#include "tommath_private.h"

#ifdef BN_S_MP_INVMOD_FAST_C

/* LibTomMath, multiple-precision integer library -- Tom St Denis */

/* SPDX-License-Identifier: Unlicense */

/* computes the modular inverse via binary extended euclidean algorithm,

 * that is c = 1/a mod b

 *

 * Based on slow invmod except this is optimized for the case where b is

 * odd as per HAC Note 14.64 on pp. 610

 */

mp_err s_mp_invmod_fast(const mp_int *a, const mp_int *b, mp_int *c)

{

   mp_int  x, y, u, v, B, D;

   mp_sign neg;

   mp_err  err;

   /* 2. [modified] b must be odd   */

   if (MP_IS_EVEN(b)) {

      return MP_VAL;

   }

   /* init all our temps */

   if ((err = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {

      return err;

   }

   /* x == modulus, y == value to invert */

   if ((err = mp_copy(b, &x)) != MP_OKAY)                         goto LBL_ERR;

   /* we need y = |a| */

   if ((err = mp_mod(a, b, &y)) != MP_OKAY)                       goto LBL_ERR;

   /* if one of x,y is zero return an error! */

   if (MP_IS_ZERO(&x) || MP_IS_ZERO(&y)) {

      err = MP_VAL;

      goto LBL_ERR;

   }

   /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */

   if ((err = mp_copy(&x, &u)) != MP_OKAY)                        goto LBL_ERR;

   if ((err = mp_copy(&y, &v)) != MP_OKAY)                        goto LBL_ERR;

   mp_set(&D, 1uL);

top:

   /* 4.  while u is even do */

   while (MP_IS_EVEN(&u)) {

      /* 4.1 u = u/2 */

      if ((err = mp_div_2(&u, &u)) != MP_OKAY)                    goto LBL_ERR;

      /* 4.2 if B is odd then */

      if (MP_IS_ODD(&B)) {

         if ((err = mp_sub(&B, &x, &B)) != MP_OKAY)               goto LBL_ERR;

      }

      /* B = B/2 */

      if ((err = mp_div_2(&B, &B)) != MP_OKAY)                    goto LBL_ERR;

   }

   /* 5.  while v is even do */

   while (MP_IS_EVEN(&v)) {

      /* 5.1 v = v/2 */

      if ((err = mp_div_2(&v, &v)) != MP_OKAY)                    goto LBL_ERR;

      /* 5.2 if D is odd then */

      if (MP_IS_ODD(&D)) {

         /* D = (D-x)/2 */

         if ((err = mp_sub(&D, &x, &D)) != MP_OKAY)               goto LBL_ERR;

      }

      /* D = D/2 */

      if ((err = mp_div_2(&D, &D)) != MP_OKAY)                    goto LBL_ERR;

   }

   /* 6.  if u >= v then */

   if (mp_cmp(&u, &v) != MP_LT) {

      /* u = u - v, B = B - D */

      if ((err = mp_sub(&u, &v, &u)) != MP_OKAY)                  goto LBL_ERR;

      if ((err = mp_sub(&B, &D, &B)) != MP_OKAY)                  goto LBL_ERR;

   } else {

      /* v - v - u, D = D - B */

      if ((err = mp_sub(&v, &u, &v)) != MP_OKAY)                  goto LBL_ERR;

      if ((err = mp_sub(&D, &B, &D)) != MP_OKAY)                  goto LBL_ERR;

   }

   /* if not zero goto step 4 */

   if (!MP_IS_ZERO(&u)) {

      goto top;

   }

   /* now a = C, b = D, gcd == g*v */

   /* if v != 1 then there is no inverse */

   if (mp_cmp_d(&v, 1uL) != MP_EQ) {

      err = MP_VAL;

      goto LBL_ERR;

   }

   /* b is now the inverse */

   neg = a->sign;

   while (D.sign == MP_NEG) {

      if ((err = mp_add(&D, b, &D)) != MP_OKAY)                   goto LBL_ERR;

   }

   /* too big */

   while (mp_cmp_mag(&D, b) != MP_LT) {

      if ((err = mp_sub(&D, b, &D)) != MP_OKAY)                   goto LBL_ERR;

   }

   mp_exch(&D, c);

   c->sign = neg;

   err = MP_OKAY;

LBL_ERR:

   mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL);

   return err;

}

#endif