montgomery reduction stuff */
int
@@ -47,7 +48,8 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
#endif
/* rho = -1/m mod b */
- *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
+ *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mul.c b/bn_mp_mul.c
index 8e11f9f..f9cfa09 100644
--- a/bn_mp_mul.c
+++ b/bn_mp_mul.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
@@ -21,12 +22,18 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
/* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
res = mp_toom_mul(a, b, c);
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
/* use Karatsuba? */
- } else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
res = mp_karatsuba_mul (a, b, c);
- } else {
+ } else
+#endif
+ {
/* can we use the fast multiplier?
*
* The fast multiplier can be used if the output will
@@ -35,14 +42,21 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
*/
int digs = a->used + b->used + 1;
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
if ((digs < MP_WARRAY) &&
MIN(a->used, b->used) <=
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
res = fast_s_mp_mul_digs (a, b, c, digs);
- } else {
- res = s_mp_mul (a, b, c);
- }
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+ res = MP_VAL;
+#endif
+
}
c->sign = (c->used > 0) ? neg : MP_ZPOS;
return res;
}
+#endif
diff --git a/bn_mp_mul_2.c b/bn_mp_mul_2.c
index f947d75..6936681 100644
--- a/bn_mp_mul_2.c
+++ b/bn_mp_mul_2.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
@@ -74,3 +75,4 @@ int mp_mul_2(mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mul_2d.c b/bn_mp_mul_2d.c
index f5fa1d0..04cb8dd 100644
--- a/bn_mp_mul_2d.c
+++ b/bn_mp_mul_2d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left by a certain bit count */
int mp_mul_2d (mp_int * a, int b, mp_int * c)
@@ -77,3 +78,4 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mul_d.c b/bn_mp_mul_d.c
index 658fe01..f936361 100644
--- a/bn_mp_mul_d.c
+++ b/bn_mp_mul_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiply by a digit */
int
@@ -70,3 +71,4 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mulmod.c b/bn_mp_mulmod.c
index 77f8459..d34e90a 100644
--- a/bn_mp_mulmod.c
+++ b/bn_mp_mulmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a * b (mod c) */
int
@@ -33,3 +34,4 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_n_root.c b/bn_mp_n_root.c
index a79af17..9489903 100644
--- a/bn_mp_n_root.c
+++ b/bn_mp_n_root.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* find the n'th root of an integer
*
@@ -124,3 +125,4 @@ __T2:mp_clear (&t2);
__T1:mp_clear (&t1);
return res;
}
+#endif
diff --git a/bn_mp_neg.c b/bn_mp_neg.c
index f9de6e4..3a991db 100644
--- a/bn_mp_neg.c
+++ b/bn_mp_neg.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = -a */
int mp_neg (mp_int * a, mp_int * b)
@@ -26,3 +27,4 @@ int mp_neg (mp_int * a, mp_int * b)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_or.c b/bn_mp_or.c
index 793e8e9..dccee7e 100644
--- a/bn_mp_or.c
+++ b/bn_mp_or.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
@@ -42,3 +43,4 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_prime_fermat.c b/bn_mp_prime_fermat.c
index 7d58785..fe17aaa 100644
--- a/bn_mp_prime_fermat.c
+++ b/bn_mp_prime_fermat.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs one Fermat test.
*
@@ -54,3 +55,4 @@ int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
__T:mp_clear (&t);
return err;
}
+#endif
diff --git a/bn_mp_prime_is_divisible.c b/bn_mp_prime_is_divisible.c
index 86392d1..22ec1ae 100644
--- a/bn_mp_prime_is_divisible.c
+++ b/bn_mp_prime_is_divisible.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if an integers is divisible by one
* of the first PRIME_SIZE primes or not
@@ -42,3 +43,4 @@ int mp_prime_is_divisible (mp_int * a, int *result)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_prime_is_prime.c b/bn_mp_prime_is_prime.c
index 88a777b..c2354d2 100644
--- a/bn_mp_prime_is_prime.c
+++ b/bn_mp_prime_is_prime.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs a variable number of rounds of Miller-Rabin
*
* Probability of error after t rounds is no more than
- * (1/4)^t when 1 <= t <= PRIME_SIZE
+
*
* Sets result to 1 if probably prime, 0 otherwise
*/
@@ -75,3 +76,4 @@ int mp_prime_is_prime (mp_int * a, int t, int *result)
__B:mp_clear (&b);
return err;
}
+#endif
diff --git a/bn_mp_prime_miller_rabin.c b/bn_mp_prime_miller_rabin.c
index 0c55d9c..22dec2f 100644
--- a/bn_mp_prime_miller_rabin.c
+++ b/bn_mp_prime_miller_rabin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
@@ -95,3 +96,4 @@ __R:mp_clear (&r);
__N1:mp_clear (&n1);
return err;
}
+#endif
diff --git a/bn_mp_prime_next_prime.c b/bn_mp_prime_next_prime.c
index f45af81..c478ce5 100644
--- a/bn_mp_prime_next_prime.c
+++ b/bn_mp_prime_next_prime.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
@@ -162,3 +163,4 @@ __ERR:
return err;
}
+#endif
diff --git a/bn_mp_prime_rabin_miller_trials.c b/bn_mp_prime_rabin_miller_trials.c
new file mode 100644
index 0000000..d1d0867
--- /dev/null
+++ b/bn_mp_prime_rabin_miller_trials.c
@@ -0,0 +1,48 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+
+static const struct {
+ int k, t;
+} sizes[] = {
+{ 128, 28 },
+{ 256, 16 },
+{ 384, 10 },
+{ 512, 7 },
+{ 640, 6 },
+{ 768, 5 },
+{ 896, 4 },
+{ 1024, 4 }
+};
+
+/* returns # of RM trials required for a given bit size */
+int mp_prime_rabin_miller_trials(int size)
+{
+ int x;
+
+ for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
+ if (sizes[x].k == size) {
+ return sizes[x].t;
+ } else if (sizes[x].k > size) {
+ return (x == 0) ? sizes[0].t : sizes[x - 1].t;
+ }
+ }
+ return sizes[x-1].t + 1;
+}
+
+
+#endif
diff --git a/bn_mp_prime_random_ex.c b/bn_mp_prime_random_ex.c
index 147721b..2c4f4f0 100644
--- a/bn_mp_prime_random_ex.c
+++ b/bn_mp_prime_random_ex.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RANDOM_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* makes a truly random prime of a given size (bits),
*
@@ -92,6 +93,9 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
/* is it prime? */
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ if (res == MP_NO) {
+ continue;
+ }
if (flags & LTM_PRIME_SAFE) {
/* see if (a-1)/2 is prime */
@@ -116,3 +120,4 @@ error:
}
+#endif
diff --git a/bn_mp_radix_size.c b/bn_mp_radix_size.c
index ae2d09a..30b78d9 100644
--- a/bn_mp_radix_size.c
+++ b/bn_mp_radix_size.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
@@ -63,3 +64,4 @@ int mp_radix_size (mp_int * a, int radix, int *size)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_radix_smap.c b/bn_mp_radix_smap.c
index 2c4d966..bc7517d 100644
--- a/bn_mp_radix_smap.c
+++ b/bn_mp_radix_smap.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,7 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+#endif
diff --git a/bn_mp_rand.c b/bn_mp_rand.c
index c744994..1cc47f1 100644
--- a/bn_mp_rand.c
+++ b/bn_mp_rand.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* makes a pseudo-random int of a given size */
int
@@ -47,3 +48,4 @@ mp_rand (mp_int * a, int digits)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_read_radix.c b/bn_mp_read_radix.c
index 653a891..704bd0f 100644
--- a/bn_mp_read_radix.c
+++ b/bn_mp_read_radix.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, char *str, int radix)
@@ -74,3 +75,4 @@ int mp_read_radix (mp_int * a, char *str, int radix)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_read_signed_bin.c b/bn_mp_read_signed_bin.c
index 39d8618..814d6c1 100644
--- a/bn_mp_read_signed_bin.c
+++ b/bn_mp_read_signed_bin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int
@@ -34,3 +35,4 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_read_unsigned_bin.c b/bn_mp_read_unsigned_bin.c
index cb11d87..946457d 100644
--- a/bn_mp_read_unsigned_bin.c
+++ b/bn_mp_read_unsigned_bin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int
@@ -48,3 +49,4 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
mp_clamp (a);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_reduce.c b/bn_mp_reduce.c
index d4c5b10..cfcb55a 100644
--- a/bn_mp_reduce.c
+++ b/bn_mp_reduce.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces x mod m, assumes 0 < x < m**2, mu is
* precomputed via mp_reduce_setup.
@@ -38,9 +39,20 @@ mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
goto CLEANUP;
}
} else {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
goto CLEANUP;
}
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
}
/* q3 = q2 / b**(k+1) */
@@ -82,3 +94,4 @@ CLEANUP:
return res;
}
+#endif
diff --git a/bn_mp_reduce_2k.c b/bn_mp_reduce_2k.c
index f6b40cf..a5a9c74 100644
--- a/bn_mp_reduce_2k.c
+++ b/bn_mp_reduce_2k.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces a modulo n where n is of the form 2**p - d */
int
@@ -54,3 +55,4 @@ ERR:
return res;
}
+#endif
diff --git a/bn_mp_reduce_2k_setup.c b/bn_mp_reduce_2k_setup.c
index 6bdfe7f..5e1fb6e 100644
--- a/bn_mp_reduce_2k_setup.c
+++ b/bn_mp_reduce_2k_setup.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines the setup value */
int
@@ -40,3 +41,4 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d)
mp_clear(&tmp);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_reduce_is_2k.c b/bn_mp_reduce_is_2k.c
index cc36115..fc81397 100644
--- a/bn_mp_reduce_is_2k.c
+++ b/bn_mp_reduce_is_2k.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
@@ -44,3 +45,4 @@ int mp_reduce_is_2k(mp_int *a)
return 1;
}
+#endif
diff --git a/bn_mp_reduce_setup.c b/bn_mp_reduce_setup.c
index 1ba69e9..99f158a 100644
--- a/bn_mp_reduce_setup.c
+++ b/bn_mp_reduce_setup.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,13 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* pre-calculate the value required for Barrett reduction
* For a given modulus "b" it calulates the value required in "a"
*/
-int
-mp_reduce_setup (mp_int * a, mp_int * b)
+int mp_reduce_setup (mp_int * a, mp_int * b)
{
int res;
@@ -27,3 +27,4 @@ mp_reduce_setup (mp_int * a, mp_int * b)
}
return mp_div (a, b, a, NULL);
}
+#endif
diff --git a/bn_mp_rshd.c b/bn_mp_rshd.c
index 87d6e3b..913dda6 100644
--- a/bn_mp_rshd.c
+++ b/bn_mp_rshd.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
@@ -64,3 +65,4 @@ void mp_rshd (mp_int * a, int b)
/* remove excess digits */
a->used -= b;
}
+#endif
diff --git a/bn_mp_set.c b/bn_mp_set.c
index 25ccf64..078fd5f 100644
--- a/bn_mp_set.c
+++ b/bn_mp_set.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
@@ -21,3 +22,4 @@ void mp_set (mp_int * a, mp_digit b)
a->dp[0] = b & MP_MASK;
a->used = (a->dp[0] != 0) ? 1 : 0;
}
+#endif
diff --git a/bn_mp_set_int.c b/bn_mp_set_int.c
index 64f1aed..bd47136 100644
--- a/bn_mp_set_int.c
+++ b/bn_mp_set_int.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
@@ -40,3 +41,4 @@ int mp_set_int (mp_int * a, unsigned long b)
mp_clamp (a);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_shrink.c b/bn_mp_shrink.c
index daefed2..b31f9d2 100644
--- a/bn_mp_shrink.c
+++ b/bn_mp_shrink.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shrink a bignum */
int mp_shrink (mp_int * a)
@@ -27,3 +28,4 @@ int mp_shrink (mp_int * a)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_signed_bin_size.c b/bn_mp_signed_bin_size.c
index 76d085c..30048cb 100644
--- a/bn_mp_signed_bin_size.c
+++ b/bn_mp_signed_bin_size.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,10 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
return 1 + mp_unsigned_bin_size (a);
}
+#endif
diff --git a/bn_mp_sqr.c b/bn_mp_sqr.c
index 4857994..b1fdb57 100644
--- a/bn_mp_sqr.c
+++ b/bn_mp_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes b = a*a */
int
@@ -20,22 +21,34 @@ mp_sqr (mp_int * a, mp_int * b)
{
int res;
+#ifdef BN_MP_TOOM_SQR_C
/* use Toom-Cook? */
if (a->used >= TOOM_SQR_CUTOFF) {
res = mp_toom_sqr(a, b);
/* Karatsuba? */
- } else if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
res = mp_karatsuba_sqr (a, b);
- } else {
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
/* can we use the fast comba multiplier? */
if ((a->used * 2 + 1) < MP_WARRAY &&
a->used <
(1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
res = fast_s_mp_sqr (a, b);
- } else {
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
res = s_mp_sqr (a, b);
- }
+#else
+ res = MP_VAL;
+#endif
}
b->sign = MP_ZPOS;
return res;
}
+#endif
diff --git a/bn_mp_sqrmod.c b/bn_mp_sqrmod.c
index 778b68e..1923be4 100644
--- a/bn_mp_sqrmod.c
+++ b/bn_mp_sqrmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a * a (mod b) */
int
@@ -33,3 +34,4 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_sqrt.c b/bn_mp_sqrt.c
index ec9d102..76cec87 100644
--- a/bn_mp_sqrt.c
+++ b/bn_mp_sqrt.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
@@ -73,3 +74,4 @@ E2: mp_clear(&t1);
return res;
}
+#endif
diff --git a/bn_mp_sub.c b/bn_mp_sub.c
index eb99583..97495f4 100644
--- a/bn_mp_sub.c
+++ b/bn_mp_sub.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level subtraction (handles signs) */
int
@@ -51,3 +52,4 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
return res;
}
+#endif
diff --git a/bn_mp_sub_d.c b/bn_mp_sub_d.c
index 6368970..4923dde 100644
--- a/bn_mp_sub_d.c
+++ b/bn_mp_sub_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit subtraction */
int
@@ -81,3 +82,4 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_submod.c b/bn_mp_submod.c
index 868dd2f..b999c85 100644
--- a/bn_mp_submod.c
+++ b/bn_mp_submod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a - b (mod c) */
int
@@ -34,3 +35,4 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_to_signed_bin.c b/bn_mp_to_signed_bin.c
index 1e21667..0e40d0f 100644
--- a/bn_mp_to_signed_bin.c
+++ b/bn_mp_to_signed_bin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in signed [big endian] format */
int
@@ -26,3 +27,4 @@ mp_to_signed_bin (mp_int * a, unsigned char *b)
b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_to_unsigned_bin.c b/bn_mp_to_unsigned_bin.c
index f7cae69..763e346 100644
--- a/bn_mp_to_unsigned_bin.c
+++ b/bn_mp_to_unsigned_bin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in unsigned [big endian] format */
int
@@ -41,3 +42,4 @@ mp_to_unsigned_bin (mp_int * a, unsigned char *b)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_toom_mul.c b/bn_mp_toom_mul.c
index 50660ff..2d66779 100644
--- a/bn_mp_toom_mul.c
+++ b/bn_mp_toom_mul.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,9 +14,13 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* multiplication using the Toom-Cook 3-way algorithm */
+/* multiplication using the Toom-Cook 3-way algorithm
+ *
+ * Much more complicated than Karatsuba but has a lower asymptotic running time of
+ * O(N**1.464). This algorithm is only particularly useful on VERY large
+ * inputs (we're talking 1000s of digits here...).
+*/
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
@@ -270,3 +276,4 @@ ERR:
return res;
}
+#endif
diff --git a/bn_mp_toom_sqr.c b/bn_mp_toom_sqr.c
index de3094a..8c46fea 100644
--- a/bn_mp_toom_sqr.c
+++ b/bn_mp_toom_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* squaring using Toom-Cook 3-way algorithm */
int
@@ -218,3 +219,4 @@ ERR:
return res;
}
+#endif
diff --git a/bn_mp_toradix.c b/bn_mp_toradix.c
index c605867..a206d5e 100644
--- a/bn_mp_toradix.c
+++ b/bn_mp_toradix.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix (mp_int * a, char *str, int radix)
@@ -67,3 +68,4 @@ int mp_toradix (mp_int * a, char *str, int radix)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_toradix_n.c b/bn_mp_toradix_n.c
index d2f6ec2..7d43558 100644
--- a/bn_mp_toradix_n.c
+++ b/bn_mp_toradix_n.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* stores a bignum as a ASCII string in a given radix (2..64)
*
@@ -81,3 +82,4 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_unsigned_bin_size.c b/bn_mp_unsigned_bin_size.c
index 47bbc64..80da415 100644
--- a/bn_mp_unsigned_bin_size.c
+++ b/bn_mp_unsigned_bin_size.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an unsigned equivalent */
int
@@ -21,3 +22,4 @@ mp_unsigned_bin_size (mp_int * a)
int size = mp_count_bits (a);
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
+#endif
diff --git a/bn_mp_xor.c b/bn_mp_xor.c
index 36e6733..192aacc 100644
--- a/bn_mp_xor.c
+++ b/bn_mp_xor.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_XOR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* XOR two ints together */
int
@@ -36,10 +37,11 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
}
for (ix = 0; ix < px; ix++) {
- t.dp[ix] ^= x->dp[ix];
+
}
mp_clamp (&t);
mp_exch (c, &t);
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_zero.c b/bn_mp_zero.c
index a888589..0097598 100644
--- a/bn_mp_zero.c
+++ b/bn_mp_zero.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ZERO_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to zero */
void
@@ -22,3 +23,4 @@ mp_zero (mp_int * a)
a->used = 0;
memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
}
+#endif
diff --git a/bn_prime_sizes_tab.c b/bn_prime_sizes_tab.c
deleted file mode 100644
index c6e1dad..0000000
--- a/bn_prime_sizes_tab.c
+++ /dev/null
@@ -1,51 +0,0 @@
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-#include <tommath.h>
-
-/* this table gives the # of rabin miller trials for a prob of failure lower than 2^-96 */
-static const struct {
- int k, t;
-} sizes[] = {
-{ 128, 28 },
-{ 256, 16 },
-{ 384, 10 },
-{ 512, 7 },
-{ 640, 6 },
-{ 768, 5 },
-{ 896, 4 },
-{ 1024, 4 },
-{ 1152, 3 },
-{ 1280, 3 },
-{ 1408, 3 },
-{ 1536, 3 },
-{ 1664, 3 },
-{ 1792, 2 } };
-
-/* returns # of RM trials required for a given bit size */
-int mp_prime_rabin_miller_trials(int size)
-{
- int x;
-
- for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
- if (sizes[x].k == size) {
- return sizes[x].t;
- } else if (sizes[x].k > size) {
- return (x == 0) ? sizes[0].t : sizes[x - 1].t;
- }
- }
- return 1;
-}
-
-
diff --git a/bn_prime_tab.c b/bn_prime_tab.c
index 7dfdc8c..18ecc47 100644
--- a/bn_prime_tab.c
+++ b/bn_prime_tab.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_PRIME_TAB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
const mp_digit __prime_tab[] = {
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
@@ -53,3 +54,4 @@ const mp_digit __prime_tab[] = {
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
};
+#endif
diff --git a/bn_reverse.c b/bn_reverse.c
index 89cbbb7..851a6e8 100644
--- a/bn_reverse.c
+++ b/bn_reverse.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reverse an array, used for radix code */
void
@@ -31,3 +32,4 @@ bn_reverse (unsigned char *s, int len)
--iy;
}
}
+#endif
diff --git a/bn_s_mp_add.c b/bn_s_mp_add.c
index e07931a..2b378ae 100644
--- a/bn_s_mp_add.c
+++ b/bn_s_mp_add.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
@@ -101,3 +102,4 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_s_mp_exptmod.c b/bn_s_mp_exptmod.c
index 28c14fd..4f1032a 100644
--- a/bn_s_mp_exptmod.c
+++ b/bn_s_mp_exptmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#ifdef MP_LOW_MEM
#define TAB_SIZE 32
@@ -232,3 +233,4 @@ __M:
}
return err;
}
+#endif
diff --git a/bn_s_mp_mul_digs.c b/bn_s_mp_mul_digs.c
index a5b1067..d9f0a56 100644
--- a/bn_s_mp_mul_digs.c
+++ b/bn_s_mp_mul_digs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and only computes upto digs digits of result
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
@@ -83,3 +84,4 @@ s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_s_mp_mul_high_digs.c b/bn_s_mp_mul_high_digs.c
index 84cc7d0..a060248 100644
--- a/bn_s_mp_mul_high_digs.c
+++ b/bn_s_mp_mul_high_digs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and does not compute the lower digs digits
* [meant to get the higher part of the product]
@@ -27,10 +28,12 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_digit tmpx, *tmpt, *tmpy;
/* can we use the fast multiplier? */
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
if (((a->used + b->used + 1) < MP_WARRAY)
&& MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_s_mp_mul_high_digs (a, b, c, digs);
}
+#endif
if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
return res;
@@ -71,3 +74,4 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_s_mp_sqr.c b/bn_s_mp_sqr.c
index 3a00a4e..4d12804 100644
--- a/bn_s_mp_sqr.c
+++ b/bn_s_mp_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int
@@ -77,3 +78,4 @@ s_mp_sqr (mp_int * a, mp_int * b)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_s_mp_sub.c b/bn_s_mp_sub.c
index 4381af8..5b7aef9 100644
--- a/bn_s_mp_sub.c
+++ b/bn_s_mp_sub.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
@@ -81,3 +82,4 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
return MP_OKAY;
}
+#endif
diff --git a/bncore.c b/bncore.c
index 918a99a..cf8a15a 100644
--- a/bncore.c
+++ b/bncore.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,22 +14,18 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Known optimal configurations
CPU /Compiler /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
- Intel P4 Northwood /GCC v3.3.3 / 59/ 81/profiled build
- Intel P4 Northwood /GCC v3.3.3 / 59/ 80/profiled_single build
- Intel P4 Northwood /ICC v8.0 / 57/ 70/profiled build
- Intel P4 Northwood /ICC v8.0 / 54/ 76/profiled_single build
- AMD Athlon XP /GCC v3.2 / 109/ 127/
+ Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
*/
-int KARATSUBA_MUL_CUTOFF = 57, /* Min. number of digits before Karatsuba multiplication is used. */
- KARATSUBA_SQR_CUTOFF = 70, /* Min. number of digits before Karatsuba squaring is used. */
+int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */
+ KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */
TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */
TOOM_SQR_CUTOFF = 400;
+#endif
diff --git a/booker.pl b/booker.pl
index de28780..5c77e53 100644
--- a/booker.pl
+++ b/booker.pl
@@ -82,7 +82,7 @@ while (<IN>) {
# scan till next end of comment, e.g. skip license
while (<SRC>) {
$text[$line++] = $_;
- last if ($_ =~ /tommath\.h/);
+ last if ($_ =~ /math\.libtomcrypt\.org/);
}
<SRC>;
}
diff --git a/callgraph.txt b/callgraph.txt
new file mode 100644
index 0000000..56d4f8b
--- /dev/null
+++ b/callgraph.txt
@@ -0,0 +1,10168 @@
+BN_PRIME_TAB_C
+
+
+BN_MP_SQRT_C
++--->BN_MP_N_ROOT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_EXPT_D_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_SET_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CMP_D_C
+
+
+BN_MP_EXCH_C
+
+
+BN_MP_IS_SQUARE_C
++--->BN_MP_MOD_D_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SET_INT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_SET_INT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_GET_INT_C
++--->BN_MP_SQRT_C
+| +--->BN_MP_N_ROOT_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_EXPT_D_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_SUB_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_NEG_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
+
+
+BN_MP_EXPTMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_INVMOD_C
+| +--->BN_FAST_MP_INVMOD_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ABS_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_CMP_D_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INVMOD_SLOW_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_CMP_D_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_ABS_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_MULTI_C
++--->BN_MP_DR_IS_MODULUS_C
++--->BN_MP_REDUCE_IS_2K_C
+| +--->BN_MP_REDUCE_2K_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_COUNT_BITS_C
++--->BN_MP_EXPTMOD_FAST_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MONTGOMERY_SETUP_C
+| +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| +--->BN_MP_MONTGOMERY_REDUCE_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| +--->BN_MP_DR_SETUP_C
+| +--->BN_MP_DR_REDUCE_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| +--->BN_MP_REDUCE_2K_SETUP_C
+| | +--->BN_MP_2EXPT_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_REDUCE_2K_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | +--->BN_MP_2EXPT_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MULMOD_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_COPY_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_SQR_C
+| | +--->BN_MP_TOOM_SQR_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_KARATSUBA_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | +--->BN_FAST_S_MP_SQR_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
++--->BN_S_MP_EXPTMOD_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_REDUCE_SETUP_C
+| | +--->BN_MP_2EXPT_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_SET_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MOD_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_SET_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_SQR_C
+| | +--->BN_MP_TOOM_SQR_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_KARATSUBA_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | +--->BN_FAST_S_MP_SQR_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_REDUCE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_D_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_OR_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_ZERO_C
+
+
+BN_MP_GROW_C
+
+
+BN_MP_COUNT_BITS_C
+
+
+BN_MP_PRIME_FERMAT_C
++--->BN_MP_CMP_D_C
++--->BN_MP_INIT_C
++--->BN_MP_EXPTMOD_C
+| +--->BN_MP_INVMOD_C
+| | +--->BN_FAST_MP_INVMOD_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ABS_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INVMOD_SLOW_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_ABS_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_DR_IS_MODULUS_C
+| +--->BN_MP_REDUCE_IS_2K_C
+| | +--->BN_MP_REDUCE_2K_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_EXPTMOD_FAST_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MONTGOMERY_SETUP_C
+| | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_DR_SETUP_C
+| | +--->BN_MP_DR_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_REDUCE_2K_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MULMOD_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_SET_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2D_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_INIT_COPY_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_COPY_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_S_MP_EXPTMOD_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_REDUCE_SETUP_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_COPY_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_COPY_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_REDUCE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_SUBMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_MOD_2D_C
++--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_TORADIX_N_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_DIV_D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CMP_C
++--->BN_MP_CMP_MAG_C
+
+
+BNCORE_C
+
+
+BN_MP_TORADIX_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_DIV_D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_ADD_D_C
++--->BN_MP_GROW_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_DIV_3_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_FAST_S_MP_MUL_DIGS_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_SQRMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_INVMOD_C
++--->BN_FAST_MP_INVMOD_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ABS_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_CMP_D_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INVMOD_SLOW_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_CMP_D_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+
+
+BN_MP_AND_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_MUL_D_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_FAST_MP_INVMOD_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ABS_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_CMP_D_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_FWRITE_C
++--->BN_MP_RADIX_SIZE_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_TORADIX_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_S_MP_SQR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_N_ROOT_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_EXPT_D_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_SQR_C
+| | +--->BN_MP_TOOM_SQR_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_KARATSUBA_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_FAST_S_MP_SQR_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+
+
+BN_MP_RADIX_SIZE_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_DIV_D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_READ_SIGNED_BIN_C
++--->BN_MP_READ_UNSIGNED_BIN_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_PRIME_RANDOM_EX_C
++--->BN_MP_READ_UNSIGNED_BIN_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_PRIME_IS_PRIME_C
+| +--->BN_MP_CMP_D_C
+| +--->BN_MP_PRIME_IS_DIVISIBLE_C
+| | +--->BN_MP_MOD_D_C
+| | | +--->BN_MP_DIV_D_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_INIT_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_INIT_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_PRIME_MILLER_RABIN_C
+| | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SUB_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CNT_LSB_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXPTMOD_C
+| | | +--->BN_MP_INVMOD_C
+| | | | +--->BN_FAST_MP_INVMOD_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ABS_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_INVMOD_SLOW_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_ABS_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_DR_IS_MODULUS_C
+| | | +--->BN_MP_REDUCE_IS_2K_C
+| | | | +--->BN_MP_REDUCE_2K_C
+| | | | | +--->BN_MP_COUNT_BITS_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_EXPTMOD_FAST_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MONTGOMERY_SETUP_C
+| | | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_DR_SETUP_C
+| | | | +--->BN_MP_DR_REDUCE_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | | | +--->BN_MP_2EXPT_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_REDUCE_2K_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | | | +--->BN_MP_2EXPT_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MULMOD_C
+| | | | | +--->BN_MP_MUL_C
+| | | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_EXCH_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_MOD_C
+| | | | | | +--->BN_MP_DIV_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_MOD_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_SQR_C
+| | | | | +--->BN_MP_TOOM_SQR_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SQR_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_S_MP_EXPTMOD_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_REDUCE_SETUP_C
+| | | | | +--->BN_MP_2EXPT_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MOD_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_SQR_C
+| | | | | +--->BN_MP_TOOM_SQR_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SQR_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_REDUCE_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_C
+| | | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_EXCH_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_SQRMOD_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_COUNT_BITS_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_KARATSUBA_SQR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
++--->BN_S_MP_ADD_C
+| +--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
++--->BN_MP_ADD_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_INIT_COPY_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
+
+
+BN_MP_CLAMP_C
+
+
+BN_MP_TOOM_SQR_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_MOD_2D_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_SQR_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_2_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_3_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_MOD_C
++--->BN_MP_INIT_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_SET_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
+
+
+BN_MP_INIT_C
+
+
+BN_MP_TOOM_MUL_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_MOD_2D_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_MUL_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_2_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_3_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_IS_PRIME_C
++--->BN_MP_CMP_D_C
++--->BN_MP_PRIME_IS_DIVISIBLE_C
+| +--->BN_MP_MOD_D_C
+| | +--->BN_MP_DIV_D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_INIT_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_PRIME_MILLER_RABIN_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CNT_LSB_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXPTMOD_C
+| | +--->BN_MP_INVMOD_C
+| | | +--->BN_FAST_MP_INVMOD_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ABS_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_INVMOD_SLOW_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_ABS_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_DR_IS_MODULUS_C
+| | +--->BN_MP_REDUCE_IS_2K_C
+| | | +--->BN_MP_REDUCE_2K_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_EXPTMOD_FAST_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MONTGOMERY_SETUP_C
+| | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_DR_SETUP_C
+| | | +--->BN_MP_DR_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_REDUCE_2K_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MULMOD_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_MOD_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_S_MP_EXPTMOD_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_REDUCE_SETUP_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_REDUCE_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_SQRMOD_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_COPY_C
++--->BN_MP_GROW_C
+
+
+BN_S_MP_SUB_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_READ_UNSIGNED_BIN_C
++--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_EXPTMOD_FAST_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MONTGOMERY_SETUP_C
++--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
++--->BN_MP_MONTGOMERY_REDUCE_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
++--->BN_MP_DR_SETUP_C
++--->BN_MP_DR_REDUCE_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
++--->BN_MP_REDUCE_2K_SETUP_C
+| +--->BN_MP_2EXPT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_GROW_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_REDUCE_2K_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| +--->BN_MP_2EXPT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MULMOD_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_MOD_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_SET_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_EXCH_C
+
+
+BN_MP_TO_UNSIGNED_BIN_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_SET_INT_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_MOD_D_C
++--->BN_MP_DIV_D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_SQR_C
++--->BN_MP_TOOM_SQR_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_KARATSUBA_SQR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| +--->BN_MP_ADD_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_SQR_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_S_MP_SQR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_MULMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_DIV_2D_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_C
++--->BN_MP_MOD_2D_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
++--->BN_MP_RSHD_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
+
+
+BN_S_MP_ADD_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_FAST_S_MP_SQR_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_S_MP_MUL_DIGS_C
++--->BN_FAST_S_MP_MUL_DIGS_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_XOR_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_RADIX_SMAP_C
+
+
+BN_MP_DR_IS_MODULUS_C
+
+
+BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_2EXPT_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_GROW_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_MUL_2_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_SUB_C
++--->BN_S_MP_ADD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_INIT_MULTI_C
++--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
+
+
+BN_S_MP_MUL_HIGH_DIGS_C
++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_NEXT_PRIME_C
++--->BN_MP_CMP_D_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_D_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_PRIME_MILLER_RABIN_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CNT_LSB_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXPTMOD_C
+| | +--->BN_MP_INVMOD_C
+| | | +--->BN_FAST_MP_INVMOD_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ABS_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_INVMOD_SLOW_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_ABS_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_DR_IS_MODULUS_C
+| | +--->BN_MP_REDUCE_IS_2K_C
+| | | +--->BN_MP_REDUCE_2K_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_EXPTMOD_FAST_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MONTGOMERY_SETUP_C
+| | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_DR_SETUP_C
+| | | +--->BN_MP_DR_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_REDUCE_2K_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MULMOD_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_MOD_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_S_MP_EXPTMOD_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_REDUCE_SETUP_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_REDUCE_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_SQRMOD_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_SIGNED_BIN_SIZE_C
++--->BN_MP_UNSIGNED_BIN_SIZE_C
+| +--->BN_MP_COUNT_BITS_C
+
+
+BN_MP_INVMOD_SLOW_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_CMP_D_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_LCM_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_GCD_C
+| +--->BN_MP_ABS_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CNT_LSB_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_EXCH_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_DIV_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_SET_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_REVERSE_C
+
+
+BN_MP_PRIME_IS_DIVISIBLE_C
++--->BN_MP_MOD_D_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+
+
+BN_MP_SET_C
++--->BN_MP_ZERO_C
+
+
+BN_MP_GCD_C
++--->BN_MP_ABS_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_READ_RADIX_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_FAST_S_MP_MUL_HIGH_DIGS_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_FAST_MP_MONTGOMERY_REDUCE_C
++--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+
+
+BN_MP_DIV_D_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_DIV_3_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_REDUCE_2K_SETUP_C
++--->BN_MP_INIT_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_2EXPT_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_INIT_SET_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
+
+
+BN_MP_REDUCE_2K_C
++--->BN_MP_INIT_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_S_MP_ADD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_ERROR_C
+
+
+BN_MP_EXPT_D_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+
+
+BN_S_MP_EXPTMOD_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
++--->BN_MP_REDUCE_SETUP_C
+| +--->BN_MP_2EXPT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_REDUCE_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_D_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_EXCH_C
+
+
+BN_MP_ABS_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
+
+
+BN_MP_INIT_SET_INT_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_INT_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_SUB_D_C
++--->BN_MP_GROW_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_TO_SIGNED_BIN_C
++--->BN_MP_TO_UNSIGNED_BIN_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_DIV_2_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_REDUCE_IS_2K_C
++--->BN_MP_REDUCE_2K_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_COUNT_BITS_C
+
+
+BN_MP_INIT_SIZE_C
++--->BN_MP_INIT_C
+
+
+BN_MP_DIV_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SET_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_INIT_C
++--->BN_MP_INIT_COPY_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
++--->BN_MP_RSHD_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CLEAR_C
+
+
+BN_MP_MONTGOMERY_REDUCE_C
++--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+
+
+BN_MP_MUL_2_C
++--->BN_MP_GROW_C
+
+
+BN_MP_UNSIGNED_BIN_SIZE_C
++--->BN_MP_COUNT_BITS_C
+
+
+BN_MP_ADDMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_ADD_C
++--->BN_S_MP_ADD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_RAND_C
++--->BN_MP_ZERO_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+
+
+BN_MP_CNT_LSB_C
+
+
+BN_MP_2EXPT_C
++--->BN_MP_ZERO_C
++--->BN_MP_GROW_C
+
+
+BN_MP_RSHD_C
++--->BN_MP_ZERO_C
+
+
+BN_MP_SHRINK_C
+
+
+BN_MP_REDUCE_C
++--->BN_MP_REDUCE_SETUP_C
+| +--->BN_MP_2EXPT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_S_MP_MUL_HIGH_DIGS_C
+| +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_2D_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_S_MP_MUL_DIGS_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_D_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_MUL_2D_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_GET_INT_C
+
+
+BN_MP_JACOBI_C
++--->BN_MP_CMP_D_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CLEAR_MULTI_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_MUL_C
++--->BN_MP_TOOM_MUL_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_KARATSUBA_MUL_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_MUL_DIGS_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_S_MP_MUL_DIGS_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_EXTEUCLID_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_DR_REDUCE_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+
+
+BN_MP_FREAD_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_D_C
+
+
+BN_MP_REDUCE_SETUP_C
++--->BN_MP_2EXPT_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_GROW_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_SET_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_MONTGOMERY_SETUP_C
+
+
+BN_MP_KARATSUBA_MUL_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_LSHD_C
++--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
+
+
+BN_MP_PRIME_MILLER_RABIN_C
++--->BN_MP_CMP_D_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_EXPTMOD_C
+| +--->BN_MP_INVMOD_C
+| | +--->BN_FAST_MP_INVMOD_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ABS_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INVMOD_SLOW_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_ABS_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_DR_IS_MODULUS_C
+| +--->BN_MP_REDUCE_IS_2K_C
+| | +--->BN_MP_REDUCE_2K_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_EXPTMOD_FAST_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MONTGOMERY_SETUP_C
+| | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_DR_SETUP_C
+| | +--->BN_MP_DR_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_REDUCE_2K_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MULMOD_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_SET_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_S_MP_EXPTMOD_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_REDUCE_SETUP_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_REDUCE_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_SQRMOD_C
+| +--->BN_MP_SQR_C
+| | +--->BN_MP_TOOM_SQR_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_KARATSUBA_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_FAST_S_MP_SQR_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_MOD_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_SET_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_DR_SETUP_C
+
+
+BN_MP_CMP_MAG_C
+
+
diff --git a/changes.txt b/changes.txt
index c90d27a..6a86209 100644
--- a/changes.txt
+++ b/changes.txt
@@ -1,3 +1,18 @@
+October 29th, 2004
+v0.32 -- Added "makefile.shared" for shared object support
+ -- Added more to the build options/configs in the manual
+ -- Started the Depends framework, wrote dep.pl to scan deps and
+ produce "callgraph.txt" ;-)
+ -- Wrote SC_RSA_1 which will enable close to the minimum required to perform
+ RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
+ -- Merged in the small/slower mp_div replacement. You can now toggle which
+ you want to use as your mp_div() at build time. Saves roughly 8KB or so.
+ -- Renamed a few files and changed some comments to make depends system work better.
+ (No changes to function names)
+ -- Merged in new Combas that perform 2 reads per inner loop instead of the older
+ 3reads/2writes per inner loop of the old code. Really though if you want speed
+ learn to use TomsFastMath ;-)
+
August 9th, 2004
v0.31 -- "profiled" builds now :-) new timings for Intel Northwoods
-- Added "pretty" build target
diff --git a/demo/demo.c b/demo/demo.c
index 8cbcb8a..53eb3cf 100644
--- a/demo/demo.c
+++ b/demo/demo.c
@@ -64,6 +64,7 @@ int main(void)
srand(time(NULL));
+#if 0
// test mp_get_int
printf("Testing: mp_get_int\n");
for(i=0;i<1000;++i) {
@@ -274,6 +275,7 @@ int main(void)
printf("Passed DR test for %d digits\n", cnt);
}
+#endif
div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = sub_d_n= 0;
diff --git a/demo/timing.c b/demo/timing.c
index 30e95ce..865c444 100644
--- a/demo/timing.c
+++ b/demo/timing.c
@@ -152,7 +152,7 @@ int main(void)
KARATSUBA_SQR_CUTOFF = (ix==0)?9999:old_kara_s;
log = fopen((ix==0)?"logs/mult.log":"logs/mult_kara.log", "w");
- for (cnt = 32; cnt <= 288; cnt += 8) {
+ for (cnt = 4; cnt <= 288; cnt += 2) {
SLEEP;
mp_rand(&a, cnt);
mp_rand(&b, cnt);
@@ -170,7 +170,7 @@ int main(void)
fclose(log);
log = fopen((ix==0)?"logs/sqr.log":"logs/sqr_kara.log", "w");
- for (cnt = 32; cnt <= 288; cnt += 8) {
+ for (cnt = 4; cnt <= 288; cnt += 2) {
SLEEP;
mp_rand(&a, cnt);
rr = 0;
diff --git a/dep.pl b/dep.pl
new file mode 100644
index 0000000..22266e3
--- /dev/null
+++ b/dep.pl
@@ -0,0 +1,121 @@
+#!/usr/bin/perl
+#
+# Walk through source, add labels and make classes
+#
+#use strict;
+
+my %deplist;
+
+#open class file and write preamble
+open(CLASS, ">tommath_class.h") or die "Couldn't open tommath_class.h for writing\n";
+print CLASS "#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))\n#if defined(LTM2)\n#define LTM3\n#endif\n#if defined(LTM1)\n#define LTM2\n#endif\n#define LTM1\n\n#if defined(LTM_ALL)\n";
+
+foreach my $filename (glob "bn*.c") {
+ my $define = $filename;
+
+ # convert filename to upper case so we can use it as a define
+ $define =~ tr/[a-z]/[A-Z]/;
+ $define =~ tr/\./_/;
+ print CLASS "#define $define\n";
+
+ # now copy text and apply #ifdef as required
+ my $apply = 0;
+ open(SRC, "<$filename");
+ open(OUT, ">tmp");
+
+ # first line will be the #ifdef
+ my $line = <SRC>;
+ if ($line =~ /include/) {
+ print OUT $line;
+ } else {
+ print OUT "#include <tommath.h>\n#ifdef $define\n$line";
+ $apply = 1;
+ }
+ while (<SRC>) {
+ if (!($_ =~ /tommath\.h/)) {
+ print OUT $_;
+ }
+ }
+ if ($apply == 1) {
+ print OUT "#endif\n";
+ }
+ close SRC;
+ close OUT;
+
+ unlink($filename);
+ rename("tmp", $filename);
+}
+print CLASS "#endif\n\n";
+
+# now do classes
+
+foreach my $filename (glob "bn*.c") {
+ open(SRC, "<$filename") or die "Can't open source file!\n";
+
+ # convert filename to upper case so we can use it as a define
+ $filename =~ tr/[a-z]/[A-Z]/;
+ $filename =~ tr/\./_/;
+
+ print CLASS "#if defined($filename)\n";
+ my $list = $filename;
+
+ # scan for mp_* and make classes
+ while (<SRC>) {
+ my $line = $_;
+ while ($line =~ m/(fast_)*(s_)*mp\_[a-z_0-9]*/) {
+ $line = $';
+ # now $& is the match, we want to skip over LTM keywords like
+ # mp_int, mp_word, mp_digit
+ if (!($& eq "mp_digit") && !($& eq "mp_word") && !($& eq "mp_int")) {
+ my $a = $&;
+ $a =~ tr/[a-z]/[A-Z]/;
+ $a = "BN_" . $a . "_C";
+ if (!($list =~ /$a/)) {
+ print CLASS " #define $a\n";
+ }
+ $list = $list . "," . $a;
+ }
+ }
+ }
+ @deplist{$filename} = $list;
+
+ print CLASS "#endif\n\n";
+ close SRC;
+}
+
+print CLASS "#ifdef LTM3\n#define LTM_LAST\n#endif\n#include <tommath_superclass.h>\n#include <tommath_class.h>\n#else\n#define LTM_LAST\n#endif\n";
+close CLASS;
+
+#now let's make a cool call graph...
+
+open(OUT,">callgraph.txt");
+$indent = 0;
+foreach (keys %deplist) {
+ $list = "";
+ draw_func(@deplist{$_});
+ print OUT "\n\n";
+}
+close(OUT);
+
+sub draw_func()
+{
+ my @funcs = split(",", $_[0]);
+ if ($list =~ /@funcs[0]/) {
+ return;
+ } else {
+ $list = $list . @funcs[0];
+ }
+ if ($indent == 0) { }
+ elsif ($indent >= 1) { print OUT "| " x ($indent - 1) . "+--->"; }
+ print OUT @funcs[0] . "\n";
+ shift @funcs;
+ my $temp = $list;
+ foreach my $i (@funcs) {
+ ++$indent;
+ draw_func(@deplist{$i});
+ --$indent;
+ }
+ $list = $temp;
+}
+
+
diff --git a/etc/tune.c b/etc/tune.c
index 11ce210..bc101be 100644
--- a/etc/tune.c
+++ b/etc/tune.c
@@ -8,7 +8,7 @@
/* how many times todo each size mult. Depends on your computer. For slow computers
* this can be low like 5 or 10. For fast [re: Athlon] should be 25 - 50 or so
*/
-#define TIMES 50
+#define TIMES (1UL<<14UL)
#ifndef X86_TIMER
@@ -23,154 +23,85 @@ extern void t_start(void);
extern ulong64 t_read(void);
#endif
-ulong64
-time_mult (int max)
+ulong64 time_mult(int size, int s)
{
- int x, y;
+ unsigned long x;
mp_int a, b, c;
+ ulong64 t1;
mp_init (&a);
mp_init (&b);
mp_init (&c);
+ mp_rand (&a, size);
+ mp_rand (&b, size);
+
+ if (s == 1) {
+ KARATSUBA_MUL_CUTOFF = size;
+ } else {
+ KARATSUBA_MUL_CUTOFF = 100000;
+ }
+
t_start();
- for (x = 32; x <= max; x += 4) {
- mp_rand (&a, x);
- mp_rand (&b, x);
- for (y = 0; y < TIMES; y++) {
- mp_mul (&a, &b, &c);
- }
+ for (x = 0; x < TIMES; x++) {
+ mp_mul(&a,&b,&c);
}
+ t1 = t_read();
mp_clear (&a);
mp_clear (&b);
mp_clear (&c);
- return t_read();
+ return t1;
}
-ulong64
-time_sqr (int max)
+ulong64 time_sqr(int size, int s)
{
- int x, y;
+ unsigned long x;
mp_int a, b;
+ ulong64 t1;
mp_init (&a);
mp_init (&b);
+ mp_rand (&a, size);
+
+ if (s == 1) {
+ KARATSUBA_SQR_CUTOFF = size;
+ } else {
+ KARATSUBA_SQR_CUTOFF = 100000;
+ }
+
t_start();
- for (x = 32; x <= max; x += 4) {
- mp_rand (&a, x);
- for (y = 0; y < TIMES; y++) {
- mp_sqr (&a, &b);
- }
+ for (x = 0; x < TIMES; x++) {
+ mp_sqr(&a,&b);
}
+ t1 = t_read();
mp_clear (&a);
mp_clear (&b);
- return t_read();
+ return t1;
}
int
main (void)
{
- int best_kmult, best_tmult, best_ksquare, best_tsquare, counter;
- ulong64 best, ti;
- FILE *log;
-
- best_kmult = best_ksquare = best_tmult = best_tsquare = 0;
- /* tune multiplication first */
-
- /* effectively turn TOOM off */
- TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 100000;
-
- log = fopen ("mult.log", "w");
- best = -1;
- counter = 16;
- for (KARATSUBA_MUL_CUTOFF = 8; KARATSUBA_MUL_CUTOFF <= 200; KARATSUBA_MUL_CUTOFF++) {
- ti = time_mult (300);
- printf ("%4d : %9llu \r", KARATSUBA_MUL_CUTOFF, ti);
- fprintf (log, "%d, %llu\n", KARATSUBA_MUL_CUTOFF, ti);
- fflush (stdout);
- if (ti < best) {
- printf ("New best: %llu, %d \r", ti, KARATSUBA_MUL_CUTOFF);
- best = ti;
- best_kmult = KARATSUBA_MUL_CUTOFF;
- counter = 16;
- } else if (--counter == 0) {
- printf("No better found in 16 trials.\n");
- break;
- }
- }
- fclose (log);
- printf("Karatsuba Multiplier Cutoff (KARATSUBA_MUL_CUTOFF) == %d\n", best_kmult);
-
- /* tune squaring */
- log = fopen ("sqr.log", "w");
- best = -1;
- counter = 16;
- for (KARATSUBA_SQR_CUTOFF = 8; KARATSUBA_SQR_CUTOFF <= 200; KARATSUBA_SQR_CUTOFF++) {
- ti = time_sqr (300);
- printf ("%4d : %9llu \r", KARATSUBA_SQR_CUTOFF, ti);
- fprintf (log, "%d, %llu\n", KARATSUBA_SQR_CUTOFF, ti);
- fflush (stdout);
- if (ti < best) {
- printf ("New best: %llu, %d \r", ti, KARATSUBA_SQR_CUTOFF);
- best = ti;
- best_ksquare = KARATSUBA_SQR_CUTOFF;
- counter = 16;
- } else if (--counter == 0) {
- printf("No better found in 16 trials.\n");
- break;
- }
- }
- fclose (log);
- printf("Karatsuba Squaring Cutoff (KARATSUBA_SQR_CUTOFF) == %d\n", best_ksquare);
-
- KARATSUBA_MUL_CUTOFF = best_kmult;
- KARATSUBA_SQR_CUTOFF = best_ksquare;
-
- /* tune TOOM mult */
- counter = 16;
- log = fopen ("tmult.log", "w");
- best = -1;
- for (TOOM_MUL_CUTOFF = best_kmult*5; TOOM_MUL_CUTOFF <= 800; TOOM_MUL_CUTOFF++) {
- ti = time_mult (1200);
- printf ("%4d : %9llu \r", TOOM_MUL_CUTOFF, ti);
- fprintf (log, "%d, %llu\n", TOOM_MUL_CUTOFF, ti);
- fflush (stdout);
- if (ti < best) {
- printf ("New best: %llu, %d \r", ti, TOOM_MUL_CUTOFF);
- best = ti;
- best_tmult = TOOM_MUL_CUTOFF;
- counter = 16;
- } else if (--counter == 0) {
- printf("No better found in 16 trials.\n");
- break;
- }
- }
- fclose (log);
- printf("Toom-Cook Multiplier Cutoff (TOOM_MUL_CUTOFF) == %d\n", best_tmult);
-
- /* tune TOOM sqr */
- log = fopen ("tsqr.log", "w");
- best = -1;
- counter = 16;
- for (TOOM_SQR_CUTOFF = best_ksquare*3; TOOM_SQR_CUTOFF <= 800; TOOM_SQR_CUTOFF++) {
- ti = time_sqr (1200);
- printf ("%4d : %9llu \r", TOOM_SQR_CUTOFF, ti);
- fprintf (log, "%d, %llu\n", TOOM_SQR_CUTOFF, ti);
- fflush (stdout);
- if (ti < best) {
- printf ("New best: %llu, %d \r", ti, TOOM_SQR_CUTOFF);
- best = ti;
- best_tsquare = TOOM_SQR_CUTOFF;
- counter = 16;
- } else if (--counter == 0) {
- printf("No better found in 16 trials.\n");
- break;
- }
+ ulong64 t1, t2;
+ int x, y;
+
+ for (x = 8; ; x += 2) {
+ t1 = time_mult(x, 0);
+ t2 = time_mult(x, 1);
+ printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
+ if (t2 < t1) break;
}
- fclose (log);
- printf("Toom-Cook Squaring Cutoff (TOOM_SQR_CUTOFF) == %d\n", best_tsquare);
+ y = x;
+ for (x = 8; ; x += 2) {
+ t1 = time_sqr(x, 0);
+ t2 = time_sqr(x, 1);
+ printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
+ if (t2 < t1) break;
+ }
+ printf("KARATSUBA_MUL_CUTOFF = %d\n", y);
+ printf("KARATSUBA_SQR_CUTOFF = %d\n", x);
return 0;
}
diff --git a/logs/add.log b/logs/add.log
index 2ba7207..d44c4cd 100644
--- a/logs/add.log
+++ b/logs/add.log
@@ -1,16 +1,16 @@
-224 1572
-448 1740
-672 1902
-896 2116
-1120 2324
-1344 2484
-1568 2548
-1792 2772
-2016 2958
-2240 3058
-2464 3276
-2688 3436
-2912 3542
-3136 3702
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-3584 4074
+224 222
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+2016 1006
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diff --git a/logs/expt.log b/logs/expt.log
index 695c936..e69de29 100644
--- a/logs/expt.log
+++ b/logs/expt.log
@@ -1,7 +0,0 @@
-513 19933908
-769 55707832
-1025 119872576
-2049 856114218
-2561 1602741360
-3073 2718192748
-4097 6264335828
diff --git a/logs/expt_2k.log b/logs/expt_2k.log
index d7c47f3..e69de29 100644
--- a/logs/expt_2k.log
+++ b/logs/expt_2k.log
@@ -1,6 +0,0 @@
-521 18847776
-607 24665920
-1279 110036220
-2203 414562036
-3217 1108350966
-4253 2286079370
diff --git a/logs/expt_dr.log b/logs/expt_dr.log
index b017e7c..e69de29 100644
--- a/logs/expt_dr.log
+++ b/logs/expt_dr.log
@@ -1,7 +0,0 @@
-532 9656134
-784 23022274
-1036 45227854
-1540 129652848
-2072 280625626
-3080 845619480
-4116 1866206400
diff --git a/logs/mult.log b/logs/mult.log
index 5b2d258..a2c9c18 100644
--- a/logs/mult.log
+++ b/logs/mult.log
@@ -1,33 +1,143 @@
-923 45612
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diff --git a/logs/mult_kara.log b/logs/mult_kara.log
index c69769b..086feaf 100644
--- a/logs/mult_kara.log
+++ b/logs/mult_kara.log
@@ -1,33 +1,33 @@
-921 92388
-1148 61410
-1372 43799
-1594 33047
-1819 26913
-2043 21996
-2268 18453
-2492 15623
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diff --git a/logs/sqr.log b/logs/sqr.log
index ec142fe..3e175ac 100644
--- a/logs/sqr.log
+++ b/logs/sqr.log
@@ -1,33 +1,143 @@
-924 26026
-1146 37682
-1370 51714
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diff --git a/logs/sqr_kara.log b/logs/sqr_kara.log
index f75256a..cafe458 100644
--- a/logs/sqr_kara.log
+++ b/logs/sqr_kara.log
@@ -1,33 +1,33 @@
-923 165854
-1146 112539
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diff --git a/logs/sub.log b/logs/sub.log
index 97ea200..cf2bcd6 100644
--- a/logs/sub.log
+++ b/logs/sub.log
@@ -1,16 +1,16 @@
-224 2012
-448 2208
-672 2366
-896 2532
-1120 2682
-1344 2838
-1568 3016
-1792 3146
-2016 3318
-2240 3538
-2464 3756
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diff --git a/makefile b/makefile
index 95bd003..4fe2256 100644
--- a/makefile
+++ b/makefile
@@ -15,7 +15,7 @@ CFLAGS += -fomit-frame-pointer
#debug
#CFLAGS += -g3
-VERSION=0.31
+VERSION=0.32
default: libtommath.a
@@ -53,9 +53,9 @@ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_prime_sizes_tab.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
-bn_mp_init_set_int.o
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o
libtommath.a: $(OBJECTS)
$(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
@@ -139,7 +139,8 @@ pretty:
clean:
rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
- *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex *~ demo/*~ etc/*~
+ *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find -type f | grep [~] | xargs` *.lo *.la
+ rm -rf .libs
cd etc ; make clean
cd pics ; make clean
diff --git a/makefile.bcc b/makefile.bcc
index b71f380..775e9ff 100644
--- a/makefile.bcc
+++ b/makefile.bcc
@@ -29,9 +29,9 @@ bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
-bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_prime_sizes_tab.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
+bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
-bn_mp_init_set.obj bn_mp_init_set_int.obj
+bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj
TARGET = libtommath.lib
diff --git a/makefile.cygwin_dll b/makefile.cygwin_dll
index 332a328..c90e5d9 100644
--- a/makefile.cygwin_dll
+++ b/makefile.cygwin_dll
@@ -34,9 +34,9 @@ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_prime_sizes_tab.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
-bn_mp_init_set_int.o
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o
# make a Windows DLL via Cygwin
windll: $(OBJECTS)
diff --git a/makefile.icc b/makefile.icc
index e4c0d19..09117b7 100644
--- a/makefile.icc
+++ b/makefile.icc
@@ -57,9 +57,9 @@ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_prime_sizes_tab.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
-bn_mp_init_set_int.o
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o
libtommath.a: $(OBJECTS)
$(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
diff --git a/makefile.msvc b/makefile.msvc
index 7d67442..cf59943 100644
--- a/makefile.msvc
+++ b/makefile.msvc
@@ -28,9 +28,9 @@ bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
-bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_prime_sizes_tab.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
+bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
-bn_mp_init_set.obj bn_mp_init_set_int.obj
+bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj
library: $(OBJECTS)
lib /out:tommath.lib $(OBJECTS)
diff --git a/makefile.shared b/makefile.shared
new file mode 100644
index 0000000..96bbf32
--- /dev/null
+++ b/makefile.shared
@@ -0,0 +1,74 @@
+#Makefile for GCC
+#
+#Tom St Denis
+VERSION=0:32
+
+CC = libtool --mode=compile gcc
+
+CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare
+
+#for speed
+CFLAGS += -O3 -funroll-loops
+
+#for size
+#CFLAGS += -Os
+
+#x86 optimizations [should be valid for any GCC install though]
+CFLAGS += -fomit-frame-pointer
+
+default: libtommath.la
+
+#default files to install
+LIBNAME=libtommath.la
+HEADERS=tommath.h
+
+#LIBPATH-The directory for libtommath to be installed to.
