kc3-lang/libtommath/s_mp_karatsuba_mul.c

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• Hash : 7a68f128
  Author :
  Date : 2019-10-19T16:24:39
  

  Execute move.sh - Rename files from bn_* to match the function names. * git blame <renamed-file> is not affected * git log --follow <renamed-file> can be used to show log across renames

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• s_mp_karatsuba_mul.c

• #include "tommath_private.h"
  #ifdef S_MP_KARATSUBA_MUL_C
  /* LibTomMath, multiple-precision integer library -- Tom St Denis */
  /* SPDX-License-Identifier: Unlicense */
  
  /* c = |a| * |b| using Karatsuba Multiplication using
   * three half size multiplications
   *
   * Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and
   * let n represent half of the number of digits in
   * the min(a,b)
   *
   * a = a1 * B**n + a0
   * b = b1 * B**n + b0
   *
   * Then, a * b =>
     a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
   *
   * Note that a1b1 and a0b0 are used twice and only need to be
   * computed once.  So in total three half size (half # of
   * digit) multiplications are performed, a0b0, a1b1 and
   * (a1+b1)(a0+b0)
   *
   * Note that a multiplication of half the digits requires
   * 1/4th the number of single precision multiplications so in
   * total after one call 25% of the single precision multiplications
   * are saved.  Note also that the call to mp_mul can end up back
   * in this function if the a0, a1, b0, or b1 are above the threshold.
   * This is known as divide-and-conquer and leads to the famous
   * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
   * the standard O(N**2) that the baseline/comba methods use.
   * Generally though the overhead of this method doesn't pay off
   * until a certain size (N ~ 80) is reached.
   */
  mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
  {
     mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
     int     B;
     mp_err  err = MP_MEM; /* default the return code to an error */
  
     /* min # of digits */
     B = MP_MIN(a->used, b->used);
  
     /* now divide in two */
     B = B >> 1;
  
     /* init copy all the temps */
     if (mp_init_size(&x0, B) != MP_OKAY) {
        goto LBL_ERR;
     }
     if (mp_init_size(&x1, a->used - B) != MP_OKAY) {
        goto X0;
     }
     if (mp_init_size(&y0, B) != MP_OKAY) {
        goto X1;
     }
     if (mp_init_size(&y1, b->used - B) != MP_OKAY) {
        goto Y0;
     }
  
     /* init temps */
     if (mp_init_size(&t1, B * 2) != MP_OKAY) {
        goto Y1;
     }
     if (mp_init_size(&x0y0, B * 2) != MP_OKAY) {
        goto T1;
     }
     if (mp_init_size(&x1y1, B * 2) != MP_OKAY) {
        goto X0Y0;
     }
  
     /* now shift the digits */
     x0.used = y0.used = B;
     x1.used = a->used - B;
     y1.used = b->used - B;
  
     {
        int x;
        mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
  
        /* we copy the digits directly instead of using higher level functions
         * since we also need to shift the digits
         */
        tmpa = a->dp;
        tmpb = b->dp;
  
        tmpx = x0.dp;
        tmpy = y0.dp;
        for (x = 0; x < B; x++) {
           *tmpx++ = *tmpa++;
           *tmpy++ = *tmpb++;
        }
  
        tmpx = x1.dp;
        for (x = B; x < a->used; x++) {
           *tmpx++ = *tmpa++;
        }
  
        tmpy = y1.dp;
        for (x = B; x < b->used; x++) {
           *tmpy++ = *tmpb++;
        }
     }
  
     /* only need to clamp the lower words since by definition the
      * upper words x1/y1 must have a known number of digits
      */
     mp_clamp(&x0);
     mp_clamp(&y0);
  
     /* now calc the products x0y0 and x1y1 */
     /* after this x0 is no longer required, free temp [x0==t2]! */
     if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) {
        goto X1Y1;          /* x0y0 = x0*y0 */
     }
     if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) {
        goto X1Y1;          /* x1y1 = x1*y1 */
     }
  
     /* now calc x1+x0 and y1+y0 */
     if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) {
        goto X1Y1;          /* t1 = x1 - x0 */
     }
     if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) {
        goto X1Y1;          /* t2 = y1 - y0 */
     }
     if (mp_mul(&t1, &x0, &t1) != MP_OKAY) {
        goto X1Y1;          /* t1 = (x1 + x0) * (y1 + y0) */
     }
  
     /* add x0y0 */
     if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
        goto X1Y1;          /* t2 = x0y0 + x1y1 */
     }
     if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) {
        goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
     }
  
     /* shift by B */
     if (mp_lshd(&t1, B) != MP_OKAY) {
        goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
     }
     if (mp_lshd(&x1y1, B * 2) != MP_OKAY) {
        goto X1Y1;          /* x1y1 = x1y1 << 2*B */
     }
  
     if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) {
        goto X1Y1;          /* t1 = x0y0 + t1 */
     }
     if (mp_add(&t1, &x1y1, c) != MP_OKAY) {
        goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */
     }
  
     /* Algorithm succeeded set the return code to MP_OKAY */
     err = MP_OKAY;
  
  X1Y1:
     mp_clear(&x1y1);
  X0Y0:
     mp_clear(&x0y0);
  T1:
     mp_clear(&t1);
  Y1:
     mp_clear(&y1);
  Y0:
     mp_clear(&y0);
  X1:
     mp_clear(&x1);
  X0:
     mp_clear(&x0);
  LBL_ERR:
     return err;
  }
  #endif
  

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