/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is 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://libtommath.iahu.ca
*/
#ifndef BN_H_
#define BN_H_
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <ctype.h>
#include <limits.h>
/* some default configurations.
*
* A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
* A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
*
* At the very least a mp_digit must be able to hold 7 bits
* [any size beyond that is ok provided it overflow the data type]
*/
#ifdef MP_8BIT
typedef unsigned char mp_digit;
typedef unsigned short mp_word;
#elif defined(MP_16BIT)
typedef unsigned short mp_digit;
typedef unsigned long mp_word;
#else
typedef unsigned long mp_digit;
typedef unsigned long long mp_word;
#define DIGIT_BIT 28U
#endif
#ifndef DIGIT_BIT
#define DIGIT_BIT ((CHAR_BIT * sizeof(mp_digit) - 1)) /* bits per digit */
#endif
#define MP_DIGIT_BIT DIGIT_BIT
#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
#define MP_DIGIT_MAX MP_MASK
/* equalities */
#define MP_LT -1 /* less than */
#define MP_EQ 0 /* equal to */
#define MP_GT 1 /* greater than */
#define MP_ZPOS 0 /* positive integer */
#define MP_NEG 1 /* negative */
#define MP_OKAY 0 /* ok result */
#define MP_MEM -2 /* out of mem */
#define MP_VAL -3 /* invalid input */
#define MP_RANGE MP_VAL
#define KARATSUBA_MUL_CUTOFF 80 /* Min. number of digits before Karatsuba multiplication is used. */
#define KARATSUBA_SQR_CUTOFF 80 /* Min. number of digits before Karatsuba squaring is used. */
typedef struct {
int used, alloc, sign;
mp_digit *dp;
} mp_int;
#define USED(m) ((m)->used)
#define DIGIT(m,k) ((m)->dp[k])
#define SIGN(m) ((m)->sign)
/* ---> init and deinit bignum functions <--- */
/* init a bignum */
int mp_init(mp_int *a);
/* free a bignum */
void mp_clear(mp_int *a);
/* exchange two ints */
void mp_exch(mp_int *a, mp_int *b);
/* shrink ram required for a bignum */
int mp_shrink(mp_int *a);
/* ---> Basic Manipulations <--- */
#define mp_iszero(a) (((a)->used == 0) ? 1 : 0)
#define mp_iseven(a) (((a)->used == 0 || (((a)->dp[0] & 1) == 0)) ? 1 : 0)
#define mp_isodd(a) (((a)->used > 0 || (((a)->dp[0] & 1) == 1)) ? 1 : 0)
/* set to zero */
void mp_zero(mp_int *a);
/* set to a digit */
void mp_set(mp_int *a, mp_digit b);
/* set a 32-bit const */
int mp_set_int(mp_int *a, unsigned long b);
/* init to a given number of digits */
int mp_init_size(mp_int *a, int size);
/* copy, b = a */
int mp_copy(mp_int *a, mp_int *b);
/* inits and copies, a = b */
int mp_init_copy(mp_int *a, mp_int *b);
/* ---> digit manipulation <--- */
/* right shift by "b" digits */
void mp_rshd(mp_int *a, int b);
/* left shift by "b" digits */
int mp_lshd(mp_int *a, int b);
/* c = a / 2^b */
int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
/* b = a/2 */
int mp_div_2(mp_int *a, mp_int *b);
/* c = a * 2^b */
int mp_mul_2d(mp_int *a, int b, mp_int *c);
/* b = a*2 */
int mp_mul_2(mp_int *a, mp_int *b);
/* c = a mod 2^d */
int mp_mod_2d(mp_int *a, int b, mp_int *c);
/* ---> Basic arithmetic <--- */
/* b = -a */
int mp_neg(mp_int *a, mp_int *b);
/* b = |a| */
int mp_abs(mp_int *a, mp_int *b);
/* compare a to b */
int mp_cmp(mp_int *a, mp_int *b);
/* compare |a| to |b| */
int mp_cmp_mag(mp_int *a, mp_int *b);
/* c = a + b */
int mp_add(mp_int *a, mp_int *b, mp_int *c);
/* c = a - b */
int mp_sub(mp_int *a, mp_int *b, mp_int *c);
/* c = a * b */
int mp_mul(mp_int *a, mp_int *b, mp_int *c);
/* b = a^2 */
int mp_sqr(mp_int *a, mp_int *b);
/* a/b => cb + d == a */
int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* c = a mod b, 0 <= c < b */
int mp_mod(mp_int *a, mp_int *b, mp_int *c);
/* ---> single digit functions <--- */
/* compare against a single digit */
int mp_cmp_d(mp_int *a, mp_digit b);
/* c = a + b */
int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
/* c = a - b */
int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
/* c = a * b */
int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
/* a/b => cb + d == a */
int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
/* c = a^b */
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
/* c = a mod b, 0 <= c < b */
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
/* ---> number theory <--- */
/* d = a + b (mod c) */
int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* d = a - b (mod c) */
int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* d = a * b (mod c) */
int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* c = a * a (mod b) */
int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
/* c = 1/a (mod b) */
int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
/* c = (a, b) */
int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
/* c = [a, b] or (a*b)/(a, b) */
int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
/* used to setup the Barrett reduction for a given modulus b */
int mp_reduce_setup(mp_int *a, mp_int *b);
/* Barrett Reduction, computes a (mod b) with a precomputed value c
*
* Assumes that 0 < a <= b^2, note if 0 > a > -(b^2) then you can merely
* compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
*/
int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
/* d = a^b (mod c) */
int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
/* ---> radix conversion <--- */
int mp_count_bits(mp_int *a);
int mp_unsigned_bin_size(mp_int *a);
int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
int mp_signed_bin_size(mp_int *a);
int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
int mp_to_signed_bin(mp_int *a, unsigned char *b);
int mp_read_radix(mp_int *a, unsigned char *str, int radix);
int mp_toradix(mp_int *a, unsigned char *str, int radix);
int mp_radix_size(mp_int *a, int radix);
#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
#define mp_raw_size(mp) mp_signed_bin_size(mp)
#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
#define mp_tohex(M, S) mp_toradix((M), (S), 16)
#endif