+#INCPATH-The directory to install the header files for libtommath.
+#DATAPATH-The directory to install the pdf docs.
+DESTDIR=
+LIBPATH=/usr/lib
+INCPATH=/usr/include
+DATAPATH=/usr/share/doc/libtommath/pdf
+
+OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
+bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
+bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
+bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
+bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
+bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
+bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
+bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
+bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
+bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
+bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
+bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \
+bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
+bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
+bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
+bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
+bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
+bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o
+
+libtommath.la: $(OBJECTS)
+ libtool --mode=link gcc *.lo -o libtommath.la -rpath $(LIBPATH) -version-info $(VERSION)
+ libtool --mode=link gcc *.o -o libtommath.a
+ libtool --mode=install install -c libtommath.la $(LIBPATH)/libtommath.la
+ install -d -g root -o root $(DESTDIR)$(INCPATH)
+ install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH)
+
+test: libtommath.a demo/demo.o
+ gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o
+ libtool --mode=link gcc -o test demo/demo.o libtommath.la
+
+mtest: test
+ cd mtest ; gcc $(CFLAGS) mtest.c -o mtest -s
+
+timing: libtommath.la
+ gcc $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s
diff --git a/mtest/mtest.c b/mtest/mtest.c
index 2c24825..ef0e093 100644
--- a/mtest/mtest.c
+++ b/mtest/mtest.c
@@ -58,7 +58,7 @@ void rand_num2(mp_int *a)
int n, size;
unsigned char buf[2048];
- size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 97;
+ size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 97;
buf[0] = (fgetc(rng)&1)?1:0;
fread(buf+1, 1, size, rng);
while (buf[1] == 0) buf[1] = fgetc(rng);
@@ -109,11 +109,12 @@ int main(void)
t1 = clock();
for (;;) {
+#if 0
if (clock() - t1 > CLOCKS_PER_SEC) {
sleep(2);
t1 = clock();
}
-
+#endif
n = fgetc(rng) % 15;
if (n == 0) {
diff --git a/poster.pdf b/poster.pdf
index 6689f2e..60999da 100644
Binary files a/poster.pdf and b/poster.pdf differ
diff --git a/pre_gen/mpi.c b/pre_gen/mpi.c
index 370b34d..78a73f0 100644
--- a/pre_gen/mpi.c
+++ b/pre_gen/mpi.c
@@ -1,4 +1,6 @@
/* Start: bn_error.c */
+#include <tommath.h>
+#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -13,7 +15,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static const struct {
int code;
@@ -40,10 +41,13 @@ char *mp_error_to_string(int code)
return "Invalid error code";
}
+#endif
/* End: bn_error.c */
/* Start: bn_fast_mp_invmod.c */
+#include <tommath.h>
+#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -58,12 +62,11 @@ char *mp_error_to_string(int code)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
- * Based on mp_invmod except this is optimized for the case where b is
+ * Based on slow invmod except this is optimized for the case where b is
* odd as per HAC Note 14.64 on pp. 610
*/
int
@@ -187,10 +190,13 @@ top:
__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
+#endif
/* End: bn_fast_mp_invmod.c */
/* Start: bn_fast_mp_montgomery_reduce.c */
+#include <tommath.h>
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -205,11 +211,10 @@ __ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction
*
- * This is an optimized implementation of mp_montgomery_reduce
+ * This is an optimized implementation of montgomery_reduce
* which uses the comba method to quickly calculate the columns of the
* reduction.
*
@@ -358,10 +363,13 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
}
return MP_OKAY;
}
+#endif
/* End: bn_fast_mp_montgomery_reduce.c */
/* Start: bn_fast_s_mp_mul_digs.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -376,7 +384,6 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Fast (comba) multiplier
*
@@ -397,8 +404,9 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
int
fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int olduse, res, pa, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
/* grow the destination as required */
if (c->alloc < digs) {
@@ -407,48 +415,39 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
}
}
- /* clear temp buf (the columns) */
- memset (W, 0, sizeof (mp_word) * digs);
-
- /* calculate the columns */
- pa = a->used;
- for (ix = 0; ix < pa; ix++) {
- /* this multiplier has been modified to allow you to
- * control how many digits of output are produced.
- * So at most we want to make upto "digs" digits of output.
- *
- * this adds products to distinct columns (at ix+iy) of W
- * note that each step through the loop is not dependent on
- * the previous which means the compiler can easily unroll
- * the loop without scheduling problems
- */
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy, pb;
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
- /* alias for the the word on the left e.g. A[ix] * A[iy] */
- tmpx = a->dp[ix];
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix <= pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
- /* alias for the right side */
- tmpy = b->dp;
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* alias for the columns, each step through the loop adds a new
- term to each column
- */
- _W = W + ix;
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* the number of digits is limited by their placement. E.g.
- we avoid multiplying digits that will end up above the # of
- digits of precision requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- pb = MIN (b->used, digs - ix);
+ iy = MIN(a->used-tx, ty+1);
- for (iy = 0; iy < pb; iy++) {
- *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
@@ -457,32 +456,11 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
register mp_digit *tmpc;
-
- /* At this point W[] contains the sums of each column. To get the
- * correct result we must take the extra bits from each column and
- * carry them down
- *
- * Note that while this adds extra code to the multiplier it
- * saves time since the carry propagation is removed from the
- * above nested loop.This has the effect of reducing the work
- * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
- * cost of the shifting. On very small numbers this is slower
- * but on most cryptographic size numbers it is faster.
- *
- * In this particular implementation we feed the carries from
- * behind which means when the loop terminates we still have one
- * last digit to copy
- */
tmpc = c->dp;
- for (ix = 1; ix < digs; ix++) {
- /* forward the carry from the previous temp */
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-
+ for (ix = 0; ix < digs; ix++) {
/* now extract the previous digit [below the carry] */
- *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ *tmpc++ = W[ix];
}
- /* fetch the last digit */
- *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
@@ -492,10 +470,13 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_mul_digs.c */
/* Start: bn_fast_s_mp_mul_high_digs.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -510,10 +491,9 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
- #include <tommath.h>
-/* this is a modified version of fast_s_mp_mul_digs that only produces
- * output digits *above* digs. See the comments for fast_s_mp_mul_digs
+/* this is a modified version of fast_s_mul_digs that only produces
+ * output digits *above* digs. See the comments for fast_s_mul_digs
* to see how it works.
*
* This is used in the Barrett reduction since for one of the multiplications
@@ -524,80 +504,78 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
int
fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int oldused, newused, res, pa, pb, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ mp_word _W;
- /* calculate size of product and allocate more space if required */
- newused = a->used + b->used + 1;
- if (c->alloc < newused) {
- if ((res = mp_grow (c, newused)) != MP_OKAY) {
+ /* grow the destination as required */
+ pa = a->used + b->used;
+ if (c->alloc < pa) {
+ if ((res = mp_grow (c, pa)) != MP_OKAY) {
return res;
}
}
- /* like the other comba method we compute the columns first */
- pa = a->used;
- pb = b->used;
- memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word));
- for (ix = 0; ix < pa; ix++) {
- {
- register mp_digit tmpx, *tmpy;
- register int iy;
- register mp_word *_W;
+ /* number of output digits to produce */
+ pa = a->used + b->used;
+ _W = 0;
+ for (ix = digs; ix <= pa; ix++) {
+ int tx, ty, iy;
+ mp_digit *tmpx, *tmpy;
- /* work todo, that is we only calculate digits that are at "digs" or above */
- iy = digs - ix;
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* copy of word on the left of A[ix] * B[iy] */
- tmpx = a->dp[ix];
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* alias for right side */
- tmpy = b->dp + iy;
-
- /* alias for the columns of output. Offset to be equal to or above the
- * smallest digit place requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- _W = W + digs;
-
- /* skip cases below zero where ix > digs */
- if (iy < 0) {
- iy = abs(iy);
- tmpy += iy;
- _W += iy;
- iy = 0;
- }
+ iy = MIN(a->used-tx, ty+1);
- /* compute column products for digits above the minimum */
- for (; iy < pb; iy++) {
- *_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
- oldused = c->used;
- c->used = newused;
+ olduse = c->used;
+ c->used = pa;
- /* now convert the array W downto what we need
- *
- * See comments in bn_fast_s_mp_mul_digs.c
- */
- for (ix = digs + 1; ix < newused; ix++) {
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
- c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
- }
- c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK));
+ {
+ register mp_digit *tmpc;
- for (; ix < oldused; ix++) {
- c->dp[ix] = 0;
+ tmpc = c->dp + digs;
+ for (ix = digs; ix <= pa; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
}
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_mul_high_digs.c */
/* Start: bn_fast_s_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -612,7 +590,6 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* fast squaring
*
@@ -631,116 +608,107 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
* Based on Algorithm 14.16 on pp.597 of HAC.
*
*/
+/* the jist of squaring...
+
+you do like mult except the offset of the tmpx [one that starts closer to zero]
+can't equal the offset of tmpy. So basically you set up iy like before then you min it with
+(ty-tx) so that it never happens. You double all those you add in the inner loop
+
+After that loop you do the squares and add them in.
+
+Remove W2 and don't memset W
+
+*/
+
int fast_s_mp_sqr (mp_int * a, mp_int * b)
{
- int olduse, newused, res, ix, pa;
- mp_word W2[MP_WARRAY], W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
- /* calculate size of product and allocate as required */
- pa = a->used;
- newused = pa + pa + 1;
- if (b->alloc < newused) {
- if ((res = mp_grow (b, newused)) != MP_OKAY) {
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
return res;
}
}
- /* zero temp buffer (columns)
- * Note that there are two buffers. Since squaring requires
- * a outer and inner product and the inner product requires
- * computing a product and doubling it (a relatively expensive
- * op to perform n**2 times if you don't have to) the inner and
- * outer products are computed in different buffers. This way
- * the inner product can be doubled using n doublings instead of
- * n**2
- */
- memset (W, 0, newused * sizeof (mp_word));
- memset (W2, 0, newused * sizeof (mp_word));
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix <= pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
- /* This computes the inner product. To simplify the inner N**2 loop
- * the multiplication by two is done afterwards in the N loop.
- */
- for (ix = 0; ix < pa; ix++) {
- /* compute the outer product
- *
- * Note that every outer product is computed
- * for a particular column only once which means that
- * there is no need todo a double precision addition
- * into the W2[] array.
- */
- W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
+ /* clear counter */
+ _W = 0;
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy;
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
- /* copy of left side */
- tmpx = a->dp[ix];
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
- /* alias for right side */
- tmpy = a->dp + (ix + 1);
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
- /* the column to store the result in */
- _W = W + (ix + ix + 1);
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
- /* inner products */
- for (iy = ix + 1; iy < pa; iy++) {
- *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
+
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+ }
+
+ /* store it */
+ W[ix] = _W;
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
olduse = b->used;
- b->used = newused;
+ b->used = a->used+a->used;
- /* now compute digits
- *
- * We have to double the inner product sums, add in the
- * outer product sums, propagate carries and convert
- * to single precision.
- */
{
- register mp_digit *tmpb;
-
- /* double first value, since the inner products are
- * half of what they should be
- */
- W[0] += W[0] + W2[0];
-
+ mp_digit *tmpb;
tmpb = b->dp;
- for (ix = 1; ix < newused; ix++) {
- /* double/add next digit */
- W[ix] += W[ix] + W2[ix];
-
- /* propagate carry forwards [from the previous digit] */
- W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-
- /* store the current digit now that the carry isn't
- * needed
- */
- *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
}
- /* set the last value. Note even if the carry is zero
- * this is required since the next step will not zero
- * it if b originally had a value at b->dp[2*a.used]
- */
- *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
- /* clear high digits of b if there were any originally */
+ /* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
-
mp_clamp (b);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_sqr.c */
/* Start: bn_mp_2expt.c */
+#include <tommath.h>
+#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -755,7 +723,6 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes a = 2**b
*
@@ -783,10 +750,13 @@ mp_2expt (mp_int * a, int b)
return MP_OKAY;
}
+#endif
/* End: bn_mp_2expt.c */
/* Start: bn_mp_abs.c */
+#include <tommath.h>
+#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -801,7 +771,6 @@ mp_2expt (mp_int * a, int b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = |a|
*
@@ -824,10 +793,13 @@ mp_abs (mp_int * a, mp_int * b)
return MP_OKAY;
}
+#endif
/* End: bn_mp_abs.c */
/* Start: bn_mp_add.c */
+#include <tommath.h>
+#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -842,7 +814,6 @@ mp_abs (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
@@ -875,10 +846,13 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
return res;
}
+#endif
/* End: bn_mp_add.c */
/* Start: bn_mp_add_d.c */
+#include <tommath.h>
+#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -893,7 +867,6 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit addition */
int
@@ -982,10 +955,13 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
/* End: bn_mp_add_d.c */
/* Start: bn_mp_addmod.c */
+#include <tommath.h>
+#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1000,7 +976,6 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a + b (mod c) */
int
@@ -1021,10 +996,13 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_addmod.c */
/* Start: bn_mp_and.c */
+#include <tommath.h>
+#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1039,7 +1017,6 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* AND two ints together */
int
@@ -1076,10 +1053,13 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_and.c */
/* Start: bn_mp_clamp.c */
+#include <tommath.h>
+#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1094,7 +1074,6 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* trim unused digits
*
@@ -1118,10 +1097,13 @@ mp_clamp (mp_int * a)
a->sign = MP_ZPOS;
}
}
+#endif
/* End: bn_mp_clamp.c */
/* Start: bn_mp_clear.c */
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1136,7 +1118,6 @@ mp_clamp (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* clear one (frees) */
void
@@ -1160,10 +1141,13 @@ mp_clear (mp_int * a)
a->sign = MP_ZPOS;
}
}
+#endif
/* End: bn_mp_clear.c */
/* Start: bn_mp_clear_multi.c */
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1178,7 +1162,6 @@ mp_clear (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
@@ -1192,10 +1175,13 @@ void mp_clear_multi(mp_int *mp, ...)
}
va_end(args);
}
+#endif
/* End: bn_mp_clear_multi.c */
/* Start: bn_mp_cmp.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1210,7 +1196,6 @@ void mp_clear_multi(mp_int *mp, ...)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare two ints (signed)*/
int
@@ -1233,10 +1218,13 @@ mp_cmp (mp_int * a, mp_int * b)
return mp_cmp_mag(a, b);
}
}
+#endif
/* End: bn_mp_cmp.c */
/* Start: bn_mp_cmp_d.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1251,7 +1239,6 @@ mp_cmp (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare a digit */
int mp_cmp_d(mp_int * a, mp_digit b)
@@ -1275,10 +1262,13 @@ int mp_cmp_d(mp_int * a, mp_digit b)
return MP_EQ;
}
}
+#endif
/* End: bn_mp_cmp_d.c */
/* Start: bn_mp_cmp_mag.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1293,7 +1283,6 @@ int mp_cmp_d(mp_int * a, mp_digit b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (mp_int * a, mp_int * b)
@@ -1328,10 +1317,13 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
}
return MP_EQ;
}
+#endif
/* End: bn_mp_cmp_mag.c */
/* Start: bn_mp_cnt_lsb.c */
+#include <tommath.h>
+#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1346,7 +1338,6 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static const int lnz[16] = {
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
@@ -1379,10 +1370,13 @@ int mp_cnt_lsb(mp_int *a)
return x;
}
+#endif
/* End: bn_mp_cnt_lsb.c */
/* Start: bn_mp_copy.c */
+#include <tommath.h>
+#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1397,7 +1391,6 @@ int mp_cnt_lsb(mp_int *a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* copy, b = a */
int
@@ -1445,10 +1438,13 @@ mp_copy (mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
+#endif
/* End: bn_mp_copy.c */
/* Start: bn_mp_count_bits.c */
+#include <tommath.h>
+#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1463,7 +1459,6 @@ mp_copy (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns the number of bits in an int */
int
@@ -1488,10 +1483,13 @@ mp_count_bits (mp_int * a)
}
return r;
}
+#endif
/* End: bn_mp_count_bits.c */
/* Start: bn_mp_div.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1506,7 +1504,78 @@ mp_count_bits (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_copy(a, &ta)) != MP_OKAY) ||
+ ((res = mp_copy(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto __ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto __ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto __ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = n;
+ }
+__ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
/* integer signed division.
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
@@ -1704,9 +1773,15 @@ __Q:mp_clear (&q);
return res;
}
+#endif
+
+#endif
+
/* End: bn_mp_div.c */
/* Start: bn_mp_div_2.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1721,7 +1796,6 @@ __Q:mp_clear (&q);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
@@ -1769,10 +1843,13 @@ int mp_div_2(mp_int * a, mp_int * b)
mp_clamp (b);
return MP_OKAY;
}
+#endif
/* End: bn_mp_div_2.c */
/* Start: bn_mp_div_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1787,7 +1864,6 @@ int mp_div_2(mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
@@ -1864,10 +1940,13 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_div_2d.c */
/* Start: bn_mp_div_3.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1882,7 +1961,6 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* divide by three (based on routine from MPI and the GMP manual) */
int
@@ -1941,10 +2019,13 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
return res;
}
+#endif
/* End: bn_mp_div_3.c */
/* Start: bn_mp_div_d.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1959,7 +2040,6 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static int s_is_power_of_two(mp_digit b, int *p)
{
@@ -2001,7 +2081,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
/* power of two ? */
if (s_is_power_of_two(b, &ix) == 1) {
if (d != NULL) {
- *d = a->dp[0] & ((1<<ix) - 1);
+ *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
}
if (c != NULL) {
return mp_div_2d(a, ix, c, NULL);
@@ -2009,10 +2089,12 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return MP_OKAY;
}
+#ifdef BN_MP_DIV_3_C
/* three? */
if (b == 3) {
return mp_div_3(a, c, d);
}
+#endif
/* no easy answer [c'est la vie]. Just division */
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
@@ -2047,10 +2129,13 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return res;
}
+#endif
/* End: bn_mp_div_d.c */
/* Start: bn_mp_dr_is_modulus.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2065,7 +2150,6 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
@@ -2088,10 +2172,13 @@ int mp_dr_is_modulus(mp_int *a)
return 1;
}
+#endif
/* End: bn_mp_dr_is_modulus.c */
/* Start: bn_mp_dr_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2106,7 +2193,6 @@ int mp_dr_is_modulus(mp_int *a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
*
@@ -2180,10 +2266,13 @@ top:
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_dr_reduce.c */
/* Start: bn_mp_dr_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2198,7 +2287,6 @@ top:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
@@ -2210,10 +2298,13 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
((mp_word)a->dp[0]));
}
+#endif
/* End: bn_mp_dr_setup.c */
/* Start: bn_mp_exch.c */
+#include <tommath.h>
+#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2228,7 +2319,6 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* swap the elements of two integers, for cases where you can't simply swap the
* mp_int pointers around
@@ -2242,10 +2332,13 @@ mp_exch (mp_int * a, mp_int * b)
*a = *b;
*b = t;
}
+#endif
/* End: bn_mp_exch.c */
/* Start: bn_mp_expt_d.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2260,7 +2353,6 @@ mp_exch (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calculate c = a**b using a square-multiply algorithm */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
@@ -2297,10 +2389,13 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
mp_clear (&g);
return MP_OKAY;
}
+#endif
/* End: bn_mp_expt_d.c */
/* Start: bn_mp_exptmod.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2315,7 +2410,6 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this is a shell function that calls either the normal or Montgomery
@@ -2334,6 +2428,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
/* if exponent X is negative we have to recurse */
if (X->sign == MP_NEG) {
+#ifdef BN_MP_INVMOD_C
mp_int tmpG, tmpX;
int err;
@@ -2360,29 +2455,51 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
err = mp_exptmod(&tmpG, &tmpX, P, Y);
mp_clear_multi(&tmpG, &tmpX, NULL);
return err;
+#else
+ /* no invmod */
+ return MP_VAL
+#endif
}
+#ifdef BN_MP_DR_IS_MODULUS_C
/* is it a DR modulus? */
dr = mp_dr_is_modulus(P);
+#else
+ dr = 0;
+#endif
+#ifdef BN_MP_REDUCE_IS_2K_C
/* if not, is it a uDR modulus? */
if (dr == 0) {
dr = mp_reduce_is_2k(P) << 1;
}
+#endif
/* if the modulus is odd or dr != 0 use the fast method */
+#ifdef BN_MP_EXPTMOD_FAST_C
if (mp_isodd (P) == 1 || dr != 0) {
return mp_exptmod_fast (G, X, P, Y, dr);
} else {
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
/* otherwise use the generic Barrett reduction technique */
return s_mp_exptmod (G, X, P, Y);
+#else
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
}
+#endif
}
+#endif
/* End: bn_mp_exptmod.c */
/* Start: bn_mp_exptmod_fast.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2397,7 +2514,6 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
*
@@ -2469,29 +2585,52 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* determine and setup reduction code */
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* now setup montgomery */
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
goto __M;
}
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
if (((P->used * 2 + 1) < MP_WARRAY) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
- } else {
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
}
} else if (redmode == 1) {
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
/* setup DR reduction for moduli of the form B**k - b */
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
} else {
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
/* setup DR reduction for moduli of the form 2**k - b */
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
goto __M;
}
redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
}
/* setup result */
@@ -2501,16 +2640,21 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* create M table
*
- * The M table contains powers of the input base, e.g. M[x] = G^x mod P
+
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
goto __RES;
}
+#else
+ err = MP_VAL;
+ goto __RES;
+#endif
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
@@ -2654,7 +2798,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
* to reduce one more time to cancel out the factor
* of R.
*/
- if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
@@ -2670,10 +2814,14 @@ __M:
}
return err;
}
+#endif
+
/* End: bn_mp_exptmod_fast.c */
/* Start: bn_mp_exteuclid.c */
+#include <tommath.h>
+#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2688,7 +2836,6 @@ __M:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Extended euclidean algorithm of (a, b) produces
a*u1 + b*u2 = u3
@@ -2743,10 +2890,13 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
return err;
}
+#endif
/* End: bn_mp_exteuclid.c */
/* Start: bn_mp_fread.c */
+#include <tommath.h>
+#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2761,7 +2911,6 @@ _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
@@ -2808,10 +2957,13 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
+#endif
/* End: bn_mp_fread.c */
/* Start: bn_mp_fwrite.c */
+#include <tommath.h>
+#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2826,7 +2978,6 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
@@ -2858,10 +3009,13 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
+#endif
/* End: bn_mp_fwrite.c */
/* Start: bn_mp_gcd.c */
+#include <tommath.h>
+#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2876,7 +3030,6 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
@@ -2969,10 +3122,13 @@ __V:mp_clear (&u);
__U:mp_clear (&v);
return res;
}
+#endif
/* End: bn_mp_gcd.c */
/* Start: bn_mp_get_int.c */
+#include <tommath.h>
+#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2987,7 +3143,6 @@ __U:mp_clear (&v);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
@@ -3012,10 +3167,13 @@ unsigned long mp_get_int(mp_int * a)
/* force result to 32-bits always so it is consistent on non 32-bit platforms */
return res & 0xFFFFFFFFUL;
}
+#endif
/* End: bn_mp_get_int.c */
/* Start: bn_mp_grow.c */
+#include <tommath.h>
+#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3030,7 +3188,6 @@ unsigned long mp_get_int(mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* grow as required */
int mp_grow (mp_int * a, int size)
@@ -3067,10 +3224,13 @@ int mp_grow (mp_int * a, int size)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_grow.c */
/* Start: bn_mp_init.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3085,7 +3245,6 @@ int mp_grow (mp_int * a, int size)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* init a new mp_int */
int mp_init (mp_int * a)
@@ -3111,10 +3270,13 @@ int mp_init (mp_int * a)
return MP_OKAY;
}
+#endif
/* End: bn_mp_init.c */
/* Start: bn_mp_init_copy.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3129,7 +3291,6 @@ int mp_init (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
@@ -3141,10 +3302,13 @@ int mp_init_copy (mp_int * a, mp_int * b)
}
return mp_copy (b, a);
}
+#endif
/* End: bn_mp_init_copy.c */
/* Start: bn_mp_init_multi.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3159,7 +3323,6 @@ int mp_init_copy (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#include <stdarg.h>
int mp_init_multi(mp_int *mp, ...)
@@ -3198,10 +3361,13 @@ int mp_init_multi(mp_int *mp, ...)
return res; /* Assumed ok, if error flagged above. */
}
+#endif
/* End: bn_mp_init_multi.c */
/* Start: bn_mp_init_set.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3216,7 +3382,6 @@ int mp_init_multi(mp_int *mp, ...)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
@@ -3228,10 +3393,13 @@ int mp_init_set (mp_int * a, mp_digit b)
mp_set(a, b);
return err;
}
+#endif
/* End: bn_mp_init_set.c */
/* Start: bn_mp_init_set_int.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3246,7 +3414,6 @@ int mp_init_set (mp_int * a, mp_digit b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
@@ -3257,10 +3424,13 @@ int mp_init_set_int (mp_int * a, unsigned long b)
}
return mp_set_int(a, b);
}
+#endif
/* End: bn_mp_init_set_int.c */
/* Start: bn_mp_init_size.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3275,29 +3445,40 @@ int mp_init_set_int (mp_int * a, unsigned long b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
+ int x;
+
/* pad size so there are always extra digits */
size += (MP_PREC * 2) - (size % MP_PREC);
/* alloc mem */
- a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size);
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
if (a->dp == NULL) {
return MP_MEM;
}
+
+ /* set the members */
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
+
return MP_OKAY;
}
+#endif
/* End: bn_mp_init_size.c */
/* Start: bn_mp_invmod.c */
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3312,24 +3493,61 @@ int mp_init_size (mp_int * a, int size)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
- mp_int x, y, u, v, A, B, C, D;
- int res;
-
/* b cannot be negative */
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
return MP_VAL;
}
+#ifdef BN_FAST_MP_INVMOD_C
/* if the modulus is odd we can use a faster routine instead */
if (mp_isodd (b) == 1) {
return fast_mp_invmod (a, b, c);
}
-
+#endif
+
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
+
+ return MP_VAL;
+}
+#endif
+
+/* End: bn_mp_invmod.c */
+
+/* Start: bn_mp_invmod_slow.c */
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_SLOW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, A, B, C, D;
+ int res;
+
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
/* init temps */
if ((res = mp_init_multi(&x, &y, &u, &v,
&A, &B, &C, &D, NULL)) != MP_OKAY) {
@@ -3472,10 +3690,13 @@ top:
__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
return res;
}
+#endif
-/* End: bn_mp_invmod.c */
+/* End: bn_mp_invmod_slow.c */
/* Start: bn_mp_is_square.c */
+#include <tommath.h>
+#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3490,7 +3711,6 @@ __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
@@ -3547,7 +3767,7 @@ int mp_is_square(mp_int *arg,int *ret)
return MP_OKAY;
}
- /* product of primes less than 2^31 */
+
if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
return res;
}
@@ -3579,10 +3799,13 @@ int mp_is_square(mp_int *arg,int *ret)
ERR:mp_clear(&t);
return res;
}
+#endif
/* End: bn_mp_is_square.c */
/* Start: bn_mp_jacobi.c */
+#include <tommath.h>
+#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3597,7 +3820,6 @@ ERR:mp_clear(&t);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
@@ -3682,10 +3904,13 @@ __P1:mp_clear (&p1);
__A1:mp_clear (&a1);
return res;
}
+#endif
/* End: bn_mp_jacobi.c */
/* Start: bn_mp_karatsuba_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3700,7 +3925,6 @@ __A1:mp_clear (&a1);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
@@ -3847,10 +4071,13 @@ X0:mp_clear (&x0);
ERR:
return err;
}
+#endif
/* End: bn_mp_karatsuba_mul.c */
/* Start: bn_mp_karatsuba_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3865,12 +4092,11 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Karatsuba squaring, computes b = a*a using three
* half size squarings
*
- * See comments of mp_karatsuba_mul for details. It
+ * See comments of karatsuba_mul for details. It
* is essentially the same algorithm but merely
* tuned to perform recursive squarings.
*/
@@ -3966,10 +4192,13 @@ X0:mp_clear (&x0);
ERR:
return err;
}
+#endif
/* End: bn_mp_karatsuba_sqr.c */
/* Start: bn_mp_lcm.c */
+#include <tommath.h>
+#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3984,7 +4213,6 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
@@ -4024,10 +4252,13 @@ __T:
mp_clear_multi (&t1, &t2, NULL);
return res;
}
+#endif
/* End: bn_mp_lcm.c */
/* Start: bn_mp_lshd.c */
+#include <tommath.h>
+#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4042,7 +4273,6 @@ __T:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
@@ -4089,10 +4319,13 @@ int mp_lshd (mp_int * a, int b)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_lshd.c */
/* Start: bn_mp_mod.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4107,7 +4340,6 @@ int mp_lshd (mp_int * a, int b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a mod b, 0 <= c < b */
int
@@ -4135,10 +4367,13 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_mod.c */
/* Start: bn_mp_mod_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4153,7 +4388,6 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calc a value mod 2**b */
int
@@ -4188,10 +4422,13 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_mp_mod_2d.c */
/* Start: bn_mp_mod_d.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4206,17 +4443,19 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
return mp_div_d(a, b, NULL, c);
}
+#endif
/* End: bn_mp_mod_d.c */
/* Start: bn_mp_montgomery_calc_normalization.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4231,31 +4470,31 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* calculates a = B^n mod b for Montgomery reduction
- * Where B is the base [e.g. 2^DIGIT_BIT].
- * B^n mod b is computed by first computing
- * A = B^(n-1) which doesn't require a reduction but a simple OR.
- * then C = A * B = B^n is computed by performing upto DIGIT_BIT
+/*
* shifts with subtractions when the result is greater than b.
*
* The method is slightly modified to shift B unconditionally upto just under
* the leading bit of b. This saves alot of multiple precision shifting.
*/
-int
-mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
{
int x, bits, res;
/* how many bits of last digit does b use */
bits = mp_count_bits (b) % DIGIT_BIT;
- /* compute A = B^(n-1) * 2^(bits-1) */
- if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
- return res;
+
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
}
+
/* now compute C = A * B mod b */
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
@@ -4270,10 +4509,13 @@ mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_calc_normalization.c */
/* Start: bn_mp_montgomery_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4288,7 +4530,6 @@ mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
@@ -4299,7 +4540,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* can the fast reduction [comba] method be used?
*
- * Note that unlike in mp_mul you're safely allowed *less*
+ * Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
@@ -4322,7 +4563,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* mu = ai * rho mod b
*
* The value of rho must be precalculated via
- * bn_mp_montgomery_setup() such that
+ * montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
@@ -4386,10 +4627,13 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_reduce.c */
/* Start: bn_mp_montgomery_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4404,7 +4648,6 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* setups the montgomery reduction stuff */
int
@@ -4439,14 +4682,17 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
#endif
/* rho = -1/m mod b */
- *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
+ *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_setup.c */
/* Start: bn_mp_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4461,7 +4707,6 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
@@ -4470,12 +4715,18 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
/* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
res = mp_toom_mul(a, b, c);
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
/* use Karatsuba? */
- } else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
res = mp_karatsuba_mul (a, b, c);
- } else {
+ } else
+#endif
+ {
/* can we use the fast multiplier?
*
* The fast multiplier can be used if the output will
@@ -4484,21 +4735,30 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
*/
int digs = a->used + b->used + 1;
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
if ((digs < MP_WARRAY) &&
MIN(a->used, b->used) <=
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
res = fast_s_mp_mul_digs (a, b, c, digs);
- } else {
- res = s_mp_mul (a, b, c);
- }
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+ res = MP_VAL;
+#endif
+
}
c->sign = (c->used > 0) ? neg : MP_ZPOS;
return res;
}
+#endif
/* End: bn_mp_mul.c */
/* Start: bn_mp_mul_2.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4513,7 +4773,6 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
@@ -4575,10 +4834,13 @@ int mp_mul_2(mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_2.c */
/* Start: bn_mp_mul_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4593,7 +4855,6 @@ int mp_mul_2(mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left by a certain bit count */
int mp_mul_2d (mp_int * a, int b, mp_int * c)
@@ -4658,10 +4919,13 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_2d.c */
/* Start: bn_mp_mul_d.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4676,7 +4940,6 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiply by a digit */
int
@@ -4734,10 +4997,13 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_d.c */
/* Start: bn_mp_mulmod.c */
+#include <tommath.h>
+#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4752,7 +5018,6 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a * b (mod c) */
int
@@ -4773,10 +5038,13 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_mulmod.c */
/* Start: bn_mp_n_root.c */
+#include <tommath.h>
+#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4791,7 +5059,6 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* find the n'th root of an integer
*
@@ -4903,10 +5170,13 @@ __T2:mp_clear (&t2);
__T1:mp_clear (&t1);
return res;
}
+#endif
/* End: bn_mp_n_root.c */
/* Start: bn_mp_neg.c */
+#include <tommath.h>
+#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4921,7 +5191,6 @@ __T1:mp_clear (&t1);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = -a */
int mp_neg (mp_int * a, mp_int * b)
@@ -4935,10 +5204,13 @@ int mp_neg (mp_int * a, mp_int * b)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_neg.c */
/* Start: bn_mp_or.c */
+#include <tommath.h>
+#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4953,7 +5225,6 @@ int mp_neg (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
@@ -4983,10 +5254,13 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_or.c */
/* Start: bn_mp_prime_fermat.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5001,7 +5275,6 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs one Fermat test.
*
@@ -5043,10 +5316,13 @@ int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
__T:mp_clear (&t);
return err;
}
+#endif
/* End: bn_mp_prime_fermat.c */
/* Start: bn_mp_prime_is_divisible.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5061,7 +5337,6 @@ __T:mp_clear (&t);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if an integers is divisible by one
* of the first PRIME_SIZE primes or not
@@ -5091,10 +5366,13 @@ int mp_prime_is_divisible (mp_int * a, int *result)
return MP_OKAY;
}
+#endif
/* End: bn_mp_prime_is_divisible.c */
/* Start: bn_mp_prime_is_prime.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5109,12 +5387,11 @@ int mp_prime_is_divisible (mp_int * a, int *result)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs a variable number of rounds of Miller-Rabin
*
* Probability of error after t rounds is no more than
- * (1/4)^t when 1 <= t <= PRIME_SIZE
+
*
* Sets result to 1 if probably prime, 0 otherwise
*/
@@ -5172,10 +5449,13 @@ int mp_prime_is_prime (mp_int * a, int t, int *result)
__B:mp_clear (&b);
return err;
}
+#endif
/* End: bn_mp_prime_is_prime.c */
/* Start: bn_mp_prime_miller_rabin.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5190,7 +5470,6 @@ __B:mp_clear (&b);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
@@ -5273,10 +5552,13 @@ __R:mp_clear (&r);
__N1:mp_clear (&n1);
return err;
}
+#endif
/* End: bn_mp_prime_miller_rabin.c */
/* Start: bn_mp_prime_next_prime.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5291,7 +5573,6 @@ __N1:mp_clear (&n1);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
@@ -5441,10 +5722,13 @@ __ERR:
return err;
}
+#endif
/* End: bn_mp_prime_next_prime.c */
-/* Start: bn_mp_prime_random_ex.c */
+/* Start: bn_mp_prime_rabin_miller_trials.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5459,7 +5743,58 @@ __ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+
+static const struct {
+ int k, t;
+} sizes[] = {
+{ 128, 28 },
+{ 256, 16 },
+{ 384, 10 },
+{ 512, 7 },
+{ 640, 6 },
+{ 768, 5 },
+{ 896, 4 },
+{ 1024, 4 }
+};
+
+/* returns # of RM trials required for a given bit size */
+int mp_prime_rabin_miller_trials(int size)
+{
+ int x;
+
+ for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
+ if (sizes[x].k == size) {
+ return sizes[x].t;
+ } else if (sizes[x].k > size) {
+ return (x == 0) ? sizes[0].t : sizes[x - 1].t;
+ }
+ }
+ return sizes[x-1].t + 1;
+}
+
+
+#endif
+
+/* End: bn_mp_prime_rabin_miller_trials.c */
+
+/* Start: bn_mp_prime_random_ex.c */
#include <tommath.h>
+#ifdef BN_MP_PRIME_RANDOM_EX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
/* makes a truly random prime of a given size (bits),
*
@@ -5539,6 +5874,9 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
/* is it prime? */
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ if (res == MP_NO) {
+ continue;
+ }
if (flags & LTM_PRIME_SAFE) {
/* see if (a-1)/2 is prime */
@@ -5563,10 +5901,13 @@ error:
}
+#endif
/* End: bn_mp_prime_random_ex.c */
/* Start: bn_mp_radix_size.c */
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5581,7 +5922,6 @@ error:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
@@ -5632,10 +5972,13 @@ int mp_radix_size (mp_int * a, int radix, int *size)
return MP_OKAY;
}
+#endif
/* End: bn_mp_radix_size.c */
/* Start: bn_mp_radix_smap.c */
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5650,14 +5993,16 @@ int mp_radix_size (mp_int * a, int radix, int *size)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+#endif
/* End: bn_mp_radix_smap.c */
/* Start: bn_mp_rand.c */
+#include <tommath.h>
+#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5672,7 +6017,6 @@ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrs
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* makes a pseudo-random int of a given size */
int
@@ -5707,10 +6051,13 @@ mp_rand (mp_int * a, int digits)
return MP_OKAY;
}
+#endif
/* End: bn_mp_rand.c */
/* Start: bn_mp_read_radix.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5725,7 +6072,6 @@ mp_rand (mp_int * a, int digits)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, char *str, int radix)
@@ -5787,10 +6133,13 @@ int mp_read_radix (mp_int * a, char *str, int radix)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_read_radix.c */
/* Start: bn_mp_read_signed_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5805,7 +6154,6 @@ int mp_read_radix (mp_int * a, char *str, int radix)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int
@@ -5827,10 +6175,13 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
return MP_OKAY;
}
+#endif
/* End: bn_mp_read_signed_bin.c */
/* Start: bn_mp_read_unsigned_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5845,7 +6196,6 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int
@@ -5881,10 +6231,13 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
mp_clamp (a);
return MP_OKAY;
}
+#endif
/* End: bn_mp_read_unsigned_bin.c */
/* Start: bn_mp_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5899,7 +6252,6 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces x mod m, assumes 0 < x < m**2, mu is
* precomputed via mp_reduce_setup.
@@ -5925,9 +6277,20 @@ mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
goto CLEANUP;
}
} else {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
goto CLEANUP;
}
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
}
/* q3 = q2 / b**(k+1) */
@@ -5969,10 +6332,13 @@ CLEANUP:
return res;
}
+#endif
/* End: bn_mp_reduce.c */
/* Start: bn_mp_reduce_2k.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5987,7 +6353,6 @@ CLEANUP:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces a modulo n where n is of the form 2**p - d */
int
@@ -6029,10 +6394,13 @@ ERR:
return res;
}
+#endif
/* End: bn_mp_reduce_2k.c */
/* Start: bn_mp_reduce_2k_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6047,7 +6415,6 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines the setup value */
int
@@ -6075,10 +6442,13 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d)
mp_clear(&tmp);
return MP_OKAY;
}
+#endif
/* End: bn_mp_reduce_2k_setup.c */
/* Start: bn_mp_reduce_is_2k.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6093,7 +6463,6 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
@@ -6125,10 +6494,13 @@ int mp_reduce_is_2k(mp_int *a)
return 1;
}
+#endif
/* End: bn_mp_reduce_is_2k.c */
/* Start: bn_mp_reduce_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6143,13 +6515,11 @@ int mp_reduce_is_2k(mp_int *a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* pre-calculate the value required for Barrett reduction
* For a given modulus "b" it calulates the value required in "a"
*/
-int
-mp_reduce_setup (mp_int * a, mp_int * b)
+int mp_reduce_setup (mp_int * a, mp_int * b)
{
int res;
@@ -6158,10 +6528,13 @@ mp_reduce_setup (mp_int * a, mp_int * b)
}
return mp_div (a, b, a, NULL);
}
+#endif
/* End: bn_mp_reduce_setup.c */
/* Start: bn_mp_rshd.c */
+#include <tommath.h>
+#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6176,7 +6549,6 @@ mp_reduce_setup (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
@@ -6228,10 +6600,13 @@ void mp_rshd (mp_int * a, int b)
/* remove excess digits */
a->used -= b;
}
+#endif
/* End: bn_mp_rshd.c */
/* Start: bn_mp_set.c */
+#include <tommath.h>
+#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6246,7 +6621,6 @@ void mp_rshd (mp_int * a, int b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
@@ -6255,10 +6629,13 @@ void mp_set (mp_int * a, mp_digit b)
a->dp[0] = b & MP_MASK;
a->used = (a->dp[0] != 0) ? 1 : 0;
}
+#endif
/* End: bn_mp_set.c */
/* Start: bn_mp_set_int.c */
+#include <tommath.h>
+#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6273,7 +6650,6 @@ void mp_set (mp_int * a, mp_digit b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
@@ -6301,10 +6677,13 @@ int mp_set_int (mp_int * a, unsigned long b)
mp_clamp (a);
return MP_OKAY;
}
+#endif
/* End: bn_mp_set_int.c */
/* Start: bn_mp_shrink.c */
+#include <tommath.h>
+#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6319,7 +6698,6 @@ int mp_set_int (mp_int * a, unsigned long b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shrink a bignum */
int mp_shrink (mp_int * a)
@@ -6334,10 +6712,13 @@ int mp_shrink (mp_int * a)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_shrink.c */
/* Start: bn_mp_signed_bin_size.c */
+#include <tommath.h>
+#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6352,17 +6733,19 @@ int mp_shrink (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
return 1 + mp_unsigned_bin_size (a);
}
+#endif
/* End: bn_mp_signed_bin_size.c */
/* Start: bn_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6377,7 +6760,6 @@ int mp_signed_bin_size (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes b = a*a */
int
@@ -6385,29 +6767,43 @@ mp_sqr (mp_int * a, mp_int * b)
{
int res;
+#ifdef BN_MP_TOOM_SQR_C
/* use Toom-Cook? */
if (a->used >= TOOM_SQR_CUTOFF) {
res = mp_toom_sqr(a, b);
/* Karatsuba? */
- } else if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
res = mp_karatsuba_sqr (a, b);
- } else {
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
/* can we use the fast comba multiplier? */
if ((a->used * 2 + 1) < MP_WARRAY &&
a->used <
(1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
res = fast_s_mp_sqr (a, b);
- } else {
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
res = s_mp_sqr (a, b);
- }
+#else
+ res = MP_VAL;
+#endif
}
b->sign = MP_ZPOS;
return res;
}
+#endif
/* End: bn_mp_sqr.c */
/* Start: bn_mp_sqrmod.c */
+#include <tommath.h>
+#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6422,7 +6818,6 @@ mp_sqr (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a * a (mod b) */
int
@@ -6443,10 +6838,13 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_sqrmod.c */
/* Start: bn_mp_sqrt.c */
+#include <tommath.h>
+#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6461,7 +6859,6 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
@@ -6522,10 +6919,13 @@ E2: mp_clear(&t1);
return res;
}
+#endif
/* End: bn_mp_sqrt.c */
/* Start: bn_mp_sub.c */
+#include <tommath.h>
+#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6540,7 +6940,6 @@ E2: mp_clear(&t1);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level subtraction (handles signs) */
int
@@ -6579,10 +6978,13 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
return res;
}
+#endif
/* End: bn_mp_sub.c */
/* Start: bn_mp_sub_d.c */
+#include <tommath.h>
+#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6597,7 +6999,6 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit subtraction */
int
@@ -6666,10 +7067,13 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
/* End: bn_mp_sub_d.c */
/* Start: bn_mp_submod.c */
+#include <tommath.h>
+#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6684,7 +7088,6 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a - b (mod c) */
int
@@ -6706,10 +7109,13 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_submod.c */
/* Start: bn_mp_to_signed_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6724,7 +7130,6 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in signed [big endian] format */
int
@@ -6738,10 +7143,13 @@ mp_to_signed_bin (mp_int * a, unsigned char *b)
b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
return MP_OKAY;
}
+#endif
/* End: bn_mp_to_signed_bin.c */
/* Start: bn_mp_to_unsigned_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6756,7 +7164,6 @@ mp_to_signed_bin (mp_int * a, unsigned char *b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in unsigned [big endian] format */
int
@@ -6785,10 +7192,13 @@ mp_to_unsigned_bin (mp_int * a, unsigned char *b)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_to_unsigned_bin.c */
/* Start: bn_mp_toom_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6803,9 +7213,13 @@ mp_to_unsigned_bin (mp_int * a, unsigned char *b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* multiplication using the Toom-Cook 3-way algorithm */
+/* multiplication using the Toom-Cook 3-way algorithm
+ *
+ * Much more complicated than Karatsuba but has a lower asymptotic running time of
+ * O(N**1.464). This algorithm is only particularly useful on VERY large
+ * inputs (we're talking 1000s of digits here...).
