kc3-lang/libtommath/s_mp_montgomery_reduce_fast.c

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• Hash : 795cd201
  Author :
  Date : 2019-10-29T21:48:50
  

  simplifications: add s_mp_zero_(digs|buf) and s_mp_copy_digs Originally I made those as macros. However we have many other small functions like mp_clamp, mp_exch which are also not implemented as macros right now. If we would use c99, I would implement them as private static inline functions. And mp_exch would be a public static inline function. But since we are bound to c89, we simply use normal functions. To achieve optimal performance one should either use link time optimization or amalgamation.

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• s_mp_montgomery_reduce_fast.c

• #include "tommath_private.h"
  #ifdef S_MP_MONTGOMERY_REDUCE_FAST_C
  /* LibTomMath, multiple-precision integer library -- Tom St Denis */
  /* SPDX-License-Identifier: Unlicense */
  
  /* computes xR**-1 == x (mod N) via Montgomery Reduction
   *
   * This is an optimized implementation of montgomery_reduce
   * which uses the comba method to quickly calculate the columns of the
   * reduction.
   *
   * Based on Algorithm 14.32 on pp.601 of HAC.
  */
  mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho)
  {
     int     ix, oldused;
     mp_err  err;
     mp_word W[MP_WARRAY];
  
     if (x->used > MP_WARRAY) {
        return MP_VAL;
     }
  
     /* get old used count */
     oldused = x->used;
  
     /* grow a as required */
     if (x->alloc < (n->used + 1)) {
        if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) {
           return err;
        }
     }
  
     /* first we have to get the digits of the input into
      * an array of double precision words W[...]
      */
  
     /* copy the digits of a into W[0..a->used-1] */
     for (ix = 0; ix < x->used; ix++) {
        W[ix] = x->dp[ix];
     }
  
     /* zero the high words of W[a->used..m->used*2] */
     if (ix < ((n->used * 2) + 1)) {
        s_mp_zero_buf(W + x->used, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix));
     }
  
     /* now we proceed to zero successive digits
      * from the least significant upwards
      */
     for (ix = 0; ix < n->used; ix++) {
        int iy;
        mp_digit mu;
  
        /* mu = ai * m' mod b
         *
         * We avoid a double precision multiplication (which isn't required)
         * by casting the value down to a mp_digit.  Note this requires
         * that W[ix-1] have  the carry cleared (see after the inner loop)
         */
        mu = ((W[ix] & MP_MASK) * rho) & MP_MASK;
  
        /* a = a + mu * m * b**i
         *
         * This is computed in place and on the fly.  The multiplication
         * by b**i is handled by offseting which columns the results
         * are added to.
         *
         * Note the comba method normally doesn't handle carries in the
         * inner loop In this case we fix the carry from the previous
         * column since the Montgomery reduction requires digits of the
         * result (so far) [see above] to work.  This is
         * handled by fixing up one carry after the inner loop.  The
         * carry fixups are done in order so after these loops the
         * first m->used words of W[] have the carries fixed
         */
        for (iy = 0; iy < n->used; iy++) {
           W[ix + iy] += (mp_word)mu * (mp_word)n->dp[iy];
        }
  
        /* now fix carry for next digit, W[ix+1] */
        W[ix + 1] += W[ix] >> (mp_word)MP_DIGIT_BIT;
     }
  
     /* now we have to propagate the carries and
      * shift the words downward [all those least
      * significant digits we zeroed].
      */
  
     for (; ix < (n->used * 2); ix++) {
        W[ix + 1] += W[ix] >> (mp_word)MP_DIGIT_BIT;
     }
  
     /* copy out, A = A/b**n
      *
      * The result is A/b**n but instead of converting from an
      * array of mp_word to mp_digit than calling mp_rshd
      * we just copy them in the right order
      */
  
     for (ix = 0; ix < (n->used + 1); ix++) {
        x->dp[ix] = W[n->used + ix] & (mp_word)MP_MASK;
     }
  
     /* set the max used */
     x->used = n->used + 1;
  
     /* zero oldused digits, if the input a was larger than
      * m->used+1 we'll have to clear the digits
      */
     s_mp_zero_digs(x->dp + x->used, oldused - x->used);
  
     mp_clamp(x);
  
     /* if A >= m then A = A - m */
     if (mp_cmp_mag(x, n) != MP_LT) {
        return s_mp_sub(x, n, x);
     }
     return MP_OKAY;
  }
  #endif
  

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