+*/
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
@@ -7061,10 +7475,13 @@ ERR:
return res;
}
+#endif
/* End: bn_mp_toom_mul.c */
/* Start: bn_mp_toom_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7079,7 +7496,6 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* squaring using Toom-Cook 3-way algorithm */
int
@@ -7285,10 +7701,13 @@ ERR:
return res;
}
+#endif
/* End: bn_mp_toom_sqr.c */
/* Start: bn_mp_toradix.c */
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7303,7 +7722,6 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix (mp_int * a, char *str, int radix)
@@ -7358,10 +7776,13 @@ int mp_toradix (mp_int * a, char *str, int radix)
return MP_OKAY;
}
+#endif
/* End: bn_mp_toradix.c */
/* Start: bn_mp_toradix_n.c */
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7376,7 +7797,6 @@ int mp_toradix (mp_int * a, char *str, int radix)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* stores a bignum as a ASCII string in a given radix (2..64)
*
@@ -7445,10 +7865,13 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
return MP_OKAY;
}
+#endif
/* End: bn_mp_toradix_n.c */
/* Start: bn_mp_unsigned_bin_size.c */
+#include <tommath.h>
+#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7463,7 +7886,6 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an unsigned equivalent */
int
@@ -7472,10 +7894,13 @@ mp_unsigned_bin_size (mp_int * a)
int size = mp_count_bits (a);
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
+#endif
/* End: bn_mp_unsigned_bin_size.c */
/* Start: bn_mp_xor.c */
+#include <tommath.h>
+#ifdef BN_MP_XOR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7490,7 +7915,6 @@ mp_unsigned_bin_size (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* XOR two ints together */
int
@@ -7514,17 +7938,20 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
}
for (ix = 0; ix < px; ix++) {
- t.dp[ix] ^= x->dp[ix];
+
}
mp_clamp (&t);
mp_exch (c, &t);
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_xor.c */
/* Start: bn_mp_zero.c */
+#include <tommath.h>
+#ifdef BN_MP_ZERO_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7539,7 +7966,6 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to zero */
void
@@ -7549,65 +7975,13 @@ mp_zero (mp_int * a)
a->used = 0;
memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
}
+#endif
/* End: bn_mp_zero.c */
-/* Start: bn_prime_sizes_tab.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-#include <tommath.h>
-
-/* this table gives the # of rabin miller trials for a prob of failure lower than 2^-96 */
-static const struct {
- int k, t;
-} sizes[] = {
-{ 128, 28 },
-{ 256, 16 },
-{ 384, 10 },
-{ 512, 7 },
-{ 640, 6 },
-{ 768, 5 },
-{ 896, 4 },
-{ 1024, 4 },
-{ 1152, 3 },
-{ 1280, 3 },
-{ 1408, 3 },
-{ 1536, 3 },
-{ 1664, 3 },
-{ 1792, 2 } };
-
-/* returns # of RM trials required for a given bit size */
-int mp_prime_rabin_miller_trials(int size)
-{
- int x;
-
- for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
- if (sizes[x].k == size) {
- return sizes[x].t;
- } else if (sizes[x].k > size) {
- return (x == 0) ? sizes[0].t : sizes[x - 1].t;
- }
- }
- return 1;
-}
-
-
-
-/* End: bn_prime_sizes_tab.c */
-
/* Start: bn_prime_tab.c */
+#include <tommath.h>
+#ifdef BN_PRIME_TAB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7622,7 +7996,6 @@ int mp_prime_rabin_miller_trials(int size)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
const mp_digit __prime_tab[] = {
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
@@ -7663,10 +8036,13 @@ const mp_digit __prime_tab[] = {
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
};
+#endif
/* End: bn_prime_tab.c */
/* Start: bn_reverse.c */
+#include <tommath.h>
+#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7681,7 +8057,6 @@ const mp_digit __prime_tab[] = {
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reverse an array, used for radix code */
void
@@ -7700,10 +8075,13 @@ bn_reverse (unsigned char *s, int len)
--iy;
}
}
+#endif
/* End: bn_reverse.c */
/* Start: bn_s_mp_add.c */
+#include <tommath.h>
+#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7718,7 +8096,6 @@ bn_reverse (unsigned char *s, int len)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
@@ -7807,10 +8184,13 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_add.c */
/* Start: bn_s_mp_exptmod.c */
+#include <tommath.h>
+#ifdef BN_S_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7825,7 +8205,6 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#ifdef MP_LOW_MEM
#define TAB_SIZE 32
@@ -8045,10 +8424,13 @@ __M:
}
return err;
}
+#endif
/* End: bn_s_mp_exptmod.c */
/* Start: bn_s_mp_mul_digs.c */
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8063,7 +8445,6 @@ __M:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and only computes upto digs digits of result
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
@@ -8134,10 +8515,13 @@ s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_mul_digs.c */
/* Start: bn_s_mp_mul_high_digs.c */
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8152,7 +8536,6 @@ s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and does not compute the lower digs digits
* [meant to get the higher part of the product]
@@ -8167,10 +8550,12 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_digit tmpx, *tmpt, *tmpy;
/* can we use the fast multiplier? */
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
if (((a->used + b->used + 1) < MP_WARRAY)
&& MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_s_mp_mul_high_digs (a, b, c, digs);
}
+#endif
if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
return res;
@@ -8211,10 +8596,13 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_mul_high_digs.c */
/* Start: bn_s_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8229,7 +8617,6 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int
@@ -8294,10 +8681,13 @@ s_mp_sqr (mp_int * a, mp_int * b)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_sqr.c */
/* Start: bn_s_mp_sub.c */
+#include <tommath.h>
+#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8312,7 +8702,6 @@ s_mp_sqr (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
@@ -8381,10 +8770,13 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_sub.c */
/* Start: bncore.c */
+#include <tommath.h>
+#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8399,25 +8791,21 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Known optimal configurations
CPU /Compiler /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
- Intel P4 Northwood /GCC v3.3.3 / 59/ 81/profiled build
- Intel P4 Northwood /GCC v3.3.3 / 59/ 80/profiled_single build
- Intel P4 Northwood /ICC v8.0 / 57/ 70/profiled build
- Intel P4 Northwood /ICC v8.0 / 54/ 76/profiled_single build
- AMD Athlon XP /GCC v3.2 / 109/ 127/
+ Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
*/
-int KARATSUBA_MUL_CUTOFF = 57, /* Min. number of digits before Karatsuba multiplication is used. */
- KARATSUBA_SQR_CUTOFF = 70, /* Min. number of digits before Karatsuba squaring is used. */
+int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */
+ KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */
TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */
TOOM_SQR_CUTOFF = 400;
+#endif
/* End: bncore.c */
diff --git a/tommath.h b/tommath.h
index 0029994..896d389 100644
--- a/tommath.h
+++ b/tommath.h
@@ -21,6 +21,8 @@
#include <ctype.h>
#include <limits.h>
+#include <tommath_class.h>
+
#undef MIN
#define MIN(x,y) ((x)<(y)?(x):(y))
#undef MAX
@@ -39,6 +41,14 @@ extern "C" {
#endif
+
+/* detect 64-bit mode if possible */
+#if defined(__x86_64__)
+ #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
+ #define MP_64BIT
+ #endif
+#endif
+
/* some default configurations.
*
* A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
@@ -60,7 +70,7 @@ extern "C" {
typedef signed long long long64;
#endif
- typedef ulong64 mp_digit;
+ typedef unsigned long mp_digit;
typedef unsigned long mp_word __attribute__ ((mode(TI)));
#define DIGIT_BIT 60
@@ -153,7 +163,7 @@ extern int KARATSUBA_MUL_CUTOFF,
/* default precision */
#ifndef MP_PREC
- #ifdef MP_LOW_MEM
+ #ifndef MP_LOW_MEM
#define MP_PREC 64 /* default digits of precision */
#else
#define MP_PREC 8 /* default digits of precision */
@@ -541,6 +551,7 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
int mp_toom_sqr(mp_int *a, mp_int *b);
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
diff --git a/tommath.pdf b/tommath.pdf
index bcc919a..18cac6f 100644
Binary files a/tommath.pdf and b/tommath.pdf differ
diff --git a/tommath.tex b/tommath.tex
index 3fbe907..d0ac947 100644
--- a/tommath.tex
+++ b/tommath.tex
@@ -822,30 +822,32 @@ decrementally.
\hspace{-5.1mm}{\bf File}: bn\_mp\_init.c
\vspace{-3mm}
\begin{alltt}
-016 /* init a new mp_int */
-017 int mp_init (mp_int * a)
-018 \{
-019 int i;
-020
-021 /* allocate memory required and clear it */
-022 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
-023 if (a->dp == NULL) \{
-024 return MP_MEM;
-025 \}
-026
-027 /* set the digits to zero */
-028 for (i = 0; i < MP_PREC; i++) \{
-029 a->dp[i] = 0;
-030 \}
-031
-032 /* set the used to zero, allocated digits to the default precision
-033 * and sign to positive */
-034 a->used = 0;
-035 a->alloc = MP_PREC;
-036 a->sign = MP_ZPOS;
-037
-038 return MP_OKAY;
-039 \}
+016
+017 /* init a new mp_int */
+018 int mp_init (mp_int * a)
+019 \{
+020 int i;
+021
+022 /* allocate memory required and clear it */
+023 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
+024 if (a->dp == NULL) \{
+025 return MP_MEM;
+026 \}
+027
+028 /* set the digits to zero */
+029 for (i = 0; i < MP_PREC; i++) \{
+030 a->dp[i] = 0;
+031 \}
+032
+033 /* set the used to zero, allocated digits to the default precision
+034 * and sign to positive */
+035 a->used = 0;
+036 a->alloc = MP_PREC;
+037 a->sign = MP_ZPOS;
+038
+039 return MP_OKAY;
+040 \}
+041 #endif
\end{alltt}
\end{small}
@@ -853,7 +855,7 @@ One immediate observation of this initializtion function is that it does not ret
is assumed that the caller has already allocated memory for the mp\_int structure, typically on the application stack. The
call to mp\_init() is used only to initialize the members of the structure to a known default state.
-Here we see (line 22) the memory allocation is performed first. This allows us to exit cleanly and quickly
+Here we see (line 23) the memory allocation is performed first. This allows us to exit cleanly and quickly
if there is an error. If the allocation fails the routine will return \textbf{MP\_MEM} to the caller to indicate there
was a memory error. The function XMALLOC is what actually allocates the memory. Technically XMALLOC is not a function
but a macro defined in ``tommath.h``. By default, XMALLOC will evaluate to malloc() which is the C library's built--in
@@ -861,11 +863,11 @@ memory allocation routine.
In order to assure the mp\_int is in a known state the digits must be set to zero. On most platforms this could have been
accomplished by using calloc() instead of malloc(). However, to correctly initialize a integer type to a given value in a
-portable fashion you have to actually assign the value. The for loop (line 28) performs this required
+portable fashion you have to actually assign the value. The for loop (line 29) performs this required
operation.
After the memory has been successfully initialized the remainder of the members are initialized
-(lines 32 through 33) to their respective default states. At this point the algorithm has succeeded and
+(lines 33 through 34) to their respective default states. At this point the algorithm has succeeded and
a success code is returned to the calling function. If this function returns \textbf{MP\_OKAY} it is safe to assume the
mp\_int structure has been properly initialized and is safe to use with other functions within the library.
@@ -910,43 +912,45 @@ with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp
\hspace{-5.1mm}{\bf File}: bn\_mp\_clear.c
\vspace{-3mm}
\begin{alltt}
-016 /* clear one (frees) */
-017 void
-018 mp_clear (mp_int * a)
-019 \{
-020 int i;
-021
-022 /* only do anything if a hasn't been freed previously */
-023 if (a->dp != NULL) \{
-024 /* first zero the digits */
-025 for (i = 0; i < a->used; i++) \{
-026 a->dp[i] = 0;
-027 \}
-028
-029 /* free ram */
-030 XFREE(a->dp);
-031
-032 /* reset members to make debugging easier */
-033 a->dp = NULL;
-034 a->alloc = a->used = 0;
-035 a->sign = MP_ZPOS;
-036 \}
-037 \}
+016
+017 /* clear one (frees) */
+018 void
+019 mp_clear (mp_int * a)
+020 \{
+021 int i;
+022
+023 /* only do anything if a hasn't been freed previously */
+024 if (a->dp != NULL) \{
+025 /* first zero the digits */
+026 for (i = 0; i < a->used; i++) \{
+027 a->dp[i] = 0;
+028 \}
+029
+030 /* free ram */
+031 XFREE(a->dp);
+032
+033 /* reset members to make debugging easier */
+034 a->dp = NULL;
+035 a->alloc = a->used = 0;
+036 a->sign = MP_ZPOS;
+037 \}
+038 \}
+039 #endif
\end{alltt}
\end{small}
-The algorithm only operates on the mp\_int if it hasn't been previously cleared. The if statement (line 23)
+The algorithm only operates on the mp\_int if it hasn't been previously cleared. The if statement (line 24)
checks to see if the \textbf{dp} member is not \textbf{NULL}. If the mp\_int is a valid mp\_int then \textbf{dp} cannot be
\textbf{NULL} in which case the if statement will evaluate to true.
-The digits of the mp\_int are cleared by the for loop (line 25) which assigns a zero to every digit. Similar to mp\_init()
+The digits of the mp\_int are cleared by the for loop (line 26) which assigns a zero to every digit. Similar to mp\_init()
the digits are assigned zero instead of using block memory operations (such as memset()) since this is more portable.
The digits are deallocated off the heap via the XFREE macro. Similar to XMALLOC the XFREE macro actually evaluates to
a standard C library function. In this case the free() function. Since free() only deallocates the memory the pointer
-still has to be reset to \textbf{NULL} manually (line 33).
+still has to be reset to \textbf{NULL} manually (line 34).
-Now that the digits have been cleared and deallocated the other members are set to their final values (lines 34 and 35).
+Now that the digits have been cleared and deallocated the other members are set to their final values (lines 35 and 36).
\section{Maintenance Algorithms}
@@ -1001,41 +1005,43 @@ assumed to contain undefined values they are initially set to zero.
\hspace{-5.1mm}{\bf File}: bn\_mp\_grow.c
\vspace{-3mm}
\begin{alltt}
-016 /* grow as required */
-017 int mp_grow (mp_int * a, int size)
-018 \{
-019 int i;
-020 mp_digit *tmp;
-021
-022 /* if the alloc size is smaller alloc more ram */
-023 if (a->alloc < size) \{
-024 /* ensure there are always at least MP_PREC digits extra on top */
-025 size += (MP_PREC * 2) - (size % MP_PREC);
-026
-027 /* reallocate the array a->dp
-028 *
-029 * We store the return in a temporary variable
-030 * in case the operation failed we don't want
-031 * to overwrite the dp member of a.
-032 */
-033 tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
-034 if (tmp == NULL) \{
-035 /* reallocation failed but "a" is still valid [can be freed] */
-036 return MP_MEM;
-037 \}
-038
-039 /* reallocation succeeded so set a->dp */
-040 a->dp = tmp;
-041
-042 /* zero excess digits */
-043 i = a->alloc;
-044 a->alloc = size;
-045 for (; i < a->alloc; i++) \{
-046 a->dp[i] = 0;
-047 \}
-048 \}
-049 return MP_OKAY;
-050 \}
+016
+017 /* grow as required */
+018 int mp_grow (mp_int * a, int size)
+019 \{
+020 int i;
+021 mp_digit *tmp;
+022
+023 /* if the alloc size is smaller alloc more ram */
+024 if (a->alloc < size) \{
+025 /* ensure there are always at least MP_PREC digits extra on top */
+026 size += (MP_PREC * 2) - (size % MP_PREC);
+027
+028 /* reallocate the array a->dp
+029 *
+030 * We store the return in a temporary variable
+031 * in case the operation failed we don't want
+032 * to overwrite the dp member of a.
+033 */
+034 tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
+035 if (tmp == NULL) \{
+036 /* reallocation failed but "a" is still valid [can be freed] */
+037 return MP_MEM;
+038 \}
+039
+040 /* reallocation succeeded so set a->dp */
+041 a->dp = tmp;
+042
+043 /* zero excess digits */
+044 i = a->alloc;
+045 a->alloc = size;
+046 for (; i < a->alloc; i++) \{
+047 a->dp[i] = 0;
+048 \}
+049 \}
+050 return MP_OKAY;
+051 \}
+052 #endif
\end{alltt}
\end{small}
@@ -1044,7 +1050,7 @@ if the \textbf{alloc} member of the mp\_int is smaller than the requested digit
the function skips the re-allocation part thus saving time.
When a re-allocation is performed it is turned into an optimal request to save time in the future. The requested digit count is
-padded upwards to 2nd multiple of \textbf{MP\_PREC} larger than \textbf{alloc} (line 25). The XREALLOC function is used
+padded upwards to 2nd multiple of \textbf{MP\_PREC} larger than \textbf{alloc} (line 26). The XREALLOC function is used
to re-allocate the memory. As per the other functions XREALLOC is actually a macro which evaluates to realloc by default. The realloc
function leaves the base of the allocation intact which means the first \textbf{alloc} digits of the mp\_int are the same as before
the re-allocation. All that is left is to clear the newly allocated digits and return.
@@ -1096,34 +1102,45 @@ correct no further memory re-allocations are required to work with the mp\_int.
\hspace{-5.1mm}{\bf File}: bn\_mp\_init\_size.c
\vspace{-3mm}
\begin{alltt}
-016 /* init an mp_init for a given size */
-017 int mp_init_size (mp_int * a, int size)
-018 \{
-019 /* pad size so there are always extra digits */
-020 size += (MP_PREC * 2) - (size % MP_PREC);
-021
-022 /* alloc mem */
-023 a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size);
-024 if (a->dp == NULL) \{
-025 return MP_MEM;
-026 \}
-027 a->used = 0;
-028 a->alloc = size;
-029 a->sign = MP_ZPOS;
+016
+017 /* init an mp_init for a given size */
+018 int mp_init_size (mp_int * a, int size)
+019 \{
+020 int x;
+021
+022 /* pad size so there are always extra digits */
+023 size += (MP_PREC * 2) - (size % MP_PREC);
+024
+025 /* alloc mem */
+026 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
+027 if (a->dp == NULL) \{
+028 return MP_MEM;
+029 \}
030
-031 return MP_OKAY;
-032 \}
+031 /* set the members */
+032 a->used = 0;
+033 a->alloc = size;
+034 a->sign = MP_ZPOS;
+035
+036 /* zero the digits */
+037 for (x = 0; x < size; x++) \{
+038 a->dp[x] = 0;
+039 \}
+040
+041 return MP_OKAY;
+042 \}
+043 #endif
\end{alltt}
\end{small}
-The number of digits $b$ requested is padded (line 20) by first augmenting it to the next multiple of
+The number of digits $b$ requested is padded (line 23) by first augmenting it to the next multiple of
\textbf{MP\_PREC} and then adding \textbf{MP\_PREC} to the result. If the memory can be successfully allocated the
mp\_int is placed in a default state representing the integer zero. Otherwise, the error code \textbf{MP\_MEM} will be
-returned (line 25).
+returned (line 28).
-The digits are allocated and set to zero at the same time with the calloc() function (line 23). The
+The digits are allocated and set to zero at the same time with the calloc() function (line @25,XCALLOC@). The
\textbf{used} count is set to zero, the \textbf{alloc} count set to the padded digit count and the \textbf{sign} flag set
-to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines 27, 28 and 29). If the function
+to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines 32, 33 and 34). If the function
returns succesfully then it is correct to assume that the mp\_int structure is in a valid state for the remainder of the
functions to work with.
@@ -1161,43 +1178,45 @@ initialization which allows for quick recovery from runtime errors.
\hspace{-5.1mm}{\bf File}: bn\_mp\_init\_multi.c
\vspace{-3mm}
\begin{alltt}
-016
-017 int mp_init_multi(mp_int *mp, ...)
-018 \{
-019 mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
-020 int n = 0; /* Number of ok inits */
-021 mp_int* cur_arg = mp;
-022 va_list args;
-023
-024 va_start(args, mp); /* init args to next argument from caller */
-025 while (cur_arg != NULL) \{
-026 if (mp_init(cur_arg) != MP_OKAY) \{
-027 /* Oops - error! Back-track and mp_clear what we already
-028 succeeded in init-ing, then return error.
-029 */
-030 va_list clean_args;
-031
-032 /* end the current list */
-033 va_end(args);
-034
-035 /* now start cleaning up */
-036 cur_arg = mp;
-037 va_start(clean_args, mp);
-038 while (n--) \{
-039 mp_clear(cur_arg);
-040 cur_arg = va_arg(clean_args, mp_int*);
-041 \}
-042 va_end(clean_args);
-043 res = MP_MEM;
-044 break;
-045 \}
-046 n++;
-047 cur_arg = va_arg(args, mp_int*);
-048 \}
-049 va_end(args);
-050 return res; /* Assumed ok, if error flagged above. */
-051 \}
-052
+016 #include <stdarg.h>
+017
+018 int mp_init_multi(mp_int *mp, ...)
+019 \{
+020 mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
+021 int n = 0; /* Number of ok inits */
+022 mp_int* cur_arg = mp;
+023 va_list args;
+024
+025 va_start(args, mp); /* init args to next argument from caller */
+026 while (cur_arg != NULL) \{
+027 if (mp_init(cur_arg) != MP_OKAY) \{
+028 /* Oops - error! Back-track and mp_clear what we already
+029 succeeded in init-ing, then return error.
+030 */
+031 va_list clean_args;
+032
+033 /* end the current list */
+034 va_end(args);
+035
+036 /* now start cleaning up */
+037 cur_arg = mp;
+038 va_start(clean_args, mp);
+039 while (n--) \{
+040 mp_clear(cur_arg);
+041 cur_arg = va_arg(clean_args, mp_int*);
+042 \}
+043 va_end(clean_args);
+044 res = MP_MEM;
+045 break;
+046 \}
+047 n++;
+048 cur_arg = va_arg(args, mp_int*);
+049 \}
+050 va_end(args);
+051 return res; /* Assumed ok, if error flagged above. */
+052 \}
+053
+054 #endif
\end{alltt}
\end{small}
@@ -1207,8 +1226,8 @@ structures in an actual C array they are simply passed as arguments to the funct
appended on the right.
The function uses the ``stdarg.h'' \textit{va} functions to step portably through the arguments to the function. A count
-$n$ of succesfully initialized mp\_int structures is maintained (line 46) such that if a failure does occur,
-the algorithm can backtrack and free the previously initialized structures (lines 26 to 45).
+$n$ of succesfully initialized mp\_int structures is maintained (line 47) such that if a failure does occur,
+the algorithm can backtrack and free the previously initialized structures (lines 27 to 46).
\subsection{Clamping Excess Digits}
@@ -1259,35 +1278,37 @@ when all of the digits are zero to ensure that the mp\_int is valid at all times
\hspace{-5.1mm}{\bf File}: bn\_mp\_clamp.c
\vspace{-3mm}
\begin{alltt}
-016 /* trim unused digits
-017 *
-018 * This is used to ensure that leading zero digits are
-019 * trimed and the leading "used" digit will be non-zero
-020 * Typically very fast. Also fixes the sign if there
-021 * are no more leading digits
-022 */
-023 void
-024 mp_clamp (mp_int * a)
-025 \{
-026 /* decrease used while the most significant digit is
-027 * zero.
-028 */
-029 while (a->used > 0 && a->dp[a->used - 1] == 0) \{
-030 --(a->used);
-031 \}
-032
-033 /* reset the sign flag if used == 0 */
-034 if (a->used == 0) \{
-035 a->sign = MP_ZPOS;
-036 \}
-037 \}
+016
+017 /* trim unused digits
+018 *
+019 * This is used to ensure that leading zero digits are
+020 * trimed and the leading "used" digit will be non-zero
+021 * Typically very fast. Also fixes the sign if there
+022 * are no more leading digits
+023 */
+024 void
+025 mp_clamp (mp_int * a)
+026 \{
+027 /* decrease used while the most significant digit is
+028 * zero.
+029 */
+030 while (a->used > 0 && a->dp[a->used - 1] == 0) \{
+031 --(a->used);
+032 \}
+033
+034 /* reset the sign flag if used == 0 */
+035 if (a->used == 0) \{
+036 a->sign = MP_ZPOS;
+037 \}
+038 \}
+039 #endif
\end{alltt}
\end{small}
-Note on line 26 how to test for the \textbf{used} count is made on the left of the \&\& operator. In the C programming
+Note on line 27 how to test for the \textbf{used} count is made on the left of the \&\& operator. In the C programming
language the terms to \&\& are evaluated left to right with a boolean short-circuit if any condition fails. This is
important since if the \textbf{used} is zero the test on the right would fetch below the array. That is obviously
-undesirable. The parenthesis on line 29 is used to make sure the \textbf{used} count is decremented and not
+undesirable. The parenthesis on line 30 is used to make sure the \textbf{used} count is decremented and not
the pointer ``a''.
\section*{Exercises}
@@ -1370,67 +1391,69 @@ implement the pseudo-code.
\hspace{-5.1mm}{\bf File}: bn\_mp\_copy.c
\vspace{-3mm}
\begin{alltt}
-016 /* copy, b = a */
-017 int
-018 mp_copy (mp_int * a, mp_int * b)
-019 \{
-020 int res, n;
-021
-022 /* if dst == src do nothing */
-023 if (a == b) \{
-024 return MP_OKAY;
-025 \}
-026
-027 /* grow dest */
-028 if (b->alloc < a->used) \{
-029 if ((res = mp_grow (b, a->used)) != MP_OKAY) \{
-030 return res;
-031 \}
-032 \}
-033
-034 /* zero b and copy the parameters over */
-035 \{
-036 register mp_digit *tmpa, *tmpb;
-037
-038 /* pointer aliases */
-039
-040 /* source */
-041 tmpa = a->dp;
-042
-043 /* destination */
-044 tmpb = b->dp;
-045
-046 /* copy all the digits */
-047 for (n = 0; n < a->used; n++) \{
-048 *tmpb++ = *tmpa++;
-049 \}
-050
-051 /* clear high digits */
-052 for (; n < b->used; n++) \{
-053 *tmpb++ = 0;
-054 \}
-055 \}
-056
-057 /* copy used count and sign */
-058 b->used = a->used;
-059 b->sign = a->sign;
-060 return MP_OKAY;
-061 \}
+016
+017 /* copy, b = a */
+018 int
+019 mp_copy (mp_int * a, mp_int * b)
+020 \{
+021 int res, n;
+022
+023 /* if dst == src do nothing */
+024 if (a == b) \{
+025 return MP_OKAY;
+026 \}
+027
+028 /* grow dest */
+029 if (b->alloc < a->used) \{
+030 if ((res = mp_grow (b, a->used)) != MP_OKAY) \{
+031 return res;
+032 \}
+033 \}
+034
+035 /* zero b and copy the parameters over */
+036 \{
+037 register mp_digit *tmpa, *tmpb;
+038
+039 /* pointer aliases */
+040
+041 /* source */
+042 tmpa = a->dp;
+043
+044 /* destination */
+045 tmpb = b->dp;
+046
+047 /* copy all the digits */
+048 for (n = 0; n < a->used; n++) \{
+049 *tmpb++ = *tmpa++;
+050 \}
+051
+052 /* clear high digits */
+053 for (; n < b->used; n++) \{
+054 *tmpb++ = 0;
+055 \}
+056 \}
+057
+058 /* copy used count and sign */
+059 b->used = a->used;
+060 b->sign = a->sign;
+061 return MP_OKAY;
+062 \}
+063 #endif
\end{alltt}
\end{small}
Occasionally a dependent algorithm may copy an mp\_int effectively into itself such as when the input and output
mp\_int structures passed to a function are one and the same. For this case it is optimal to return immediately without
-copying digits (line 23).
+copying digits (line 24).
The mp\_int $b$ must have enough digits to accomodate the used digits of the mp\_int $a$. If $b.alloc$ is less than
-$a.used$ the algorithm mp\_grow is used to augment the precision of $b$ (lines 28 to 32). In order to
+$a.used$ the algorithm mp\_grow is used to augment the precision of $b$ (lines 29 to 33). In order to
simplify the inner loop that copies the digits from $a$ to $b$, two aliases $tmpa$ and $tmpb$ point directly at the digits
-of the mp\_ints $a$ and $b$ respectively. These aliases (lines 41 and 44) allow the compiler to access the digits without first dereferencing the
+of the mp\_ints $a$ and $b$ respectively. These aliases (lines 42 and 45) allow the compiler to access the digits without first dereferencing the
mp\_int pointers and then subsequently the pointer to the digits.
-After the aliases are established the digits from $a$ are copied into $b$ (lines 47 to 49) and then the excess
-digits of $b$ are set to zero (lines 52 to 55). Both ``for'' loops make use of the pointer aliases and in
+After the aliases are established the digits from $a$ are copied into $b$ (lines 48 to 50) and then the excess
+digits of $b$ are set to zero (lines 53 to 55). Both ``for'' loops make use of the pointer aliases and in
fact the alias for $b$ is carried through into the second ``for'' loop to clear the excess digits. This optimization
allows the alias to stay in a machine register fairly easy between the two loops.
@@ -1518,16 +1541,18 @@ such this algorithm will perform two operations in one step.
\hspace{-5.1mm}{\bf File}: bn\_mp\_init\_copy.c
\vspace{-3mm}
\begin{alltt}
-016 /* creates "a" then copies b into it */
-017 int mp_init_copy (mp_int * a, mp_int * b)
-018 \{
-019 int res;
-020
-021 if ((res = mp_init (a)) != MP_OKAY) \{
-022 return res;
-023 \}
-024 return mp_copy (b, a);
-025 \}
+016
+017 /* creates "a" then copies b into it */
+018 int mp_init_copy (mp_int * a, mp_int * b)
+019 \{
+020 int res;
+021
+022 if ((res = mp_init (a)) != MP_OKAY) \{
+023 return res;
+024 \}
+025 return mp_copy (b, a);
+026 \}
+027 #endif
\end{alltt}
\end{small}
@@ -1563,14 +1588,16 @@ This algorithm simply resets a mp\_int to the default state.
\hspace{-5.1mm}{\bf File}: bn\_mp\_zero.c
\vspace{-3mm}
\begin{alltt}
-016 /* set to zero */
-017 void
-018 mp_zero (mp_int * a)
-019 \{
-020 a->sign = MP_ZPOS;
-021 a->used = 0;
-022 memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
-023 \}
+016
+017 /* set to zero */
+018 void
+019 mp_zero (mp_int * a)
+020 \{
+021 a->sign = MP_ZPOS;
+022 a->used = 0;
+023 memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
+024 \}
+025 #endif
\end{alltt}
\end{small}
@@ -1609,27 +1636,29 @@ logic to handle it.
\hspace{-5.1mm}{\bf File}: bn\_mp\_abs.c
\vspace{-3mm}
\begin{alltt}
-016 /* b = |a|
-017 *
-018 * Simple function copies the input and fixes the sign to positive
-019 */
-020 int
-021 mp_abs (mp_int * a, mp_int * b)
-022 \{
-023 int res;
-024
-025 /* copy a to b */
-026 if (a != b) \{
-027 if ((res = mp_copy (a, b)) != MP_OKAY) \{
-028 return res;
-029 \}
-030 \}
-031
-032 /* force the sign of b to positive */
-033 b->sign = MP_ZPOS;
-034
-035 return MP_OKAY;
-036 \}
+016
+017 /* b = |a|
+018 *
+019 * Simple function copies the input and fixes the sign to positive
+020 */
+021 int
+022 mp_abs (mp_int * a, mp_int * b)
+023 \{
+024 int res;
+025
+026 /* copy a to b */
+027 if (a != b) \{
+028 if ((res = mp_copy (a, b)) != MP_OKAY) \{
+029 return res;
+030 \}
+031 \}
+032
+033 /* force the sign of b to positive */
+034 b->sign = MP_ZPOS;
+035
+036 return MP_OKAY;
+037 \}
+038 #endif
\end{alltt}
\end{small}
@@ -1668,18 +1697,20 @@ zero as negative.
\hspace{-5.1mm}{\bf File}: bn\_mp\_neg.c
\vspace{-3mm}
\begin{alltt}
-016 /* b = -a */
-017 int mp_neg (mp_int * a, mp_int * b)
-018 \{
-019 int res;
-020 if ((res = mp_copy (a, b)) != MP_OKAY) \{
-021 return res;
-022 \}
-023 if (mp_iszero(b) != MP_YES) \{
-024 b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
-025 \}
-026 return MP_OKAY;
-027 \}
+016
+017 /* b = -a */
+018 int mp_neg (mp_int * a, mp_int * b)
+019 \{
+020 int res;
+021 if ((res = mp_copy (a, b)) != MP_OKAY) \{
+022 return res;
+023 \}
+024 if (mp_iszero(b) != MP_YES) \{
+025 b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+026 \}
+027 return MP_OKAY;
+028 \}
+029 #endif
\end{alltt}
\end{small}
@@ -1714,20 +1745,22 @@ single digit is set (\textit{modulo $\beta$}) and the \textbf{used} count is adj
\hspace{-5.1mm}{\bf File}: bn\_mp\_set.c
\vspace{-3mm}
\begin{alltt}
-016 /* set to a digit */
-017 void mp_set (mp_int * a, mp_digit b)
-018 \{
-019 mp_zero (a);
-020 a->dp[0] = b & MP_MASK;
-021 a->used = (a->dp[0] != 0) ? 1 : 0;
-022 \}
+016
+017 /* set to a digit */
+018 void mp_set (mp_int * a, mp_digit b)
+019 \{
+020 mp_zero (a);
+021 a->dp[0] = b & MP_MASK;
+022 a->used = (a->dp[0] != 0) ? 1 : 0;
+023 \}
+024 #endif
\end{alltt}
\end{small}
-Line 19 calls mp\_zero() to clear the mp\_int and reset the sign. Line 20 copies the digit
+Line 20 calls mp\_zero() to clear the mp\_int and reset the sign. Line 21 copies the digit
into the least significant location. Note the usage of a new constant \textbf{MP\_MASK}. This constant is used to quickly
reduce an integer modulo $\beta$. Since $\beta$ is of the form $2^k$ for any suitable $k$ it suffices to perform a binary AND with
-$MP\_MASK = 2^k - 1$ to perform the reduction. Finally line 21 will set the \textbf{used} member with respect to the
+$MP\_MASK = 2^k - 1$ to perform the reduction. Finally line 22 will set the \textbf{used} member with respect to the
digit actually set. This function will always make the integer positive.
One important limitation of this function is that it will only set one digit. The size of a digit is not fixed, meaning source that uses
@@ -1770,39 +1803,41 @@ Excess zero digits are trimmed in steps 2.1 and 3 by using higher level algorith
\hspace{-5.1mm}{\bf File}: bn\_mp\_set\_int.c
\vspace{-3mm}
\begin{alltt}
-016 /* set a 32-bit const */
-017 int mp_set_int (mp_int * a, unsigned long b)
-018 \{
-019 int x, res;
-020
-021 mp_zero (a);
-022
-023 /* set four bits at a time */
-024 for (x = 0; x < 8; x++) \{
-025 /* shift the number up four bits */
-026 if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) \{
-027 return res;
-028 \}
-029
-030 /* OR in the top four bits of the source */
-031 a->dp[0] |= (b >> 28) & 15;
-032
-033 /* shift the source up to the next four bits */
-034 b <<= 4;
-035
-036 /* ensure that digits are not clamped off */
-037 a->used += 1;
-038 \}
-039 mp_clamp (a);
-040 return MP_OKAY;
-041 \}
+016
+017 /* set a 32-bit const */
+018 int mp_set_int (mp_int * a, unsigned long b)
+019 \{
+020 int x, res;
+021
+022 mp_zero (a);
+023
+024 /* set four bits at a time */
+025 for (x = 0; x < 8; x++) \{
+026 /* shift the number up four bits */
+027 if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) \{
+028 return res;
+029 \}
+030
+031 /* OR in the top four bits of the source */
+032 a->dp[0] |= (b >> 28) & 15;
+033
+034 /* shift the source up to the next four bits */
+035 b <<= 4;
+036
+037 /* ensure that digits are not clamped off */
+038 a->used += 1;
+039 \}
+040 mp_clamp (a);
+041 return MP_OKAY;
+042 \}
+043 #endif
\end{alltt}
\end{small}
This function sets four bits of the number at a time to handle all practical \textbf{DIGIT\_BIT} sizes. The weird
-addition on line 37 ensures that the newly added in bits are added to the number of digits. While it may not
-seem obvious as to why the digit counter does not grow exceedingly large it is because of the shift on line 26
-as well as the call to mp\_clamp() on line 39. Both functions will clamp excess leading digits which keeps
+addition on line 38 ensures that the newly added in bits are added to the number of digits. While it may not
+seem obvious as to why the digit counter does not grow exceedingly large it is because of the shift on line 27
+as well as the call to mp\_clamp() on line 40. Both functions will clamp excess leading digits which keeps
the number of used digits low.
\section{Comparisons}
@@ -1863,43 +1898,45 @@ the zero'th digit. If after all of the digits have been compared, no difference
\hspace{-5.1mm}{\bf File}: bn\_mp\_cmp\_mag.c
\vspace{-3mm}
\begin{alltt}
-016 /* compare maginitude of two ints (unsigned) */
-017 int mp_cmp_mag (mp_int * a, mp_int * b)
-018 \{
-019 int n;
-020 mp_digit *tmpa, *tmpb;
-021
-022 /* compare based on # of non-zero digits */
-023 if (a->used > b->used) \{
-024 return MP_GT;
-025 \}
-026
-027 if (a->used < b->used) \{
-028 return MP_LT;
-029 \}
-030
-031 /* alias for a */
-032 tmpa = a->dp + (a->used - 1);
-033
-034 /* alias for b */
-035 tmpb = b->dp + (a->used - 1);
-036
-037 /* compare based on digits */
-038 for (n = 0; n < a->used; ++n, --tmpa, --tmpb) \{
-039 if (*tmpa > *tmpb) \{
-040 return MP_GT;
-041 \}
-042
-043 if (*tmpa < *tmpb) \{
-044 return MP_LT;
-045 \}
-046 \}
-047 return MP_EQ;
-048 \}
+016
+017 /* compare maginitude of two ints (unsigned) */
+018 int mp_cmp_mag (mp_int * a, mp_int * b)
+019 \{
+020 int n;
+021 mp_digit *tmpa, *tmpb;
+022
+023 /* compare based on # of non-zero digits */
+024 if (a->used > b->used) \{
+025 return MP_GT;
+026 \}
+027
+028 if (a->used < b->used) \{
+029 return MP_LT;
+030 \}
+031
+032 /* alias for a */
+033 tmpa = a->dp + (a->used - 1);
+034
+035 /* alias for b */
+036 tmpb = b->dp + (a->used - 1);
+037
+038 /* compare based on digits */
+039 for (n = 0; n < a->used; ++n, --tmpa, --tmpb) \{
+040 if (*tmpa > *tmpb) \{
+041 return MP_GT;
+042 \}
+043
+044 if (*tmpa < *tmpb) \{
+045 return MP_LT;
+046 \}
+047 \}
+048 return MP_EQ;
+049 \}
+050 #endif
\end{alltt}
\end{small}
-The two if statements on lines 23 and 27 compare the number of digits in the two inputs. These two are performed before all of the digits
+The two if statements on lines 24 and 28 compare the number of digits in the two inputs. These two are performed before all of the digits
are compared since it is a very cheap test to perform and can potentially save considerable time. The implementation given is also not valid
without those two statements. $b.alloc$ may be smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the
array of digits.
@@ -1937,33 +1974,35 @@ $\vert a \vert < \vert b \vert$. Step number four will compare the two when the
\hspace{-5.1mm}{\bf File}: bn\_mp\_cmp.c
\vspace{-3mm}
\begin{alltt}
-016 /* compare two ints (signed)*/
-017 int
-018 mp_cmp (mp_int * a, mp_int * b)
-019 \{
-020 /* compare based on sign */
-021 if (a->sign != b->sign) \{
-022 if (a->sign == MP_NEG) \{
-023 return MP_LT;
-024 \} else \{
-025 return MP_GT;
-026 \}
-027 \}
-028
-029 /* compare digits */
-030 if (a->sign == MP_NEG) \{
-031 /* if negative compare opposite direction */
-032 return mp_cmp_mag(b, a);
-033 \} else \{
-034 return mp_cmp_mag(a, b);
-035 \}
-036 \}
+016
+017 /* compare two ints (signed)*/
+018 int
+019 mp_cmp (mp_int * a, mp_int * b)
+020 \{
+021 /* compare based on sign */
+022 if (a->sign != b->sign) \{
+023 if (a->sign == MP_NEG) \{
+024 return MP_LT;
+025 \} else \{
+026 return MP_GT;
+027 \}
+028 \}
+029
+030 /* compare digits */
+031 if (a->sign == MP_NEG) \{
+032 /* if negative compare opposite direction */
+033 return mp_cmp_mag(b, a);
+034 \} else \{
+035 return mp_cmp_mag(a, b);
+036 \}
+037 \}
+038 #endif
\end{alltt}
\end{small}
-The two if statements on lines 22 and 30 perform the initial sign comparison. If the signs are not the equal then which ever
-has the positive sign is larger. At line 30, the inputs are compared based on magnitudes. If the signs were both negative then
-the unsigned comparison is performed in the opposite direction (\textit{line 32}). Otherwise, the signs are assumed to
+The two if statements on lines 22 and 23 perform the initial sign comparison. If the signs are not the equal then which ever
+has the positive sign is larger. At line 31, the inputs are compared based on magnitudes. If the signs were both negative then
+the unsigned comparison is performed in the opposite direction (\textit{line 33}). Otherwise, the signs are assumed to
be both positive and a forward direction unsigned comparison is performed.
\section*{Exercises}
@@ -2087,109 +2126,111 @@ The final carry is stored in $c_{max}$ and digits above $max$ upto $oldused$ are
\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_add.c
\vspace{-3mm}
\begin{alltt}
-016 /* low level addition, based on HAC pp.594, Algorithm 14.7 */
-017 int
-018 s_mp_add (mp_int * a, mp_int * b, mp_int * c)
-019 \{
-020 mp_int *x;
-021 int olduse, res, min, max;
-022
-023 /* find sizes, we let |a| <= |b| which means we have to sort
-024 * them. "x" will point to the input with the most digits
-025 */
-026 if (a->used > b->used) \{
-027 min = b->used;
-028 max = a->used;
-029 x = a;
-030 \} else \{
-031 min = a->used;
-032 max = b->used;
-033 x = b;
-034 \}
-035
-036 /* init result */
-037 if (c->alloc < max + 1) \{
-038 if ((res = mp_grow (c, max + 1)) != MP_OKAY) \{
-039 return res;
-040 \}
-041 \}
-042
-043 /* get old used digit count and set new one */
-044 olduse = c->used;
-045 c->used = max + 1;
-046
-047 \{
-048 register mp_digit u, *tmpa, *tmpb, *tmpc;
-049 register int i;
-050
-051 /* alias for digit pointers */
-052
-053 /* first input */
-054 tmpa = a->dp;
-055
-056 /* second input */
-057 tmpb = b->dp;
-058
-059 /* destination */
-060 tmpc = c->dp;
-061
-062 /* zero the carry */
-063 u = 0;
-064 for (i = 0; i < min; i++) \{
-065 /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
-066 *tmpc = *tmpa++ + *tmpb++ + u;
-067
-068 /* U = carry bit of T[i] */
-069 u = *tmpc >> ((mp_digit)DIGIT_BIT);
-070
-071 /* take away carry bit from T[i] */
-072 *tmpc++ &= MP_MASK;
-073 \}
-074
-075 /* now copy higher words if any, that is in A+B
-076 * if A or B has more digits add those in
-077 */
-078 if (min != max) \{
-079 for (; i < max; i++) \{
-080 /* T[i] = X[i] + U */
-081 *tmpc = x->dp[i] + u;
-082
-083 /* U = carry bit of T[i] */
-084 u = *tmpc >> ((mp_digit)DIGIT_BIT);
-085
-086 /* take away carry bit from T[i] */
-087 *tmpc++ &= MP_MASK;
-088 \}
-089 \}
-090
-091 /* add carry */
-092 *tmpc++ = u;
-093
-094 /* clear digits above oldused */
-095 for (i = c->used; i < olduse; i++) \{
-096 *tmpc++ = 0;
-097 \}
-098 \}
-099
-100 mp_clamp (c);
-101 return MP_OKAY;
-102 \}
+016
+017 /* low level addition, based on HAC pp.594, Algorithm 14.7 */
+018 int
+019 s_mp_add (mp_int * a, mp_int * b, mp_int * c)
+020 \{
+021 mp_int *x;
+022 int olduse, res, min, max;
+023
+024 /* find sizes, we let |a| <= |b| which means we have to sort
+025 * them. "x" will point to the input with the most digits
+026 */
+027 if (a->used > b->used) \{
+028 min = b->used;
+029 max = a->used;
+030 x = a;
+031 \} else \{
+032 min = a->used;
+033 max = b->used;
+034 x = b;
+035 \}
+036
+037 /* init result */
+038 if (c->alloc < max + 1) \{
+039 if ((res = mp_grow (c, max + 1)) != MP_OKAY) \{
+040 return res;
+041 \}
+042 \}
+043
+044 /* get old used digit count and set new one */
+045 olduse = c->used;
+046 c->used = max + 1;
+047
+048 \{
+049 register mp_digit u, *tmpa, *tmpb, *tmpc;
+050 register int i;
+051
+052 /* alias for digit pointers */
+053
+054 /* first input */
+055 tmpa = a->dp;
+056
+057 /* second input */
+058 tmpb = b->dp;
+059
+060 /* destination */
+061 tmpc = c->dp;
+062
+063 /* zero the carry */
+064 u = 0;
+065 for (i = 0; i < min; i++) \{
+066 /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
+067 *tmpc = *tmpa++ + *tmpb++ + u;
+068
+069 /* U = carry bit of T[i] */
+070 u = *tmpc >> ((mp_digit)DIGIT_BIT);
+071
+072 /* take away carry bit from T[i] */
+073 *tmpc++ &= MP_MASK;
+074 \}
+075
+076 /* now copy higher words if any, that is in A+B
+077 * if A or B has more digits add those in
+078 */
+079 if (min != max) \{
+080 for (; i < max; i++) \{
+081 /* T[i] = X[i] + U */
+082 *tmpc = x->dp[i] + u;
+083
+084 /* U = carry bit of T[i] */
+085 u = *tmpc >> ((mp_digit)DIGIT_BIT);
+086
+087 /* take away carry bit from T[i] */
+088 *tmpc++ &= MP_MASK;
+089 \}
+090 \}
+091
+092 /* add carry */
+093 *tmpc++ = u;
+094
+095 /* clear digits above oldused */
+096 for (i = c->used; i < olduse; i++) \{
+097 *tmpc++ = 0;
+098 \}
+099 \}
+100
+101 mp_clamp (c);
+102 return MP_OKAY;
+103 \}
+104 #endif
\end{alltt}
\end{small}
-Lines 26 to 34 perform the initial sorting of the inputs and determine the $min$ and $max$ variables. Note that $x$ is a pointer to a
-mp\_int assigned to the largest input, in effect it is a local alias. Lines 36 to 41 ensure that the destination is grown to
+Lines 27 to 35 perform the initial sorting of the inputs and determine the $min$ and $max$ variables. Note that $x$ is a pointer to a
+mp\_int assigned to the largest input, in effect it is a local alias. Lines 37 to 42 ensure that the destination is grown to
accomodate the result of the addition.
Similar to the implementation of mp\_copy this function uses the braced code and local aliases coding style. The three aliases that are on
-lines 54, 57 and 60 represent the two inputs and destination variables respectively. These aliases are used to ensure the
+lines 55, 58 and 61 represent the two inputs and destination variables respectively. These aliases are used to ensure the
compiler does not have to dereference $a$, $b$ or $c$ (respectively) to access the digits of the respective mp\_int.
-The initial carry $u$ is cleared on line 63, note that $u$ is of type mp\_digit which ensures type compatibility within the
-implementation. The initial addition loop begins on line 64 and ends on line 73. Similarly the conditional addition loop
-begins on line 79 and ends on line 89. The addition is finished with the final carry being stored in $tmpc$ on line 96.
-Note the ``++'' operator on the same line. After line 96 $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$. This is useful
-for the next loop on lines 95 to 98 which set any old upper digits to zero.
+The initial carry $u$ is cleared on line 64, note that $u$ is of type mp\_digit which ensures type compatibility within the
+implementation. The initial addition loop begins on line 65 and ends on line 74. Similarly the conditional addition loop
+begins on line 80 and ends on line 90. The addition is finished with the final carry being stored in $tmpc$ on line 93.
+Note the ``++'' operator on the same line. After line 93 $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$. This is useful
+for the next loop on lines 96 to 99 which set any old upper digits to zero.
\subsection{Low Level Subtraction}
The low level unsigned subtraction algorithm is very similar to the low level unsigned addition algorithm. The principle difference is that the
@@ -2273,90 +2314,92 @@ If $b$ has a smaller magnitude than $a$ then step 9 will force the carry and cop
\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_sub.c
\vspace{-3mm}
\begin{alltt}
-016 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
-017 int
-018 s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
-019 \{
-020 int olduse, res, min, max;
-021
-022 /* find sizes */
-023 min = b->used;
-024 max = a->used;
-025
-026 /* init result */
-027 if (c->alloc < max) \{
-028 if ((res = mp_grow (c, max)) != MP_OKAY) \{
-029 return res;
-030 \}
-031 \}
-032 olduse = c->used;
-033 c->used = max;
-034
-035 \{
-036 register mp_digit u, *tmpa, *tmpb, *tmpc;
-037 register int i;
-038
-039 /* alias for digit pointers */
-040 tmpa = a->dp;
-041 tmpb = b->dp;
-042 tmpc = c->dp;
-043
-044 /* set carry to zero */
-045 u = 0;
-046 for (i = 0; i < min; i++) \{
-047 /* T[i] = A[i] - B[i] - U */
-048 *tmpc = *tmpa++ - *tmpb++ - u;
-049
-050 /* U = carry bit of T[i]
-051 * Note this saves performing an AND operation since
-052 * if a carry does occur it will propagate all the way to the
-053 * MSB. As a result a single shift is enough to get the carry
-054 */
-055 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
-056
-057 /* Clear carry from T[i] */
-058 *tmpc++ &= MP_MASK;
-059 \}
-060
-061 /* now copy higher words if any, e.g. if A has more digits than B */
-062 for (; i < max; i++) \{
-063 /* T[i] = A[i] - U */
-064 *tmpc = *tmpa++ - u;
-065
-066 /* U = carry bit of T[i] */
-067 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
-068
-069 /* Clear carry from T[i] */
-070 *tmpc++ &= MP_MASK;
-071 \}
-072
-073 /* clear digits above used (since we may not have grown result above) */
+016
+017 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
+018 int
+019 s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
+020 \{
+021 int olduse, res, min, max;
+022
+023 /* find sizes */
+024 min = b->used;
+025 max = a->used;
+026
+027 /* init result */
+028 if (c->alloc < max) \{
+029 if ((res = mp_grow (c, max)) != MP_OKAY) \{
+030 return res;
+031 \}
+032 \}
+033 olduse = c->used;
+034 c->used = max;
+035
+036 \{
+037 register mp_digit u, *tmpa, *tmpb, *tmpc;
+038 register int i;
+039
+040 /* alias for digit pointers */
+041 tmpa = a->dp;
+042 tmpb = b->dp;
+043 tmpc = c->dp;
+044
+045 /* set carry to zero */
+046 u = 0;
+047 for (i = 0; i < min; i++) \{
+048 /* T[i] = A[i] - B[i] - U */
+049 *tmpc = *tmpa++ - *tmpb++ - u;
+050
+051 /* U = carry bit of T[i]
+052 * Note this saves performing an AND operation since
+053 * if a carry does occur it will propagate all the way to the
+054 * MSB. As a result a single shift is enough to get the carry
+055 */
+056 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+057
+058 /* Clear carry from T[i] */
+059 *tmpc++ &= MP_MASK;
+060 \}
+061
+062 /* now copy higher words if any, e.g. if A has more digits than B */
+063 for (; i < max; i++) \{
+064 /* T[i] = A[i] - U */
+065 *tmpc = *tmpa++ - u;
+066
+067 /* U = carry bit of T[i] */
+068 u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+069
+070 /* Clear carry from T[i] */
+071 *tmpc++ &= MP_MASK;
+072 \}
+073
+074 /* clear digits above used (since we may not have grown result above) */
-074 for (i = c->used; i < olduse; i++) \{
-075 *tmpc++ = 0;
-076 \}
-077 \}
-078
-079 mp_clamp (c);
-080 return MP_OKAY;
-081 \}
-082
+075 for (i = c->used; i < olduse; i++) \{
+076 *tmpc++ = 0;
+077 \}
+078 \}
+079
+080 mp_clamp (c);
+081 return MP_OKAY;
+082 \}
+083
+084 #endif
\end{alltt}
\end{small}
-Line 23 and 24 perform the initial hardcoded sorting of the inputs. In reality the $min$ and $max$ variables are only aliases and are only
-used to make the source code easier to read. Again the pointer alias optimization is used within this algorithm. Lines 40, 41 and 42 initialize the aliases for
+Line 24 and 25 perform the initial hardcoded sorting of the inputs. In reality the $min$ and $max$ variables are only aliases and are only
+used to make the source code easier to read. Again the pointer alias optimization is used within this algorithm. Lines 41, 42 and 43 initialize the aliases for
$a$, $b$ and $c$ respectively.
-The first subtraction loop occurs on lines 45 through 59. The theory behind the subtraction loop is exactly the same as that for
+The first subtraction loop occurs on lines 46 through 60. The theory behind the subtraction loop is exactly the same as that for
the addition loop. As remarked earlier there is an implementation reason for using the ``awkward'' method of extracting the carry
-(\textit{see line 55}). The traditional method for extracting the carry would be to shift by $lg(\beta)$ positions and logically AND
+(\textit{see line 56}). The traditional method for extracting the carry would be to shift by $lg(\beta)$ positions and logically AND
the least significant bit. The AND operation is required because all of the bits above the $\lg(\beta)$'th bit will be set to one after a carry
occurs from subtraction. This carry extraction requires two relatively cheap operations to extract the carry. The other method is to simply
shift the most significant bit to the least significant bit thus extracting the carry with a single cheap operation. This optimization only works on
twos compliment machines which is a safe assumption to make.
-If $a$ has a larger magnitude than $b$ an additional loop (\textit{see lines 62 through 71}) is required to propagate the carry through
+If $a$ has a larger magnitude than $b$ an additional loop (\textit{see lines 63 through 72}) is required to propagate the carry through
$a$ and copy the result to $c$.
\subsection{High Level Addition}
@@ -2440,37 +2483,39 @@ within algorithm s\_mp\_add will force $-0$ to become $0$.
\hspace{-5.1mm}{\bf File}: bn\_mp\_add.c
\vspace{-3mm}
\begin{alltt}
-016 /* high level addition (handles signs) */
-017 int mp_add (mp_int * a, mp_int * b, mp_int * c)
-018 \{
-019 int sa, sb, res;
-020
-021 /* get sign of both inputs */
-022 sa = a->sign;
-023 sb = b->sign;
-024
-025 /* handle two cases, not four */
-026 if (sa == sb) \{
-027 /* both positive or both negative */
-028 /* add their magnitudes, copy the sign */
-029 c->sign = sa;
-030 res = s_mp_add (a, b, c);
-031 \} else \{
-032 /* one positive, the other negative */
-033 /* subtract the one with the greater magnitude from */
-034 /* the one of the lesser magnitude. The result gets */
-035 /* the sign of the one with the greater magnitude. */
-036 if (mp_cmp_mag (a, b) == MP_LT) \{
-037 c->sign = sb;
-038 res = s_mp_sub (b, a, c);
-039 \} else \{
-040 c->sign = sa;
-041 res = s_mp_sub (a, b, c);
-042 \}
-043 \}
-044 return res;
-045 \}
-046
+016
+017 /* high level addition (handles signs) */
+018 int mp_add (mp_int * a, mp_int * b, mp_int * c)
+019 \{
+020 int sa, sb, res;
+021
+022 /* get sign of both inputs */
+023 sa = a->sign;
+024 sb = b->sign;
+025
+026 /* handle two cases, not four */
+027 if (sa == sb) \{
+028 /* both positive or both negative */
+029 /* add their magnitudes, copy the sign */
+030 c->sign = sa;
+031 res = s_mp_add (a, b, c);
+032 \} else \{
+033 /* one positive, the other negative */
+034 /* subtract the one with the greater magnitude from */
+035 /* the one of the lesser magnitude. The result gets */
+036 /* the sign of the one with the greater magnitude. */
+037 if (mp_cmp_mag (a, b) == MP_LT) \{
+038 c->sign = sb;
+039 res = s_mp_sub (b, a, c);
+040 \} else \{
+041 c->sign = sa;
+042 res = s_mp_sub (a, b, c);
+043 \}
+044 \}
+045 return res;
+046 \}
+047
+048 #endif
\end{alltt}
\end{small}
@@ -2544,48 +2589,50 @@ algorithm from producing $-a - -a = -0$ as a result.
\hspace{-5.1mm}{\bf File}: bn\_mp\_sub.c
\vspace{-3mm}
\begin{alltt}
-016 /* high level subtraction (handles signs) */
-017 int
-018 mp_sub (mp_int * a, mp_int * b, mp_int * c)
-019 \{
-020 int sa, sb, res;
-021
-022 sa = a->sign;
-023 sb = b->sign;
-024
-025 if (sa != sb) \{
-026 /* subtract a negative from a positive, OR */
-027 /* subtract a positive from a negative. */
-028 /* In either case, ADD their magnitudes, */
-029 /* and use the sign of the first number. */
-030 c->sign = sa;
-031 res = s_mp_add (a, b, c);
-032 \} else \{
-033 /* subtract a positive from a positive, OR */
-034 /* subtract a negative from a negative. */
-035 /* First, take the difference between their */
-036 /* magnitudes, then... */
-037 if (mp_cmp_mag (a, b) != MP_LT) \{
-038 /* Copy the sign from the first */
-039 c->sign = sa;
-040 /* The first has a larger or equal magnitude */
-041 res = s_mp_sub (a, b, c);
-042 \} else \{
-043 /* The result has the *opposite* sign from */
-044 /* the first number. */
-045 c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
-046 /* The second has a larger magnitude */
-047 res = s_mp_sub (b, a, c);
-048 \}
-049 \}
-050 return res;
-051 \}
-052
+016
+017 /* high level subtraction (handles signs) */
+018 int
+019 mp_sub (mp_int * a, mp_int * b, mp_int * c)
+020 \{
+021 int sa, sb, res;
+022
+023 sa = a->sign;
+024 sb = b->sign;
+025
+026 if (sa != sb) \{
+027 /* subtract a negative from a positive, OR */
+028 /* subtract a positive from a negative. */
+029 /* In either case, ADD their magnitudes, */
+030 /* and use the sign of the first number. */
+031 c->sign = sa;
+032 res = s_mp_add (a, b, c);
+033 \} else \{
+034 /* subtract a positive from a positive, OR */
+035 /* subtract a negative from a negative. */
+036 /* First, take the difference between their */
+037 /* magnitudes, then... */
+038 if (mp_cmp_mag (a, b) != MP_LT) \{
+039 /* Copy the sign from the first */
+040 c->sign = sa;
+041 /* The first has a larger or equal magnitude */
+042 res = s_mp_sub (a, b, c);
+043 \} else \{
+044 /* The result has the *opposite* sign from */
+045 /* the first number. */
+046 c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+047 /* The second has a larger magnitude */
+048 res = s_mp_sub (b, a, c);
+049 \}
+050 \}
+051 return res;
+052 \}
+053
+054 #endif
\end{alltt}
\end{small}
Much like the implementation of algorithm mp\_add the variable $res$ is used to catch the return code of the unsigned addition or subtraction operations
-and forward it to the end of the function. On line 37 the ``not equal to'' \textbf{MP\_LT} expression is used to emulate a
+and forward it to the end of the function. On line 38 the ``not equal to'' \textbf{MP\_LT} expression is used to emulate a
``greater than or equal to'' comparison.
\section{Bit and Digit Shifting}
@@ -2653,71 +2700,73 @@ Step 8 clears any leading digits of $b$ in case it originally had a larger magni
\hspace{-5.1mm}{\bf File}: bn\_mp\_mul\_2.c
\vspace{-3mm}
\begin{alltt}
-016 /* b = a*2 */
-017 int mp_mul_2(mp_int * a, mp_int * b)
-018 \{
-019 int x, res, oldused;
-020
-021 /* grow to accomodate result */
-022 if (b->alloc < a->used + 1) \{
-023 if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) \{
-024 return res;
-025 \}
-026 \}
-027
-028 oldused = b->used;
-029 b->used = a->used;
-030
-031 \{
-032 register mp_digit r, rr, *tmpa, *tmpb;
-033
-034 /* alias for source */
-035 tmpa = a->dp;
-036
-037 /* alias for dest */
-038 tmpb = b->dp;
-039
-040 /* carry */
-041 r = 0;
-042 for (x = 0; x < a->used; x++) \{
-043
-044 /* get what will be the *next* carry bit from the
-045 * MSB of the current digit
-046 */
-047 rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
-048
-049 /* now shift up this digit, add in the carry [from the previous] */
-050 *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
-051
-052 /* copy the carry that would be from the source
-053 * digit into the next iteration
-054 */
-055 r = rr;
-056 \}
-057
-058 /* new leading digit? */
-059 if (r != 0) \{
-060 /* add a MSB which is always 1 at this point */
-061 *tmpb = 1;
-062 ++(b->used);
-063 \}
-064
-065 /* now zero any excess digits on the destination
-066 * that we didn't write to
-067 */
-068 tmpb = b->dp + b->used;
-069 for (x = b->used; x < oldused; x++) \{
-070 *tmpb++ = 0;
-071 \}
-072 \}
-073 b->sign = a->sign;
-074 return MP_OKAY;
-075 \}
+016
+017 /* b = a*2 */
+018 int mp_mul_2(mp_int * a, mp_int * b)
+019 \{
+020 int x, res, oldused;
+021
+022 /* grow to accomodate result */
+023 if (b->alloc < a->used + 1) \{
+024 if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) \{
+025 return res;
+026 \}
+027 \}
+028
+029 oldused = b->used;
+030 b->used = a->used;
+031
+032 \{
+033 register mp_digit r, rr, *tmpa, *tmpb;
+034
+035 /* alias for source */
+036 tmpa = a->dp;
+037
+038 /* alias for dest */
+039 tmpb = b->dp;
+040
+041 /* carry */
+042 r = 0;
+043 for (x = 0; x < a->used; x++) \{
+044
+045 /* get what will be the *next* carry bit from the
+046 * MSB of the current digit
+047 */
+048 rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
+049
+050 /* now shift up this digit, add in the carry [from the previous] */
+051 *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
+052
+053 /* copy the carry that would be from the source
+054 * digit into the next iteration
+055 */
+056 r = rr;
+057 \}
+058
+059 /* new leading digit? */
+060 if (r != 0) \{
+061 /* add a MSB which is always 1 at this point */
+062 *tmpb = 1;
+063 ++(b->used);
+064 \}
+065
+066 /* now zero any excess digits on the destination
+067 * that we didn't write to
+068 */
+069 tmpb = b->dp + b->used;
+070 for (x = b->used; x < oldused; x++) \{
+071 *tmpb++ = 0;
+072 \}
+073 \}
+074 b->sign = a->sign;
+075 return MP_OKAY;
+076 \}
+077 #endif
\end{alltt}
\end{small}
This implementation is essentially an optimized implementation of s\_mp\_add for the case of doubling an input. The only noteworthy difference
-is the use of the logical shift operator on line 50 to perform a single precision doubling.
+is the use of the logical shift operator on line 51 to perform a single precision doubling.
\subsection{Division by Two}
A division by two can just as easily be accomplished with a logical shift right as multiplication by two can be with a logical shift left.
@@ -2765,52 +2814,54 @@ least significant bit not the most significant bit.
\hspace{-5.1mm}{\bf File}: bn\_mp\_div\_2.c
\vspace{-3mm}
\begin{alltt}
-016 /* b = a/2 */
-017 int mp_div_2(mp_int * a, mp_int * b)
-018 \{
-019 int x, res, oldused;
-020
-021 /* copy */
-022 if (b->alloc < a->used) \{
-023 if ((res = mp_grow (b, a->used)) != MP_OKAY) \{
-024 return res;
-025 \}
-026 \}
-027
-028 oldused = b->used;
-029 b->used = a->used;
-030 \{
-031 register mp_digit r, rr, *tmpa, *tmpb;
-032
-033 /* source alias */
-034 tmpa = a->dp + b->used - 1;
-035
-036 /* dest alias */
-037 tmpb = b->dp + b->used - 1;
-038
-039 /* carry */
-040 r = 0;
-041 for (x = b->used - 1; x >= 0; x--) \{
-042 /* get the carry for the next iteration */
-043 rr = *tmpa & 1;
-044
-045 /* shift the current digit, add in carry and store */
-046 *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
-047
-048 /* forward carry to next iteration */
-049 r = rr;
-050 \}
-051
-052 /* zero excess digits */
-053 tmpb = b->dp + b->used;
-054 for (x = b->used; x < oldused; x++) \{
-055 *tmpb++ = 0;
-056 \}
-057 \}
-058 b->sign = a->sign;
-059 mp_clamp (b);
-060 return MP_OKAY;
-061 \}
+016
+017 /* b = a/2 */
+018 int mp_div_2(mp_int * a, mp_int * b)
+019 \{
+020 int x, res, oldused;
+021
+022 /* copy */
+023 if (b->alloc < a->used) \{
+024 if ((res = mp_grow (b, a->used)) != MP_OKAY) \{
+025 return res;
+026 \}
+027 \}
+028
+029 oldused = b->used;
+030 b->used = a->used;
+031 \{
+032 register mp_digit r, rr, *tmpa, *tmpb;
+033
+034 /* source alias */
+035 tmpa = a->dp + b->used - 1;
+036
+037 /* dest alias */
+038 tmpb = b->dp + b->used - 1;
+039
+040 /* carry */
+041 r = 0;
+042 for (x = b->used - 1; x >= 0; x--) \{
+043 /* get the carry for the next iteration */
+044 rr = *tmpa & 1;
+045
+046 /* shift the current digit, add in carry and store */
+047 *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
+048
+049 /* forward carry to next iteration */
+050 r = rr;
+051 \}
+052
+053 /* zero excess digits */
+054 tmpb = b->dp + b->used;
+055 for (x = b->used; x < oldused; x++) \{
+056 *tmpb++ = 0;
+057 \}
+058 \}
+059 b->sign = a->sign;
+060 mp_clamp (b);
+061 return MP_OKAY;
+062 \}
+063 #endif
\end{alltt}
\end{small}
@@ -2884,57 +2935,59 @@ step 8 sets the lower $b$ digits to zero.
\hspace{-5.1mm}{\bf File}: bn\_mp\_lshd.c
\vspace{-3mm}
\begin{alltt}
-016 /* shift left a certain amount of digits */
-017 int mp_lshd (mp_int * a, int b)
-018 \{
-019 int x, res;
-020
-021 /* if its less than zero return */
-022 if (b <= 0) \{
-023 return MP_OKAY;
-024 \}
-025
-026 /* grow to fit the new digits */
-027 if (a->alloc < a->used + b) \{
-028 if ((res = mp_grow (a, a->used + b)) != MP_OKAY) \{
-029 return res;
-030 \}
-031 \}
-032
-033 \{
-034 register mp_digit *top, *bottom;
-035
-036 /* increment the used by the shift amount then copy upwards */
-037 a->used += b;
-038
-039 /* top */
-040 top = a->dp + a->used - 1;
-041
-042 /* base */
-043 bottom = a->dp + a->used - 1 - b;
-044
-045 /* much like mp_rshd this is implemented using a sliding window
-046 * except the window goes the otherway around. Copying from
-047 * the bottom to the top. see bn_mp_rshd.c for more info.
-048 */
-049 for (x = a->used - 1; x >= b; x--) \{
-050 *top-- = *bottom--;
-051 \}
-052
-053 /* zero the lower digits */
-054 top = a->dp;
-055 for (x = 0; x < b; x++) \{
-056 *top++ = 0;
-057 \}
-058 \}
-059 return MP_OKAY;
-060 \}
+016
+017 /* shift left a certain amount of digits */
+018 int mp_lshd (mp_int * a, int b)
+019 \{
+020 int x, res;
+021
+022 /* if its less than zero return */
+023 if (b <= 0) \{
+024 return MP_OKAY;
+025 \}
+026
+027 /* grow to fit the new digits */
+028 if (a->alloc < a->used + b) \{
+029 if ((res = mp_grow (a, a->used + b)) != MP_OKAY) \{
+030 return res;
+031 \}
+032 \}
+033
+034 \{
+035 register mp_digit *top, *bottom;
+036
+037 /* increment the used by the shift amount then copy upwards */
+038 a->used += b;
+039
+040 /* top */
+041 top = a->dp + a->used - 1;
+042
+043 /* base */
+044 bottom = a->dp + a->used - 1 - b;
+045
+046 /* much like mp_rshd this is implemented using a sliding window
+047 * except the window goes the otherway around. Copying from
+048 * the bottom to the top. see bn_mp_rshd.c for more info.
+049 */
+050 for (x = a->used - 1; x >= b; x--) \{
+051 *top-- = *bottom--;
+052 \}
+053
+054 /* zero the lower digits */
+055 top = a->dp;
+056 for (x = 0; x < b; x++) \{
+057 *top++ = 0;
+058 \}
+059 \}
+060 return MP_OKAY;
+061 \}
+062 #endif
\end{alltt}
\end{small}
-The if statement on line 22 ensures that the $b$ variable is greater than zero. The \textbf{used} count is incremented by $b$ before
-the copy loop begins. This elminates the need for an additional variable in the for loop. The variable $top$ on line 40 is an alias
-for the leading digit while $bottom$ on line 47 is an alias for the trailing edge. The aliases form a window of exactly $b$ digits
+The if statement on line 23 ensures that the $b$ variable is greater than zero. The \textbf{used} count is incremented by $b$ before
+the copy loop begins. This elminates the need for an additional variable in the for loop. The variable $top$ on line 41 is an alias
+for the leading digit while $bottom$ on line 44 is an alias for the trailing edge. The aliases form a window of exactly $b$ digits
over the input.
\subsection{Division by $x$}
@@ -2987,56 +3040,58 @@ Once the window copy is complete the upper digits must be zeroed and the \textbf
\hspace{-5.1mm}{\bf File}: bn\_mp\_rshd.c
\vspace{-3mm}
\begin{alltt}
-016 /* shift right a certain amount of digits */
-017 void mp_rshd (mp_int * a, int b)
-018 \{
-019 int x;
-020
-021 /* if b <= 0 then ignore it */
-022 if (b <= 0) \{
-023 return;
-024 \}
-025
-026 /* if b > used then simply zero it and return */
-027 if (a->used <= b) \{
-028 mp_zero (a);
-029 return;
-030 \}
-031
-032 \{
-033 register mp_digit *bottom, *top;
-034
-035 /* shift the digits down */
-036
-037 /* bottom */
-038 bottom = a->dp;
-039
-040 /* top [offset into digits] */
-041 top = a->dp + b;
-042
-043 /* this is implemented as a sliding window where
-044 * the window is b-digits long and digits from
-045 * the top of the window are copied to the bottom
-046 *
-047 * e.g.
-048
-049 b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
-050 /\symbol{92} | ---->
-051 \symbol{92}-------------------/ ---->
-052 */
-053 for (x = 0; x < (a->used - b); x++) \{
-054 *bottom++ = *top++;
-055 \}
-056
-057 /* zero the top digits */
-058 for (; x < a->used; x++) \{
-059 *bottom++ = 0;
-060 \}
-061 \}
-062
-063 /* remove excess digits */
-064 a->used -= b;
-065 \}
+016
+017 /* shift right a certain amount of digits */
+018 void mp_rshd (mp_int * a, int b)
+019 \{
+020 int x;
+021
+022 /* if b <= 0 then ignore it */
+023 if (b <= 0) \{
+024 return;
+025 \}
+026
+027 /* if b > used then simply zero it and return */
+028 if (a->used <= b) \{
+029 mp_zero (a);
+030 return;
+031 \}
+032
+033 \{
+034 register mp_digit *bottom, *top;
+035
+036 /* shift the digits down */
+037
+038 /* bottom */
+039 bottom = a->dp;
+040
+041 /* top [offset into digits] */
+042 top = a->dp + b;
+043
+044 /* this is implemented as a sliding window where
+045 * the window is b-digits long and digits from
+046 * the top of the window are copied to the bottom
+047 *
+048 * e.g.
+049
+050 b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
+051 /\symbol{92} | ---->
+052 \symbol{92}-------------------/ ---->
+053 */
+054 for (x = 0; x < (a->used - b); x++) \{
+055 *bottom++ = *top++;
+056 \}
+057
+058 /* zero the top digits */
+059 for (; x < a->used; x++) \{
+060 *bottom++ = 0;
+061 \}
+062 \}
+063
+064 /* remove excess digits */
+065 a->used -= b;
+066 \}
+067 #endif
\end{alltt}
\end{small}
@@ -3105,69 +3160,71 @@ complete. It is possible to optimize this algorithm down to a $O(n)$ algorithm
\hspace{-5.1mm}{\bf File}: bn\_mp\_mul\_2d.c
\vspace{-3mm}
\begin{alltt}
-016 /* shift left by a certain bit count */
-017 int mp_mul_2d (mp_int * a, int b, mp_int * c)
-018 \{
-019 mp_digit d;
-020 int res;
-021
-022 /* copy */
-023 if (a != c) \{
-024 if ((res = mp_copy (a, c)) != MP_OKAY) \{
-025 return res;
-026 \}
-027 \}
-028
-029 if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) \{
-030 if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) \{
-031 return res;
-032 \}
-033 \}
-034
-035 /* shift by as many digits in the bit count */
-036 if (b >= (int)DIGIT_BIT) \{
-037 if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) \{
-038 return res;
-039 \}
-040 \}
-041
-042 /* shift any bit count < DIGIT_BIT */
-043 d = (mp_digit) (b % DIGIT_BIT);
-044 if (d != 0) \{
-045 register mp_digit *tmpc, shift, mask, r, rr;
-046 register int x;
-047
-048 /* bitmask for carries */
-049 mask = (((mp_digit)1) << d) - 1;
-050
-051 /* shift for msbs */
-052 shift = DIGIT_BIT - d;
-053
-054 /* alias */
-055 tmpc = c->dp;
-056
-057 /* carry */
-058 r = 0;
-059 for (x = 0; x < c->used; x++) \{
-060 /* get the higher bits of the current word */
-061 rr = (*tmpc >> shift) & mask;
-062
-063 /* shift the current word and OR in the carry */
-064 *tmpc = ((*tmpc << d) | r) & MP_MASK;
-065 ++tmpc;
-066
-067 /* set the carry to the carry bits of the current word */
-068 r = rr;
-069 \}
-070
-071 /* set final carry */
-072 if (r != 0) \{
-073 c->dp[(c->used)++] = r;
-074 \}
-075 \}
-076 mp_clamp (c);
-077 return MP_OKAY;
-078 \}
+016
+017 /* shift left by a certain bit count */
+018 int mp_mul_2d (mp_int * a, int b, mp_int * c)
+019 \{
+020 mp_digit d;
+021 int res;
+022
+023 /* copy */
+024 if (a != c) \{
+025 if ((res = mp_copy (a, c)) != MP_OKAY) \{
+026 return res;
+027 \}
+028 \}
+029
+030 if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) \{
+031 if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) \{
+032 return res;
+033 \}
+034 \}
+035
+036 /* shift by as many digits in the bit count */
+037 if (b >= (int)DIGIT_BIT) \{
+038 if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) \{
+039 return res;
+040 \}
+041 \}
+042
+043 /* shift any bit count < DIGIT_BIT */
+044 d = (mp_digit) (b % DIGIT_BIT);
+045 if (d != 0) \{
+046 register mp_digit *tmpc, shift, mask, r, rr;
+047 register int x;
+048
+049 /* bitmask for carries */
+050 mask = (((mp_digit)1) << d) - 1;
+051
+052 /* shift for msbs */
+053 shift = DIGIT_BIT - d;
+054
+055 /* alias */
+056 tmpc = c->dp;
+057
+058 /* carry */
+059 r = 0;
+060 for (x = 0; x < c->used; x++) \{
+061 /* get the higher bits of the current word */
+062 rr = (*tmpc >> shift) & mask;
+063
+064 /* shift the current word and OR in the carry */
+065 *tmpc = ((*tmpc << d) | r) & MP_MASK;
+066 ++tmpc;
+067
+068 /* set the carry to the carry bits of the current word */
+069 r = rr;
+070 \}
+071
+072 /* set final carry */
+073 if (r != 0) \{
+074 c->dp[(c->used)++] = r;
+075 \}
+076 \}
+077 mp_clamp (c);
+078 return MP_OKAY;
+079 \}
+080 #endif
\end{alltt}
\end{small}
@@ -3217,83 +3274,85 @@ by using algorithm mp\_mod\_2d.
\hspace{-5.1mm}{\bf File}: bn\_mp\_div\_2d.c
\vspace{-3mm}
\begin{alltt}
-016 /* shift right by a certain bit count (store quotient in c, optional remaind
+016
+017 /* shift right by a certain bit count (store quotient in c, optional remaind
er in d) */
-017 int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
-018 \{
-019 mp_digit D, r, rr;
-020 int x, res;
-021 mp_int t;
-022
+018 int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
+019 \{
+020 mp_digit D, r, rr;
+021 int x, res;
+022 mp_int t;
023
-024 /* if the shift count is <= 0 then we do no work */
-025 if (b <= 0) \{
-026 res = mp_copy (a, c);
-027 if (d != NULL) \{
-028 mp_zero (d);
-029 \}
-030 return res;
-031 \}
-032
-033 if ((res = mp_init (&t)) != MP_OKAY) \{
-034 return res;
-035 \}
-036
-037 /* get the remainder */
-038 if (d != NULL) \{
-039 if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) \{
-040 mp_clear (&t);
-041 return res;
-042 \}
-043 \}
-044
-045 /* copy */
-046 if ((res = mp_copy (a, c)) != MP_OKAY) \{
-047 mp_clear (&t);
-048 return res;
-049 \}
-050
-051 /* shift by as many digits in the bit count */
-052 if (b >= (int)DIGIT_BIT) \{
-053 mp_rshd (c, b / DIGIT_BIT);
-054 \}
-055
-056 /* shift any bit count < DIGIT_BIT */
-057 D = (mp_digit) (b % DIGIT_BIT);
-058 if (D != 0) \{
-059 register mp_digit *tmpc, mask, shift;
-060
-061 /* mask */
-062 mask = (((mp_digit)1) << D) - 1;
-063
-064 /* shift for lsb */
-065 shift = DIGIT_BIT - D;
-066
-067 /* alias */
-068 tmpc = c->dp + (c->used - 1);
-069
-070 /* carry */
-071 r = 0;
-072 for (x = c->used - 1; x >= 0; x--) \{
-073 /* get the lower bits of this word in a temp */
-074 rr = *tmpc & mask;
-075
-076 /* shift the current word and mix in the carry bits from the previous
+024
+025 /* if the shift count is <= 0 then we do no work */
+026 if (b <= 0) \{
+027 res = mp_copy (a, c);
+028 if (d != NULL) \{
+029 mp_zero (d);
+030 \}
+031 return res;
+032 \}
+033
+034 if ((res = mp_init (&t)) != MP_OKAY) \{
+035 return res;
+036 \}
+037
+038 /* get the remainder */
+039 if (d != NULL) \{
+040 if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) \{
+041 mp_clear (&t);
+042 return res;
+043 \}
+044 \}
+045
+046 /* copy */
+047 if ((res = mp_copy (a, c)) != MP_OKAY) \{
+048 mp_clear (&t);
+049 return res;
+050 \}
+051
+052 /* shift by as many digits in the bit count */
+053 if (b >= (int)DIGIT_BIT) \{
+054 mp_rshd (c, b / DIGIT_BIT);
+055 \}
+056
+057 /* shift any bit count < DIGIT_BIT */
+058 D = (mp_digit) (b % DIGIT_BIT);
+059 if (D != 0) \{
+060 register mp_digit *tmpc, mask, shift;
+061
+062 /* mask */
+063 mask = (((mp_digit)1) << D) - 1;
+064
+065 /* shift for lsb */
+066 shift = DIGIT_BIT - D;
+067
+068 /* alias */
+069 tmpc = c->dp + (c->used - 1);
+070
+071 /* carry */
+072 r = 0;
+073 for (x = c->used - 1; x >= 0; x--) \{
+074 /* get the lower bits of this word in a temp */
+075 rr = *tmpc & mask;
+076
+077 /* shift the current word and mix in the carry bits from the previous
word */
-077 *tmpc = (*tmpc >> D) | (r << shift);
-078 --tmpc;
-079
-080 /* set the carry to the carry bits of the current word found above */
-081 r = rr;
-082 \}
-083 \}
-084 mp_clamp (c);
-085 if (d != NULL) \{
-086 mp_exch (&t, d);
-087 \}
-088 mp_clear (&t);
-089 return MP_OKAY;
-090 \}
+078 *tmpc = (*tmpc >> D) | (r << shift);
+079 --tmpc;
+080
+081 /* set the carry to the carry bits of the current word found above */
+082 r = rr;
+083 \}
+084 \}
+085 mp_clamp (c);
+086 if (d != NULL) \{
+087 mp_exch (&t, d);
+088 \}
+089 mp_clear (&t);
+090 return MP_OKAY;
+091 \}
+092 #endif
\end{alltt}
\end{small}
@@ -3347,41 +3406,43 @@ is copied to $b$, leading digits are removed and the remaining leading digit is
\hspace{-5.1mm}{\bf File}: bn\_mp\_mod\_2d.c
\vspace{-3mm}
\begin{alltt}
-016 /* calc a value mod 2**b */
-017 int
-018 mp_mod_2d (mp_int * a, int b, mp_int * c)
-019 \{
-020 int x, res;
-021
-022 /* if b is <= 0 then zero the int */
-023 if (b <= 0) \{
-024 mp_zero (c);
-025 return MP_OKAY;
-026 \}
-027
-028 /* if the modulus is larger than the value than return */
-029 if (b > (int) (a->used * DIGIT_BIT)) \{
-030 res = mp_copy (a, c);
-031 return res;
-032 \}
-033
-034 /* copy */
-035 if ((res = mp_copy (a, c)) != MP_OKAY) \{
-036 return res;
-037 \}
-038
-039 /* zero digits above the last digit of the modulus */
-040 for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x+
+016
+017 /* calc a value mod 2**b */
+018 int
+019 mp_mod_2d (mp_int * a, int b, mp_int * c)
+020 \{
+021 int x, res;
+022
+023 /* if b is <= 0 then zero the int */
+024 if (b <= 0) \{
+025 mp_zero (c);
+026 return MP_OKAY;
+027 \}
+028
+029 /* if the modulus is larger than the value than return */
+030 if (b > (int) (a->used * DIGIT_BIT)) \{
+031 res = mp_copy (a, c);
+032 return res;
+033 \}
+034
+035 /* copy */
+036 if ((res = mp_copy (a, c)) != MP_OKAY) \{
+037 return res;
+038 \}
+039
+040 /* zero digits above the last digit of the modulus */
+041 for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x+
+) \{
-041 c->dp[x] = 0;
-042 \}
-043 /* clear the digit that is not completely outside/inside the modulus */
-044 c->dp[b / DIGIT_BIT] &=
-045 (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digi
+042 c->dp[x] = 0;
+043 \}
+044 /* clear the digit that is not completely outside/inside the modulus */
+045 c->dp[b / DIGIT_BIT] &=
+046 (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digi
t) 1));
-046 mp_clamp (c);
-047 return MP_OKAY;
-048 \}
+047 mp_clamp (c);
+048 return MP_OKAY;
+049 \}
+050 #endif
\end{alltt}
\end{small}
@@ -3545,85 +3606,87 @@ exceed the precision requested.
\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_mul\_digs.c
\vspace{-3mm}
\begin{alltt}
-016 /* multiplies |a| * |b| and only computes upto digs digits of result
-017 * HAC pp. 595, Algorithm 14.12 Modified so you can control how
-018 * many digits of output are created.
-019 */
-020 int
-021 s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-022 \{
-023 mp_int t;
-024 int res, pa, pb, ix, iy;
-025 mp_digit u;
-026 mp_word r;
-027 mp_digit tmpx, *tmpt, *tmpy;
-028
-029 /* can we use the fast multiplier? */
-030 if (((digs) < MP_WARRAY) &&
-031 MIN (a->used, b->used) <
-032 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{
-033 return fast_s_mp_mul_digs (a, b, c, digs);
-034 \}
-035
-036 if ((res = mp_init_size (&t, digs)) != MP_OKAY) \{
-037 return res;
-038 \}
-039 t.used = digs;
-040
-041 /* compute the digits of the product directly */
-042 pa = a->used;
-043 for (ix = 0; ix < pa; ix++) \{
-044 /* set the carry to zero */
-045 u = 0;
-046
-047 /* limit ourselves to making digs digits of output */
-048 pb = MIN (b->used, digs - ix);
-049
-050 /* setup some aliases */
-051 /* copy of the digit from a used within the nested loop */
-052 tmpx = a->dp[ix];
-053
-054 /* an alias for the destination shifted ix places */
-055 tmpt = t.dp + ix;
-056
-057 /* an alias for the digits of b */
-058 tmpy = b->dp;
-059
-060 /* compute the columns of the output and propagate the carry */
-061 for (iy = 0; iy < pb; iy++) \{
-062 /* compute the column as a mp_word */
-063 r = ((mp_word)*tmpt) +
-064 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
-065 ((mp_word) u);
-066
-067 /* the new column is the lower part of the result */
-068 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-069
-070 /* get the carry word from the result */
-071 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-072 \}
-073 /* set carry if it is placed below digs */
-074 if (ix + iy < digs) \{
-075 *tmpt = u;
-076 \}
-077 \}
-078
-079 mp_clamp (&t);
-080 mp_exch (&t, c);
-081
-082 mp_clear (&t);
-083 return MP_OKAY;
-084 \}
+016
+017 /* multiplies |a| * |b| and only computes upto digs digits of result
+018 * HAC pp. 595, Algorithm 14.12 Modified so you can control how
+019 * many digits of output are created.
+020 */
+021 int
+022 s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+023 \{
+024 mp_int t;
+025 int res, pa, pb, ix, iy;
+026 mp_digit u;
+027 mp_word r;
+028 mp_digit tmpx, *tmpt, *tmpy;
+029
+030 /* can we use the fast multiplier? */
+031 if (((digs) < MP_WARRAY) &&
+032 MIN (a->used, b->used) <
+033 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{
+034 return fast_s_mp_mul_digs (a, b, c, digs);
+035 \}
+036
+037 if ((res = mp_init_size (&t, digs)) != MP_OKAY) \{
+038 return res;
+039 \}
+040 t.used = digs;
+041
+042 /* compute the digits of the product directly */
+043 pa = a->used;
+044 for (ix = 0; ix < pa; ix++) \{
+045 /* set the carry to zero */
+046 u = 0;
+047
+048 /* limit ourselves to making digs digits of output */
+049 pb = MIN (b->used, digs - ix);
+050
+051 /* setup some aliases */
+052 /* copy of the digit from a used within the nested loop */
+053 tmpx = a->dp[ix];
+054
+055 /* an alias for the destination shifted ix places */
+056 tmpt = t.dp + ix;
+057
+058 /* an alias for the digits of b */
+059 tmpy = b->dp;
+060
+061 /* compute the columns of the output and propagate the carry */
+062 for (iy = 0; iy < pb; iy++) \{
+063 /* compute the column as a mp_word */
+064 r = ((mp_word)*tmpt) +
+065 ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+066 ((mp_word) u);
+067
+068 /* the new column is the lower part of the result */
+069 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+070
+071 /* get the carry word from the result */
+072 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+073 \}
+074 /* set carry if it is placed below digs */
+075 if (ix + iy < digs) \{
+076 *tmpt = u;
+077 \}
+078 \}
+079
+080 mp_clamp (&t);
+081 mp_exch (&t, c);
+082
+083 mp_clear (&t);
+084 return MP_OKAY;
+085 \}
+086 #endif
\end{alltt}
\end{small}
-Lines 30 to 34 determine if the Comba method can be used first. The conditions for using the Comba routine are that min$(a.used, b.used) < \delta$ and
+Lines 31 to 35 determine if the Comba method can be used first. The conditions for using the Comba routine are that min$(a.used, b.used) < \delta$ and
the number of digits of output is less than \textbf{MP\_WARRAY}. This new constant is used to control
the stack usage in the Comba routines. By default it is set to $\delta$ but can be reduced when memory is at a premium.
-Of particular importance is the calculation of the $ix+iy$'th column on lines 64, 65 and 65. Note how all of the
+Of particular importance is the calculation of the $ix+iy$'th column on lines 64, 65 and 66. Note how all of the
variables are cast to the type \textbf{mp\_word}, which is also the type of variable $\hat r$. That is to ensure that double precision operations
-are used instead of single precision. The multiplication on line 64 makes use of a specific GCC optimizer behaviour. On the outset it looks like
+are used instead of single precision. The multiplication on line 65 makes use of a specific GCC optimizer behaviour. On the outset it looks like
the compiler will have to use a double precision multiplication to produce the result required. Such an operation would be horribly slow on most
processors and drag this to a crawl. However, GCC is smart enough to realize that double wide output single precision multipliers can be used. For
example, the instruction ``MUL'' on the x86 processor can multiply two 32-bit values and produce a 64-bit result.
@@ -3797,128 +3860,102 @@ and addition operations in the nested loop in parallel.
\hspace{-5.1mm}{\bf File}: bn\_fast\_s\_mp\_mul\_digs.c
\vspace{-3mm}
\begin{alltt}
-016 /* Fast (comba) multiplier
-017 *
-018 * This is the fast column-array [comba] multiplier. It is
-019 * designed to compute the columns of the product first
-020 * then handle the carries afterwards. This has the effect
-021 * of making the nested loops that compute the columns very
-022 * simple and schedulable on super-scalar processors.
-023 *
-024 * This has been modified to produce a variable number of
-025 * digits of output so if say only a half-product is required
-026 * you don't have to compute the upper half (a feature
-027 * required for fast Barrett reduction).
-028 *
-029 * Based on Algorithm 14.12 on pp.595 of HAC.
-030 *
-031 */
-032 int
-033 fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-034 \{
-035 int olduse, res, pa, ix;
-036 mp_word W[MP_WARRAY];
-037
-038 /* grow the destination as required */
-039 if (c->alloc < digs) \{
-040 if ((res = mp_grow (c, digs)) != MP_OKAY) \{
-041 return res;
-042 \}
-043 \}
-044
-045 /* clear temp buf (the columns) */
-046 memset (W, 0, sizeof (mp_word) * digs);
-047
-048 /* calculate the columns */
-049 pa = a->used;
-050 for (ix = 0; ix < pa; ix++) \{
-051 /* this multiplier has been modified to allow you to
-052 * control how many digits of output are produced.
-053 * So at most we want to make upto "digs" digits of output.
-054 *
-055 * this adds products to distinct columns (at ix+iy) of W
-056 * note that each step through the loop is not dependent on
-057 * the previous which means the compiler can easily unroll
-058 * the loop without scheduling problems
-059 */
-060 \{
-061 register mp_digit tmpx, *tmpy;
-062 register mp_word *_W;
-063 register int iy, pb;
+016
+017 /* Fast (comba) multiplier
+018 *
+019 * This is the fast column-array [comba] multiplier. It is
+020 * designed to compute the columns of the product first
+021 * then handle the carries afterwards. This has the effect
+022 * of making the nested loops that compute the columns very
+023 * simple and schedulable on super-scalar processors.
+024 *
+025 * This has been modified to produce a variable number of
+026 * digits of output so if say only a half-product is required
+027 * you don't have to compute the upper half (a feature
+028 * required for fast Barrett reduction).
+029 *
+030 * Based on Algorithm 14.12 on pp.595 of HAC.
+031 *
+032 */
+033 int
+034 fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+035 \{
+036 int olduse, res, pa, ix, iz;
+037 mp_digit W[MP_WARRAY];
+038 register mp_word _W;
+039
+040 /* grow the destination as required */
+041 if (c->alloc < digs) \{
+042 if ((res = mp_grow (c, digs)) != MP_OKAY) \{
+043 return res;
+044 \}
+045 \}
+046
+047 /* number of output digits to produce */
+048 pa = MIN(digs, a->used + b->used);
+049
+050 /* clear the carry */
+051 _W = 0;
+052 for (ix = 0; ix <= pa; ix++) \{
+053 int tx, ty;
+054 int iy;
+055 mp_digit *tmpx, *tmpy;
+056
+057 /* get offsets into the two bignums */
+058 ty = MIN(b->used-1, ix);
+059 tx = ix - ty;
+060
+061 /* setup temp aliases */
+062 tmpx = a->dp + tx;
+063 tmpy = b->dp + ty;
064
-065 /* alias for the the word on the left e.g. A[ix] * A[iy] */
-066 tmpx = a->dp[ix];
-067
-068 /* alias for the right side */
-069 tmpy = b->dp;
-070
-071 /* alias for the columns, each step through the loop adds a new
-072 term to each column
-073 */
-074 _W = W + ix;
-075
-076 /* the number of digits is limited by their placement. E.g.
-077 we avoid multiplying digits that will end up above the # of
-078 digits of precision requested
-079 */
-080 pb = MIN (b->used, digs - ix);
+065 /* this is the number of times the loop will iterrate, essentially its
+
+066 while (tx++ < a->used && ty-- >= 0) \{ ... \}
+067 */
+068 iy = MIN(a->used-tx, ty+1);
+069
+070 /* execute loop */
+071 for (iz = 0; iz < iy; ++iz) \{
+072 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+073 \}
+074
+075 /* store term */
+076 W[ix] = ((mp_digit)_W) & MP_MASK;
+077
+078 /* make next carry */
+079 _W = _W >> ((mp_word)DIGIT_BIT);
+080 \}
081
-082 for (iy = 0; iy < pb; iy++) \{
-083 *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
-084 \}
-085 \}
-086
-087 \}
-088
-089 /* setup dest */
-090 olduse = c->used;
-091 c->used = digs;
-092
-093 \{
-094 register mp_digit *tmpc;
-095
-096 /* At this point W[] contains the sums of each column. To get the
-097 * correct result we must take the extra bits from each column and
-098 * carry them down
-099 *
-100 * Note that while this adds extra code to the multiplier it
-101 * saves time since the carry propagation is removed from the
-102 * above nested loop.This has the effect of reducing the work
-103 * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
-104 * cost of the shifting. On very small numbers this is slower
-105 * but on most cryptographic size numbers it is faster.
-106 *
-107 * In this particular implementation we feed the carries from
-108 * behind which means when the loop terminates we still have one
-109 * last digit to copy
-110 */
-111 tmpc = c->dp;
-112 for (ix = 1; ix < digs; ix++) \{
-113 /* forward the carry from the previous temp */
-114 W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-115
-116 /* now extract the previous digit [below the carry] */
-117 *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
-118 \}
-119 /* fetch the last digit */
-120 *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
-121
-122 /* clear unused digits [that existed in the old copy of c] */
-123 for (; ix < olduse; ix++) \{
-124 *tmpc++ = 0;
-125 \}
-126 \}
-127 mp_clamp (c);
-128 return MP_OKAY;
-129 \}
+082 /* setup dest */
+083 olduse = c->used;
+084 c->used = digs;
+085
+086 \{
+087 register mp_digit *tmpc;
+088 tmpc = c->dp;
+089 for (ix = 0; ix < digs; ix++) \{
+090 /* now extract the previous digit [below the carry] */
+091 *tmpc++ = W[ix];
+092 \}
+093
+094 /* clear unused digits [that existed in the old copy of c] */
+095 for (; ix < olduse; ix++) \{
+096 *tmpc++ = 0;
+097 \}
+098 \}
+099 mp_clamp (c);
+100 return MP_OKAY;
+101 \}
+102 #endif
\end{alltt}
\end{small}
-The memset on line 46 clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication
-implementation a series of aliases (\textit{lines 66, 69 and 74}) are used to simplify the inner $O(n^2)$ loop.
+The memset on line @47,memset@ clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication
+implementation a series of aliases (\textit{lines 62, 63 and 76}) are used to simplify the inner $O(n^2)$ loop.
In this case a new alias $\_\hat W$ has been added which refers to the double precision columns offset by $ix$ in each pass.
-The inner loop on lines 82, 83 and 85 is where the algorithm will spend the majority of the time, which is why it has been
+The inner loop on lines 89, 79 and 80 is where the algorithm will spend the majority of the time, which is why it has been
stripped to the bones of any extra baggage\footnote{Hence the pointer aliases.}. On x86 processors the multiplication and additions amount to at the
very least five instructions (\textit{two loads, two additions, one multiply}) while on the ARMv4 processors they amount to only three
(\textit{one load, one store, one multiply-add}). For both of the x86 and ARMv4 processors the GCC compiler performs a good job at unrolling the loop
@@ -4115,157 +4152,159 @@ The remaining steps 13 through 18 compute the Karatsuba polynomial through a var
\hspace{-5.1mm}{\bf File}: bn\_mp\_karatsuba\_mul.c
\vspace{-3mm}
\begin{alltt}
-016 /* c = |a| * |b| using Karatsuba Multiplication using
-017 * three half size multiplications
-018 *
-019 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
-020 * let n represent half of the number of digits in
-021 * the min(a,b)
-022 *
-023 * a = a1 * B**n + a0
-024 * b = b1 * B**n + b0
-025 *
-026 * Then, a * b =>
-027 a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0
-028 *
-029 * Note that a1b1 and a0b0 are used twice and only need to be
-030 * computed once. So in total three half size (half # of
-031 * digit) multiplications are performed, a0b0, a1b1 and
-032 * (a1-b1)(a0-b0)
-033 *
-034 * Note that a multiplication of half the digits requires
-035 * 1/4th the number of single precision multiplications so in
-036 * total after one call 25% of the single precision multiplications
-037 * are saved. Note also that the call to mp_mul can end up back
-038 * in this function if the a0, a1, b0, or b1 are above the threshold.
-039 * This is known as divide-and-conquer and leads to the famous
-040 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
-041 * the standard O(N**2) that the baseline/comba methods use.
-042 * Generally though the overhead of this method doesn't pay off
-043 * until a certain size (N ~ 80) is reached.
-044 */
-045 int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
-046 \{
-047 mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
-048 int B, err;
-049
-050 /* default the return code to an error */
-051 err = MP_MEM;
-052
-053 /* min # of digits */
-054 B = MIN (a->used, b->used);
-055
-056 /* now divide in two */
-057 B = B >> 1;
-058
-059 /* init copy all the temps */
-060 if (mp_init_size (&x0, B) != MP_OKAY)
-061 goto ERR;
-062 if (mp_init_size (&x1, a->used - B) != MP_OKAY)
-063 goto X0;
-064 if (mp_init_size (&y0, B) != MP_OKAY)
-065 goto X1;
-066 if (mp_init_size (&y1, b->used - B) != MP_OKAY)
-067 goto Y0;
-068
-069 /* init temps */
-070 if (mp_init_size (&t1, B * 2) != MP_OKAY)
-071 goto Y1;
-072 if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
-073 goto T1;
-074 if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
-075 goto X0Y0;
-076
-077 /* now shift the digits */
-078 x0.used = y0.used = B;
-079 x1.used = a->used - B;
-080 y1.used = b->used - B;
-081
-082 \{
-083 register int x;
-084 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
-085
-086 /* we copy the digits directly instead of using higher level functions
-087 * since we also need to shift the digits
-088 */
-089 tmpa = a->dp;
-090 tmpb = b->dp;
-091
-092 tmpx = x0.dp;
-093 tmpy = y0.dp;
-094 for (x = 0; x < B; x++) \{
-095 *tmpx++ = *tmpa++;
-096 *tmpy++ = *tmpb++;
-097 \}
-098
-099 tmpx = x1.dp;
-100 for (x = B; x < a->used; x++) \{
-101 *tmpx++ = *tmpa++;
-102 \}
-103
-104 tmpy = y1.dp;
-105 for (x = B; x < b->used; x++) \{
-106 *tmpy++ = *tmpb++;
-107 \}
-108 \}
-109
-110 /* only need to clamp the lower words since by definition the
-111 * upper words x1/y1 must have a known number of digits
-112 */
-113 mp_clamp (&x0);
-114 mp_clamp (&y0);
-115
-116 /* now calc the products x0y0 and x1y1 */
-117 /* after this x0 is no longer required, free temp [x0==t2]! */
-118 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
-119 goto X1Y1; /* x0y0 = x0*y0 */
-120 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
-121 goto X1Y1; /* x1y1 = x1*y1 */
-122
-123 /* now calc x1-x0 and y1-y0 */
-124 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
-125 goto X1Y1; /* t1 = x1 - x0 */
-126 if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
-127 goto X1Y1; /* t2 = y1 - y0 */
-128 if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
-129 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
-130
-131 /* add x0y0 */
-132 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
-133 goto X1Y1; /* t2 = x0y0 + x1y1 */
-134 if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
-135 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
-136
-137 /* shift by B */
-138 if (mp_lshd (&t1, B) != MP_OKAY)
-139 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
-140 if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
-141 goto X1Y1; /* x1y1 = x1y1 << 2*B */
-142
-143 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
-144 goto X1Y1; /* t1 = x0y0 + t1 */
-145 if (mp_add (&t1, &x1y1, c) != MP_OKAY)
-146 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
-147
-148 /* Algorithm succeeded set the return code to MP_OKAY */
-149 err = MP_OKAY;
-150
-151 X1Y1:mp_clear (&x1y1);
-152 X0Y0:mp_clear (&x0y0);
-153 T1:mp_clear (&t1);
-154 Y1:mp_clear (&y1);
-155 Y0:mp_clear (&y0);
-156 X1:mp_clear (&x1);
-157 X0:mp_clear (&x0);
-158 ERR:
-159 return err;
-160 \}
+016
+017 /* c = |a| * |b| using Karatsuba Multiplication using
+018 * three half size multiplications
+019 *
+020 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
+021 * let n represent half of the number of digits in
+022 * the min(a,b)
+023 *
+024 * a = a1 * B**n + a0
+025 * b = b1 * B**n + b0
+026 *
+027 * Then, a * b =>
+028 a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0
+029 *
+030 * Note that a1b1 and a0b0 are used twice and only need to be
+031 * computed once. So in total three half size (half # of
+032 * digit) multiplications are performed, a0b0, a1b1 and
+033 * (a1-b1)(a0-b0)
+034 *
+035 * Note that a multiplication of half the digits requires
+036 * 1/4th the number of single precision multiplications so in
+037 * total after one call 25% of the single precision multiplications
+038 * are saved. Note also that the call to mp_mul can end up back
+039 * in this function if the a0, a1, b0, or b1 are above the threshold.
+040 * This is known as divide-and-conquer and leads to the famous
+041 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
+042 * the standard O(N**2) that the baseline/comba methods use.
+043 * Generally though the overhead of this method doesn't pay off
+044 * until a certain size (N ~ 80) is reached.
+045 */
+046 int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
+047 \{
+048 mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
+049 int B, err;
+050
+051 /* default the return code to an error */
+052 err = MP_MEM;
+053
+054 /* min # of digits */
+055 B = MIN (a->used, b->used);
+056
+057 /* now divide in two */
+058 B = B >> 1;
+059
+060 /* init copy all the temps */
+061 if (mp_init_size (&x0, B) != MP_OKAY)
+062 goto ERR;
+063 if (mp_init_size (&x1, a->used - B) != MP_OKAY)
+064 goto X0;
+065 if (mp_init_size (&y0, B) != MP_OKAY)
+066 goto X1;
+067 if (mp_init_size (&y1, b->used - B) != MP_OKAY)
+068 goto Y0;
+069
+070 /* init temps */
+071 if (mp_init_size (&t1, B * 2) != MP_OKAY)
+072 goto Y1;
+073 if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
+074 goto T1;
+075 if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
+076 goto X0Y0;
+077
+078 /* now shift the digits */
+079 x0.used = y0.used = B;
+080 x1.used = a->used - B;
+081 y1.used = b->used - B;
+082
+083 \{
+084 register int x;
+085 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
+086
+087 /* we copy the digits directly instead of using higher level functions
+088 * since we also need to shift the digits
+089 */
+090 tmpa = a->dp;
+091 tmpb = b->dp;
+092
+093 tmpx = x0.dp;
+094 tmpy = y0.dp;
+095 for (x = 0; x < B; x++) \{
+096 *tmpx++ = *tmpa++;
+097 *tmpy++ = *tmpb++;
+098 \}
+099
+100 tmpx = x1.dp;
+101 for (x = B; x < a->used; x++) \{
+102 *tmpx++ = *tmpa++;
+103 \}
+104
+105 tmpy = y1.dp;
+106 for (x = B; x < b->used; x++) \{
+107 *tmpy++ = *tmpb++;
+108 \}
+109 \}
+110
+111 /* only need to clamp the lower words since by definition the
+112 * upper words x1/y1 must have a known number of digits
+113 */
+114 mp_clamp (&x0);
+115 mp_clamp (&y0);
+116
+117 /* now calc the products x0y0 and x1y1 */
+118 /* after this x0 is no longer required, free temp [x0==t2]! */
+119 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
+120 goto X1Y1; /* x0y0 = x0*y0 */
+121 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
+122 goto X1Y1; /* x1y1 = x1*y1 */
+123
+124 /* now calc x1-x0 and y1-y0 */
+125 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
+126 goto X1Y1; /* t1 = x1 - x0 */
+127 if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
+128 goto X1Y1; /* t2 = y1 - y0 */
+129 if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
+130 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
+131
+132 /* add x0y0 */
+133 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
+134 goto X1Y1; /* t2 = x0y0 + x1y1 */
+135 if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
+136 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
+137
+138 /* shift by B */
+139 if (mp_lshd (&t1, B) != MP_OKAY)
+140 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
+141 if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
+142 goto X1Y1; /* x1y1 = x1y1 << 2*B */
+143
+144 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
+145 goto X1Y1; /* t1 = x0y0 + t1 */
+146 if (mp_add (&t1, &x1y1, c) != MP_OKAY)
+147 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
+148
+149 /* Algorithm succeeded set the return code to MP_OKAY */
+150 err = MP_OKAY;
+151
+152 X1Y1:mp_clear (&x1y1);
+153 X0Y0:mp_clear (&x0y0);
+154 T1:mp_clear (&t1);
+155 Y1:mp_clear (&y1);
+156 Y0:mp_clear (&y0);
+157 X1:mp_clear (&x1);
+158 X0:mp_clear (&x0);
+159 ERR:
+160 return err;
+161 \}
+162 #endif
\end{alltt}
\end{small}
The new coding element in this routine, not seen in previous routines, is the usage of goto statements. The conventional
wisdom is that goto statements should be avoided. This is generally true, however when every single function call can fail, it makes sense
-to handle error recovery with a single piece of code. Lines 62 to 74 handle initializing all of the temporary variables
+to handle error recovery with a single piece of code. Lines 61 to 75 handle initializing all of the temporary variables
required. Note how each of the if statements goes to a different label in case of failure. This allows the routine to correctly free only
the temporaries that have been successfully allocated so far.
@@ -4275,13 +4314,13 @@ number of digits for the next section of code.
The first algebraic portion of the algorithm is to split the two inputs into their halves. However, instead of using mp\_mod\_2d and mp\_rshd
to extract the halves, the respective code has been placed inline within the body of the function. To initialize the halves, the \textbf{used} and
-\textbf{sign} members are copied first. The first for loop on line 100 copies the lower halves. Since they are both the same magnitude it
-is simpler to calculate both lower halves in a single loop. The for loop on lines 105 and 105 calculate the upper halves $x1$ and
+\textbf{sign} members are copied first. The first for loop on line 101 copies the lower halves. Since they are both the same magnitude it
+is simpler to calculate both lower halves in a single loop. The for loop on lines 106 and 106 calculate the upper halves $x1$ and
$y1$ respectively.
By inlining the calculation of the halves, the Karatsuba multiplier has a slightly lower overhead and can be used for smaller magnitude inputs.
-When line 149 is reached, the algorithm has completed succesfully. The ``error status'' variable $err$ is set to \textbf{MP\_OKAY} so that
+When line 150 is reached, the algorithm has completed succesfully. The ``error status'' variable $err$ is set to \textbf{MP\_OKAY} so that
the same code that handles errors can be used to clear the temporary variables and return.
\subsection{Toom-Cook $3$-Way Multiplication}
@@ -4399,262 +4438,270 @@ result $a \cdot b$ is produced.
\hspace{-5.1mm}{\bf File}: bn\_mp\_toom\_mul.c
\vspace{-3mm}
\begin{alltt}
-016 /* multiplication using the Toom-Cook 3-way algorithm */
-017 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
-018 \{
-019 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
-020 int res, B;
-021
-022 /* init temps */
-023 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
-024 &a0, &a1, &a2, &b0, &b1,
-025 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{
-026 return res;
-027 \}
-028
-029 /* B */
-030 B = MIN(a->used, b->used) / 3;
-031
-032 /* a = a2 * B**2 + a1 * B + a0 */
-033 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{
-034 goto ERR;
-035 \}
-036
-037 if ((res = mp_copy(a, &a1)) != MP_OKAY) \{
-038 goto ERR;
-039 \}
-040 mp_rshd(&a1, B);
-041 mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+016
+017 /* multiplication using the Toom-Cook 3-way algorithm
+018 *
+019 * Much more complicated than Karatsuba but has a lower asymptotic running t
+ ime of
+020 * O(N**1.464). This algorithm is only particularly useful on VERY large
+021 * inputs (we're talking 1000s of digits here...).
+022 */
+023 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
+024 \{
+025 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
+026 int res, B;
+027
+028 /* init temps */
+029 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
+030 &a0, &a1, &a2, &b0, &b1,
+031 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{
+032 return res;
+033 \}
+034
+035 /* B */
+036 B = MIN(a->used, b->used) / 3;
+037
+038 /* a = a2 * B**2 + a1 * B + a0 */
+039 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{
+040 goto ERR;
+041 \}
042
-043 if ((res = mp_copy(a, &a2)) != MP_OKAY) \{
+043 if ((res = mp_copy(a, &a1)) != MP_OKAY) \{
044 goto ERR;
045 \}
-046 mp_rshd(&a2, B*2);
-047
-048 /* b = b2 * B**2 + b1 * B + b0 */
-049 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{
+046 mp_rshd(&a1, B);
+047 mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+048
+049 if ((res = mp_copy(a, &a2)) != MP_OKAY) \{
050 goto ERR;
051 \}
-052
-053 if ((res = mp_copy(b, &b1)) != MP_OKAY) \{
-054 goto ERR;
-055 \}
-056 mp_rshd(&b1, B);
-057 mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
+052 mp_rshd(&a2, B*2);
+053
+054 /* b = b2 * B**2 + b1 * B + b0 */
+055 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{
+056 goto ERR;
+057 \}
058
-059 if ((res = mp_copy(b, &b2)) != MP_OKAY) \{
+059 if ((res = mp_copy(b, &b1)) != MP_OKAY) \{
060 goto ERR;
061 \}
-062 mp_rshd(&b2, B*2);
-063
-064 /* w0 = a0*b0 */
-065 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{
+062 mp_rshd(&b1, B);
+063 mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
+064
+065 if ((res = mp_copy(b, &b2)) != MP_OKAY) \{
066 goto ERR;
067 \}
-068
-069 /* w4 = a2 * b2 */
-070 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{
-071 goto ERR;
-072 \}
-073
-074 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
-075 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{
-076 goto ERR;
-077 \}
-078 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
-079 goto ERR;
-080 \}
-081 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
+068 mp_rshd(&b2, B*2);
+069
+070 /* w0 = a0*b0 */
+071 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{
+072 goto ERR;
+073 \}
+074
+075 /* w4 = a2 * b2 */
+076 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{
+077 goto ERR;
+078 \}
+079
+080 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
+081 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{
082 goto ERR;
083 \}
-084 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{
+084 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
085 goto ERR;
086 \}
-087
-088 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{
-089 goto ERR;
-090 \}
-091 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
-092 goto ERR;
-093 \}
-094 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
+087 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
+088 goto ERR;
+089 \}
+090 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{
+091 goto ERR;
+092 \}
+093
+094 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{
095 goto ERR;
096 \}
-097 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{
+097 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
098 goto ERR;
099 \}
-100
-101 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{
-102 goto ERR;
-103 \}
-104
-105 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
-106 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{
-107 goto ERR;
-108 \}
-109 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
-110 goto ERR;
-111 \}
-112 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
+100 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
+101 goto ERR;
+102 \}
+103 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{
+104 goto ERR;
+105 \}
+106
+107 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{
+108 goto ERR;
+109 \}
+110
+111 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
+112 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{
113 goto ERR;
114 \}
-115 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
+115 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
116 goto ERR;
117 \}
-118
-119 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{
-120 goto ERR;
-121 \}
-122 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
-123 goto ERR;
-124 \}
-125 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
+118 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
+119 goto ERR;
+120 \}
+121 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
+122 goto ERR;
+123 \}
+124
+125 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{
126 goto ERR;
127 \}
-128 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
+128 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
129 goto ERR;
130 \}
-131
-132 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{
-133 goto ERR;
-134 \}
-135
-136
-137 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
-138 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{
+131 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
+132 goto ERR;
+133 \}
+134 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
+135 goto ERR;
+136 \}
+137
+138 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{
139 goto ERR;
140 \}
-141 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
-142 goto ERR;
-143 \}
-144 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{
+141
+142
+143 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
+144 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{
145 goto ERR;
146 \}
-147 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
+147 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
148 goto ERR;
149 \}
-150 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{
+150 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{
151 goto ERR;
152 \}
-153
-154 /* now solve the matrix
-155
-156 0 0 0 0 1
-157 1 2 4 8 16
-158 1 1 1 1 1
-159 16 8 4 2 1
-160 1 0 0 0 0
-161
-162 using 12 subtractions, 4 shifts,
-163 2 small divisions and 1 small multiplication
-164 */
-165
-166 /* r1 - r4 */
-167 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{
-168 goto ERR;
-169 \}
-170 /* r3 - r0 */
-171 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{
-172 goto ERR;
-173 \}
-174 /* r1/2 */
-175 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{
-176 goto ERR;
-177 \}
-178 /* r3/2 */
-179 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{
-180 goto ERR;
-181 \}
-182 /* r2 - r0 - r4 */
-183 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{
-184 goto ERR;
-185 \}
-186 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{
-187 goto ERR;
-188 \}
-189 /* r1 - r2 */
-190 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
-191 goto ERR;
-192 \}
-193 /* r3 - r2 */
-194 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
-195 goto ERR;
-196 \}
-197 /* r1 - 8r0 */
-198 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{
-199 goto ERR;
-200 \}
-201 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{
-202 goto ERR;
-203 \}
-204 /* r3 - 8r4 */
-205 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{
-206 goto ERR;
-207 \}
-208 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{
-209 goto ERR;
-210 \}
-211 /* 3r2 - r1 - r3 */
-212 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{
-213 goto ERR;
-214 \}
-215 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{
-216 goto ERR;
-217 \}
-218 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{
+153 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
+154 goto ERR;
+155 \}
+156 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{
+157 goto ERR;
+158 \}
+159
+160 /* now solve the matrix
+161
+162 0 0 0 0 1
+163 1 2 4 8 16
+164 1 1 1 1 1
+165 16 8 4 2 1
+166 1 0 0 0 0
+167
+168 using 12 subtractions, 4 shifts,
+169 2 small divisions and 1 small multiplication
+170 */
+171
+172 /* r1 - r4 */
+173 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{
+174 goto ERR;
+175 \}
+176 /* r3 - r0 */
+177 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{
+178 goto ERR;
+179 \}
+180 /* r1/2 */
+181 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{
+182 goto ERR;
+183 \}
+184 /* r3/2 */
+185 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{
+186 goto ERR;
+187 \}
+188 /* r2 - r0 - r4 */
+189 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{
+190 goto ERR;
+191 \}
+192 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{
+193 goto ERR;
+194 \}
+195 /* r1 - r2 */
+196 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
+197 goto ERR;
+198 \}
+199 /* r3 - r2 */
+200 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
+201 goto ERR;
+202 \}
+203 /* r1 - 8r0 */
+204 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{
+205 goto ERR;
+206 \}
+207 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{
+208 goto ERR;
+209 \}
+210 /* r3 - 8r4 */
+211 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{
+212 goto ERR;
+213 \}
+214 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{
+215 goto ERR;
+216 \}
+217 /* 3r2 - r1 - r3 */
+218 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{
219 goto ERR;
220 \}
-221 /* r1 - r2 */
-222 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
-223 goto ERR;
-224 \}
-225 /* r3 - r2 */
-226 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
-227 goto ERR;
-228 \}
-229 /* r1/3 */
-230 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{
-231 goto ERR;
-232 \}
-233 /* r3/3 */
-234 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{
-235 goto ERR;
-236 \}
-237
-238 /* at this point shift W[n] by B*n */
-239 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{
-240 goto ERR;
-241 \}
-242 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{
-243 goto ERR;
-244 \}
-245 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{
+221 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{
+222 goto ERR;
+223 \}
+224 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{
+225 goto ERR;
+226 \}
+227 /* r1 - r2 */
+228 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
+229 goto ERR;
+230 \}
+231 /* r3 - r2 */
+232 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
+233 goto ERR;
+234 \}
+235 /* r1/3 */
+236 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{
+237 goto ERR;
+238 \}
+239 /* r3/3 */
+240 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{
+241 goto ERR;
+242 \}
+243
+244 /* at this point shift W[n] by B*n */
+245 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{
246 goto ERR;
247 \}
-248 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{
+248 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{
249 goto ERR;
-250 \}
-251
-252 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{
-253 goto ERR;
-254 \}
-255 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{
-256 goto ERR;
-257 \}
-258 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{
+250 \}
+251 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{
+252 goto ERR;
+253 \}
+254 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{
+255 goto ERR;
+256 \}
+257
+258 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{
259 goto ERR;
260 \}
-261 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{
+261 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{
262 goto ERR;
-263 \}
-264
-265 ERR:
-266 mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
-267 &a0, &a1, &a2, &b0, &b1,
-268 &b2, &tmp1, &tmp2, NULL);
-269 return res;
-270 \}
-271
+263 \}
+264 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{
+265 goto ERR;
+266 \}
+267 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{
+268 goto ERR;
+269 \}
+270
+271 ERR:
+272 mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
+273 &a0, &a1, &a2, &b0, &b1,
+274 &b2, &tmp1, &tmp2, NULL);
+275 return res;
+276 \}
+277
+278 #endif
\end{alltt}
\end{small}
@@ -4704,43 +4751,57 @@ s\_mp\_mul\_digs will clear it.
\hspace{-5.1mm}{\bf File}: bn\_mp\_mul.c
\vspace{-3mm}
\begin{alltt}
-016 /* high level multiplication (handles sign) */
-017 int mp_mul (mp_int * a, mp_int * b, mp_int * c)
-018 \{
-019 int res, neg;
-020 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-021
-022 /* use Toom-Cook? */
-023 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) \{
-024 res = mp_toom_mul(a, b, c);
-025 /* use Karatsuba? */
-026 \} else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) \{
-027 res = mp_karatsuba_mul (a, b, c);
-028 \} else \{
-029 /* can we use the fast multiplier?
-030 *
-031 * The fast multiplier can be used if the output will
-032 * have less than MP_WARRAY digits and the number of
-033 * digits won't affect carry propagation
-034 */
-035 int digs = a->used + b->used + 1;
-036
-037 if ((digs < MP_WARRAY) &&
-038 MIN(a->used, b->used) <=
-039 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{
-040 res = fast_s_mp_mul_digs (a, b, c, digs);
-041 \} else \{
-042 res = s_mp_mul (a, b, c);
-043 \}
-044 \}
-045 c->sign = (c->used > 0) ? neg : MP_ZPOS;
-046 return res;
-047 \}
+016
+017 /* high level multiplication (handles sign) */
+018 int mp_mul (mp_int * a, mp_int * b, mp_int * c)
+019 \{
+020 int res, neg;
+021 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+022
+023 /* use Toom-Cook? */
+024 #ifdef BN_MP_TOOM_MUL_C
+025 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) \{
+026 res = mp_toom_mul(a, b, c);
+027 \} else
+028 #endif
+029 #ifdef BN_MP_KARATSUBA_MUL_C
+030 /* use Karatsuba? */
+031 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) \{
+032 res = mp_karatsuba_mul (a, b, c);
+033 \} else
+034 #endif
+035 \{
+036 /* can we use the fast multiplier?
+037 *
+038 * The fast multiplier can be used if the output will
+039 * have less than MP_WARRAY digits and the number of
+040 * digits won't affect carry propagation
+041 */
+042 int digs = a->used + b->used + 1;
+043
+044 #ifdef BN_FAST_S_MP_MUL_DIGS_C
+045 if ((digs < MP_WARRAY) &&
+046 MIN(a->used, b->used) <=
+047 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{
+048 res = fast_s_mp_mul_digs (a, b, c, digs);
+049 \} else
+050 #endif
+051 #ifdef BN_S_MP_MUL_DIGS_C
+052 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+053 #else
+054 res = MP_VAL;
+055 #endif
+056
+057 \}
+058 c->sign = (c->used > 0) ? neg : MP_ZPOS;
+059 return res;
+060 \}
+061 #endif
\end{alltt}
\end{small}
-The implementation is rather simplistic and is not particularly noteworthy. Line 22 computes the sign of the result using the ``?''
-operator from the C programming language. Line 39 computes $\delta$ using the fact that $1 << k$ is equal to $2^k$.
+The implementation is rather simplistic and is not particularly noteworthy. Line 23 computes the sign of the result using the ``?''
+operator from the C programming language. Line 47 computes $\delta$ using the fact that $1 << k$ is equal to $2^k$.
\section{Squaring}
\label{sec:basesquare}
@@ -4841,75 +4902,77 @@ results calculated so far. This involves expensive carry propagation which will
\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_sqr.c
\vspace{-3mm}
\begin{alltt}
-016 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
-017 int
-018 s_mp_sqr (mp_int * a, mp_int * b)
-019 \{
-020 mp_int t;
-021 int res, ix, iy, pa;
-022 mp_word r;
-023 mp_digit u, tmpx, *tmpt;
-024
-025 pa = a->used;
-026 if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) \{
-027 return res;
-028 \}
-029
-030 /* default used is maximum possible size */
-031 t.used = 2*pa + 1;
-032
-033 for (ix = 0; ix < pa; ix++) \{
-034 /* first calculate the digit at 2*ix */
-035 /* calculate double precision result */
-036 r = ((mp_word) t.dp[2*ix]) +
-037 ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
-038
-039 /* store lower part in result */
-040 t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
-041
-042 /* get the carry */
-043 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-044
-045 /* left hand side of A[ix] * A[iy] */
-046 tmpx = a->dp[ix];
-047
-048 /* alias for where to store the results */
-049 tmpt = t.dp + (2*ix + 1);
-050
-051 for (iy = ix + 1; iy < pa; iy++) \{
-052 /* first calculate the product */
-053 r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
-054
-055 /* now calculate the double precision result, note we use
-056 * addition instead of *2 since it's easier to optimize
-057 */
-058 r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
-059
-060 /* store lower part */
-061 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-062
-063 /* get carry */
-064 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-065 \}
-066 /* propagate upwards */
-067 while (u != ((mp_digit) 0)) \{
-068 r = ((mp_word) *tmpt) + ((mp_word) u);
-069 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-070 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-071 \}
-072 \}
-073
-074 mp_clamp (&t);
-075 mp_exch (&t, b);
-076 mp_clear (&t);
-077 return MP_OKAY;
-078 \}
+016
+017 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
+018 int
+019 s_mp_sqr (mp_int * a, mp_int * b)
+020 \{
+021 mp_int t;
+022 int res, ix, iy, pa;
+023 mp_word r;
+024 mp_digit u, tmpx, *tmpt;
+025
+026 pa = a->used;
+027 if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) \{
+028 return res;
+029 \}
+030
+031 /* default used is maximum possible size */
+032 t.used = 2*pa + 1;
+033
+034 for (ix = 0; ix < pa; ix++) \{
+035 /* first calculate the digit at 2*ix */
+036 /* calculate double precision result */
+037 r = ((mp_word) t.dp[2*ix]) +
+038 ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
+039
+040 /* store lower part in result */
+041 t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
+042
+043 /* get the carry */
+044 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+045
+046 /* left hand side of A[ix] * A[iy] */
+047 tmpx = a->dp[ix];
+048
+049 /* alias for where to store the results */
+050 tmpt = t.dp + (2*ix + 1);
+051
+052 for (iy = ix + 1; iy < pa; iy++) \{
+053 /* first calculate the product */
+054 r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
+055
+056 /* now calculate the double precision result, note we use
+057 * addition instead of *2 since it's easier to optimize
+058 */
+059 r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
+060
+061 /* store lower part */
+062 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+063
+064 /* get carry */
+065 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+066 \}
+067 /* propagate upwards */
+068 while (u != ((mp_digit) 0)) \{
+069 r = ((mp_word) *tmpt) + ((mp_word) u);
+070 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+071 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+072 \}
+073 \}
+074
+075 mp_clamp (&t);
+076 mp_exch (&t, b);
+077 mp_clear (&t);
+078 return MP_OKAY;
+079 \}
+080 #endif
\end{alltt}
\end{small}
-Inside the outer loop (\textit{see line 33}) the square term is calculated on line 36. Line 43 extracts the carry from the square
-term. Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized on lines 46 and 49 respectively. The doubling is performed using two
-additions (\textit{see line 58}) since it is usually faster than shifting,if not at least as fast.
+Inside the outer loop (\textit{see line 34}) the square term is calculated on line 37. Line 44 extracts the carry from the square
+term. Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized on lines 47 and 50 respectively. The doubling is performed using two
+additions (\textit{see line 59}) since it is usually faster than shifting,if not at least as fast.
\subsection{Faster Squaring by the ``Comba'' Method}
A major drawback to the baseline method is the requirement for single precision shifting inside the $O(n^2)$ nested loop. Squaring has an additional
@@ -4988,129 +5051,123 @@ squares in place.
\hspace{-5.1mm}{\bf File}: bn\_fast\_s\_mp\_sqr.c
\vspace{-3mm}
\begin{alltt}
-016 /* fast squaring
-017 *
-018 * This is the comba method where the columns of the product
-019 * are computed first then the carries are computed. This
-020 * has the effect of making a very simple inner loop that
-021 * is executed the most
-022 *
-023 * W2 represents the outer products and W the inner.
-024 *
-025 * A further optimizations is made because the inner
-026 * products are of the form "A * B * 2". The *2 part does
-027 * not need to be computed until the end which is good
-028 * because 64-bit shifts are slow!
-029 *
-030 * Based on Algorithm 14.16 on pp.597 of HAC.
-031 *
-032 */
-033 int fast_s_mp_sqr (mp_int * a, mp_int * b)
-034 \{
-035 int olduse, newused, res, ix, pa;
-036 mp_word W2[MP_WARRAY], W[MP_WARRAY];
-037
-038 /* calculate size of product and allocate as required */
-039 pa = a->used;
-040 newused = pa + pa + 1;
-041 if (b->alloc < newused) \{
-042 if ((res = mp_grow (b, newused)) != MP_OKAY) \{
-043 return res;
-044 \}
-045 \}
-046
-047 /* zero temp buffer (columns)
-048 * Note that there are two buffers. Since squaring requires
-049 * a outer and inner product and the inner product requires
-050 * computing a product and doubling it (a relatively expensive
-051 * op to perform n**2 times if you don't have to) the inner and
-052 * outer products are computed in different buffers. This way
-053 * the inner product can be doubled using n doublings instead of
-054 * n**2
-055 */
-056 memset (W, 0, newused * sizeof (mp_word));
-057 memset (W2, 0, newused * sizeof (mp_word));
-058
-059 /* This computes the inner product. To simplify the inner N**2 loop
-060 * the multiplication by two is done afterwards in the N loop.
-061 */
-062 for (ix = 0; ix < pa; ix++) \{
-063 /* compute the outer product
-064 *
-065 * Note that every outer product is computed
-066 * for a particular column only once which means that
-067 * there is no need todo a double precision addition
-068 * into the W2[] array.
-069 */
-070 W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
-071
-072 \{
-073 register mp_digit tmpx, *tmpy;
-074 register mp_word *_W;
-075 register int iy;
-076
-077 /* copy of left side */
-078 tmpx = a->dp[ix];
-079
-080 /* alias for right side */
-081 tmpy = a->dp + (ix + 1);
+016
+017 /* fast squaring
+018 *
+019 * This is the comba method where the columns of the product
+020 * are computed first then the carries are computed. This
+021 * has the effect of making a very simple inner loop that
+022 * is executed the most
+023 *
+024 * W2 represents the outer products and W the inner.
+025 *
+026 * A further optimizations is made because the inner
+027 * products are of the form "A * B * 2". The *2 part does
+028 * not need to be computed until the end which is good
+029 * because 64-bit shifts are slow!
+030 *
+031 * Based on Algorithm 14.16 on pp.597 of HAC.
+032 *
+033 */
+034 /* the jist of squaring...
+035
+036 you do like mult except the offset of the tmpx [one that starts closer to ze
+ ro]
+037 can't equal the offset of tmpy. So basically you set up iy like before then
+ you min it with
+038 (ty-tx) so that it never happens. You double all those you add in the inner
+ loop
+039
+040 After that loop you do the squares and add them in.
+041
+042 Remove W2 and don't memset W
+043
+044 */
+045
+046 int fast_s_mp_sqr (mp_int * a, mp_int * b)
+047 \{
+048 int olduse, res, pa, ix, iz;
+049 mp_digit W[MP_WARRAY], *tmpx;
+050 mp_word W1;
+051
+052 /* grow the destination as required */
+053 pa = a->used + a->used;
+054 if (b->alloc < pa) \{
+055 if ((res = mp_grow (b, pa)) != MP_OKAY) \{
+056 return res;
+057 \}
+058 \}
+059
+060 /* number of output digits to produce */
+061 W1 = 0;
+062 for (ix = 0; ix <= pa; ix++) \{
+063 int tx, ty, iy;
+064 mp_word _W;
+065 mp_digit *tmpy;
+066
+067 /* clear counter */
+068 _W = 0;
+069
+070 /* get offsets into the two bignums */
+071 ty = MIN(a->used-1, ix);
+072 tx = ix - ty;
+073
+074 /* setup temp aliases */
+075 tmpx = a->dp + tx;
+076 tmpy = a->dp + ty;
+077
+078 /* this is the number of times the loop will iterrate, essentially its
+
+079 while (tx++ < a->used && ty-- >= 0) \{ ... \}
+080 */
+081 iy = MIN(a->used-tx, ty+1);
082
-083 /* the column to store the result in */
-084 _W = W + (ix + ix + 1);
-085
-086 /* inner products */
-087 for (iy = ix + 1; iy < pa; iy++) \{
-088 *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
-089 \}
-090 \}
-091 \}
-092
-093 /* setup dest */
-094 olduse = b->used;
-095 b->used = newused;
+083 /* now for squaring tx can never equal ty
+084 * we halve the distance since they approach at a rate of 2x
+085 * and we have to round because odd cases need to be executed
+086 */
+087 iy = MIN(iy, (ty-tx+1)>>1);
+088
+089 /* execute loop */
+090 for (iz = 0; iz < iy; iz++) \{
+091 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+092 \}
+093
+094 /* double the inner product and add carry */
+095 _W = _W + _W + W1;
096
-097 /* now compute digits
-098 *
-099 * We have to double the inner product sums, add in the
-100 * outer product sums, propagate carries and convert
-101 * to single precision.
-102 */
-103 \{
-104 register mp_digit *tmpb;
-105
-106 /* double first value, since the inner products are
-107 * half of what they should be
-108 */
-109 W[0] += W[0] + W2[0];
-110
-111 tmpb = b->dp;
-112 for (ix = 1; ix < newused; ix++) \{
-113 /* double/add next digit */
-114 W[ix] += W[ix] + W2[ix];
-115
-116 /* propagate carry forwards [from the previous digit] */
-117 W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-118
-119 /* store the current digit now that the carry isn't
-120 * needed
-121 */
-122 *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+097 /* even columns have the square term in them */
+098 if ((ix&1) == 0) \{
+099 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+100 \}
+101
+102 /* store it */
+103 W[ix] = _W;
+104
+105 /* make next carry */
+106 W1 = _W >> ((mp_word)DIGIT_BIT);
+107 \}
+108
+109 /* setup dest */
+110 olduse = b->used;
+111 b->used = a->used+a->used;
+112
+113 \{
+114 mp_digit *tmpb;
+115 tmpb = b->dp;
+116 for (ix = 0; ix < pa; ix++) \{
+117 *tmpb++ = W[ix] & MP_MASK;
+118 \}
+119
+120 /* clear unused digits [that existed in the old copy of c] */
+121 for (; ix < olduse; ix++) \{
+122 *tmpb++ = 0;
123 \}
-124 /* set the last value. Note even if the carry is zero
-125 * this is required since the next step will not zero
-126 * it if b originally had a value at b->dp[2*a.used]
-127 */
-128 *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
-129
-130 /* clear high digits of b if there were any originally */
-131 for (; ix < olduse; ix++) \{
-132 *tmpb++ = 0;
-133 \}
-134 \}
-135
-136 mp_clamp (b);
-137 return MP_OKAY;
-138 \}
+124 \}
+125 mp_clamp (b);
+126 return MP_OKAY;
+127 \}
+128 #endif
\end{alltt}
\end{small}
@@ -5219,110 +5276,112 @@ ratio of 1:7. } than simpler operations such as addition.
\hspace{-5.1mm}{\bf File}: bn\_mp\_karatsuba\_sqr.c
\vspace{-3mm}
\begin{alltt}
-016 /* Karatsuba squaring, computes b = a*a using three
-017 * half size squarings
-018 *
-019 * See comments of mp_karatsuba_mul for details. It
-020 * is essentially the same algorithm but merely
-021 * tuned to perform recursive squarings.
-022 */
-023 int mp_karatsuba_sqr (mp_int * a, mp_int * b)
-024 \{
-025 mp_int x0, x1, t1, t2, x0x0, x1x1;
-026 int B, err;
-027
-028 err = MP_MEM;
-029
-030 /* min # of digits */
-031 B = a->used;
-032
-033 /* now divide in two */
-034 B = B >> 1;
-035
-036 /* init copy all the temps */
-037 if (mp_init_size (&x0, B) != MP_OKAY)
-038 goto ERR;
-039 if (mp_init_size (&x1, a->used - B) != MP_OKAY)
-040 goto X0;
-041
-042 /* init temps */
-043 if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
-044 goto X1;
-045 if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
-046 goto T1;
-047 if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
-048 goto T2;
-049 if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
-050 goto X0X0;
-051
-052 \{
-053 register int x;
-054 register mp_digit *dst, *src;
-055
-056 src = a->dp;
-057
-058 /* now shift the digits */
-059 dst = x0.dp;
-060 for (x = 0; x < B; x++) \{
-061 *dst++ = *src++;
-062 \}
-063
-064 dst = x1.dp;
-065 for (x = B; x < a->used; x++) \{
-066 *dst++ = *src++;
-067 \}
-068 \}
-069
-070 x0.used = B;
-071 x1.used = a->used - B;
-072
-073 mp_clamp (&x0);
-074
-075 /* now calc the products x0*x0 and x1*x1 */
-076 if (mp_sqr (&x0, &x0x0) != MP_OKAY)
-077 goto X1X1; /* x0x0 = x0*x0 */
-078 if (mp_sqr (&x1, &x1x1) != MP_OKAY)
-079 goto X1X1; /* x1x1 = x1*x1 */
-080
-081 /* now calc (x1-x0)**2 */
-082 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
-083 goto X1X1; /* t1 = x1 - x0 */
-084 if (mp_sqr (&t1, &t1) != MP_OKAY)
-085 goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
-086
-087 /* add x0y0 */
-088 if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
-089 goto X1X1; /* t2 = x0x0 + x1x1 */
-090 if (mp_sub (&t2, &t1, &t1) != MP_OKAY)
-091 goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */
-092
-093 /* shift by B */
-094 if (mp_lshd (&t1, B) != MP_OKAY)
-095 goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
-096 if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
-097 goto X1X1; /* x1x1 = x1x1 << 2*B */
-098
-099 if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
-100 goto X1X1; /* t1 = x0x0 + t1 */
-101 if (mp_add (&t1, &x1x1, b) != MP_OKAY)
-102 goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
-103
-104 err = MP_OKAY;
-105
-106 X1X1:mp_clear (&x1x1);
-107 X0X0:mp_clear (&x0x0);
-108 T2:mp_clear (&t2);
-109 T1:mp_clear (&t1);
-110 X1:mp_clear (&x1);
-111 X0:mp_clear (&x0);
-112 ERR:
-113 return err;
-114 \}
+016
+017 /* Karatsuba squaring, computes b = a*a using three
+018 * half size squarings
+019 *
+020 * See comments of karatsuba_mul for details. It
+021 * is essentially the same algorithm but merely
+022 * tuned to perform recursive squarings.
+023 */
+024 int mp_karatsuba_sqr (mp_int * a, mp_int * b)
+025 \{
+026 mp_int x0, x1, t1, t2, x0x0, x1x1;
+027 int B, err;
+028
+029 err = MP_MEM;
+030
+031 /* min # of digits */
+032 B = a->used;
+033
+034 /* now divide in two */
+035 B = B >> 1;
+036
+037 /* init copy all the temps */
+038 if (mp_init_size (&x0, B) != MP_OKAY)
+039 goto ERR;
+040 if (mp_init_size (&x1, a->used - B) != MP_OKAY)
+041 goto X0;
+042
+043 /* init temps */
+044 if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
+045 goto X1;
+046 if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
+047 goto T1;
+048 if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
+049 goto T2;
+050 if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
+051 goto X0X0;
+052
+053 \{
+054 register int x;
+055 register mp_digit *dst, *src;
+056
+057 src = a->dp;
+058
+059 /* now shift the digits */
+060 dst = x0.dp;
+061 for (x = 0; x < B; x++) \{
+062 *dst++ = *src++;
+063 \}
+064
+065 dst = x1.dp;
+066 for (x = B; x < a->used; x++) \{
+067 *dst++ = *src++;
+068 \}
+069 \}
+070
+071 x0.used = B;
+072 x1.used = a->used - B;
+073
+074 mp_clamp (&x0);
+075
+076 /* now calc the products x0*x0 and x1*x1 */
+077 if (mp_sqr (&x0, &x0x0) != MP_OKAY)
+078 goto X1X1; /* x0x0 = x0*x0 */
+079 if (mp_sqr (&x1, &x1x1) != MP_OKAY)
+080 goto X1X1; /* x1x1 = x1*x1 */
+081
+082 /* now calc (x1-x0)**2 */
+083 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
+084 goto X1X1; /* t1 = x1 - x0 */
+085 if (mp_sqr (&t1, &t1) != MP_OKAY)
+086 goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
+087
+088 /* add x0y0 */
+089 if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
+090 goto X1X1; /* t2 = x0x0 + x1x1 */
+091 if (mp_sub (&t2, &t1, &t1) != MP_OKAY)
+092 goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */
+093
+094 /* shift by B */
+095 if (mp_lshd (&t1, B) != MP_OKAY)
+096 goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
+097 if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
+098 goto X1X1; /* x1x1 = x1x1 << 2*B */
+099
+100 if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
+101 goto X1X1; /* t1 = x0x0 + t1 */
+102 if (mp_add (&t1, &x1x1, b) != MP_OKAY)
+103 goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
+104
+105 err = MP_OKAY;
+106
+107 X1X1:mp_clear (&x1x1);
+108 X0X0:mp_clear (&x0x0);
+109 T2:mp_clear (&t2);
+110 T1:mp_clear (&t1);
+111 X1:mp_clear (&x1);
+112 X0:mp_clear (&x0);
+113 ERR:
+114 return err;
+115 \}
+116 #endif
\end{alltt}
\end{small}
This implementation is largely based on the implementation of algorithm mp\_karatsuba\_mul. It uses the same inline style to copy and
-shift the input into the two halves. The loop from line 52 to line 68 has been modified since only one input exists. The \textbf{used}
+shift the input into the two halves. The loop from line 53 to line 69 has been modified since only one input exists. The \textbf{used}
count of both $x0$ and $x1$ is fixed up and $x0$ is clamped before the calculations begin. At this point $x1$ and $x0$ are valid equivalents
to the respective halves as if mp\_rshd and mp\_mod\_2d had been used.
@@ -5377,31 +5436,44 @@ neither of the polynomial basis algorithms should be used then either the Comba
\hspace{-5.1mm}{\bf File}: bn\_mp\_sqr.c
\vspace{-3mm}
\begin{alltt}
-016 /* computes b = a*a */
-017 int
-018 mp_sqr (mp_int * a, mp_int * b)
-019 \{
-020 int res;
-021
-022 /* use Toom-Cook? */
-023 if (a->used >= TOOM_SQR_CUTOFF) \{
-024 res = mp_toom_sqr(a, b);
-025 /* Karatsuba? */
-026 \} else if (a->used >= KARATSUBA_SQR_CUTOFF) \{
-027 res = mp_karatsuba_sqr (a, b);
-028 \} else \{
-029 /* can we use the fast comba multiplier? */
-030 if ((a->used * 2 + 1) < MP_WARRAY &&
-031 a->used <
-032 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) \{
-033 res = fast_s_mp_sqr (a, b);
-034 \} else \{
-035 res = s_mp_sqr (a, b);
-036 \}
-037 \}
-038 b->sign = MP_ZPOS;
-039 return res;
-040 \}
+016
+017 /* computes b = a*a */
+018 int
+019 mp_sqr (mp_int * a, mp_int * b)
+020 \{
+021 int res;
+022
+023 #ifdef BN_MP_TOOM_SQR_C
+024 /* use Toom-Cook? */
+025 if (a->used >= TOOM_SQR_CUTOFF) \{
+026 res = mp_toom_sqr(a, b);
+027 /* Karatsuba? */
+028 \} else
+029 #endif
+030 #ifdef BN_MP_KARATSUBA_SQR_C
+031 if (a->used >= KARATSUBA_SQR_CUTOFF) \{
+032 res = mp_karatsuba_sqr (a, b);
+033 \} else
+034 #endif
+035 \{
+036 #ifdef BN_FAST_S_MP_SQR_C
+037 /* can we use the fast comba multiplier? */
+038 if ((a->used * 2 + 1) < MP_WARRAY &&
+039 a->used <
+040 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) \{
+041 res = fast_s_mp_sqr (a, b);
+042 \} else
+043 #endif
+044 #ifdef BN_S_MP_SQR_C
+045 res = s_mp_sqr (a, b);
+046 #else
+047 res = MP_VAL;
+048 #endif
+049 \}
+050 b->sign = MP_ZPOS;
+051 return res;
+052 \}
+053 #endif
\end{alltt}
\end{small}
@@ -5650,80 +5722,93 @@ performed at most twice, and on average once. However, if $a \ge b^2$ than it wi
\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce.c
\vspace{-3mm}
\begin{alltt}
-016 /* reduces x mod m, assumes 0 < x < m**2, mu is
-017 * precomputed via mp_reduce_setup.
-018 * From HAC pp.604 Algorithm 14.42
-019 */
-020 int
-021 mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
-022 \{
-023 mp_int q;
-024 int res, um = m->used;
-025
-026 /* q = x */
-027 if ((res = mp_init_copy (&q, x)) != MP_OKAY) \{
-028 return res;
-029 \}
-030
-031 /* q1 = x / b**(k-1) */
-032 mp_rshd (&q, um - 1);
-033
-034 /* according to HAC this optimization is ok */
-035 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) \{
-036 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) \{
-037 goto CLEANUP;
-038 \}
-039 \} else \{
-040 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{
-041 goto CLEANUP;
-042 \}
-043 \}
-044
-045 /* q3 = q2 / b**(k+1) */
-046 mp_rshd (&q, um + 1);
-047
-048 /* x = x mod b**(k+1), quick (no division) */
-049 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{
-050 goto CLEANUP;
-051 \}
-052
-053 /* q = q * m mod b**(k+1), quick (no division) */
-054 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{
-055 goto CLEANUP;
-056 \}
-057
-058 /* x = x - q */
-059 if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{
-060 goto CLEANUP;
-061 \}
-062
-063 /* If x < 0, add b**(k+1) to it */
-064 if (mp_cmp_d (x, 0) == MP_LT) \{
-065 mp_set (&q, 1);
-066 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
-067 goto CLEANUP;
-068 if ((res = mp_add (x, &q, x)) != MP_OKAY)
-069 goto CLEANUP;
-070 \}
-071
-072 /* Back off if it's too big */
-073 while (mp_cmp (x, m) != MP_LT) \{
-074 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{
-075 goto CLEANUP;
-076 \}
-077 \}
-078
-079 CLEANUP:
-080 mp_clear (&q);
-081
-082 return res;
-083 \}
+016
+017 /* reduces x mod m, assumes 0 < x < m**2, mu is
+018 * precomputed via mp_reduce_setup.
+019 * From HAC pp.604 Algorithm 14.42
+020 */
+021 int
+022 mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
+023 \{
+024 mp_int q;
+025 int res, um = m->used;
+026
+027 /* q = x */
+028 if ((res = mp_init_copy (&q, x)) != MP_OKAY) \{
+029 return res;
+030 \}
+031
+032 /* q1 = x / b**(k-1) */
+033 mp_rshd (&q, um - 1);
+034
+035 /* according to HAC this optimization is ok */
+036 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) \{
+037 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) \{
+038 goto CLEANUP;
+039 \}
+040 \} else \{
+041 #ifdef BN_S_MP_MUL_HIGH_DIGS_C
+042 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{
+043 goto CLEANUP;
+044 \}
+045 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+046 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{
+047 goto CLEANUP;
+048 \}
+049 #else
+050 \{
+051 res = MP_VAL;
+052 goto CLEANUP;
+053 \}
+054 #endif
+055 \}
+056
+057 /* q3 = q2 / b**(k+1) */
+058 mp_rshd (&q, um + 1);
+059
+060 /* x = x mod b**(k+1), quick (no division) */
+061 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{
+062 goto CLEANUP;
+063 \}
+064
+065 /* q = q * m mod b**(k+1), quick (no division) */
+066 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{
+067 goto CLEANUP;
+068 \}
+069
+070 /* x = x - q */
+071 if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{
+072 goto CLEANUP;
+073 \}
+074
+075 /* If x < 0, add b**(k+1) to it */
+076 if (mp_cmp_d (x, 0) == MP_LT) \{
+077 mp_set (&q, 1);
+078 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
+079 goto CLEANUP;
+080 if ((res = mp_add (x, &q, x)) != MP_OKAY)
+081 goto CLEANUP;
+082 \}
+083
+084 /* Back off if it's too big */
+085 while (mp_cmp (x, m) != MP_LT) \{
+086 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{
+087 goto CLEANUP;
+088 \}
+089 \}
+090
+091 CLEANUP:
+092 mp_clear (&q);
+093
+094 return res;
+095 \}
+096 #endif
\end{alltt}
\end{small}
The first multiplication that determines the quotient can be performed by only producing the digits from $m - 1$ and up. This essentially halves
the number of single precision multiplications required. However, the optimization is only safe if $\beta$ is much larger than the number of digits
-in the modulus. In the source code this is evaluated on lines 36 to 43 where algorithm s\_mp\_mul\_high\_digs is used when it is
+in the modulus. In the source code this is evaluated on lines 36 to 44 where algorithm s\_mp\_mul\_high\_digs is used when it is
safe to do so.
\subsection{The Barrett Setup Algorithm}
@@ -5756,11 +5841,11 @@ is equivalent and much faster. The final value is computed by taking the intege
\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce\_setup.c
\vspace{-3mm}
\begin{alltt}
-016 /* pre-calculate the value required for Barrett reduction
-017 * For a given modulus "b" it calulates the value required in "a"
-018 */
-019 int
-020 mp_reduce_setup (mp_int * a, mp_int * b)
+016
+017 /* pre-calculate the value required for Barrett reduction
+018 * For a given modulus "b" it calulates the value required in "a"
+019 */
+020 int mp_reduce_setup (mp_int * a, mp_int * b)
021 \{
022 int res;
023
@@ -5769,6 +5854,7 @@ is equivalent and much faster. The final value is computed by taking the intege
026 \}
027 return mp_div (a, b, a, NULL);
028 \}
+029 #endif
\end{alltt}
\end{small}
@@ -6026,107 +6112,109 @@ multiplications.
\hspace{-5.1mm}{\bf File}: bn\_mp\_montgomery\_reduce.c
\vspace{-3mm}
\begin{alltt}
-016 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
-017 int
-018 mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-019 \{
-020 int ix, res, digs;
-021 mp_digit mu;
-022
-023 /* can the fast reduction [comba] method be used?
-024 *
-025 * Note that unlike in mp_mul you're safely allowed *less*
-026 * than the available columns [255 per default] since carries
-027 * are fixed up in the inner loop.
-028 */
-029 digs = n->used * 2 + 1;
-030 if ((digs < MP_WARRAY) &&
-031 n->used <
-032 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{
-033 return fast_mp_montgomery_reduce (x, n, rho);
-034 \}
-035
-036 /* grow the input as required */
-037 if (x->alloc < digs) \{
-038 if ((res = mp_grow (x, digs)) != MP_OKAY) \{
-039 return res;
-040 \}
-041 \}
-042 x->used = digs;
-043
-044 for (ix = 0; ix < n->used; ix++) \{
-045 /* mu = ai * rho mod b
-046 *
-047 * The value of rho must be precalculated via
-048 * bn_mp_montgomery_setup() such that
-049 * it equals -1/n0 mod b this allows the
-050 * following inner loop to reduce the
-051 * input one digit at a time
-052 */
-053 mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
-054
-055 /* a = a + mu * m * b**i */
-056 \{
-057 register int iy;
-058 register mp_digit *tmpn, *tmpx, u;
-059 register mp_word r;
-060
-061 /* alias for digits of the modulus */
-062 tmpn = n->dp;
-063
-064 /* alias for the digits of x [the input] */
-065 tmpx = x->dp + ix;
-066
-067 /* set the carry to zero */
-068 u = 0;
-069
-070 /* Multiply and add in place */
-071 for (iy = 0; iy < n->used; iy++) \{
-072 /* compute product and sum */
-073 r = ((mp_word)mu) * ((mp_word)*tmpn++) +
-074 ((mp_word) u) + ((mp_word) * tmpx);
-075
-076 /* get carry */
-077 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-078
-079 /* fix digit */
-080 *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
-081 \}
-082 /* At this point the ix'th digit of x should be zero */
-083
+016
+017 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
+018 int
+019 mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+020 \{
+021 int ix, res, digs;
+022 mp_digit mu;
+023
+024 /* can the fast reduction [comba] method be used?
+025 *
+026 * Note that unlike in mul you're safely allowed *less*
+027 * than the available columns [255 per default] since carries
+028 * are fixed up in the inner loop.
+029 */
+030 digs = n->used * 2 + 1;
+031 if ((digs < MP_WARRAY) &&
+032 n->used <
+033 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{
+034 return fast_mp_montgomery_reduce (x, n, rho);
+035 \}
+036
+037 /* grow the input as required */
+038 if (x->alloc < digs) \{
+039 if ((res = mp_grow (x, digs)) != MP_OKAY) \{
+040 return res;
+041 \}
+042 \}
+043 x->used = digs;
+044
+045 for (ix = 0; ix < n->used; ix++) \{
+046 /* mu = ai * rho mod b
+047 *
+048 * The value of rho must be precalculated via
+049 * montgomery_setup() such that
+050 * it equals -1/n0 mod b this allows the
+051 * following inner loop to reduce the
+052 * input one digit at a time
+053 */
+054 mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
+055
+056 /* a = a + mu * m * b**i */
+057 \{
+058 register int iy;
+059 register mp_digit *tmpn, *tmpx, u;
+060 register mp_word r;
+061
+062 /* alias for digits of the modulus */
+063 tmpn = n->dp;
+064
+065 /* alias for the digits of x [the input] */
+066 tmpx = x->dp + ix;
+067
+068 /* set the carry to zero */
+069 u = 0;
+070
+071 /* Multiply and add in place */
+072 for (iy = 0; iy < n->used; iy++) \{
+073 /* compute product and sum */
+074 r = ((mp_word)mu) * ((mp_word)*tmpn++) +
+075 ((mp_word) u) + ((mp_word) * tmpx);
+076
+077 /* get carry */
+078 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+079
+080 /* fix digit */
+081 *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
+082 \}
+083 /* At this point the ix'th digit of x should be zero */
084
-085 /* propagate carries upwards as required*/
-086 while (u) \{
-087 *tmpx += u;
-088 u = *tmpx >> DIGIT_BIT;
-089 *tmpx++ &= MP_MASK;
-090 \}
-091 \}
-092 \}
-093
-094 /* at this point the n.used'th least
-095 * significant digits of x are all zero
-096 * which means we can shift x to the
-097 * right by n.used digits and the
-098 * residue is unchanged.
-099 */
-100
-101 /* x = x/b**n.used */
-102 mp_clamp(x);
-103 mp_rshd (x, n->used);
-104
-105 /* if x >= n then x = x - n */
-106 if (mp_cmp_mag (x, n) != MP_LT) \{
-107 return s_mp_sub (x, n, x);
-108 \}
-109
-110 return MP_OKAY;
-111 \}
+085
+086 /* propagate carries upwards as required*/
+087 while (u) \{
+088 *tmpx += u;
+089 u = *tmpx >> DIGIT_BIT;
+090 *tmpx++ &= MP_MASK;
+091 \}
+092 \}
+093 \}
+094
+095 /* at this point the n.used'th least
+096 * significant digits of x are all zero
+097 * which means we can shift x to the
+098 * right by n.used digits and the
+099 * residue is unchanged.
+100 */
+101
+102 /* x = x/b**n.used */
+103 mp_clamp(x);
+104 mp_rshd (x, n->used);
+105
+106 /* if x >= n then x = x - n */
+107 if (mp_cmp_mag (x, n) != MP_LT) \{
+108 return s_mp_sub (x, n, x);
+109 \}
+110
+111 return MP_OKAY;
+112 \}
+113 #endif
\end{alltt}
\end{small}
-This is the baseline implementation of the Montgomery reduction algorithm. Lines 30 to 34 determine if the Comba based
-routine can be used instead. Line 47 computes the value of $\mu$ for that particular iteration of the outer loop.
+This is the baseline implementation of the Montgomery reduction algorithm. Lines 30 to 35 determine if the Comba based
+routine can be used instead. Line 48 computes the value of $\mu$ for that particular iteration of the outer loop.
The multiplication $\mu n \beta^{ix}$ is performed in one step in the inner loop. The alias $tmpx$ refers to the $ix$'th digit of $x$ and
the alias $tmpn$ refers to the modulus $n$.
@@ -6214,168 +6302,170 @@ stored in the destination $x$.
\hspace{-5.1mm}{\bf File}: bn\_fast\_mp\_montgomery\_reduce.c
\vspace{-3mm}
\begin{alltt}
-016 /* computes xR**-1 == x (mod N) via Montgomery Reduction
-017 *
-018 * This is an optimized implementation of mp_montgomery_reduce
-019 * which uses the comba method to quickly calculate the columns of the
-020 * reduction.
-021 *
-022 * Based on Algorithm 14.32 on pp.601 of HAC.
-023 */
-024 int
-025 fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-026 \{
-027 int ix, res, olduse;
-028 mp_word W[MP_WARRAY];
-029
-030 /* get old used count */
-031 olduse = x->used;
-032
-033 /* grow a as required */
-034 if (x->alloc < n->used + 1) \{
-035 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) \{
-036 return res;
-037 \}
-038 \}
-039
-040 /* first we have to get the digits of the input into
-041 * an array of double precision words W[...]
-042 */
-043 \{
-044 register mp_word *_W;
-045 register mp_digit *tmpx;
-046
-047 /* alias for the W[] array */
-048 _W = W;
-049
-050 /* alias for the digits of x*/
-051 tmpx = x->dp;
-052
-053 /* copy the digits of a into W[0..a->used-1] */
-054 for (ix = 0; ix < x->used; ix++) \{
-055 *_W++ = *tmpx++;
-056 \}
-057
-058 /* zero the high words of W[a->used..m->used*2] */
-059 for (; ix < n->used * 2 + 1; ix++) \{
-060 *_W++ = 0;
-061 \}
-062 \}
-063
-064 /* now we proceed to zero successive digits
-065 * from the least significant upwards
-066 */
-067 for (ix = 0; ix < n->used; ix++) \{
-068 /* mu = ai * m' mod b
-069 *
-070 * We avoid a double precision multiplication (which isn't required)
-071 * by casting the value down to a mp_digit. Note this requires
-072 * that W[ix-1] have the carry cleared (see after the inner loop)
-073 */
-074 register mp_digit mu;
-075 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
-076
-077 /* a = a + mu * m * b**i
-078 *
-079 * This is computed in place and on the fly. The multiplication
-080 * by b**i is handled by offseting which columns the results
-081 * are added to.
-082 *
-083 * Note the comba method normally doesn't handle carries in the
-084 * inner loop In this case we fix the carry from the previous
-085 * column since the Montgomery reduction requires digits of the
-086 * result (so far) [see above] to work. This is
-087 * handled by fixing up one carry after the inner loop. The
-088 * carry fixups are done in order so after these loops the
-089 * first m->used words of W[] have the carries fixed
-090 */
-091 \{
-092 register int iy;
-093 register mp_digit *tmpn;
-094 register mp_word *_W;
-095
-096 /* alias for the digits of the modulus */
-097 tmpn = n->dp;
-098
-099 /* Alias for the columns set by an offset of ix */
-100 _W = W + ix;
-101
-102 /* inner loop */
-103 for (iy = 0; iy < n->used; iy++) \{
-104 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
-105 \}
-106 \}
-107
-108 /* now fix carry for next digit, W[ix+1] */
-109 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
-110 \}
-111
-112 /* now we have to propagate the carries and
-113 * shift the words downward [all those least
-114 * significant digits we zeroed].
-115 */
-116 \{
-117 register mp_digit *tmpx;
-118 register mp_word *_W, *_W1;
-119
-120 /* nox fix rest of carries */
-121
-122 /* alias for current word */
-123 _W1 = W + ix;
-124
-125 /* alias for next word, where the carry goes */
-126 _W = W + ++ix;
-127
-128 for (; ix <= n->used * 2 + 1; ix++) \{
-129 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
-130 \}
-131
-132 /* copy out, A = A/b**n
-133 *
-134 * The result is A/b**n but instead of converting from an
-135 * array of mp_word to mp_digit than calling mp_rshd
-136 * we just copy them in the right order
-137 */
-138
-139 /* alias for destination word */
-140 tmpx = x->dp;
-141
-142 /* alias for shifted double precision result */
-143 _W = W + n->used;
-144
-145 for (ix = 0; ix < n->used + 1; ix++) \{
-146 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
-147 \}
-148
-149 /* zero oldused digits, if the input a was larger than
-150 * m->used+1 we'll have to clear the digits
-151 */
-152 for (; ix < olduse; ix++) \{
-153 *tmpx++ = 0;
-154 \}
-155 \}
-156
-157 /* set the max used and clamp */
-158 x->used = n->used + 1;
-159 mp_clamp (x);
-160
-161 /* if A >= m then A = A - m */
-162 if (mp_cmp_mag (x, n) != MP_LT) \{
-163 return s_mp_sub (x, n, x);
-164 \}
-165 return MP_OKAY;
-166 \}
+016
+017 /* computes xR**-1 == x (mod N) via Montgomery Reduction
+018 *
+019 * This is an optimized implementation of montgomery_reduce
+020 * which uses the comba method to quickly calculate the columns of the
+021 * reduction.
+022 *
+023 * Based on Algorithm 14.32 on pp.601 of HAC.
+024 */
+025 int
+026 fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+027 \{
+028 int ix, res, olduse;
+029 mp_word W[MP_WARRAY];
+030
+031 /* get old used count */
+032 olduse = x->used;
+033
+034 /* grow a as required */
+035 if (x->alloc < n->used + 1) \{
+036 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) \{
+037 return res;
+038 \}
+039 \}
+040
+041 /* first we have to get the digits of the input into
+042 * an array of double precision words W[...]
+043 */
+044 \{
+045 register mp_word *_W;
+046 register mp_digit *tmpx;
+047
+048 /* alias for the W[] array */
+049 _W = W;
+050
+051 /* alias for the digits of x*/
+052 tmpx = x->dp;
+053
+054 /* copy the digits of a into W[0..a->used-1] */
+055 for (ix = 0; ix < x->used; ix++) \{
+056 *_W++ = *tmpx++;
+057 \}
+058
+059 /* zero the high words of W[a->used..m->used*2] */
+060 for (; ix < n->used * 2 + 1; ix++) \{
+061 *_W++ = 0;
+062 \}
+063 \}
+064
+065 /* now we proceed to zero successive digits
+066 * from the least significant upwards
+067 */
+068 for (ix = 0; ix < n->used; ix++) \{
+069 /* mu = ai * m' mod b
+070 *
+071 * We avoid a double precision multiplication (which isn't required)
+072 * by casting the value down to a mp_digit. Note this requires
+073 * that W[ix-1] have the carry cleared (see after the inner loop)
+074 */
+075 register mp_digit mu;
+076 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
+077
+078 /* a = a + mu * m * b**i
+079 *
+080 * This is computed in place and on the fly. The multiplication
+081 * by b**i is handled by offseting which columns the results
+082 * are added to.
+083 *
+084 * Note the comba method normally doesn't handle carries in the
+085 * inner loop In this case we fix the carry from the previous
+086 * column since the Montgomery reduction requires digits of the
+087 * result (so far) [see above] to work. This is
+088 * handled by fixing up one carry after the inner loop. The
+089 * carry fixups are done in order so after these loops the
+090 * first m->used words of W[] have the carries fixed
+091 */
+092 \{
+093 register int iy;
+094 register mp_digit *tmpn;
+095 register mp_word *_W;
+096
+097 /* alias for the digits of the modulus */
+098 tmpn = n->dp;
+099
+100 /* Alias for the columns set by an offset of ix */
+101 _W = W + ix;
+102
+103 /* inner loop */
+104 for (iy = 0; iy < n->used; iy++) \{
+105 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
+106 \}
+107 \}
+108
+109 /* now fix carry for next digit, W[ix+1] */
+110 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
+111 \}
+112
+113 /* now we have to propagate the carries and
+114 * shift the words downward [all those least
+115 * significant digits we zeroed].
+116 */
+117 \{
+118 register mp_digit *tmpx;
+119 register mp_word *_W, *_W1;
+120
+121 /* nox fix rest of carries */
+122
+123 /* alias for current word */
+124 _W1 = W + ix;
+125
+126 /* alias for next word, where the carry goes */
+127 _W = W + ++ix;
+128
+129 for (; ix <= n->used * 2 + 1; ix++) \{
+130 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
+131 \}
+132
+133 /* copy out, A = A/b**n
+134 *
+135 * The result is A/b**n but instead of converting from an
+136 * array of mp_word to mp_digit than calling mp_rshd
+137 * we just copy them in the right order
+138 */
+139
+140 /* alias for destination word */
+141 tmpx = x->dp;
+142
+143 /* alias for shifted double precision result */
+144 _W = W + n->used;
+145
+146 for (ix = 0; ix < n->used + 1; ix++) \{
+147 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
+148 \}
+149
+150 /* zero oldused digits, if the input a was larger than
+151 * m->used+1 we'll have to clear the digits
+152 */
+153 for (; ix < olduse; ix++) \{
+154 *tmpx++ = 0;
+155 \}
+156 \}
+157
+158 /* set the max used and clamp */
+159 x->used = n->used + 1;
+160 mp_clamp (x);
+161
+162 /* if A >= m then A = A - m */
+163 if (mp_cmp_mag (x, n) != MP_LT) \{
+164 return s_mp_sub (x, n, x);
+165 \}
+166 return MP_OKAY;
+167 \}
+168 #endif
\end{alltt}
\end{small}
-The $\hat W$ array is first filled with digits of $x$ on line 50 then the rest of the digits are zeroed on line 54. Both loops share
+The $\hat W$ array is first filled with digits of $x$ on line 48 then the rest of the digits are zeroed on line 55. Both loops share
the same alias variables to make the code easier to read.
The value of $\mu$ is calculated in an interesting fashion. First the value $\hat W_{ix}$ is reduced modulo $\beta$ and cast to a mp\_digit. This
-forces the compiler to use a single precision multiplication and prevents any concerns about loss of precision. Line 109 fixes the carry
+forces the compiler to use a single precision multiplication and prevents any concerns about loss of precision. Line 110 fixes the carry
for the next iteration of the loop by propagating the carry from $\hat W_{ix}$ to $\hat W_{ix+1}$.
-The for loop on line 108 propagates the rest of the carries upwards through the columns. The for loop on line 125 reduces the columns
+The for loop on line 109 propagates the rest of the carries upwards through the columns. The for loop on line 126 reduces the columns
modulo $\beta$ and shifts them $k$ places at the same time. The alias $\_ \hat W$ actually refers to the array $\hat W$ starting at the $n.used$'th
digit, that is $\_ \hat W_{t} = \hat W_{n.used + t}$.
@@ -6412,43 +6502,45 @@ to calculate $1/n_0$ when $\beta$ is a power of two.
\hspace{-5.1mm}{\bf File}: bn\_mp\_montgomery\_setup.c
\vspace{-3mm}
\begin{alltt}
-016 /* setups the montgomery reduction stuff */
-017 int
-018 mp_montgomery_setup (mp_int * n, mp_digit * rho)
-019 \{
-020 mp_digit x, b;
-021
-022 /* fast inversion mod 2**k
-023 *
-024 * Based on the fact that
-025 *
-026 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
-027 * => 2*X*A - X*X*A*A = 1
-028 * => 2*(1) - (1) = 1
-029 */
-030 b = n->dp[0];
-031
-032 if ((b & 1) == 0) \{
-033 return MP_VAL;
-034 \}
-035
-036 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
-037 x *= 2 - b * x; /* here x*a==1 mod 2**8 */
-038 #if !defined(MP_8BIT)
-039 x *= 2 - b * x; /* here x*a==1 mod 2**16 */
-040 #endif
-041 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
-042 x *= 2 - b * x; /* here x*a==1 mod 2**32 */
-043 #endif
-044 #ifdef MP_64BIT
-045 x *= 2 - b * x; /* here x*a==1 mod 2**64 */
-046 #endif
-047
-048 /* rho = -1/m mod b */
-049 *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
-050
-051 return MP_OKAY;
-052 \}
+016
+017 /* setups the montgomery reduction stuff */
+018 int
+019 mp_montgomery_setup (mp_int * n, mp_digit * rho)
+020 \{
+021 mp_digit x, b;
+022
+023 /* fast inversion mod 2**k
+024 *
+025 * Based on the fact that
+026 *
+027 * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
+028 * => 2*X*A - X*X*A*A = 1
+029 * => 2*(1) - (1) = 1
+030 */
+031 b = n->dp[0];
+032
+033 if ((b & 1) == 0) \{
+034 return MP_VAL;
+035 \}
+036
+037 x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
+038 x *= 2 - b * x; /* here x*a==1 mod 2**8 */
+039 #if !defined(MP_8BIT)
+040 x *= 2 - b * x; /* here x*a==1 mod 2**16 */
+041 #endif
+042 #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
+043 x *= 2 - b * x; /* here x*a==1 mod 2**32 */
+044 #endif
+045 #ifdef MP_64BIT
+046 x *= 2 - b * x; /* here x*a==1 mod 2**64 */
+047 #endif
+048
+049 /* rho = -1/m mod b */
+050 *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
+051
+052 return MP_OKAY;
+053 \}
+054 #endif
\end{alltt}
\end{small}
@@ -6641,94 +6733,96 @@ at step 3.
\hspace{-5.1mm}{\bf File}: bn\_mp\_dr\_reduce.c
\vspace{-3mm}
\begin{alltt}
-016 /* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
-017 *
-018 * Based on algorithm from the paper
-019 *
-020 * "Generating Efficient Primes for Discrete Log Cryptosystems"
-021 * Chae Hoon Lim, Pil Loong Lee,
-022 * POSTECH Information Research Laboratories
-023 *
-024 * The modulus must be of a special format [see manual]
-025 *
-026 * Has been modified to use algorithm 7.10 from the LTM book instead
-027 *
-028 * Input x must be in the range 0 <= x <= (n-1)**2
-029 */
-030 int
-031 mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
-032 \{
-033 int err, i, m;
-034 mp_word r;
-035 mp_digit mu, *tmpx1, *tmpx2;
-036
-037 /* m = digits in modulus */
-038 m = n->used;
-039
-040 /* ensure that "x" has at least 2m digits */
-041 if (x->alloc < m + m) \{
-042 if ((err = mp_grow (x, m + m)) != MP_OKAY) \{
-043 return err;
-044 \}
-045 \}
-046
-047 /* top of loop, this is where the code resumes if
-048 * another reduction pass is required.
-049 */
-050 top:
-051 /* aliases for digits */
-052 /* alias for lower half of x */
-053 tmpx1 = x->dp;
-054
-055 /* alias for upper half of x, or x/B**m */
-056 tmpx2 = x->dp + m;
-057
-058 /* set carry to zero */
-059 mu = 0;
-060
-061 /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
-062 for (i = 0; i < m; i++) \{
-063 r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
-064 *tmpx1++ = (mp_digit)(r & MP_MASK);
-065 mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
-066 \}
-067
-068 /* set final carry */
-069 *tmpx1++ = mu;
-070
-071 /* zero words above m */
-072 for (i = m + 1; i < x->used; i++) \{
-073 *tmpx1++ = 0;
-074 \}
-075
-076 /* clamp, sub and return */
-077 mp_clamp (x);
-078
-079 /* if x >= n then subtract and reduce again
-080 * Each successive "recursion" makes the input smaller and smaller.
-081 */
-082 if (mp_cmp_mag (x, n) != MP_LT) \{
-083 s_mp_sub(x, n, x);
-084 goto top;
-085 \}
-086 return MP_OKAY;
-087 \}
+016
+017 /* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
+018 *
+019 * Based on algorithm from the paper
+020 *
+021 * "Generating Efficient Primes for Discrete Log Cryptosystems"
+022 * Chae Hoon Lim, Pil Loong Lee,
+023 * POSTECH Information Research Laboratories
+024 *
+025 * The modulus must be of a special format [see manual]
+026 *
+027 * Has been modified to use algorithm 7.10 from the LTM book instead
+028 *
+029 * Input x must be in the range 0 <= x <= (n-1)**2
+030 */
+031 int
+032 mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
+033 \{
+034 int err, i, m;
+035 mp_word r;
+036 mp_digit mu, *tmpx1, *tmpx2;
+037
+038 /* m = digits in modulus */
+039 m = n->used;
+040
+041 /* ensure that "x" has at least 2m digits */
+042 if (x->alloc < m + m) \{
+043 if ((err = mp_grow (x, m + m)) != MP_OKAY) \{
+044 return err;
+045 \}
+046 \}
+047
+048 /* top of loop, this is where the code resumes if
+049 * another reduction pass is required.
+050 */
+051 top:
+052 /* aliases for digits */
+053 /* alias for lower half of x */
+054 tmpx1 = x->dp;
+055
+056 /* alias for upper half of x, or x/B**m */
+057 tmpx2 = x->dp + m;
+058
+059 /* set carry to zero */
+060 mu = 0;
+061
+062 /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
+063 for (i = 0; i < m; i++) \{
+064 r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
+065 *tmpx1++ = (mp_digit)(r & MP_MASK);
+066 mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
+067 \}
+068
+069 /* set final carry */
+070 *tmpx1++ = mu;
+071
+072 /* zero words above m */
+073 for (i = m + 1; i < x->used; i++) \{
+074 *tmpx1++ = 0;
+075 \}
+076
+077 /* clamp, sub and return */
+078 mp_clamp (x);
+079
+080 /* if x >= n then subtract and reduce again
+081 * Each successive "recursion" makes the input smaller and smaller.
+082 */
+083 if (mp_cmp_mag (x, n) != MP_LT) \{
+084 s_mp_sub(x, n, x);
+085 goto top;
+086 \}
+087 return MP_OKAY;
+088 \}
+089 #endif
\end{alltt}
\end{small}
-The first step is to grow $x$ as required to $2m$ digits since the reduction is performed in place on $x$. The label on line 50 is where
+The first step is to grow $x$ as required to $2m$ digits since the reduction is performed in place on $x$. The label on line 51 is where
the algorithm will resume if further reduction passes are required. In theory it could be placed at the top of the function however, the size of
the modulus and question of whether $x$ is large enough are invariant after the first pass meaning that it would be a waste of time.
The aliases $tmpx1$ and $tmpx2$ refer to the digits of $x$ where the latter is offset by $m$ digits. By reading digits from $x$ offset by $m$ digits
-a division by $\beta^m$ can be simulated virtually for free. The loop on line 62 performs the bulk of the work (\textit{corresponds to step 4 of algorithm 7.11})
+a division by $\beta^m$ can be simulated virtually for free. The loop on line 63 performs the bulk of the work (\textit{corresponds to step 4 of algorithm 7.11})
in this algorithm.
-By line 69 the pointer $tmpx1$ points to the $m$'th digit of $x$ which is where the final carry will be placed. Similarly by line 72 the
+By line 70 the pointer $tmpx1$ points to the $m$'th digit of $x$ which is where the final carry will be placed. Similarly by line 73 the
same pointer will point to the $m+1$'th digit where the zeroes will be placed.
Since the algorithm is only valid if both $x$ and $n$ are greater than zero an unsigned comparison suffices to determine if another pass is required.
-With the same logic at line 83 the value of $x$ is known to be greater than or equal to $n$ meaning that an unsigned subtraction can be used
+With the same logic at line 84 the value of $x$ is known to be greater than or equal to $n$ meaning that an unsigned subtraction can be used
as well. Since the destination of the subtraction is the larger of the inputs the call to algorithm s\_mp\_sub cannot fail and the return code
does not need to be checked.
@@ -6756,16 +6850,18 @@ completeness.
\hspace{-5.1mm}{\bf File}: bn\_mp\_dr\_setup.c
\vspace{-3mm}
\begin{alltt}
-016 /* determines the setup value */
-017 void mp_dr_setup(mp_int *a, mp_digit *d)
-018 \{
-019 /* the casts are required if DIGIT_BIT is one less than
-020 * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
-021 */
-022 *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
-023 ((mp_word)a->dp[0]));
-024 \}
-025
+016
+017 /* determines the setup value */
+018 void mp_dr_setup(mp_int *a, mp_digit *d)
+019 \{
+020 /* the casts are required if DIGIT_BIT is one less than
+021 * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
+022 */
+023 *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
+024 ((mp_word)a->dp[0]));
+025 \}
+026
+027 #endif
\end{alltt}
\end{small}
@@ -6801,27 +6897,29 @@ step 3 then $n$ must be of Diminished Radix form.
\hspace{-5.1mm}{\bf File}: bn\_mp\_dr\_is\_modulus.c
\vspace{-3mm}
\begin{alltt}
-016 /* determines if a number is a valid DR modulus */
-017 int mp_dr_is_modulus(mp_int *a)
-018 \{
-019 int ix;
-020
-021 /* must be at least two digits */
-022 if (a->used < 2) \{
-023 return 0;
-024 \}
-025
-026 /* must be of the form b**k - a [a <= b] so all
-027 * but the first digit must be equal to -1 (mod b).
-028 */
-029 for (ix = 1; ix < a->used; ix++) \{
-030 if (a->dp[ix] != MP_MASK) \{
-031 return 0;
-032 \}
-033 \}
-034 return 1;
-035 \}
-036
+016
+017 /* determines if a number is a valid DR modulus */
+018 int mp_dr_is_modulus(mp_int *a)
+019 \{
+020 int ix;
+021
+022 /* must be at least two digits */
+023 if (a->used < 2) \{
+024 return 0;
+025 \}
+026
+027 /* must be of the form b**k - a [a <= b] so all
+028 * but the first digit must be equal to -1 (mod b).
+029 */
+030 for (ix = 1; ix < a->used; ix++) \{
+031 if (a->dp[ix] != MP_MASK) \{
+032 return 0;
+033 \}
+034 \}
+035 return 1;
+036 \}
+037
+038 #endif
\end{alltt}
\end{small}
@@ -6865,51 +6963,53 @@ shift which makes the algorithm fairly inexpensive to use.
\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce\_2k.c
\vspace{-3mm}
\begin{alltt}
-016 /* reduces a modulo n where n is of the form 2**p - d */
-017 int
-018 mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
-019 \{
-020 mp_int q;
-021 int p, res;
-022
-023 if ((res = mp_init(&q)) != MP_OKAY) \{
-024 return res;
-025 \}
-026
-027 p = mp_count_bits(n);
-028 top:
-029 /* q = a/2**p, a = a mod 2**p */
-030 if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) \{
-031 goto ERR;
-032 \}
-033
-034 if (d != 1) \{
-035 /* q = q * d */
-036 if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) \{
-037 goto ERR;
-038 \}
-039 \}
-040
-041 /* a = a + q */
-042 if ((res = s_mp_add(a, &q, a)) != MP_OKAY) \{
-043 goto ERR;
-044 \}
-045
-046 if (mp_cmp_mag(a, n) != MP_LT) \{
-047 s_mp_sub(a, n, a);
-048 goto top;
-049 \}
-050
-051 ERR:
-052 mp_clear(&q);
-053 return res;
-054 \}
-055
+016
+017 /* reduces a modulo n where n is of the form 2**p - d */
+018 int
+019 mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
+020 \{
+021 mp_int q;
+022 int p, res;
+023
+024 if ((res = mp_init(&q)) != MP_OKAY) \{
+025 return res;
+026 \}
+027
+028 p = mp_count_bits(n);
+029 top:
+030 /* q = a/2**p, a = a mod 2**p */
+031 if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) \{
+032 goto ERR;
+033 \}
+034
+035 if (d != 1) \{
+036 /* q = q * d */
+037 if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) \{
+038 goto ERR;
+039 \}
+040 \}
+041
+042 /* a = a + q */
+043 if ((res = s_mp_add(a, &q, a)) != MP_OKAY) \{
+044 goto ERR;
+045 \}
+046
+047 if (mp_cmp_mag(a, n) != MP_LT) \{
+048 s_mp_sub(a, n, a);
+049 goto top;
+050 \}
+051
+052 ERR:
+053 mp_clear(&q);
+054 return res;
+055 \}
+056
+057 #endif
\end{alltt}
\end{small}
The algorithm mp\_count\_bits calculates the number of bits in an mp\_int which is used to find the initial value of $p$. The call to mp\_div\_2d
-on line 30 calculates both the quotient $q$ and the remainder $a$ required. By doing both in a single function call the code size
+on line 31 calculates both the quotient $q$ and the remainder $a$ required. By doing both in a single function call the code size
is kept fairly small. The multiplication by $k$ is only performed if $k > 1$. This allows reductions modulo $2^p - 1$ to be performed without
any multiplications.
@@ -6947,32 +7047,34 @@ is sufficient to solve for $k$. Alternatively if $n$ has more than one digit th
\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce\_2k\_setup.c
\vspace{-3mm}
\begin{alltt}
-016 /* determines the setup value */
-017 int
-018 mp_reduce_2k_setup(mp_int *a, mp_digit *d)
-019 \{
-020 int res, p;
-021 mp_int tmp;
-022
-023 if ((res = mp_init(&tmp)) != MP_OKAY) \{
-024 return res;
-025 \}
-026
-027 p = mp_count_bits(a);
-028 if ((res = mp_2expt(&tmp, p)) != MP_OKAY) \{
-029 mp_clear(&tmp);
-030 return res;
-031 \}
-032
-033 if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) \{
-034 mp_clear(&tmp);
-035 return res;
-036 \}
-037
-038 *d = tmp.dp[0];
-039 mp_clear(&tmp);
-040 return MP_OKAY;
-041 \}
+016
+017 /* determines the setup value */
+018 int
+019 mp_reduce_2k_setup(mp_int *a, mp_digit *d)
+020 \{
+021 int res, p;
+022 mp_int tmp;
+023
+024 if ((res = mp_init(&tmp)) != MP_OKAY) \{
+025 return res;
+026 \}
+027
+028 p = mp_count_bits(a);
+029 if ((res = mp_2expt(&tmp, p)) != MP_OKAY) \{
+030 mp_clear(&tmp);
+031 return res;
+032 \}
+033
+034 if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) \{
+035 mp_clear(&tmp);
+036 return res;
+037 \}
+038
+039 *d = tmp.dp[0];
+040 mp_clear(&tmp);
+041 return MP_OKAY;
+042 \}
+043 #endif
\end{alltt}
\end{small}
@@ -7017,36 +7119,38 @@ This algorithm quickly determines if a modulus is of the form required for algor
\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce\_is\_2k.c
\vspace{-3mm}
\begin{alltt}
-016 /* determines if mp_reduce_2k can be used */
-017 int mp_reduce_is_2k(mp_int *a)
-018 \{
-019 int ix, iy, iw;
-020 mp_digit iz;
-021
-022 if (a->used == 0) \{
-023 return 0;
-024 \} else if (a->used == 1) \{
-025 return 1;
-026 \} else if (a->used > 1) \{
-027 iy = mp_count_bits(a);
-028 iz = 1;
-029 iw = 1;
-030
-031 /* Test every bit from the second digit up, must be 1 */
-032 for (ix = DIGIT_BIT; ix < iy; ix++) \{
-033 if ((a->dp[iw] & iz) == 0) \{
-034 return 0;
-035 \}
-036 iz <<= 1;
-037 if (iz > (mp_digit)MP_MASK) \{
-038 ++iw;
-039 iz = 1;
-040 \}
-041 \}
-042 \}
-043 return 1;
-044 \}
-045
+016
+017 /* determines if mp_reduce_2k can be used */
+018 int mp_reduce_is_2k(mp_int *a)
+019 \{
+020 int ix, iy, iw;
+021 mp_digit iz;
+022
+023 if (a->used == 0) \{
+024 return 0;
+025 \} else if (a->used == 1) \{
+026 return 1;
+027 \} else if (a->used > 1) \{
+028 iy = mp_count_bits(a);
+029 iz = 1;
+030 iw = 1;
+031
+032 /* Test every bit from the second digit up, must be 1 */
+033 for (ix = DIGIT_BIT; ix < iy; ix++) \{
+034 if ((a->dp[iw] & iz) == 0) \{
+035 return 0;
+036 \}
+037 iz <<= 1;
+038 if (iz > (mp_digit)MP_MASK) \{
+039 ++iw;
+040 iz = 1;
+041 \}
+042 \}
+043 \}
+044 return 1;
+045 \}
+046
+047 #endif
\end{alltt}
\end{small}
@@ -7219,48 +7323,50 @@ iteration of the loop moves the bits of the exponent $b$ upwards to the most sig
\hspace{-5.1mm}{\bf File}: bn\_mp\_expt\_d.c
\vspace{-3mm}
\begin{alltt}
-016 /* calculate c = a**b using a square-multiply algorithm */
-017 int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
-018 \{
-019 int res, x;
-020 mp_int g;
-021
-022 if ((res = mp_init_copy (&g, a)) != MP_OKAY) \{
-023 return res;
-024 \}
-025
-026 /* set initial result */
-027 mp_set (c, 1);
-028
-029 for (x = 0; x < (int) DIGIT_BIT; x++) \{
-030 /* square */
-031 if ((res = mp_sqr (c, c)) != MP_OKAY) \{
-032 mp_clear (&g);
-033 return res;
-034 \}
-035
-036 /* if the bit is set multiply */
-037 if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) \{
-038 if ((res = mp_mul (c, &g, c)) != MP_OKAY) \{
-039 mp_clear (&g);
-040 return res;
-041 \}
-042 \}
-043
-044 /* shift to next bit */
-045 b <<= 1;
-046 \}
-047
-048 mp_clear (&g);
-049 return MP_OKAY;
-050 \}
+016
+017 /* calculate c = a**b using a square-multiply algorithm */
+018 int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
+019 \{
+020 int res, x;
+021 mp_int g;
+022
+023 if ((res = mp_init_copy (&g, a)) != MP_OKAY) \{
+024 return res;
+025 \}
+026
+027 /* set initial result */
+028 mp_set (c, 1);
+029
+030 for (x = 0; x < (int) DIGIT_BIT; x++) \{
+031 /* square */
+032 if ((res = mp_sqr (c, c)) != MP_OKAY) \{
+033 mp_clear (&g);
+034 return res;
+035 \}
+036
+037 /* if the bit is set multiply */
+038 if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) \{
+039 if ((res = mp_mul (c, &g, c)) != MP_OKAY) \{
+040 mp_clear (&g);
+041 return res;
+042 \}
+043 \}
+044
+045 /* shift to next bit */
+046 b <<= 1;
+047 \}
+048
+049 mp_clear (&g);
+050 return MP_OKAY;
+051 \}
+052 #endif
\end{alltt}
\end{small}
-Line 27 sets the initial value of the result to $1$. Next the loop on line 29 steps through each bit of the exponent starting from
-the most significant down towards the least significant. The invariant squaring operation placed on line 31 is performed first. After
+Line 28 sets the initial value of the result to $1$. Next the loop on line 30 steps through each bit of the exponent starting from
+the most significant down towards the least significant. The invariant squaring operation placed on line 32 is performed first. After
the squaring the result $c$ is multiplied by the base $g$ if and only if the most significant bit of the exponent is set. The shift on line
-45 moves all of the bits of the exponent upwards towards the most significant location.
+46 moves all of the bits of the exponent upwards towards the most significant location.
\section{$k$-ary Exponentiation}
When calculating an exponentiation the most time consuming bottleneck is the multiplications which are in general a small factor
@@ -7442,77 +7548,99 @@ algorithm since their arguments are essentially the same (\textit{two mp\_ints a
\vspace{-3mm}
\begin{alltt}
016
-017 /* this is a shell function that calls either the normal or Montgomery
-018 * exptmod functions. Originally the call to the montgomery code was
-019 * embedded in the normal function but that wasted alot of stack space
-020 * for nothing (since 99% of the time the Montgomery code would be called)
-021 */
-022 int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-023 \{
-024 int dr;
-025
-026 /* modulus P must be positive */
-027 if (P->sign == MP_NEG) \{
-028 return MP_VAL;
-029 \}
-030
-031 /* if exponent X is negative we have to recurse */
-032 if (X->sign == MP_NEG) \{
-033 mp_int tmpG, tmpX;
-034 int err;
-035
-036 /* first compute 1/G mod P */
-037 if ((err = mp_init(&tmpG)) != MP_OKAY) \{
-038 return err;
-039 \}
-040 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) \{
-041 mp_clear(&tmpG);
-042 return err;
-043 \}
-044
-045 /* now get |X| */
-046 if ((err = mp_init(&tmpX)) != MP_OKAY) \{
-047 mp_clear(&tmpG);
-048 return err;
-049 \}
-050 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) \{
-051 mp_clear_multi(&tmpG, &tmpX, NULL);
-052 return err;
-053 \}
-054
-055 /* and now compute (1/G)**|X| instead of G**X [X < 0] */
-056 err = mp_exptmod(&tmpG, &tmpX, P, Y);
-057 mp_clear_multi(&tmpG, &tmpX, NULL);
-058 return err;
-059 \}
-060
-061 /* is it a DR modulus? */
-062 dr = mp_dr_is_modulus(P);
-063
-064 /* if not, is it a uDR modulus? */
-065 if (dr == 0) \{
-066 dr = mp_reduce_is_2k(P) << 1;
-067 \}
-068
-069 /* if the modulus is odd or dr != 0 use the fast method */
-070 if (mp_isodd (P) == 1 || dr != 0) \{
-071 return mp_exptmod_fast (G, X, P, Y, dr);
-072 \} else \{
-073 /* otherwise use the generic Barrett reduction technique */
-074 return s_mp_exptmod (G, X, P, Y);
-075 \}
-076 \}
-077
+017
+018 /* this is a shell function that calls either the normal or Montgomery
+019 * exptmod functions. Originally the call to the montgomery code was
+020 * embedded in the normal function but that wasted alot of stack space
+021 * for nothing (since 99% of the time the Montgomery code would be called)
+022 */
+023 int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+024 \{
+025 int dr;
+026
+027 /* modulus P must be positive */
+028 if (P->sign == MP_NEG) \{
+029 return MP_VAL;
+030 \}
+031
+032 /* if exponent X is negative we have to recurse */
+033 if (X->sign == MP_NEG) \{
+034 #ifdef BN_MP_INVMOD_C
+035 mp_int tmpG, tmpX;
+036 int err;
+037
+038 /* first compute 1/G mod P */
+039 if ((err = mp_init(&tmpG)) != MP_OKAY) \{
+040 return err;
+041 \}
+042 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) \{
+043 mp_clear(&tmpG);
+044 return err;
+045 \}
+046
+047 /* now get |X| */
+048 if ((err = mp_init(&tmpX)) != MP_OKAY) \{
+049 mp_clear(&tmpG);
+050 return err;
+051 \}
+052 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) \{
+053 mp_clear_multi(&tmpG, &tmpX, NULL);
+054 return err;
+055 \}
+056
+057 /* and now compute (1/G)**|X| instead of G**X [X < 0] */
+058 err = mp_exptmod(&tmpG, &tmpX, P, Y);
+059 mp_clear_multi(&tmpG, &tmpX, NULL);
+060 return err;
+061 #else
+062 /* no invmod */
+063 return MP_VAL
+064 #endif
+065 \}
+066
+067 #ifdef BN_MP_DR_IS_MODULUS_C
+068 /* is it a DR modulus? */
+069 dr = mp_dr_is_modulus(P);
+070 #else
+071 dr = 0;
+072 #endif
+073
+074 #ifdef BN_MP_REDUCE_IS_2K_C
+075 /* if not, is it a uDR modulus? */
+076 if (dr == 0) \{
+077 dr = mp_reduce_is_2k(P) << 1;
+078 \}
+079 #endif
+080
+081 /* if the modulus is odd or dr != 0 use the fast method */
+082 #ifdef BN_MP_EXPTMOD_FAST_C
+083 if (mp_isodd (P) == 1 || dr != 0) \{
+084 return mp_exptmod_fast (G, X, P, Y, dr);
+085 \} else \{
+086 #endif
+087 #ifdef BN_S_MP_EXPTMOD_C
+088 /* otherwise use the generic Barrett reduction technique */
+089 return s_mp_exptmod (G, X, P, Y);
+090 #else
+091 /* no exptmod for evens */
+092 return MP_VAL;
+093 #endif
+094 #ifdef BN_MP_EXPTMOD_FAST_C
+095 \}
+096 #endif
+097 \}
+098
+099 #endif
\end{alltt}
\end{small}
-In order to keep the algorithms in a known state the first step on line 31 is to reject any negative modulus as input. If the exponent is
+In order to keep the algorithms in a known state the first step on line 28 is to reject any negative modulus as input. If the exponent is
negative the algorithm tries to perform a modular exponentiation with the modular inverse of the base $G$. The temporary variable $tmpG$ is assigned
the modular inverse of $G$ and $tmpX$ is assigned the absolute value of $X$. The algorithm will recuse with these new values with a positive
exponent.
-If the exponent is positive the algorithm resumes the exponentiation. Line 62 determines if the modulus is of the restricted Diminished Radix
-form. If it is not line 66 attempts to determine if it is of a unrestricted Diminished Radix form. The integer $dr$ will take on one
+If the exponent is positive the algorithm resumes the exponentiation. Line 69 determines if the modulus is of the restricted Diminished Radix
+form. If it is not line 77 attempts to determine if it is of a unrestricted Diminished Radix form. The integer $dr$ will take on one
of three values.
\begin{enumerate}
@@ -7521,7 +7649,7 @@ of three values.
\item $dr = 2$ means that the modulus is of unrestricted Diminished Radix form.
\end{enumerate}
-Line 69 determines if the fast modular exponentiation algorithm can be used. It is allowed if $dr \ne 0$ or if the modulus is odd. Otherwise,
+Line 67 determines if the fast modular exponentiation algorithm can be used. It is allowed if $dr \ne 0$ or if the modulus is odd. Otherwise,
the slower s\_mp\_exptmod algorithm is used which uses Barrett reduction.
\subsection{Barrett Modular Exponentiation}
@@ -7682,249 +7810,251 @@ a Left-to-Right algorithm is used to process the remaining few bits.
\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_exptmod.c
\vspace{-3mm}
\begin{alltt}
-016 #ifdef MP_LOW_MEM
-017 #define TAB_SIZE 32
-018 #else
-019 #define TAB_SIZE 256
-020 #endif
-021
-022 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-023 \{
-024 mp_int M[TAB_SIZE], res, mu;
-025 mp_digit buf;
-026 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-027
-028 /* find window size */
-029 x = mp_count_bits (X);
-030 if (x <= 7) \{
-031 winsize = 2;
-032 \} else if (x <= 36) \{
-033 winsize = 3;
-034 \} else if (x <= 140) \{
-035 winsize = 4;
-036 \} else if (x <= 450) \{
-037 winsize = 5;
-038 \} else if (x <= 1303) \{
-039 winsize = 6;
-040 \} else if (x <= 3529) \{
-041 winsize = 7;
-042 \} else \{
-043 winsize = 8;
-044 \}
-045
-046 #ifdef MP_LOW_MEM
-047 if (winsize > 5) \{
-048 winsize = 5;
-049 \}
-050 #endif
-051
-052 /* init M array */
-053 /* init first cell */
-054 if ((err = mp_init(&M[1])) != MP_OKAY) \{
-055 return err;
-056 \}
-057
-058 /* now init the second half of the array */
-059 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{
-060 if ((err = mp_init(&M[x])) != MP_OKAY) \{
-061 for (y = 1<<(winsize-1); y < x; y++) \{
-062 mp_clear (&M[y]);
-063 \}
-064 mp_clear(&M[1]);
-065 return err;
-066 \}
-067 \}
-068
-069 /* create mu, used for Barrett reduction */
-070 if ((err = mp_init (&mu)) != MP_OKAY) \{
-071 goto __M;
-072 \}
-073 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) \{
-074 goto __MU;
-075 \}
-076
-077 /* create M table
-078 *
-079 * The M table contains powers of the base,
-080 * e.g. M[x] = G**x mod P
-081 *
-082 * The first half of the table is not
-083 * computed though accept for M[0] and M[1]
-084 */
-085 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) \{
-086 goto __MU;
-087 \}
-088
-089 /* compute the value at M[1<<(winsize-1)] by squaring
-090 * M[1] (winsize-1) times
-091 */
-092 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) \{
-093 goto __MU;
-094 \}
-095
-096 for (x = 0; x < (winsize - 1); x++) \{
-097 if ((err = mp_sqr (&M[1 << (winsize - 1)],
-098 &M[1 << (winsize - 1)])) != MP_OKAY) \{
-099 goto __MU;
-100 \}
-101 if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) \{
-102 goto __MU;
-103 \}
-104 \}
-105
-106 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
-107 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
-108 */
-109 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) \{
-110 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) \{
-111 goto __MU;
-112 \}
-113 if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) \{
-114 goto __MU;
-115 \}
-116 \}
-117
-118 /* setup result */
-119 if ((err = mp_init (&res)) != MP_OKAY) \{
-120 goto __MU;
-121 \}
-122 mp_set (&res, 1);
-123
-124 /* set initial mode and bit cnt */
-125 mode = 0;
-126 bitcnt = 1;
-127 buf = 0;
-128 digidx = X->used - 1;
-129 bitcpy = 0;
-130 bitbuf = 0;
-131
-132 for (;;) \{
-133 /* grab next digit as required */
-134 if (--bitcnt == 0) \{
-135 /* if digidx == -1 we are out of digits */
-136 if (digidx == -1) \{
-137 break;
-138 \}
-139 /* read next digit and reset the bitcnt */
-140 buf = X->dp[digidx--];
-141 bitcnt = (int) DIGIT_BIT;
-142 \}
-143
-144 /* grab the next msb from the exponent */
-145 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
-146 buf <<= (mp_digit)1;
-147
-148 /* if the bit is zero and mode == 0 then we ignore it
-149 * These represent the leading zero bits before the first 1 bit
-150 * in the exponent. Technically this opt is not required but it
-151 * does lower the # of trivial squaring/reductions used
-152 */
-153 if (mode == 0 && y == 0) \{
-154 continue;
-155 \}
-156
-157 /* if the bit is zero and mode == 1 then we square */
-158 if (mode == 1 && y == 0) \{
-159 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
-160 goto __RES;
-161 \}
-162 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
-163 goto __RES;
-164 \}
-165 continue;
-166 \}
-167
-168 /* else we add it to the window */
-169 bitbuf |= (y << (winsize - ++bitcpy));
-170 mode = 2;
-171
-172 if (bitcpy == winsize) \{
-173 /* ok window is filled so square as required and multiply */
-174 /* square first */
-175 for (x = 0; x < winsize; x++) \{
-176 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
-177 goto __RES;
-178 \}
-179 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
-180 goto __RES;
-181 \}
-182 \}
-183
-184 /* then multiply */
-185 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) \{
-186 goto __RES;
-187 \}
-188 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
-189 goto __RES;
-190 \}
-191
-192 /* empty window and reset */
-193 bitcpy = 0;
-194 bitbuf = 0;
-195 mode = 1;
-196 \}
-197 \}
-198
-199 /* if bits remain then square/multiply */
-200 if (mode == 2 && bitcpy > 0) \{
-201 /* square then multiply if the bit is set */
-202 for (x = 0; x < bitcpy; x++) \{
-203 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
-204 goto __RES;
-205 \}
-206 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
-207 goto __RES;
-208 \}
-209
-210 bitbuf <<= 1;
-211 if ((bitbuf & (1 << winsize)) != 0) \{
-212 /* then multiply */
-213 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) \{
-214 goto __RES;
-215 \}
-216 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
-217 goto __RES;
-218 \}
-219 \}
-220 \}
-221 \}
-222
-223 mp_exch (&res, Y);
-224 err = MP_OKAY;
-225 __RES:mp_clear (&res);
-226 __MU:mp_clear (&mu);
-227 __M:
-228 mp_clear(&M[1]);
-229 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{
-230 mp_clear (&M[x]);
-231 \}
-232 return err;
-233 \}
-\end{alltt}
-\end{small}
-
-Lines 30 through 40 determine the optimal window size based on the length of the exponent in bits. The window divisions are sorted
-from smallest to greatest so that in each \textbf{if} statement only one condition must be tested. For example, by the \textbf{if} statement
-on line 32 the value of $x$ is already known to be greater than $140$.
-
-The conditional piece of code beginning on line 46 allows the window size to be restricted to five bits. This logic is used to ensure
-the table of precomputed powers of $G$ remains relatively small.
-
-The for loop on line 59 initializes the $M$ array while lines 60 and 73 compute the value of $\mu$ required for
-Barrett reduction.
-
--- More later.
-
-\section{Quick Power of Two}
-Calculating $b = 2^a$ can be performed much quicker than with any of the previous algorithms. Recall that a logical shift left $m << k$ is
-equivalent to $m \cdot 2^k$. By this logic when $m = 1$ a quick power of two can be achieved.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_2expt}. \\
-\textbf{Input}. integer $b$ \\
+016
+017 #ifdef MP_LOW_MEM
+018 #define TAB_SIZE 32
+019 #else
+020 #define TAB_SIZE 256
+021 #endif
+022
+023 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+024 \{
+025 mp_int M[TAB_SIZE], res, mu;
+026 mp_digit buf;
+027 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+028
+029 /* find window size */
+030 x = mp_count_bits (X);
+031 if (x <= 7) \{
+032 winsize = 2;
+033 \} else if (x <= 36) \{
+034 winsize = 3;
+035 \} else if (x <= 140) \{
+036 winsize = 4;
+037 \} else if (x <= 450) \{
+038 winsize = 5;
+039 \} else if (x <= 1303) \{
+040 winsize = 6;
+041 \} else if (x <= 3529) \{
+042 winsize = 7;
+043 \} else \{
+044 winsize = 8;
+045 \}
+046
+047 #ifdef MP_LOW_MEM
+048 if (winsize > 5) \{
+049 winsize = 5;
+050 \}
+051 #endif
+052
+053 /* init M array */
+054 /* init first cell */
+055 if ((err = mp_init(&M[1])) != MP_OKAY) \{
+056 return err;
+057 \}
+058
+059 /* now init the second half of the array */
+060 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{
+061 if ((err = mp_init(&M[x])) != MP_OKAY) \{
+062 for (y = 1<<(winsize-1); y < x; y++) \{
+063 mp_clear (&M[y]);
+064 \}
+065 mp_clear(&M[1]);
+066 return err;
+067 \}
+068 \}
+069
+070 /* create mu, used for Barrett reduction */
+071 if ((err = mp_init (&mu)) != MP_OKAY) \{
+072 goto __M;
+073 \}
+074 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) \{
+075 goto __MU;
+076 \}
+077
+078 /* create M table
+079 *
+080 * The M table contains powers of the base,
+081 * e.g. M[x] = G**x mod P
+082 *
+083 * The first half of the table is not
+084 * computed though accept for M[0] and M[1]
+085 */
+086 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) \{
+087 goto __MU;
+088 \}
+089
+090 /* compute the value at M[1<<(winsize-1)] by squaring
+091 * M[1] (winsize-1) times
+092 */
+093 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) \{
+094 goto __MU;
+095 \}
+096
+097 for (x = 0; x < (winsize - 1); x++) \{
+098 if ((err = mp_sqr (&M[1 << (winsize - 1)],
+099 &M[1 << (winsize - 1)])) != MP_OKAY) \{
+100 goto __MU;
+101 \}
+102 if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) \{
+103 goto __MU;
+104 \}
+105 \}
+106
+107 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
+108 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
+109 */
+110 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) \{
+111 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) \{
+112 goto __MU;
+113 \}
+114 if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) \{
+115 goto __MU;
+116 \}
+117 \}
+118
+119 /* setup result */
+120 if ((err = mp_init (&res)) != MP_OKAY) \{
+121 goto __MU;
+122 \}
+123 mp_set (&res, 1);
+124
+125 /* set initial mode and bit cnt */
+126 mode = 0;
+127 bitcnt = 1;
+128 buf = 0;
+129 digidx = X->used - 1;
+130 bitcpy = 0;
+131 bitbuf = 0;
+132
+133 for (;;) \{
+134 /* grab next digit as required */
+135 if (--bitcnt == 0) \{
+136 /* if digidx == -1 we are out of digits */
+137 if (digidx == -1) \{
+138 break;
+139 \}
+140 /* read next digit and reset the bitcnt */
+141 buf = X->dp[digidx--];
+142 bitcnt = (int) DIGIT_BIT;
+143 \}
+144
+145 /* grab the next msb from the exponent */
+146 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
+147 buf <<= (mp_digit)1;
+148
+149 /* if the bit is zero and mode == 0 then we ignore it
+150 * These represent the leading zero bits before the first 1 bit
+151 * in the exponent. Technically this opt is not required but it
+152 * does lower the # of trivial squaring/reductions used
+153 */
+154 if (mode == 0 && y == 0) \{
+155 continue;
+156 \}
+157
+158 /* if the bit is zero and mode == 1 then we square */
+159 if (mode == 1 && y == 0) \{
+160 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
+161 goto __RES;
+162 \}
+163 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
+164 goto __RES;
+165 \}
+166 continue;
+167 \}
+168
+169 /* else we add it to the window */
+170 bitbuf |= (y << (winsize - ++bitcpy));
+171 mode = 2;
+172
+173 if (bitcpy == winsize) \{
+174 /* ok window is filled so square as required and multiply */
+175 /* square first */
+176 for (x = 0; x < winsize; x++) \{
+177 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
+178 goto __RES;
+179 \}
+180 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
+181 goto __RES;
+182 \}
+183 \}
+184
+185 /* then multiply */
+186 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) \{
+187 goto __RES;
+188 \}
+189 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
+190 goto __RES;
+191 \}
+192
+193 /* empty window and reset */
+194 bitcpy = 0;
+195 bitbuf = 0;
+196 mode = 1;
+197 \}
+198 \}
+199
+200 /* if bits remain then square/multiply */
+201 if (mode == 2 && bitcpy > 0) \{
+202 /* square then multiply if the bit is set */
+203 for (x = 0; x < bitcpy; x++) \{
+204 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
+205 goto __RES;
+206 \}
+207 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
+208 goto __RES;
+209 \}
+210
+211 bitbuf <<= 1;
+212 if ((bitbuf & (1 << winsize)) != 0) \{
+213 /* then multiply */
+214 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) \{
+215 goto __RES;
+216 \}
+217 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{
+218 goto __RES;
+219 \}
+220 \}
+221 \}
+222 \}
+223
+224 mp_exch (&res, Y);
+225 err = MP_OKAY;
+226 __RES:mp_clear (&res);
+227 __MU:mp_clear (&mu);
+228 __M:
+229 mp_clear(&M[1]);
+230 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{
+231 mp_clear (&M[x]);
+232 \}
+233 return err;
+234 \}
+235 #endif
+\end{alltt}
+\end{small}
+
+Lines 31 through 41 determine the optimal window size based on the length of the exponent in bits. The window divisions are sorted
+from smallest to greatest so that in each \textbf{if} statement only one condition must be tested. For example, by the \textbf{if} statement
+on line 33 the value of $x$ is already known to be greater than $140$.
+
+The conditional piece of code beginning on line 47 allows the window size to be restricted to five bits. This logic is used to ensure
+the table of precomputed powers of $G$ remains relatively small.
+
+The for loop on line 60 initializes the $M$ array while lines 61 and 74 compute the value of $\mu$ required for
+Barrett reduction.
+
+-- More later.
+
+\section{Quick Power of Two}
+Calculating $b = 2^a$ can be performed much quicker than with any of the previous algorithms. Recall that a logical shift left $m << k$ is
+equivalent to $m \cdot 2^k$. By this logic when $m = 1$ a quick power of two can be achieved.
+
+\begin{figure}[!here]
+\begin{small}
+\begin{center}
+\begin{tabular}{l}
+\hline Algorithm \textbf{mp\_2expt}. \\
+\textbf{Input}. integer $b$ \\
\textbf{Output}. $a \leftarrow 2^b$ \\
\hline \\
1. $a \leftarrow 0$ \\
@@ -7945,32 +8075,34 @@ equivalent to $m \cdot 2^k$. By this logic when $m = 1$ a quick power of two ca
\hspace{-5.1mm}{\bf File}: bn\_mp\_2expt.c
\vspace{-3mm}
\begin{alltt}
-016 /* computes a = 2**b
-017 *
-018 * Simple algorithm which zeroes the int, grows it then just sets one bit
-019 * as required.
-020 */
-021 int
-022 mp_2expt (mp_int * a, int b)
-023 \{
-024 int res;
-025
-026 /* zero a as per default */
-027 mp_zero (a);
-028
-029 /* grow a to accomodate the single bit */
-030 if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) \{
-031 return res;
-032 \}
-033
-034 /* set the used count of where the bit will go */
-035 a->used = b / DIGIT_BIT + 1;
-036
-037 /* put the single bit in its place */
-038 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
-039
-040 return MP_OKAY;
-041 \}
+016
+017 /* computes a = 2**b
+018 *
+019 * Simple algorithm which zeroes the int, grows it then just sets one bit
+020 * as required.
+021 */
+022 int
+023 mp_2expt (mp_int * a, int b)
+024 \{
+025 int res;
+026
+027 /* zero a as per default */
+028 mp_zero (a);
+029
+030 /* grow a to accomodate the single bit */
+031 if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) \{
+032 return res;
+033 \}
+034
+035 /* set the used count of where the bit will go */
+036 a->used = b / DIGIT_BIT + 1;
+037
+038 /* put the single bit in its place */
+039 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
+040
+041 return MP_OKAY;
+042 \}
+043 #endif
\end{alltt}
\end{small}
@@ -8219,201 +8351,278 @@ respectively be replaced with a zero.
\hspace{-5.1mm}{\bf File}: bn\_mp\_div.c
\vspace{-3mm}
\begin{alltt}
-016 /* integer signed division.
-017 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
-018 * HAC pp.598 Algorithm 14.20
-019 *
-020 * Note that the description in HAC is horribly
-021 * incomplete. For example, it doesn't consider
-022 * the case where digits are removed from 'x' in
-023 * the inner loop. It also doesn't consider the
-024 * case that y has fewer than three digits, etc..
-025 *
-026 * The overall algorithm is as described as
-027 * 14.20 from HAC but fixed to treat these cases.
-028 */
-029 int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-030 \{
-031 mp_int q, x, y, t1, t2;
-032 int res, n, t, i, norm, neg;
-033
-034 /* is divisor zero ? */
-035 if (mp_iszero (b) == 1) \{
-036 return MP_VAL;
-037 \}
-038
-039 /* if a < b then q=0, r = a */
-040 if (mp_cmp_mag (a, b) == MP_LT) \{
-041 if (d != NULL) \{
-042 res = mp_copy (a, d);
-043 \} else \{
-044 res = MP_OKAY;
-045 \}
-046 if (c != NULL) \{
-047 mp_zero (c);
-048 \}
-049 return res;
-050 \}
-051
-052 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) \{
-053 return res;
-054 \}
-055 q.used = a->used + 2;
-056
-057 if ((res = mp_init (&t1)) != MP_OKAY) \{
-058 goto __Q;
-059 \}
-060
-061 if ((res = mp_init (&t2)) != MP_OKAY) \{
-062 goto __T1;
-063 \}
-064
-065 if ((res = mp_init_copy (&x, a)) != MP_OKAY) \{
-066 goto __T2;
-067 \}
-068
-069 if ((res = mp_init_copy (&y, b)) != MP_OKAY) \{
-070 goto __X;
-071 \}
-072
-073 /* fix the sign */
-074 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-075 x.sign = y.sign = MP_ZPOS;
-076
-077 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
-078 norm = mp_count_bits(&y) % DIGIT_BIT;
-079 if (norm < (int)(DIGIT_BIT-1)) \{
-080 norm = (DIGIT_BIT-1) - norm;
-081 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) \{
-082 goto __Y;
-083 \}
-084 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) \{
-085 goto __Y;
-086 \}
-087 \} else \{
-088 norm = 0;
-089 \}
-090
-091 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
-092 n = x.used - 1;
-093 t = y.used - 1;
-094
-095 /* while (x >= y*b**n-t) do \{ q[n-t] += 1; x -= y*b**\{n-t\} \} */
-096 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) \{ /* y = y*b**\{n-t\} */
-097 goto __Y;
-098 \}
-099
-100 while (mp_cmp (&x, &y) != MP_LT) \{
-101 ++(q.dp[n - t]);
-102 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) \{
-103 goto __Y;
-104 \}
-105 \}
+016
+017 #ifdef BN_MP_DIV_SMALL
+018
+019 /* slower bit-bang division... also smaller */
+020 int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+021 \{
+022 mp_int ta, tb, tq, q;
+023 int res, n, n2;
+024
+025 /* is divisor zero ? */
+026 if (mp_iszero (b) == 1) \{
+027 return MP_VAL;
+028 \}
+029
+030 /* if a < b then q=0, r = a */
+031 if (mp_cmp_mag (a, b) == MP_LT) \{
+032 if (d != NULL) \{
+033 res = mp_copy (a, d);
+034 \} else \{
+035 res = MP_OKAY;
+036 \}
+037 if (c != NULL) \{
+038 mp_zero (c);
+039 \}
+040 return res;
+041 \}
+042
+043 /* init our temps */
+044 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) \{
+045 return res;
+046 \}
+047
+048
+049 mp_set(&tq, 1);
+050 n = mp_count_bits(a) - mp_count_bits(b);
+051 if (((res = mp_copy(a, &ta)) != MP_OKAY) ||
+052 ((res = mp_copy(b, &tb)) != MP_OKAY) ||
+053 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+054 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) \{
+055 goto __ERR;
+056 \}
+057
+058 while (n-- >= 0) \{
+059 if (mp_cmp(&tb, &ta) != MP_GT) \{
+060 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+061 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) \{
+062 goto __ERR;
+063 \}
+064 \}
+065 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+066 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) \{
+067 goto __ERR;
+068 \}
+069 \}
+070
+071 /* now q == quotient and ta == remainder */
+072 n = a->sign;
+073 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+074 if (c != NULL) \{
+075 mp_exch(c, &q);
+076 c->sign = n2;
+077 \}
+078 if (d != NULL) \{
+079 mp_exch(d, &ta);
+080 d->sign = n;
+081 \}
+082 __ERR:
+083 mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+084 return res;
+085 \}
+086
+087 #else
+088
+089 /* integer signed division.
+090 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
+091 * HAC pp.598 Algorithm 14.20
+092 *
+093 * Note that the description in HAC is horribly
+094 * incomplete. For example, it doesn't consider
+095 * the case where digits are removed from 'x' in
+096 * the inner loop. It also doesn't consider the
+097 * case that y has fewer than three digits, etc..
+098 *
+099 * The overall algorithm is as described as
+100 * 14.20 from HAC but fixed to treat these cases.
+101 */
+102 int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+103 \{
+104 mp_int q, x, y, t1, t2;
+105 int res, n, t, i, norm, neg;
106
-107 /* reset y by shifting it back down */
-108 mp_rshd (&y, n - t);
-109
-110 /* step 3. for i from n down to (t + 1) */
-111 for (i = n; i >= (t + 1); i--) \{
-112 if (i > x.used) \{
-113 continue;
-114 \}
-115
-116 /* step 3.1 if xi == yt then set q\{i-t-1\} to b-1,
-117 * otherwise set q\{i-t-1\} to (xi*b + x\{i-1\})/yt */
-118 if (x.dp[i] == y.dp[t]) \{
-119 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
-120 \} else \{
-121 mp_word tmp;
-122 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
-123 tmp |= ((mp_word) x.dp[i - 1]);
-124 tmp /= ((mp_word) y.dp[t]);
-125 if (tmp > (mp_word) MP_MASK)
-126 tmp = MP_MASK;
-127 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
-128 \}
+107 /* is divisor zero ? */
+108 if (mp_iszero (b) == 1) \{
+109 return MP_VAL;
+110 \}
+111
+112 /* if a < b then q=0, r = a */
+113 if (mp_cmp_mag (a, b) == MP_LT) \{
+114 if (d != NULL) \{
+115 res = mp_copy (a, d);
+116 \} else \{
+117 res = MP_OKAY;
+118 \}
+119 if (c != NULL) \{
+120 mp_zero (c);
+121 \}
+122 return res;
+123 \}
+124
+125 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) \{
+126 return res;
+127 \}
+128 q.used = a->used + 2;
129
-130 /* while (q\{i-t-1\} * (yt * b + y\{t-1\})) >
-131 xi * b**2 + xi-1 * b + xi-2
-132
-133 do q\{i-t-1\} -= 1;
-134 */
-135 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
-136 do \{
-137 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
-138
-139 /* find left hand */
-140 mp_zero (&t1);
-141 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
-142 t1.dp[1] = y.dp[t];
-143 t1.used = 2;
-144 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) \{
-145 goto __Y;
-146 \}
-147
-148 /* find right hand */
-149 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
-150 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
-151 t2.dp[2] = x.dp[i];
-152 t2.used = 3;
-153 \} while (mp_cmp_mag(&t1, &t2) == MP_GT);
-154
-155 /* step 3.3 x = x - q\{i-t-1\} * y * b**\{i-t-1\} */
-156 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) \{
-157 goto __Y;
-158 \}
-159
-160 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{
-161 goto __Y;
-162 \}
+130 if ((res = mp_init (&t1)) != MP_OKAY) \{
+131 goto __Q;
+132 \}
+133
+134 if ((res = mp_init (&t2)) != MP_OKAY) \{
+135 goto __T1;
+136 \}
+137
+138 if ((res = mp_init_copy (&x, a)) != MP_OKAY) \{
+139 goto __T2;
+140 \}
+141
+142 if ((res = mp_init_copy (&y, b)) != MP_OKAY) \{
+143 goto __X;
+144 \}
+145
+146 /* fix the sign */
+147 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+148 x.sign = y.sign = MP_ZPOS;
+149
+150 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
+151 norm = mp_count_bits(&y) % DIGIT_BIT;
+152 if (norm < (int)(DIGIT_BIT-1)) \{
+153 norm = (DIGIT_BIT-1) - norm;
+154 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) \{
+155 goto __Y;
+156 \}
+157 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) \{
+158 goto __Y;
+159 \}
+160 \} else \{
+161 norm = 0;
+162 \}
163
-164 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) \{
-165 goto __Y;
-166 \}
+164 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
+165 n = x.used - 1;
+166 t = y.used - 1;
167
-168 /* if x < 0 then \{ x = x + y*b**\{i-t-1\}; q\{i-t-1\} -= 1; \} */
-169 if (x.sign == MP_NEG) \{
-170 if ((res = mp_copy (&y, &t1)) != MP_OKAY) \{
-171 goto __Y;
-172 \}
-173 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{
-174 goto __Y;
-175 \}
-176 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) \{
-177 goto __Y;
-178 \}
+168 /* while (x >= y*b**n-t) do \{ q[n-t] += 1; x -= y*b**\{n-t\} \} */
+169 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) \{ /* y = y*b**\{n-t\} */
+170 goto __Y;
+171 \}
+172
+173 while (mp_cmp (&x, &y) != MP_LT) \{
+174 ++(q.dp[n - t]);
+175 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) \{
+176 goto __Y;
+177 \}
+178 \}
179
-180 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
-181 \}
-182 \}
-183
-184 /* now q is the quotient and x is the remainder
-185 * [which we have to normalize]
-186 */
-187
-188 /* get sign before writing to c */
-189 x.sign = x.used == 0 ? MP_ZPOS : a->sign;
-190
-191 if (c != NULL) \{
-192 mp_clamp (&q);
-193 mp_exch (&q, c);
-194 c->sign = neg;
-195 \}
-196
-197 if (d != NULL) \{
-198 mp_div_2d (&x, norm, &x, NULL);
-199 mp_exch (&x, d);
-200 \}
-201
-202 res = MP_OKAY;
-203
-204 __Y:mp_clear (&y);
-205 __X:mp_clear (&x);
-206 __T2:mp_clear (&t2);
-207 __T1:mp_clear (&t1);
-208 __Q:mp_clear (&q);
-209 return res;
-210 \}
+180 /* reset y by shifting it back down */
+181 mp_rshd (&y, n - t);
+182
+183 /* step 3. for i from n down to (t + 1) */
+184 for (i = n; i >= (t + 1); i--) \{
+185 if (i > x.used) \{
+186 continue;
+187 \}
+188
+189 /* step 3.1 if xi == yt then set q\{i-t-1\} to b-1,
+190 * otherwise set q\{i-t-1\} to (xi*b + x\{i-1\})/yt */
+191 if (x.dp[i] == y.dp[t]) \{
+192 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
+193 \} else \{
+194 mp_word tmp;
+195 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
+196 tmp |= ((mp_word) x.dp[i - 1]);
+197 tmp /= ((mp_word) y.dp[t]);
+198 if (tmp > (mp_word) MP_MASK)
+199 tmp = MP_MASK;
+200 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
+201 \}
+202
+203 /* while (q\{i-t-1\} * (yt * b + y\{t-1\})) >
+204 xi * b**2 + xi-1 * b + xi-2
+205
+206 do q\{i-t-1\} -= 1;
+207 */
+208 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
+209 do \{
+210 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
+211
+212 /* find left hand */
+213 mp_zero (&t1);
+214 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
+215 t1.dp[1] = y.dp[t];
+216 t1.used = 2;
+217 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) \{
+218 goto __Y;
+219 \}
+220
+221 /* find right hand */
+222 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
+223 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
+224 t2.dp[2] = x.dp[i];
+225 t2.used = 3;
+226 \} while (mp_cmp_mag(&t1, &t2) == MP_GT);
+227
+228 /* step 3.3 x = x - q\{i-t-1\} * y * b**\{i-t-1\} */
+229 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) \{
+230 goto __Y;
+231 \}
+232
+233 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{
+234 goto __Y;
+235 \}
+236
+237 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) \{
+238 goto __Y;
+239 \}
+240
+241 /* if x < 0 then \{ x = x + y*b**\{i-t-1\}; q\{i-t-1\} -= 1; \} */
+242 if (x.sign == MP_NEG) \{
+243 if ((res = mp_copy (&y, &t1)) != MP_OKAY) \{
+244 goto __Y;
+245 \}
+246 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{
+247 goto __Y;
+248 \}
+249 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) \{
+250 goto __Y;
+251 \}
+252
+253 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
+254 \}
+255 \}
+256
+257 /* now q is the quotient and x is the remainder
+258 * [which we have to normalize]
+259 */
+260
+261 /* get sign before writing to c */
+262 x.sign = x.used == 0 ? MP_ZPOS : a->sign;
+263
+264 if (c != NULL) \{
+265 mp_clamp (&q);
+266 mp_exch (&q, c);
+267 c->sign = neg;
+268 \}
+269
+270 if (d != NULL) \{
+271 mp_div_2d (&x, norm, &x, NULL);
+272 mp_exch (&x, d);
+273 \}
+274
+275 res = MP_OKAY;
+276
+277 __Y:mp_clear (&y);
+278 __X:mp_clear (&x);
+279 __T2:mp_clear (&t2);
+280 __T1:mp_clear (&t1);
+281 __Q:mp_clear (&q);
+282 return res;
+283 \}
+284
+285 #endif
+286
+287 #endif
\end{alltt}
\end{small}
@@ -8425,23 +8634,23 @@ algorithm with only the quotient is
mp_div(&a, &b, &c, NULL); /* c = [a/b] */
\end{verbatim}
-Lines 39 and 41 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor
-respectively. After the two trivial cases all of the temporary variables are initialized. Line 74 determines the sign of
-the quotient and line 75 ensures that both $x$ and $y$ are positive.
+Lines 37 and 44 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor
+respectively. After the two trivial cases all of the temporary variables are initialized. Line 105 determines the sign of
+the quotient and line 76 ensures that both $x$ and $y$ are positive.
-The number of bits in the leading digit is calculated on line 80. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits
+The number of bits in the leading digit is calculated on line 105. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits
of precision which when reduced modulo $lg(\beta)$ produces the value of $k$. In this case $k$ is the number of bits in the leading digit which is
exactly what is required. For the algorithm to operate $k$ must equal $lg(\beta) - 1$ and when it does not the inputs must be normalized by shifting
them to the left by $lg(\beta) - 1 - k$ bits.
Throughout the variables $n$ and $t$ will represent the highest digit of $x$ and $y$ respectively. These are first used to produce the
-leading digit of the quotient. The loop beginning on line 111 will produce the remainder of the quotient digits.
+leading digit of the quotient. The loop beginning on line 183 will produce the remainder of the quotient digits.
-The conditional ``continue'' on line 116 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the
+The conditional ``continue'' on line 114 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the
algorithm eliminates multiple non-zero digits in a single iteration. This ensures that $x_i$ is always non-zero since by definition the digits
above the $i$'th position $x$ must be zero in order for the quotient to be precise\footnote{Precise as far as integer division is concerned.}.
-Lines 142, 143 and 150 through 152 manually construct the high accuracy estimations by setting the digits of the two mp\_int
+Lines 130, 130 and 134 through 134 manually construct the high accuracy estimations by setting the digits of the two mp\_int
variables directly.
\section{Single Digit Helpers}
@@ -8479,93 +8688,95 @@ This algorithm initiates a temporary mp\_int with the value of the single digit
\hspace{-5.1mm}{\bf File}: bn\_mp\_add\_d.c
\vspace{-3mm}
\begin{alltt}
-016 /* single digit addition */
-017 int
-018 mp_add_d (mp_int * a, mp_digit b, mp_int * c)
-019 \{
-020 int res, ix, oldused;
-021 mp_digit *tmpa, *tmpc, mu;
-022
-023 /* grow c as required */
-024 if (c->alloc < a->used + 1) \{
-025 if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) \{
-026 return res;
-027 \}
-028 \}
-029
-030 /* if a is negative and |a| >= b, call c = |a| - b */
-031 if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) \{
-032 /* temporarily fix sign of a */
-033 a->sign = MP_ZPOS;
-034
-035 /* c = |a| - b */
-036 res = mp_sub_d(a, b, c);
-037
-038 /* fix sign */
-039 a->sign = c->sign = MP_NEG;
-040
-041 return res;
-042 \}
-043
-044 /* old number of used digits in c */
-045 oldused = c->used;
-046
-047 /* sign always positive */
-048 c->sign = MP_ZPOS;
-049
-050 /* source alias */
-051 tmpa = a->dp;
-052
-053 /* destination alias */
-054 tmpc = c->dp;
-055
-056 /* if a is positive */
-057 if (a->sign == MP_ZPOS) \{
-058 /* add digit, after this we're propagating
-059 * the carry.
-060 */
-061 *tmpc = *tmpa++ + b;
-062 mu = *tmpc >> DIGIT_BIT;
-063 *tmpc++ &= MP_MASK;
-064
-065 /* now handle rest of the digits */
-066 for (ix = 1; ix < a->used; ix++) \{
-067 *tmpc = *tmpa++ + mu;
-068 mu = *tmpc >> DIGIT_BIT;
-069 *tmpc++ &= MP_MASK;
-070 \}
-071 /* set final carry */
-072 ix++;
-073 *tmpc++ = mu;
-074
-075 /* setup size */
-076 c->used = a->used + 1;
-077 \} else \{
-078 /* a was negative and |a| < b */
-079 c->used = 1;
-080
-081 /* the result is a single digit */
-082 if (a->used == 1) \{
-083 *tmpc++ = b - a->dp[0];
-084 \} else \{
-085 *tmpc++ = b;
-086 \}
-087
-088 /* setup count so the clearing of oldused
-089 * can fall through correctly
-090 */
-091 ix = 1;
-092 \}
-093
-094 /* now zero to oldused */
-095 while (ix++ < oldused) \{
-096 *tmpc++ = 0;
-097 \}
-098 mp_clamp(c);
-099
-100 return MP_OKAY;
-101 \}
-102
+016
+017 /* single digit addition */
+018 int
+019 mp_add_d (mp_int * a, mp_digit b, mp_int * c)
+020 \{
+021 int res, ix, oldused;
+022 mp_digit *tmpa, *tmpc, mu;
+023
+024 /* grow c as required */
+025 if (c->alloc < a->used + 1) \{
+026 if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) \{
+027 return res;
+028 \}
+029 \}
+030
+031 /* if a is negative and |a| >= b, call c = |a| - b */
+032 if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) \{
+033 /* temporarily fix sign of a */
+034 a->sign = MP_ZPOS;
+035
+036 /* c = |a| - b */
+037 res = mp_sub_d(a, b, c);
+038
+039 /* fix sign */
+040 a->sign = c->sign = MP_NEG;
+041
+042 return res;
+043 \}
+044
+045 /* old number of used digits in c */
+046 oldused = c->used;
+047
+048 /* sign always positive */
+049 c->sign = MP_ZPOS;
+050
+051 /* source alias */
+052 tmpa = a->dp;
+053
+054 /* destination alias */
+055 tmpc = c->dp;
+056
+057 /* if a is positive */
+058 if (a->sign == MP_ZPOS) \{
+059 /* add digit, after this we're propagating
+060 * the carry.
+061 */
+062 *tmpc = *tmpa++ + b;
+063 mu = *tmpc >> DIGIT_BIT;
+064 *tmpc++ &= MP_MASK;
+065
+066 /* now handle rest of the digits */
+067 for (ix = 1; ix < a->used; ix++) \{
+068 *tmpc = *tmpa++ + mu;
+069 mu = *tmpc >> DIGIT_BIT;
+070 *tmpc++ &= MP_MASK;
+071 \}
+072 /* set final carry */
+073 ix++;
+074 *tmpc++ = mu;
+075
+076 /* setup size */
+077 c->used = a->used + 1;
+078 \} else \{
+079 /* a was negative and |a| < b */
+080 c->used = 1;
+081
+082 /* the result is a single digit */
+083 if (a->used == 1) \{
+084 *tmpc++ = b - a->dp[0];
+085 \} else \{
+086 *tmpc++ = b;
+087 \}
+088
+089 /* setup count so the clearing of oldused
+090 * can fall through correctly
+091 */
+092 ix = 1;
+093 \}
+094
+095 /* now zero to oldused */
+096 while (ix++ < oldused) \{
+097 *tmpc++ = 0;
+098 \}
+099 mp_clamp(c);
+100
+101 return MP_OKAY;
+102 \}
+103
+104 #endif
\end{alltt}
\end{small}
@@ -8616,62 +8827,64 @@ Unlike the full multiplication algorithms this algorithm does not require any si
\hspace{-5.1mm}{\bf File}: bn\_mp\_mul\_d.c
\vspace{-3mm}
\begin{alltt}
-016 /* multiply by a digit */
-017 int
-018 mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
-019 \{
-020 mp_digit u, *tmpa, *tmpc;
-021 mp_word r;
-022 int ix, res, olduse;
-023
-024 /* make sure c is big enough to hold a*b */
-025 if (c->alloc < a->used + 1) \{
-026 if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) \{
-027 return res;
-028 \}
-029 \}
-030
-031 /* get the original destinations used count */
-032 olduse = c->used;
-033
-034 /* set the sign */
-035 c->sign = a->sign;
-036
-037 /* alias for a->dp [source] */
-038 tmpa = a->dp;
-039
-040 /* alias for c->dp [dest] */
-041 tmpc = c->dp;
-042
-043 /* zero carry */
-044 u = 0;
-045
-046 /* compute columns */
-047 for (ix = 0; ix < a->used; ix++) \{
-048 /* compute product and carry sum for this term */
-049 r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
-050
-051 /* mask off higher bits to get a single digit */
-052 *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
-053
-054 /* send carry into next iteration */
-055 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-056 \}
-057
-058 /* store final carry [if any] */
-059 *tmpc++ = u;
-060
-061 /* now zero digits above the top */
-062 while (ix++ < olduse) \{
-063 *tmpc++ = 0;
-064 \}
-065
-066 /* set used count */
-067 c->used = a->used + 1;
-068 mp_clamp(c);
-069
-070 return MP_OKAY;
-071 \}
+016
+017 /* multiply by a digit */
+018 int
+019 mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
+020 \{
+021 mp_digit u, *tmpa, *tmpc;
+022 mp_word r;
+023 int ix, res, olduse;
+024
+025 /* make sure c is big enough to hold a*b */
+026 if (c->alloc < a->used + 1) \{
+027 if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) \{
+028 return res;
+029 \}
+030 \}
+031
+032 /* get the original destinations used count */
+033 olduse = c->used;
+034
+035 /* set the sign */
+036 c->sign = a->sign;
+037
+038 /* alias for a->dp [source] */
+039 tmpa = a->dp;
+040
+041 /* alias for c->dp [dest] */
+042 tmpc = c->dp;
+043
+044 /* zero carry */
+045 u = 0;
+046
+047 /* compute columns */
+048 for (ix = 0; ix < a->used; ix++) \{
+049 /* compute product and carry sum for this term */
+050 r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
+051
+052 /* mask off higher bits to get a single digit */
+053 *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
+054
+055 /* send carry into next iteration */
+056 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+057 \}
+058
+059 /* store final carry [if any] */
+060 *tmpc++ = u;
+061
+062 /* now zero digits above the top */
+063 while (ix++ < olduse) \{
+064 *tmpc++ = 0;
+065 \}
+066
+067 /* set used count */
+068 c->used = a->used + 1;
+069 mp_clamp(c);
+070
+071 return MP_OKAY;
+072 \}
+073 #endif
\end{alltt}
\end{small}
@@ -8727,99 +8940,103 @@ from chapter seven.
\hspace{-5.1mm}{\bf File}: bn\_mp\_div\_d.c
\vspace{-3mm}
\begin{alltt}
-016 static int s_is_power_of_two(mp_digit b, int *p)
-017 \{
-018 int x;
-019
-020 for (x = 1; x < DIGIT_BIT; x++) \{
-021 if (b == (((mp_digit)1)<<x)) \{
-022 *p = x;
-023 return 1;
-024 \}
-025 \}
-026 return 0;
-027 \}
-028
-029 /* single digit division (based on routine from MPI) */
-030 int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
-031 \{
-032 mp_int q;
-033 mp_word w;
-034 mp_digit t;
-035 int res, ix;
-036
-037 /* cannot divide by zero */
-038 if (b == 0) \{
-039 return MP_VAL;
-040 \}
-041
-042 /* quick outs */
-043 if (b == 1 || mp_iszero(a) == 1) \{
-044 if (d != NULL) \{
-045 *d = 0;
-046 \}
-047 if (c != NULL) \{
-048 return mp_copy(a, c);
-049 \}
-050 return MP_OKAY;
-051 \}
-052
-053 /* power of two ? */
-054 if (s_is_power_of_two(b, &ix) == 1) \{
-055 if (d != NULL) \{
-056 *d = a->dp[0] & ((1<<ix) - 1);
-057 \}
-058 if (c != NULL) \{
-059 return mp_div_2d(a, ix, c, NULL);
-060 \}
-061 return MP_OKAY;
-062 \}
-063
-064 /* three? */
-065 if (b == 3) \{
-066 return mp_div_3(a, c, d);
-067 \}
-068
-069 /* no easy answer [c'est la vie]. Just division */
-070 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) \{
-071 return res;
-072 \}
-073
-074 q.used = a->used;
-075 q.sign = a->sign;
-076 w = 0;
-077 for (ix = a->used - 1; ix >= 0; ix--) \{
-078 w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-079
-080 if (w >= b) \{
-081 t = (mp_digit)(w / b);
-082 w -= ((mp_word)t) * ((mp_word)b);
-083 \} else \{
-084 t = 0;
-085 \}
-086 q.dp[ix] = (mp_digit)t;
-087 \}
-088
-089 if (d != NULL) \{
-090 *d = (mp_digit)w;
-091 \}
-092
-093 if (c != NULL) \{
-094 mp_clamp(&q);
-095 mp_exch(&q, c);
-096 \}
-097 mp_clear(&q);
-098
-099 return res;
-100 \}
-101
+016
+017 static int s_is_power_of_two(mp_digit b, int *p)
+018 \{
+019 int x;
+020
+021 for (x = 1; x < DIGIT_BIT; x++) \{
+022 if (b == (((mp_digit)1)<<x)) \{
+023 *p = x;
+024 return 1;
+025 \}
+026 \}
+027 return 0;
+028 \}
+029
+030 /* single digit division (based on routine from MPI) */
+031 int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
+032 \{
+033 mp_int q;
+034 mp_word w;
+035 mp_digit t;
+036 int res, ix;
+037
+038 /* cannot divide by zero */
+039 if (b == 0) \{
+040 return MP_VAL;
+041 \}
+042
+043 /* quick outs */
+044 if (b == 1 || mp_iszero(a) == 1) \{
+045 if (d != NULL) \{
+046 *d = 0;
+047 \}
+048 if (c != NULL) \{
+049 return mp_copy(a, c);
+050 \}
+051 return MP_OKAY;
+052 \}
+053
+054 /* power of two ? */
+055 if (s_is_power_of_two(b, &ix) == 1) \{
+056 if (d != NULL) \{
+057 *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
+058 \}
+059 if (c != NULL) \{
+060 return mp_div_2d(a, ix, c, NULL);
+061 \}
+062 return MP_OKAY;
+063 \}
+064
+065 #ifdef BN_MP_DIV_3_C
+066 /* three? */
+067 if (b == 3) \{
+068 return mp_div_3(a, c, d);
+069 \}
+070 #endif
+071
+072 /* no easy answer [c'est la vie]. Just division */
+073 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) \{
+074 return res;
+075 \}
+076
+077 q.used = a->used;
+078 q.sign = a->sign;
+079 w = 0;
+080 for (ix = a->used - 1; ix >= 0; ix--) \{
+081 w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+082
+083 if (w >= b) \{
+084 t = (mp_digit)(w / b);
+085 w -= ((mp_word)t) * ((mp_word)b);
+086 \} else \{
+087 t = 0;
+088 \}
+089 q.dp[ix] = (mp_digit)t;
+090 \}
+091
+092 if (d != NULL) \{
+093 *d = (mp_digit)w;
+094 \}
+095
+096 if (c != NULL) \{
+097 mp_clamp(&q);
+098 mp_exch(&q, c);
+099 \}
+100 mp_clear(&q);
+101
+102 return res;
+103 \}
+104
+105 #endif
\end{alltt}
\end{small}
Like the implementation of algorithm mp\_div this algorithm allows either of the quotient or remainder to be passed as a \textbf{NULL} pointer to
indicate the respective value is not required. This allows a trivial single digit modular reduction algorithm, mp\_mod\_d to be created.
-The division and remainder on lines 42 and @45,%@ can be replaced often by a single division on most processors. For example, the 32-bit x86 based
+The division and remainder on lines 43 and @45,%@ can be replaced often by a single division on most processors. For example, the 32-bit x86 based
processors can divide a 64-bit quantity by a 32-bit quantity and produce the quotient and remainder simultaneously. Unfortunately the GCC
compiler does not recognize that optimization and will actually produce two function calls to find the quotient and remainder respectively.
@@ -8887,116 +9104,118 @@ root. Ideally this algorithm is meant to find the $n$'th root of an input where
\hspace{-5.1mm}{\bf File}: bn\_mp\_n\_root.c
\vspace{-3mm}
\begin{alltt}
-016 /* find the n'th root of an integer
-017 *
-018 * Result found such that (c)**b <= a and (c+1)**b > a
-019 *
-020 * This algorithm uses Newton's approximation
-021 * x[i+1] = x[i] - f(x[i])/f'(x[i])
-022 * which will find the root in log(N) time where
-023 * each step involves a fair bit. This is not meant to
-024 * find huge roots [square and cube, etc].
-025 */
-026 int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
-027 \{
-028 mp_int t1, t2, t3;
-029 int res, neg;
-030
-031 /* input must be positive if b is even */
-032 if ((b & 1) == 0 && a->sign == MP_NEG) \{
-033 return MP_VAL;
-034 \}
-035
-036 if ((res = mp_init (&t1)) != MP_OKAY) \{
-037 return res;
-038 \}
-039
-040 if ((res = mp_init (&t2)) != MP_OKAY) \{
-041 goto __T1;
-042 \}
-043
-044 if ((res = mp_init (&t3)) != MP_OKAY) \{
-045 goto __T2;
-046 \}
-047
-048 /* if a is negative fudge the sign but keep track */
-049 neg = a->sign;
-050 a->sign = MP_ZPOS;
-051
-052 /* t2 = 2 */
-053 mp_set (&t2, 2);
-054
-055 do \{
-056 /* t1 = t2 */
-057 if ((res = mp_copy (&t2, &t1)) != MP_OKAY) \{
-058 goto __T3;
-059 \}
-060
-061 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
-062
-063 /* t3 = t1**(b-1) */
-064 if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) \{
-065 goto __T3;
-066 \}
-067
-068 /* numerator */
-069 /* t2 = t1**b */
-070 if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) \{
-071 goto __T3;
-072 \}
-073
-074 /* t2 = t1**b - a */
-075 if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) \{
-076 goto __T3;
-077 \}
-078
-079 /* denominator */
-080 /* t3 = t1**(b-1) * b */
-081 if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) \{
-082 goto __T3;
-083 \}
-084
-085 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
-086 if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) \{
-087 goto __T3;
-088 \}
-089
-090 if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) \{
-091 goto __T3;
-092 \}
-093 \} while (mp_cmp (&t1, &t2) != MP_EQ);
-094
-095 /* result can be off by a few so check */
-096 for (;;) \{
-097 if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) \{
-098 goto __T3;
-099 \}
-100
-101 if (mp_cmp (&t2, a) == MP_GT) \{
-102 if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) \{
-103 goto __T3;
-104 \}
-105 \} else \{
-106 break;
-107 \}
-108 \}
-109
-110 /* reset the sign of a first */
-111 a->sign = neg;
-112
-113 /* set the result */
-114 mp_exch (&t1, c);
-115
-116 /* set the sign of the result */
-117 c->sign = neg;
-118
-119 res = MP_OKAY;
-120
-121 __T3:mp_clear (&t3);
-122 __T2:mp_clear (&t2);
-123 __T1:mp_clear (&t1);
-124 return res;
-125 \}
+016
+017 /* find the n'th root of an integer
+018 *
+019 * Result found such that (c)**b <= a and (c+1)**b > a
+020 *
+021 * This algorithm uses Newton's approximation
+022 * x[i+1] = x[i] - f(x[i])/f'(x[i])
+023 * which will find the root in log(N) time where
+024 * each step involves a fair bit. This is not meant to
+025 * find huge roots [square and cube, etc].
+026 */
+027 int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
+028 \{
+029 mp_int t1, t2, t3;
+030 int res, neg;
+031
+032 /* input must be positive if b is even */
+033 if ((b & 1) == 0 && a->sign == MP_NEG) \{
+034 return MP_VAL;
+035 \}
+036
+037 if ((res = mp_init (&t1)) != MP_OKAY) \{
+038 return res;
+039 \}
+040
+041 if ((res = mp_init (&t2)) != MP_OKAY) \{
+042 goto __T1;
+043 \}
+044
+045 if ((res = mp_init (&t3)) != MP_OKAY) \{
+046 goto __T2;
+047 \}
+048
+049 /* if a is negative fudge the sign but keep track */
+050 neg = a->sign;
+051 a->sign = MP_ZPOS;
+052
+053 /* t2 = 2 */
+054 mp_set (&t2, 2);
+055
+056 do \{
+057 /* t1 = t2 */
+058 if ((res = mp_copy (&t2, &t1)) != MP_OKAY) \{
+059 goto __T3;
+060 \}
+061
+062 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
+063
+064 /* t3 = t1**(b-1) */
+065 if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) \{
+066 goto __T3;
+067 \}
+068
+069 /* numerator */
+070 /* t2 = t1**b */
+071 if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) \{
+072 goto __T3;
+073 \}
+074
+075 /* t2 = t1**b - a */
+076 if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) \{
+077 goto __T3;
+078 \}
+079
+080 /* denominator */
+081 /* t3 = t1**(b-1) * b */
+082 if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) \{
+083 goto __T3;
+084 \}
+085
+086 /* t3 = (t1**b - a)/(b * t1**(b-1)) */
+087 if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) \{
+088 goto __T3;
+089 \}
+090
+091 if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) \{
+092 goto __T3;
+093 \}
+094 \} while (mp_cmp (&t1, &t2) != MP_EQ);
+095
+096 /* result can be off by a few so check */
+097 for (;;) \{
+098 if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) \{
+099 goto __T3;
+100 \}
+101
+102 if (mp_cmp (&t2, a) == MP_GT) \{
+103 if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) \{
+104 goto __T3;
+105 \}
+106 \} else \{
+107 break;
+108 \}
+109 \}
+110
+111 /* reset the sign of a first */
+112 a->sign = neg;
+113
+114 /* set the result */
+115 mp_exch (&t1, c);
+116
+117 /* set the sign of the result */
+118 c->sign = neg;
+119
+120 res = MP_OKAY;
+121
+122 __T3:mp_clear (&t3);
+123 __T2:mp_clear (&t2);
+124 __T1:mp_clear (&t1);
+125 return res;
+126 \}
+127 #endif
\end{alltt}
\end{small}
@@ -9038,39 +9257,41 @@ the integers from $0$ to $\beta - 1$.
\hspace{-5.1mm}{\bf File}: bn\_mp\_rand.c
\vspace{-3mm}
\begin{alltt}
-016 /* makes a pseudo-random int of a given size */
-017 int
-018 mp_rand (mp_int * a, int digits)
-019 \{
-020 int res;
-021 mp_digit d;
-022
-023 mp_zero (a);
-024 if (digits <= 0) \{
-025 return MP_OKAY;
-026 \}
-027
-028 /* first place a random non-zero digit */
-029 do \{
-030 d = ((mp_digit) abs (rand ()));
-031 \} while (d == 0);
-032
-033 if ((res = mp_add_d (a, d, a)) != MP_OKAY) \{
-034 return res;
-035 \}
-036
-037 while (digits-- > 0) \{
-038 if ((res = mp_lshd (a, 1)) != MP_OKAY) \{
-039 return res;
-040 \}
-041
-042 if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) \{
-043 return res;
-044 \}
-045 \}
-046
-047 return MP_OKAY;
-048 \}
+016
+017 /* makes a pseudo-random int of a given size */
+018 int
+019 mp_rand (mp_int * a, int digits)
+020 \{
+021 int res;
+022 mp_digit d;
+023
+024 mp_zero (a);
+025 if (digits <= 0) \{
+026 return MP_OKAY;
+027 \}
+028
+029 /* first place a random non-zero digit */
+030 do \{
+031 d = ((mp_digit) abs (rand ()));
+032 \} while (d == 0);
+033
+034 if ((res = mp_add_d (a, d, a)) != MP_OKAY) \{
+035 return res;
+036 \}
+037
+038 while (digits-- > 0) \{
+039 if ((res = mp_lshd (a, 1)) != MP_OKAY) \{
+040 return res;
+041 \}
+042
+043 if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) \{
+044 return res;
+045 \}
+046 \}
+047
+048 return MP_OKAY;
+049 \}
+050 #endif
\end{alltt}
\end{small}
@@ -9153,66 +9374,68 @@ as part of larger input without any significant problem.
\hspace{-5.1mm}{\bf File}: bn\_mp\_read\_radix.c
\vspace{-3mm}
\begin{alltt}
-016 /* read a string [ASCII] in a given radix */
-017 int mp_read_radix (mp_int * a, char *str, int radix)
-018 \{
-019 int y, res, neg;
-020 char ch;
-021
-022 /* make sure the radix is ok */
-023 if (radix < 2 || radix > 64) \{
-024 return MP_VAL;
-025 \}
-026
-027 /* if the leading digit is a
-028 * minus set the sign to negative.
-029 */
-030 if (*str == '-') \{
-031 ++str;
-032 neg = MP_NEG;
-033 \} else \{
-034 neg = MP_ZPOS;
-035 \}
-036
-037 /* set the integer to the default of zero */
-038 mp_zero (a);
-039
-040 /* process each digit of the string */
-041 while (*str) \{
-042 /* if the radix < 36 the conversion is case insensitive
-043 * this allows numbers like 1AB and 1ab to represent the same value
-044 * [e.g. in hex]
-045 */
-046 ch = (char) ((radix < 36) ? toupper (*str) : *str);
-047 for (y = 0; y < 64; y++) \{
-048 if (ch == mp_s_rmap[y]) \{
-049 break;
-050 \}
-051 \}
-052
-053 /* if the char was found in the map
-054 * and is less than the given radix add it
-055 * to the number, otherwise exit the loop.
-056 */
-057 if (y < radix) \{
-058 if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) \{
-059 return res;
-060 \}
-061 if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) \{
-062 return res;
-063 \}
-064 \} else \{
-065 break;
-066 \}
-067 ++str;
-068 \}
-069
-070 /* set the sign only if a != 0 */
-071 if (mp_iszero(a) != 1) \{
-072 a->sign = neg;
-073 \}
-074 return MP_OKAY;
-075 \}
+016
+017 /* read a string [ASCII] in a given radix */
+018 int mp_read_radix (mp_int * a, char *str, int radix)
+019 \{
+020 int y, res, neg;
+021 char ch;
+022
+023 /* make sure the radix is ok */
+024 if (radix < 2 || radix > 64) \{
+025 return MP_VAL;
+026 \}
+027
+028 /* if the leading digit is a
+029 * minus set the sign to negative.
+030 */
+031 if (*str == '-') \{
+032 ++str;
+033 neg = MP_NEG;
+034 \} else \{
+035 neg = MP_ZPOS;
+036 \}
+037
+038 /* set the integer to the default of zero */
+039 mp_zero (a);
+040
+041 /* process each digit of the string */
+042 while (*str) \{
+043 /* if the radix < 36 the conversion is case insensitive
+044 * this allows numbers like 1AB and 1ab to represent the same value
+045 * [e.g. in hex]
+046 */
+047 ch = (char) ((radix < 36) ? toupper (*str) : *str);
+048 for (y = 0; y < 64; y++) \{
+049 if (ch == mp_s_rmap[y]) \{
+050 break;
+051 \}
+052 \}
+053
+054 /* if the char was found in the map
+055 * and is less than the given radix add it
+056 * to the number, otherwise exit the loop.
+057 */
+058 if (y < radix) \{
+059 if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) \{
+060 return res;
+061 \}
+062 if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) \{
+063 return res;
+064 \}
+065 \} else \{
+066 break;
+067 \}
+068 ++str;
+069 \}
+070
+071 /* set the sign only if a != 0 */
+072 if (mp_iszero(a) != 1) \{
+073 a->sign = neg;
+074 \}
+075 return MP_OKAY;
+076 \}
+077 #endif
\end{alltt}
\end{small}
@@ -9277,59 +9500,61 @@ are required instead of a series of $n \times k$ divisions. One design flaw of
\hspace{-5.1mm}{\bf File}: bn\_mp\_toradix.c
\vspace{-3mm}
\begin{alltt}
-016 /* stores a bignum as a ASCII string in a given radix (2..64) */
-017 int mp_toradix (mp_int * a, char *str, int radix)
-018 \{
-019 int res, digs;
-020 mp_int t;
-021 mp_digit d;
-022 char *_s = str;
-023
-024 /* check range of the radix */
-025 if (radix < 2 || radix > 64) \{
-026 return MP_VAL;
-027 \}
-028
-029 /* quick out if its zero */
-030 if (mp_iszero(a) == 1) \{
-031 *str++ = '0';
-032 *str = '\symbol{92}0';
-033 return MP_OKAY;
-034 \}
-035
-036 if ((res = mp_init_copy (&t, a)) != MP_OKAY) \{
-037 return res;
-038 \}
-039
-040 /* if it is negative output a - */
-041 if (t.sign == MP_NEG) \{
-042 ++_s;
-043 *str++ = '-';
-044 t.sign = MP_ZPOS;
-045 \}
-046
-047 digs = 0;
-048 while (mp_iszero (&t) == 0) \{
-049 if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) \{
-050 mp_clear (&t);
-051 return res;
-052 \}
-053 *str++ = mp_s_rmap[d];
-054 ++digs;
-055 \}
-056
-057 /* reverse the digits of the string. In this case _s points
-058 * to the first digit [exluding the sign] of the number]
-059 */
-060 bn_reverse ((unsigned char *)_s, digs);
-061
-062 /* append a NULL so the string is properly terminated */
-063 *str = '\symbol{92}0';
-064
-065 mp_clear (&t);
-066 return MP_OKAY;
-067 \}
-068
+016
+017 /* stores a bignum as a ASCII string in a given radix (2..64) */
+018 int mp_toradix (mp_int * a, char *str, int radix)
+019 \{
+020 int res, digs;
+021 mp_int t;
+022 mp_digit d;
+023 char *_s = str;
+024
+025 /* check range of the radix */
+026 if (radix < 2 || radix > 64) \{
+027 return MP_VAL;
+028 \}
+029
+030 /* quick out if its zero */
+031 if (mp_iszero(a) == 1) \{
+032 *str++ = '0';
+033 *str = '\symbol{92}0';
+034 return MP_OKAY;
+035 \}
+036
+037 if ((res = mp_init_copy (&t, a)) != MP_OKAY) \{
+038 return res;
+039 \}
+040
+041 /* if it is negative output a - */
+042 if (t.sign == MP_NEG) \{
+043 ++_s;
+044 *str++ = '-';
+045 t.sign = MP_ZPOS;
+046 \}
+047
+048 digs = 0;
+049 while (mp_iszero (&t) == 0) \{
+050 if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) \{
+051 mp_clear (&t);
+052 return res;
+053 \}
+054 *str++ = mp_s_rmap[d];
+055 ++digs;
+056 \}
+057
+058 /* reverse the digits of the string. In this case _s points
+059 * to the first digit [exluding the sign] of the number]
+060 */
+061 bn_reverse ((unsigned char *)_s, digs);
+062
+063 /* append a NULL so the string is properly terminated */
+064 *str = '\symbol{92}0';
+065
+066 mp_clear (&t);
+067 return MP_OKAY;
+068 \}
+069
+070 #endif
\end{alltt}
\end{small}
@@ -9509,122 +9734,124 @@ they cannot both be even.
By step nine both of $u$ and $v$ are odd which is required for the inner logic. First the pair are swapped such that $v$ is equal to
or greater than $u$. This ensures that the subtraction on step 9.2 will always produce a positive and even result. Step 9.3 removes any
factors of two from the difference $u$ to ensure that in the next iteration of the loop both are once again odd.
-
-After $v = 0$ occurs the variable $u$ has the greatest common divisor of the pair $\left < u, v \right >$ just after step six. The result
-must be adjusted by multiplying by the common factors of two ($2^k$) removed earlier.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_gcd.c
-\vspace{-3mm}
-\begin{alltt}
-016 /* Greatest Common Divisor using the binary method */
-017 int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
-018 \{
-019 mp_int u, v;
-020 int k, u_lsb, v_lsb, res;
-021
-022 /* either zero than gcd is the largest */
-023 if (mp_iszero (a) == 1 && mp_iszero (b) == 0) \{
-024 return mp_abs (b, c);
-025 \}
-026 if (mp_iszero (a) == 0 && mp_iszero (b) == 1) \{
-027 return mp_abs (a, c);
-028 \}
-029
-030 /* optimized. At this point if a == 0 then
-031 * b must equal zero too
-032 */
-033 if (mp_iszero (a) == 1) \{
-034 mp_zero(c);
-035 return MP_OKAY;
-036 \}
-037
-038 /* get copies of a and b we can modify */
-039 if ((res = mp_init_copy (&u, a)) != MP_OKAY) \{
-040 return res;
-041 \}
-042
-043 if ((res = mp_init_copy (&v, b)) != MP_OKAY) \{
-044 goto __U;
-045 \}
-046
-047 /* must be positive for the remainder of the algorithm */
-048 u.sign = v.sign = MP_ZPOS;
-049
-050 /* B1. Find the common power of two for u and v */
-051 u_lsb = mp_cnt_lsb(&u);
-052 v_lsb = mp_cnt_lsb(&v);
-053 k = MIN(u_lsb, v_lsb);
-054
-055 if (k > 0) \{
-056 /* divide the power of two out */
-057 if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) \{
-058 goto __V;
-059 \}
-060
-061 if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) \{
-062 goto __V;
-063 \}
-064 \}
-065
-066 /* divide any remaining factors of two out */
-067 if (u_lsb != k) \{
-068 if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) \{
-069 goto __V;
-070 \}
-071 \}
-072
-073 if (v_lsb != k) \{
-074 if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) \{
-075 goto __V;
-076 \}
-077 \}
-078
-079 while (mp_iszero(&v) == 0) \{
-080 /* make sure v is the largest */
-081 if (mp_cmp_mag(&u, &v) == MP_GT) \{
-082 /* swap u and v to make sure v is >= u */
-083 mp_exch(&u, &v);
-084 \}
-085
-086 /* subtract smallest from largest */
-087 if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) \{
-088 goto __V;
-089 \}
-090
-091 /* Divide out all factors of two */
-092 if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) \{
-093 goto __V;
-094 \}
-095 \}
-096
-097 /* multiply by 2**k which we divided out at the beginning */
-098 if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) \{
-099 goto __V;
-100 \}
-101 c->sign = MP_ZPOS;
-102 res = MP_OKAY;
-103 __V:mp_clear (&u);
-104 __U:mp_clear (&v);
-105 return res;
-106 \}
+
+After $v = 0$ occurs the variable $u$ has the greatest common divisor of the pair $\left < u, v \right >$ just after step six. The result
+must be adjusted by multiplying by the common factors of two ($2^k$) removed earlier.
+
+\vspace{+3mm}\begin{small}
+\hspace{-5.1mm}{\bf File}: bn\_mp\_gcd.c
+\vspace{-3mm}
+\begin{alltt}
+016
+017 /* Greatest Common Divisor using the binary method */
+018 int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
+019 \{
+020 mp_int u, v;
+021 int k, u_lsb, v_lsb, res;
+022
+023 /* either zero than gcd is the largest */
+024 if (mp_iszero (a) == 1 && mp_iszero (b) == 0) \{
+025 return mp_abs (b, c);
+026 \}
+027 if (mp_iszero (a) == 0 && mp_iszero (b) == 1) \{
+028 return mp_abs (a, c);
+029 \}
+030
+031 /* optimized. At this point if a == 0 then
+032 * b must equal zero too
+033 */
+034 if (mp_iszero (a) == 1) \{
+035 mp_zero(c);
+036 return MP_OKAY;
+037 \}
+038
+039 /* get copies of a and b we can modify */
+040 if ((res = mp_init_copy (&u, a)) != MP_OKAY) \{
+041 return res;
+042 \}
+043
+044 if ((res = mp_init_copy (&v, b)) != MP_OKAY) \{
+045 goto __U;
+046 \}
+047
+048 /* must be positive for the remainder of the algorithm */
+049 u.sign = v.sign = MP_ZPOS;
+050
+051 /* B1. Find the common power of two for u and v */
+052 u_lsb = mp_cnt_lsb(&u);
+053 v_lsb = mp_cnt_lsb(&v);
+054 k = MIN(u_lsb, v_lsb);
+055
+056 if (k > 0) \{
+057 /* divide the power of two out */
+058 if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) \{
+059 goto __V;
+060 \}
+061
+062 if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) \{
+063 goto __V;
+064 \}
+065 \}
+066
+067 /* divide any remaining factors of two out */
+068 if (u_lsb != k) \{
+069 if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) \{
+070 goto __V;
+071 \}
+072 \}
+073
+074 if (v_lsb != k) \{
+075 if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) \{
+076 goto __V;
+077 \}
+078 \}
+079
+080 while (mp_iszero(&v) == 0) \{
+081 /* make sure v is the largest */
+082 if (mp_cmp_mag(&u, &v) == MP_GT) \{
+083 /* swap u and v to make sure v is >= u */
+084 mp_exch(&u, &v);
+085 \}
+086
+087 /* subtract smallest from largest */
+088 if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) \{
+089 goto __V;
+090 \}
+091
+092 /* Divide out all factors of two */
+093 if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) \{
+094 goto __V;
+095 \}
+096 \}
+097
+098 /* multiply by 2**k which we divided out at the beginning */
+099 if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) \{
+100 goto __V;
+101 \}
+102 c->sign = MP_ZPOS;
+103 res = MP_OKAY;
+104 __V:mp_clear (&u);
+105 __U:mp_clear (&v);
+106 return res;
+107 \}
+108 #endif
\end{alltt}
\end{small}
This function makes use of the macros mp\_iszero and mp\_iseven. The former evaluates to $1$ if the input mp\_int is equivalent to the
integer zero otherwise it evaluates to $0$. The latter evaluates to $1$ if the input mp\_int represents a non-zero even integer otherwise
it evaluates to $0$. Note that just because mp\_iseven may evaluate to $0$ does not mean the input is odd, it could also be zero. The three
-trivial cases of inputs are handled on lines 26 through 36. After those lines the inputs are assumed to be non-zero.
+trivial cases of inputs are handled on lines 24 through 37. After those lines the inputs are assumed to be non-zero.
-Lines 38 and 39 make local copies $u$ and $v$ of the inputs $a$ and $b$ respectively. At this point the common factors of two
-must be divided out of the two inputs. The while loop on line 79 iterates so long as both are even. The local integer $k$ is used to
+Lines 34 and 40 make local copies $u$ and $v$ of the inputs $a$ and $b$ respectively. At this point the common factors of two
+must be divided out of the two inputs. The while loop on line 80 iterates so long as both are even. The local integer $k$ is used to
keep track of how many factors of $2$ are pulled out of both values. It is assumed that the number of factors will not exceed the maximum
value of a C ``int'' data type\footnote{Strictly speaking no array in C may have more than entries than are accessible by an ``int'' so this is not
a limitation.}.
-At this point there are no more common factors of two in the two values. The while loops on lines 79 and 79 remove any independent
+At this point there are no more common factors of two in the two values. The while loops on lines 80 and 80 remove any independent
factors of two such that both $u$ and $v$ are guaranteed to be an odd integer before hitting the main body of the algorithm. The while loop
-on line 79 performs the reduction of the pair until $v$ is equal to zero. The unsigned comparison and subtraction algorithms are used in
+on line 80 performs the reduction of the pair until $v$ is equal to zero. The unsigned comparison and subtraction algorithms are used in
place of the full signed routines since both values are guaranteed to be positive and the result of the subtraction is guaranteed to be non-negative.
\section{Least Common Multiple}
@@ -9663,44 +9890,46 @@ dividing the product of the two inputs by their greatest common divisor.
\hspace{-5.1mm}{\bf File}: bn\_mp\_lcm.c
\vspace{-3mm}
\begin{alltt}
-016 /* computes least common multiple as |a*b|/(a, b) */
-017 int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
-018 \{
-019 int res;
-020 mp_int t1, t2;
-021
+016
+017 /* computes least common multiple as |a*b|/(a, b) */
+018 int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
+019 \{
+020 int res;
+021 mp_int t1, t2;
022
-023 if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) \{
-024 return res;
-025 \}
-026
-027 /* t1 = get the GCD of the two inputs */
-028 if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) \{
-029 goto __T;
-030 \}
-031
-032 /* divide the smallest by the GCD */
-033 if (mp_cmp_mag(a, b) == MP_LT) \{
-034 /* store quotient in t2 such that t2 * b is the LCM */
-035 if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) \{
-036 goto __T;
-037 \}
-038 res = mp_mul(b, &t2, c);
-039 \} else \{
-040 /* store quotient in t2 such that t2 * a is the LCM */
-041 if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) \{
-042 goto __T;
-043 \}
-044 res = mp_mul(a, &t2, c);
-045 \}
-046
-047 /* fix the sign to positive */
-048 c->sign = MP_ZPOS;
-049
-050 __T:
-051 mp_clear_multi (&t1, &t2, NULL);
-052 return res;
-053 \}
+023
+024 if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) \{
+025 return res;
+026 \}
+027
+028 /* t1 = get the GCD of the two inputs */
+029 if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) \{
+030 goto __T;
+031 \}
+032
+033 /* divide the smallest by the GCD */
+034 if (mp_cmp_mag(a, b) == MP_LT) \{
+035 /* store quotient in t2 such that t2 * b is the LCM */
+036 if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) \{
+037 goto __T;
+038 \}
+039 res = mp_mul(b, &t2, c);
+040 \} else \{
+041 /* store quotient in t2 such that t2 * a is the LCM */
+042 if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) \{
+043 goto __T;
+044 \}
+045 res = mp_mul(a, &t2, c);
+046 \}
+047
+048 /* fix the sign to positive */
+049 c->sign = MP_ZPOS;
+050
+051 __T:
+052 mp_clear_multi (&t1, &t2, NULL);
+053 return res;
+054 \}
+055 #endif
\end{alltt}
\end{small}
@@ -9858,89 +10087,91 @@ $\left ( {p' \over a'} \right )$ which is multiplied against the current Jacobi
\hspace{-5.1mm}{\bf File}: bn\_mp\_jacobi.c
\vspace{-3mm}
\begin{alltt}
-016 /* computes the jacobi c = (a | n) (or Legendre if n is prime)
-017 * HAC pp. 73 Algorithm 2.149
-018 */
-019 int mp_jacobi (mp_int * a, mp_int * p, int *c)
-020 \{
-021 mp_int a1, p1;
-022 int k, s, r, res;
-023 mp_digit residue;
-024
-025 /* if p <= 0 return MP_VAL */
-026 if (mp_cmp_d(p, 0) != MP_GT) \{
-027 return MP_VAL;
-028 \}
-029
-030 /* step 1. if a == 0, return 0 */
-031 if (mp_iszero (a) == 1) \{
-032 *c = 0;
-033 return MP_OKAY;
-034 \}
-035
-036 /* step 2. if a == 1, return 1 */
-037 if (mp_cmp_d (a, 1) == MP_EQ) \{
-038 *c = 1;
-039 return MP_OKAY;
-040 \}
-041
-042 /* default */
-043 s = 0;
-044
-045 /* step 3. write a = a1 * 2**k */
-046 if ((res = mp_init_copy (&a1, a)) != MP_OKAY) \{
-047 return res;
-048 \}
-049
-050 if ((res = mp_init (&p1)) != MP_OKAY) \{
-051 goto __A1;
-052 \}
-053
-054 /* divide out larger power of two */
-055 k = mp_cnt_lsb(&a1);
-056 if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) \{
-057 goto __P1;
-058 \}
-059
-060 /* step 4. if e is even set s=1 */
-061 if ((k & 1) == 0) \{
-062 s = 1;
-063 \} else \{
-064 /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
-065 residue = p->dp[0] & 7;
-066
-067 if (residue == 1 || residue == 7) \{
-068 s = 1;
-069 \} else if (residue == 3 || residue == 5) \{
-070 s = -1;
-071 \}
-072 \}
-073
-074 /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
-075 if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) \{
-076 s = -s;
-077 \}
-078
-079 /* if a1 == 1 we're done */
-080 if (mp_cmp_d (&a1, 1) == MP_EQ) \{
-081 *c = s;
-082 \} else \{
-083 /* n1 = n mod a1 */
-084 if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) \{
-085 goto __P1;
-086 \}
-087 if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) \{
-088 goto __P1;
-089 \}
-090 *c = s * r;
-091 \}
-092
-093 /* done */
-094 res = MP_OKAY;
-095 __P1:mp_clear (&p1);
-096 __A1:mp_clear (&a1);
-097 return res;
-098 \}
+016
+017 /* computes the jacobi c = (a | n) (or Legendre if n is prime)
+018 * HAC pp. 73 Algorithm 2.149
+019 */
+020 int mp_jacobi (mp_int * a, mp_int * p, int *c)
+021 \{
+022 mp_int a1, p1;
+023 int k, s, r, res;
+024 mp_digit residue;
+025
+026 /* if p <= 0 return MP_VAL */
+027 if (mp_cmp_d(p, 0) != MP_GT) \{
+028 return MP_VAL;
+029 \}
+030
+031 /* step 1. if a == 0, return 0 */
+032 if (mp_iszero (a) == 1) \{
+033 *c = 0;
+034 return MP_OKAY;
+035 \}
+036
+037 /* step 2. if a == 1, return 1 */
+038 if (mp_cmp_d (a, 1) == MP_EQ) \{
+039 *c = 1;
+040 return MP_OKAY;
+041 \}
+042
+043 /* default */
+044 s = 0;
+045
+046 /* step 3. write a = a1 * 2**k */
+047 if ((res = mp_init_copy (&a1, a)) != MP_OKAY) \{
+048 return res;
+049 \}
+050
+051 if ((res = mp_init (&p1)) != MP_OKAY) \{
+052 goto __A1;
+053 \}
+054
+055 /* divide out larger power of two */
+056 k = mp_cnt_lsb(&a1);
+057 if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) \{
+058 goto __P1;
+059 \}
+060
+061 /* step 4. if e is even set s=1 */
+062 if ((k & 1) == 0) \{
+063 s = 1;
+064 \} else \{
+065 /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
+066 residue = p->dp[0] & 7;
+067
+068 if (residue == 1 || residue == 7) \{
+069 s = 1;
+070 \} else if (residue == 3 || residue == 5) \{
+071 s = -1;
+072 \}
+073 \}
+074
+075 /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
+076 if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) \{
+077 s = -s;
+078 \}
+079
+080 /* if a1 == 1 we're done */
+081 if (mp_cmp_d (&a1, 1) == MP_EQ) \{
+082 *c = s;
+083 \} else \{
+084 /* n1 = n mod a1 */
+085 if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) \{
+086 goto __P1;
+087 \}
+088 if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) \{
+089 goto __P1;
+090 \}
+091 *c = s * r;
+092 \}
+093
+094 /* done */
+095 res = MP_OKAY;
+096 __P1:mp_clear (&p1);
+097 __A1:mp_clear (&a1);
+098 return res;
+099 \}
+100 #endif
\end{alltt}
\end{small}
@@ -9955,9 +10186,9 @@ After a local copy of $a$ is made all of the factors of two are divided out and
bit of $k$ is required, however, it makes the algorithm simpler to follow to perform an addition. In practice an exclusive-or and addition have the same
processor requirements and neither is faster than the other.
-Line 60 through 71 determines the value of $\left ( { 2 \over p } \right )^k$. If the least significant bit of $k$ is zero than
+Line 61 through 70 determines the value of $\left ( { 2 \over p } \right )^k$. If the least significant bit of $k$ is zero than
$k$ is even and the value is one. Otherwise, the value of $s$ depends on which residue class $p$ belongs to modulo eight. The value of
-$(-1)^{(p-1)(a'-1)/4}$ is compute and multiplied against $s$ on lines 74 through 77.
+$(-1)^{(p-1)(a'-1)/4}$ is compute and multiplied against $s$ on lines 75 through 73.
Finally, if $a1$ does not equal one the algorithm must recurse and compute $\left ( {p' \over a'} \right )$.
@@ -10066,164 +10297,29 @@ then only a couple of additions or subtractions will be required to adjust the i
\hspace{-5.1mm}{\bf File}: bn\_mp\_invmod.c
\vspace{-3mm}
\begin{alltt}
-016 /* hac 14.61, pp608 */
-017 int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-018 \{
-019 mp_int x, y, u, v, A, B, C, D;
-020 int res;
-021
-022 /* b cannot be negative */
-023 if (b->sign == MP_NEG || mp_iszero(b) == 1) \{
-024 return MP_VAL;
-025 \}
-026
-027 /* if the modulus is odd we can use a faster routine instead */
-028 if (mp_isodd (b) == 1) \{
-029 return fast_mp_invmod (a, b, c);
-030 \}
-031
-032 /* init temps */
-033 if ((res = mp_init_multi(&x, &y, &u, &v,
-034 &A, &B, &C, &D, NULL)) != MP_OKAY) \{
-035 return res;
-036 \}
-037
-038 /* x = a, y = b */
-039 if ((res = mp_copy (a, &x)) != MP_OKAY) \{
-040 goto __ERR;
-041 \}
-042 if ((res = mp_copy (b, &y)) != MP_OKAY) \{
-043 goto __ERR;
-044 \}
-045
-046 /* 2. [modified] if x,y are both even then return an error! */
-047 if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) \{
-048 res = MP_VAL;
-049 goto __ERR;
-050 \}
-051
-052 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
-053 if ((res = mp_copy (&x, &u)) != MP_OKAY) \{
-054 goto __ERR;
-055 \}
-056 if ((res = mp_copy (&y, &v)) != MP_OKAY) \{
-057 goto __ERR;
-058 \}
-059 mp_set (&A, 1);
-060 mp_set (&D, 1);
-061
-062 top:
-063 /* 4. while u is even do */
-064 while (mp_iseven (&u) == 1) \{
-065 /* 4.1 u = u/2 */
-066 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) \{
-067 goto __ERR;
-068 \}
-069 /* 4.2 if A or B is odd then */
-070 if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) \{
-071 /* A = (A+y)/2, B = (B-x)/2 */
-072 if ((res = mp_add (&A, &y, &A)) != MP_OKAY) \{
-073 goto __ERR;
-074 \}
-075 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) \{
-076 goto __ERR;
-077 \}
-078 \}
-079 /* A = A/2, B = B/2 */
-080 if ((res = mp_div_2 (&A, &A)) != MP_OKAY) \{
-081 goto __ERR;
-082 \}
-083 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) \{
-084 goto __ERR;
-085 \}
-086 \}
-087
-088 /* 5. while v is even do */
-089 while (mp_iseven (&v) == 1) \{
-090 /* 5.1 v = v/2 */
-091 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) \{
-092 goto __ERR;
-093 \}
-094 /* 5.2 if C or D is odd then */
-095 if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) \{
-096 /* C = (C+y)/2, D = (D-x)/2 */
-097 if ((res = mp_add (&C, &y, &C)) != MP_OKAY) \{
-098 goto __ERR;
-099 \}
-100 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) \{
-101 goto __ERR;
-102 \}
-103 \}
-104 /* C = C/2, D = D/2 */
-105 if ((res = mp_div_2 (&C, &C)) != MP_OKAY) \{
-106 goto __ERR;
-107 \}
-108 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) \{
-109 goto __ERR;
-110 \}
-111 \}
-112
-113 /* 6. if u >= v then */
-114 if (mp_cmp (&u, &v) != MP_LT) \{
-115 /* u = u - v, A = A - C, B = B - D */
-116 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) \{
-117 goto __ERR;
-118 \}
-119
-120 if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) \{
-121 goto __ERR;
-122 \}
-123
-124 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) \{
-125 goto __ERR;
-126 \}
-127 \} else \{
-128 /* v - v - u, C = C - A, D = D - B */
-129 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) \{
-130 goto __ERR;
-131 \}
-132
-133 if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) \{
-134 goto __ERR;
-135 \}
-136
-137 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) \{
-138 goto __ERR;
-139 \}
-140 \}
-141
-142 /* if not zero goto step 4 */
-143 if (mp_iszero (&u) == 0)
-144 goto top;
-145
-146 /* now a = C, b = D, gcd == g*v */
-147
-148 /* if v != 1 then there is no inverse */
-149 if (mp_cmp_d (&v, 1) != MP_EQ) \{
-150 res = MP_VAL;
-151 goto __ERR;
-152 \}
-153
-154 /* if its too low */
-155 while (mp_cmp_d(&C, 0) == MP_LT) \{
-156 if ((res = mp_add(&C, b, &C)) != MP_OKAY) \{
-157 goto __ERR;
-158 \}
-159 \}
-160
-161 /* too big */
-162 while (mp_cmp_mag(&C, b) != MP_LT) \{
-163 if ((res = mp_sub(&C, b, &C)) != MP_OKAY) \{
-164 goto __ERR;
-165 \}
-166 \}
-167
-168 /* C is now the inverse */
-169 mp_exch (&C, c);
-170 res = MP_OKAY;
-171 __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
-172 return res;
-173 \}
+016
+017 /* hac 14.61, pp608 */
+018 int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+019 \{
+020 /* b cannot be negative */
+021 if (b->sign == MP_NEG || mp_iszero(b) == 1) \{
+022 return MP_VAL;
+023 \}
+024
+025 #ifdef BN_FAST_MP_INVMOD_C
+026 /* if the modulus is odd we can use a faster routine instead */
+027 if (mp_isodd (b) == 1) \{
+028 return fast_mp_invmod (a, b, c);
+029 \}
+030 #endif
+031
+032 #ifdef BN_MP_INVMOD_SLOW_C
+033 return mp_invmod_slow(a, b, c);
+034 #endif
+035
+036 return MP_VAL;
+037 \}
+038 #endif
\end{alltt}
\end{small}
@@ -10295,34 +10391,36 @@ This algorithm attempts to determine if a candidate integer $n$ is composite by
\hspace{-5.1mm}{\bf File}: bn\_mp\_prime\_is\_divisible.c
\vspace{-3mm}
\begin{alltt}
-016 /* determines if an integers is divisible by one
-017 * of the first PRIME_SIZE primes or not
-018 *
-019 * sets result to 0 if not, 1 if yes
-020 */
-021 int mp_prime_is_divisible (mp_int * a, int *result)
-022 \{
-023 int err, ix;
-024 mp_digit res;
-025
-026 /* default to not */
-027 *result = MP_NO;
-028
-029 for (ix = 0; ix < PRIME_SIZE; ix++) \{
-030 /* what is a mod __prime_tab[ix] */
-031 if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) \{
-032 return err;
-033 \}
-034
-035 /* is the residue zero? */
-036 if (res == 0) \{
-037 *result = MP_YES;
-038 return MP_OKAY;
-039 \}
-040 \}
-041
-042 return MP_OKAY;
-043 \}
+016
+017 /* determines if an integers is divisible by one
+018 * of the first PRIME_SIZE primes or not
+019 *
+020 * sets result to 0 if not, 1 if yes
+021 */
+022 int mp_prime_is_divisible (mp_int * a, int *result)
+023 \{
+024 int err, ix;
+025 mp_digit res;
+026
+027 /* default to not */
+028 *result = MP_NO;
+029
+030 for (ix = 0; ix < PRIME_SIZE; ix++) \{
+031 /* what is a mod __prime_tab[ix] */
+032 if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) \{
+033 return err;
+034 \}
+035
+036 /* is the residue zero? */
+037 if (res == 0) \{
+038 *result = MP_YES;
+039 return MP_OKAY;
+040 \}
+041 \}
+042
+043 return MP_OKAY;
+044 \}
+045 #endif
\end{alltt}
\end{small}
@@ -10333,45 +10431,47 @@ mp\_digit. The table \_\_prime\_tab is defined in the following file.
\hspace{-5.1mm}{\bf File}: bn\_prime\_tab.c
\vspace{-3mm}
\begin{alltt}
-016 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
-017 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
-018 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
-019 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
-020 #ifndef MP_8BIT
-021 0x0083,
-022 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
-023 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
-024 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
-025 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
-026
-027 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
-028 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
-029 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
-030 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
-031 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
-032 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
-033 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
-034 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
-035
-036 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
-037 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
-038 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
-039 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
-040 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
-041 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
-042 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
-043 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
-044
-045 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
-046 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
-047 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
-048 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
-049 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
-050 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
-051 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
-052 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
-053 #endif
-054 \};
+016 const mp_digit __prime_tab[] = \{
+017 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
+018 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
+019 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
+020 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
+021 #ifndef MP_8BIT
+022 0x0083,
+023 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
+024 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
+025 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
+026 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
+027
+028 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
+029 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
+030 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
+031 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
+032 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
+033 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
+034 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
+035 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
+036
+037 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
+038 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
+039 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
+040 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
+041 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
+042 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
+043 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
+044 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
+045
+046 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
+047 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
+048 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
+049 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
+050 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
+051 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
+052 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
+053 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
+054 #endif
+055 \};
+056 #endif
\end{alltt}
\end{small}
@@ -10418,46 +10518,48 @@ determine the result.
\hspace{-5.1mm}{\bf File}: bn\_mp\_prime\_fermat.c
\vspace{-3mm}
\begin{alltt}
-016 /* performs one Fermat test.
-017 *
-018 * If "a" were prime then b**a == b (mod a) since the order of
-019 * the multiplicative sub-group would be phi(a) = a-1. That means
-020 * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
-021 *
-022 * Sets result to 1 if the congruence holds, or zero otherwise.
-023 */
-024 int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
-025 \{
-026 mp_int t;
-027 int err;
-028
-029 /* default to composite */
-030 *result = MP_NO;
-031
-032 /* ensure b > 1 */
-033 if (mp_cmp_d(b, 1) != MP_GT) \{
-034 return MP_VAL;
-035 \}
-036
-037 /* init t */
-038 if ((err = mp_init (&t)) != MP_OKAY) \{
-039 return err;
-040 \}
-041
-042 /* compute t = b**a mod a */
-043 if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) \{
-044 goto __T;
-045 \}
-046
-047 /* is it equal to b? */
-048 if (mp_cmp (&t, b) == MP_EQ) \{
-049 *result = MP_YES;
-050 \}
-051
-052 err = MP_OKAY;
-053 __T:mp_clear (&t);
-054 return err;
-055 \}
+016
+017 /* performs one Fermat test.
+018 *
+019 * If "a" were prime then b**a == b (mod a) since the order of
+020 * the multiplicative sub-group would be phi(a) = a-1. That means
+021 * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
+022 *
+023 * Sets result to 1 if the congruence holds, or zero otherwise.
+024 */
+025 int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
+026 \{
+027 mp_int t;
+028 int err;
+029
+030 /* default to composite */
+031 *result = MP_NO;
+032
+033 /* ensure b > 1 */
+034 if (mp_cmp_d(b, 1) != MP_GT) \{
+035 return MP_VAL;
+036 \}
+037
+038 /* init t */
+039 if ((err = mp_init (&t)) != MP_OKAY) \{
+040 return err;
+041 \}
+042
+043 /* compute t = b**a mod a */
+044 if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) \{
+045 goto __T;
+046 \}
+047
+048 /* is it equal to b? */
+049 if (mp_cmp (&t, b) == MP_EQ) \{
+050 *result = MP_YES;
+051 \}
+052
+053 err = MP_OKAY;
+054 __T:mp_clear (&t);
+055 return err;
+056 \}
+057 #endif
\end{alltt}
\end{small}
@@ -10510,87 +10612,89 @@ composite then it is \textit{probably} prime.
\hspace{-5.1mm}{\bf File}: bn\_mp\_prime\_miller\_rabin.c
\vspace{-3mm}
\begin{alltt}
-016 /* Miller-Rabin test of "a" to the base of "b" as described in
-017 * HAC pp. 139 Algorithm 4.24
-018 *
-019 * Sets result to 0 if definitely composite or 1 if probably prime.
-020 * Randomly the chance of error is no more than 1/4 and often
-021 * very much lower.
-022 */
-023 int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
-024 \{
-025 mp_int n1, y, r;
-026 int s, j, err;
-027
-028 /* default */
-029 *result = MP_NO;
-030
-031 /* ensure b > 1 */
-032 if (mp_cmp_d(b, 1) != MP_GT) \{
-033 return MP_VAL;
-034 \}
-035
-036 /* get n1 = a - 1 */
-037 if ((err = mp_init_copy (&n1, a)) != MP_OKAY) \{
-038 return err;
-039 \}
-040 if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) \{
-041 goto __N1;
-042 \}
-043
-044 /* set 2**s * r = n1 */
-045 if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) \{
-046 goto __N1;
-047 \}
-048
-049 /* count the number of least significant bits
-050 * which are zero
-051 */
-052 s = mp_cnt_lsb(&r);
-053
-054 /* now divide n - 1 by 2**s */
-055 if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) \{
-056 goto __R;
-057 \}
-058
-059 /* compute y = b**r mod a */
-060 if ((err = mp_init (&y)) != MP_OKAY) \{
-061 goto __R;
-062 \}
-063 if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) \{
-064 goto __Y;
-065 \}
-066
-067 /* if y != 1 and y != n1 do */
-068 if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) \{
-069 j = 1;
-070 /* while j <= s-1 and y != n1 */
-071 while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) \{
-072 if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) \{
-073 goto __Y;
-074 \}
-075
-076 /* if y == 1 then composite */
-077 if (mp_cmp_d (&y, 1) == MP_EQ) \{
-078 goto __Y;
-079 \}
-080
-081 ++j;
-082 \}
-083
-084 /* if y != n1 then composite */
-085 if (mp_cmp (&y, &n1) != MP_EQ) \{
-086 goto __Y;
-087 \}
-088 \}
-089
-090 /* probably prime now */
-091 *result = MP_YES;
-092 __Y:mp_clear (&y);
-093 __R:mp_clear (&r);
-094 __N1:mp_clear (&n1);
-095 return err;
-096 \}
+016
+017 /* Miller-Rabin test of "a" to the base of "b" as described in
+018 * HAC pp. 139 Algorithm 4.24
+019 *
+020 * Sets result to 0 if definitely composite or 1 if probably prime.
+021 * Randomly the chance of error is no more than 1/4 and often
+022 * very much lower.
+023 */
+024 int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
+025 \{
+026 mp_int n1, y, r;
+027 int s, j, err;
+028
+029 /* default */
+030 *result = MP_NO;
+031
+032 /* ensure b > 1 */
+033 if (mp_cmp_d(b, 1) != MP_GT) \{
+034 return MP_VAL;
+035 \}
+036
+037 /* get n1 = a - 1 */
+038 if ((err = mp_init_copy (&n1, a)) != MP_OKAY) \{
+039 return err;
+040 \}
+041 if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) \{
+042 goto __N1;
+043 \}
+044
+045 /* set 2**s * r = n1 */
+046 if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) \{
+047 goto __N1;
+048 \}
+049
+050 /* count the number of least significant bits
+051 * which are zero
+052 */
+053 s = mp_cnt_lsb(&r);
+054
+055 /* now divide n - 1 by 2**s */
+056 if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) \{
+057 goto __R;
+058 \}
+059
+060 /* compute y = b**r mod a */
+061 if ((err = mp_init (&y)) != MP_OKAY) \{
+062 goto __R;
+063 \}
+064 if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) \{
+065 goto __Y;
+066 \}
+067
+068 /* if y != 1 and y != n1 do */
+069 if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) \{
+070 j = 1;
+071 /* while j <= s-1 and y != n1 */
+072 while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) \{
+073 if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) \{
+074 goto __Y;
+075 \}
+076
+077 /* if y == 1 then composite */
+078 if (mp_cmp_d (&y, 1) == MP_EQ) \{
+079 goto __Y;
+080 \}
+081
+082 ++j;
+083 \}
+084
+085 /* if y != n1 then composite */
+086 if (mp_cmp (&y, &n1) != MP_EQ) \{
+087 goto __Y;
+088 \}
+089 \}
+090
+091 /* probably prime now */
+092 *result = MP_YES;
+093 __Y:mp_clear (&y);
+094 __R:mp_clear (&r);
+095 __N1:mp_clear (&n1);
+096 return err;
+097 \}
+098 #endif
\end{alltt}
\end{small}
diff --git a/tommath_class.h b/tommath_class.h
new file mode 100644
index 0000000..2a17d43
--- /dev/null
+++ b/tommath_class.h
@@ -0,0 +1,951 @@
+#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))
+#if defined(LTM2)
+#define LTM3
+#endif
+#if defined(LTM1)
+#define LTM2
+#endif
+#define LTM1
+
+#if defined(LTM_ALL)
+#define BN_ERROR_C
+#define BN_FAST_MP_INVMOD_C
+#define BN_FAST_MP_MONTGOMERY_REDUCE_C
+#define BN_FAST_S_MP_MUL_DIGS_C
+#define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+#define BN_FAST_S_MP_SQR_C
+#define BN_MP_2EXPT_C
+#define BN_MP_ABS_C
+#define BN_MP_ADD_C
+#define BN_MP_ADD_D_C
+#define BN_MP_ADDMOD_C
+#define BN_MP_AND_C
+#define BN_MP_CLAMP_C
+#define BN_MP_CLEAR_C
+#define BN_MP_CLEAR_MULTI_C
+#define BN_MP_CMP_C
+#define BN_MP_CMP_D_C
+#define BN_MP_CMP_MAG_C
+#define BN_MP_CNT_LSB_C
+#define BN_MP_COPY_C
+#define BN_MP_COUNT_BITS_C
+#define BN_MP_DIV_C
+#define BN_MP_DIV_2_C
+#define BN_MP_DIV_2D_C
+#define BN_MP_DIV_3_C
+#define BN_MP_DIV_D_C
+#define BN_MP_DR_IS_MODULUS_C
+#define BN_MP_DR_REDUCE_C
+#define BN_MP_DR_SETUP_C
+#define BN_MP_EXCH_C
+#define BN_MP_EXPT_D_C
+#define BN_MP_EXPTMOD_C
+#define BN_MP_EXPTMOD_FAST_C
+#define BN_MP_EXTEUCLID_C
+#define BN_MP_FREAD_C
+#define BN_MP_FWRITE_C
+#define BN_MP_GCD_C
+#define BN_MP_GET_INT_C
+#define BN_MP_GROW_C
+#define BN_MP_INIT_C
+#define BN_MP_INIT_COPY_C
+#define BN_MP_INIT_MULTI_C
+#define BN_MP_INIT_SET_C
+#define BN_MP_INIT_SET_INT_C
+#define BN_MP_INIT_SIZE_C
+#define BN_MP_INVMOD_C
+#define BN_MP_INVMOD_SLOW_C
+#define BN_MP_IS_SQUARE_C
+#define BN_MP_JACOBI_C
+#define BN_MP_KARATSUBA_MUL_C
+#define BN_MP_KARATSUBA_SQR_C
+#define BN_MP_LCM_C
+#define BN_MP_LSHD_C
+#define BN_MP_MOD_C
+#define BN_MP_MOD_2D_C
+#define BN_MP_MOD_D_C
+#define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+#define BN_MP_MONTGOMERY_REDUCE_C
+#define BN_MP_MONTGOMERY_SETUP_C
+#define BN_MP_MUL_C
+#define BN_MP_MUL_2_C
+#define BN_MP_MUL_2D_C
+#define BN_MP_MUL_D_C
+#define BN_MP_MULMOD_C
+#define BN_MP_N_ROOT_C
+#define BN_MP_NEG_C
+#define BN_MP_OR_C
+#define BN_MP_PRIME_FERMAT_C
+#define BN_MP_PRIME_IS_DIVISIBLE_C
+#define BN_MP_PRIME_IS_PRIME_C
+#define BN_MP_PRIME_MILLER_RABIN_C
+#define BN_MP_PRIME_NEXT_PRIME_C
+#define BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+#define BN_MP_PRIME_RANDOM_EX_C
+#define BN_MP_RADIX_SIZE_C
+#define BN_MP_RADIX_SMAP_C
+#define BN_MP_RAND_C
+#define BN_MP_READ_RADIX_C
+#define BN_MP_READ_SIGNED_BIN_C
+#define BN_MP_READ_UNSIGNED_BIN_C
+#define BN_MP_REDUCE_C
+#define BN_MP_REDUCE_2K_C
+#define BN_MP_REDUCE_2K_SETUP_C
+#define BN_MP_REDUCE_IS_2K_C
+#define BN_MP_REDUCE_SETUP_C
+#define BN_MP_RSHD_C
+#define BN_MP_SET_C
+#define BN_MP_SET_INT_C
+#define BN_MP_SHRINK_C
+#define BN_MP_SIGNED_BIN_SIZE_C
+#define BN_MP_SQR_C
+#define BN_MP_SQRMOD_C
+#define BN_MP_SQRT_C
+#define BN_MP_SUB_C
+#define BN_MP_SUB_D_C
+#define BN_MP_SUBMOD_C
+#define BN_MP_TO_SIGNED_BIN_C
+#define BN_MP_TO_UNSIGNED_BIN_C
+#define BN_MP_TOOM_MUL_C
+#define BN_MP_TOOM_SQR_C
+#define BN_MP_TORADIX_C
+#define BN_MP_TORADIX_N_C
+#define BN_MP_UNSIGNED_BIN_SIZE_C
+#define BN_MP_XOR_C
+#define BN_MP_ZERO_C
+#define BN_PRIME_TAB_C
+#define BN_REVERSE_C
+#define BN_S_MP_ADD_C
+#define BN_S_MP_EXPTMOD_C
+#define BN_S_MP_MUL_DIGS_C
+#define BN_S_MP_MUL_HIGH_DIGS_C
+#define BN_S_MP_SQR_C
+#define BN_S_MP_SUB_C
+#define BNCORE_C
+#endif
+
+#if defined(BN_ERROR_C)
+ #define BN_MP_ERROR_TO_STRING_C
+#endif
+
+#if defined(BN_FAST_MP_INVMOD_C)
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ABS_C
+ #define BN_MP_SET_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_ADD_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_FAST_MP_MONTGOMERY_REDUCE_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_FAST_S_MP_MUL_DIGS_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_FAST_S_MP_SQR_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_2EXPT_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_ABS_C)
+ #define BN_MP_COPY_C
+#endif
+
+#if defined(BN_MP_ADD_C)
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_ADD_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_ADDMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_AND_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_CLAMP_C)
+#endif
+
+#if defined(BN_MP_CLEAR_C)
+#endif
+
+#if defined(BN_MP_CLEAR_MULTI_C)
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_CMP_C)
+ #define BN_MP_CMP_MAG_C
+#endif
+
+#if defined(BN_MP_CMP_D_C)
+#endif
+
+#if defined(BN_MP_CMP_MAG_C)
+#endif
+
+#if defined(BN_MP_CNT_LSB_C)
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_COPY_C)
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_COUNT_BITS_C)
+#endif
+
+#if defined(BN_MP_DIV_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_SET_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SUB_C
+ #define BN_MP_ADD_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_INIT_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DIV_2_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_DIV_2D_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_DIV_3_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DIV_D_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_COPY_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DR_IS_MODULUS_C)
+#endif
+
+#if defined(BN_MP_DR_REDUCE_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_DR_SETUP_C)
+#endif
+
+#if defined(BN_MP_EXCH_C)
+#endif
+
+#if defined(BN_MP_EXPT_D_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_SET_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MUL_C
+#endif
+
+#if defined(BN_MP_EXPTMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_INVMOD_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_ABS_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_DR_IS_MODULUS_C
+ #define BN_MP_REDUCE_IS_2K_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_EXPTMOD_FAST_C
+ #define BN_S_MP_EXPTMOD_C
+#endif
+
+#if defined(BN_MP_EXPTMOD_FAST_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MONTGOMERY_SETUP_C
+ #define BN_FAST_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_DR_SETUP_C
+ #define BN_MP_DR_REDUCE_C
+ #define BN_MP_REDUCE_2K_SETUP_C
+ #define BN_MP_REDUCE_2K_C
+ #define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+ #define BN_MP_MULMOD_C
+ #define BN_MP_SET_C
+ #define BN_MP_MOD_C
+ #define BN_MP_COPY_C
+ #define BN_MP_SQR_C
+ #define BN_MP_MUL_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_EXTEUCLID_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_SET_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SUB_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_FREAD_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_S_RMAP_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_CMP_D_C
+#endif
+
+#if defined(BN_MP_FWRITE_C)
+ #define BN_MP_RADIX_SIZE_C
+ #define BN_MP_TORADIX_C
+#endif
+
+#if defined(BN_MP_GCD_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ABS_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_GET_INT_C)
+#endif
+
+#if defined(BN_MP_GROW_C)
+#endif
+
+#if defined(BN_MP_INIT_C)
+#endif
+
+#if defined(BN_MP_INIT_COPY_C)
+ #define BN_MP_COPY_C
+#endif
+
+#if defined(BN_MP_INIT_MULTI_C)
+ #define BN_MP_ERR_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_INIT_SET_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+#endif
+
+#if defined(BN_MP_INIT_SET_INT_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_INT_C
+#endif
+
+#if defined(BN_MP_INIT_SIZE_C)
+ #define BN_MP_INIT_C
+#endif
+
+#if defined(BN_MP_INVMOD_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ISODD_C
+ #define BN_FAST_MP_INVMOD_C
+ #define BN_MP_INVMOD_SLOW_C
+#endif
+
+#if defined(BN_MP_INVMOD_SLOW_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_SET_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_IS_SQUARE_C)
+ #define BN_MP_MOD_D_C
+ #define BN_MP_INIT_SET_INT_C
+ #define BN_MP_MOD_C
+ #define BN_MP_GET_INT_C
+ #define BN_MP_SQRT_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_JACOBI_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_MOD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_KARATSUBA_MUL_C)
+ #define BN_MP_MUL_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_SUB_C
+ #define BN_MP_ADD_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_KARATSUBA_SQR_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_SQR_C
+ #define BN_MP_SUB_C
+ #define BN_S_MP_ADD_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_LCM_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_GCD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_DIV_C
+ #define BN_MP_MUL_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_LSHD_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_RSHD_C
+#endif
+
+#if defined(BN_MP_MOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_DIV_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_ADD_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_MOD_2D_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_COPY_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MOD_D_C)
+ #define BN_MP_DIV_D_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_CALC_NORMALIZATION_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_2EXPT_C
+ #define BN_MP_SET_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_REDUCE_C)
+ #define BN_FAST_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_SETUP_C)
+#endif
+
+#if defined(BN_MP_MUL_C)
+ #define BN_MP_TOOM_MUL_C
+ #define BN_MP_KARATSUBA_MUL_C
+ #define BN_FAST_S_MP_MUL_DIGS_C
+ #define BN_S_MP_MUL_C
+ #define BN_S_MP_MUL_DIGS_C
+#endif
+
+#if defined(BN_MP_MUL_2_C)
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_MUL_2D_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_GROW_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MUL_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MULMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_MUL_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_N_ROOT_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+ #define BN_MP_COPY_C
+ #define BN_MP_EXPT_D_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SUB_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_NEG_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_OR_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_FERMAT_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_INIT_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_CMP_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_IS_DIVISIBLE_C)
+ #define BN_MP_MOD_D_C
+#endif
+
+#if defined(BN_MP_PRIME_IS_PRIME_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_PRIME_IS_DIVISIBLE_C
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+ #define BN_MP_PRIME_MILLER_RABIN_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_MILLER_RABIN_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SQRMOD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_NEXT_PRIME_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_SET_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_MOD_D_C
+ #define BN_MP_INIT_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_PRIME_MILLER_RABIN_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_RABIN_MILLER_TRIALS_C)
+#endif
+
+#if defined(BN_MP_PRIME_RANDOM_EX_C)
+ #define BN_MP_READ_UNSIGNED_BIN_C
+ #define BN_MP_PRIME_IS_PRIME_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_D_C
+#endif
+
+#if defined(BN_MP_RADIX_SIZE_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_RADIX_SMAP_C)
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_RAND_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_LSHD_C
+#endif
+
+#if defined(BN_MP_READ_RADIX_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_S_RMAP_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_READ_SIGNED_BIN_C)
+ #define BN_MP_READ_UNSIGNED_BIN_C
+#endif
+
+#if defined(BN_MP_READ_UNSIGNED_BIN_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_REDUCE_C)
+ #define BN_MP_REDUCE_SETUP_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_C
+ #define BN_S_MP_MUL_HIGH_DIGS_C
+ #define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #define BN_MP_MOD_2D_C
+ #define BN_S_MP_MUL_DIGS_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_SET_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CMP_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_REDUCE_2K_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_REDUCE_2K_SETUP_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_2EXPT_C
+ #define BN_MP_CLEAR_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_REDUCE_IS_2K_C)
+ #define BN_MP_REDUCE_2K_C
+ #define BN_MP_COUNT_BITS_C
+#endif
+
+#if defined(BN_MP_REDUCE_SETUP_C)
+ #define BN_MP_2EXPT_C
+ #define BN_MP_DIV_C
+#endif
+
+#if defined(BN_MP_RSHD_C)
+ #define BN_MP_ZERO_C
+#endif
+
+#if defined(BN_MP_SET_C)
+ #define BN_MP_ZERO_C
+#endif
+
+#if defined(BN_MP_SET_INT_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_SHRINK_C)
+#endif
+
+#if defined(BN_MP_SIGNED_BIN_SIZE_C)
+ #define BN_MP_UNSIGNED_BIN_SIZE_C
+#endif
+
+#if defined(BN_MP_SQR_C)
+ #define BN_MP_TOOM_SQR_C
+ #define BN_MP_KARATSUBA_SQR_C
+ #define BN_FAST_S_MP_SQR_C
+ #define BN_S_MP_SQR_C
+#endif
+
+#if defined(BN_MP_SQRMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_SQRT_C)
+ #define BN_MP_N_ROOT_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_DIV_C
+ #define BN_MP_ADD_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_SUB_C)
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_SUB_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_SUBMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_TO_SIGNED_BIN_C)
+ #define BN_MP_TO_UNSIGNED_BIN_C
+#endif
+
+#if defined(BN_MP_TO_UNSIGNED_BIN_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_TOOM_MUL_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_TOOM_SQR_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_SQR_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_TORADIX_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_TORADIX_N_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_UNSIGNED_BIN_SIZE_C)
+ #define BN_MP_COUNT_BITS_C
+#endif
+
+#if defined(BN_MP_XOR_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_ZERO_C)
+#endif
+
+#if defined(BN_PRIME_TAB_C)
+#endif
+
+#if defined(BN_REVERSE_C)
+#endif
+
+#if defined(BN_S_MP_ADD_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_S_MP_EXPTMOD_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_REDUCE_SETUP_C
+ #define BN_MP_MOD_C
+ #define BN_MP_COPY_C
+ #define BN_MP_SQR_C
+ #define BN_MP_REDUCE_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SET_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_S_MP_MUL_DIGS_C)
+ #define BN_FAST_S_MP_MUL_DIGS_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_MUL_HIGH_DIGS_C)
+ #define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_SQR_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_SUB_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BNCORE_C)
+#endif
+
+#ifdef LTM3
+#define LTM_LAST
+#endif
+#include <tommath_superclass.h>
+#include <tommath_class.h>
+#else
+#define LTM_LAST
+#endif
diff --git a/tommath_superclass.h b/tommath_superclass.h
new file mode 100644
index 0000000..b50ecb0
--- /dev/null
+++ b/tommath_superclass.h
@@ -0,0 +1,72 @@
+/* super class file for PK algos */
+
+/* default ... include all MPI */
+#define LTM_ALL
+
+/* RSA only (does not support DH/DSA/ECC) */
+// #define SC_RSA_1
+
+/* For reference.... On an Athlon64 optimizing for speed...
+
+ LTM's mpi.o with all functions [striped] is 142KiB in size.
+
+*/
+
+/* Works for RSA only, mpi.o is 68KiB */
+#ifdef SC_RSA_1
+ #define BN_MP_SHRINK_C
+ #define BN_MP_LCM_C
+ #define BN_MP_PRIME_RANDOM_EX_C
+ #define BN_MP_INVMOD_C
+ #define BN_MP_GCD_C
+ #define BN_MP_MOD_C
+ #define BN_MP_MULMOD_C
+ #define BN_MP_ADDMOD_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_SET_INT_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_UNSIGNED_BIN_SIZE_C
+ #define BN_MP_TO_UNSIGNED_BIN_C
+ #define BN_MP_MOD_D_C
+ #define BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+ #define BN_REVERSE_C
+ #define BN_PRIME_TAB_C
+
+ /* other modifiers */
+ #define BN_MP_DIV_SMALL /* Slower division, not critical */
+
+ /* here we are on the last pass so we turn things off. The functions classes are still there
+ * but we remove them specifically from the build. This also invokes tweaks in functions
+ * like removing support for even moduli, etc...
+ */
+#ifdef LTM_LAST
+ #undef BN_MP_TOOM_MUL_C
+ #undef BN_MP_TOOM_SQR_C
+ #undef BN_MP_KARATSUBA_MUL_C
+ #undef BN_MP_KARATSUBA_SQR_C
+ #undef BN_MP_REDUCE_C
+ #undef BN_MP_REDUCE_SETUP_C
+ #undef BN_MP_DR_IS_MODULUS_C
+ #undef BN_MP_DR_SETUP_C
+ #undef BN_MP_DR_REDUCE_C
+ #undef BN_MP_REDUCE_IS_2K_C
+ #undef BN_MP_REDUCE_2K_SETUP_C
+ #undef BN_MP_REDUCE_2K_C
+ #undef BN_S_MP_EXPTMOD_C
+ #undef BN_MP_DIV_3_C
+ #undef BN_S_MP_MUL_HIGH_DIGS_C
+ #undef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #undef BN_FAST_MP_INVMOD_C
+
+ /* To safely undefine these you have to make sure your RSA key won't exceed the Comba threshold
+ * which is roughly 255 digits [7140 bits for 32-bit machines, 15300 bits for 64-bit machines]
+ * which means roughly speaking you can handle upto 2536-bit RSA keys with these defined without
+ * trouble.
+ */
+ #undef BN_S_MP_MUL_DIGS_C
+ #undef BN_S_MP_SQR_C
+ #undef BN_MP_MONTGOMERY_REDUCE_C
+#endif
+
+#endif