libtommath/bn_mp_karatsuba_sqr.c

#include <tommath_private.h>
#ifdef BN_MP_KARATSUBA_SQR_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, tstdenis82@gmail.com, http://libtom.org
 */

/* Karatsuba squaring, computes b = a*a using three
 * half size squarings
 *
 * See comments of karatsuba_mul for details.  It
 * is essentially the same algorithm but merely
 * tuned to perform recursive squarings.
 */
int mp_karatsuba_sqr(mp_int *a, mp_int *b)
{
  mp_int  x0, x1, t1, t2, x0x0, x1x1;
  int     B, err;

  err = MP_MEM;

  /* min # of digits */
  B = a->used;

  /* now divide in two */
  B = B >> 1;

  /* init copy all the temps */
  if (mp_init_size(&x0, B) != MP_OKAY)
    goto ERR;
  if (mp_init_size(&x1, a->used - B) != MP_OKAY)
    goto X0;

  /* init temps */
  if (mp_init_size(&t1, a->used * 2) != MP_OKAY)
    goto X1;
  if (mp_init_size(&t2, a->used * 2) != MP_OKAY)
    goto T1;
  if (mp_init_size(&x0x0, B * 2) != MP_OKAY)
    goto T2;
  if (mp_init_size(&x1x1, (a->used - B) * 2) != MP_OKAY)
    goto X0X0;

  {
    int x;
    mp_digit *dst, *src;

    src = a->dp;

    /* now shift the digits */
    dst = x0.dp;
    for (x = 0; x < B; x++) {
      *dst++ = *src++;
    }

    dst = x1.dp;
    for (x = B; x < a->used; x++) {
      *dst++ = *src++;
    }
  }

  x0.used = B;
  x1.used = a->used - B;

  mp_clamp(&x0);

  /* now calc the products x0*x0 and x1*x1 */
  if (mp_sqr(&x0, &x0x0) != MP_OKAY)
    goto X1X1;           /* x0x0 = x0*x0 */
  if (mp_sqr(&x1, &x1x1) != MP_OKAY)
    goto X1X1;           /* x1x1 = x1*x1 */

  /* now calc (x1+x0)**2 */
  if (s_mp_add(&x1, &x0, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = x1 - x0 */
  if (mp_sqr(&t1, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = (x1 - x0) * (x1 - x0) */

  /* add x0y0 */
  if (s_mp_add(&x0x0, &x1x1, &t2) != MP_OKAY)
    goto X1X1;           /* t2 = x0x0 + x1x1 */
  if (s_mp_sub(&t1, &t2, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */

  /* shift by B */
  if (mp_lshd(&t1, B) != MP_OKAY)
    goto X1X1;           /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
  if (mp_lshd(&x1x1, B * 2) != MP_OKAY)
    goto X1X1;           /* x1x1 = x1x1 << 2*B */

  if (mp_add(&x0x0, &t1, &t1) != MP_OKAY)
    goto X1X1;           /* t1 = x0x0 + t1 */
  if (mp_add(&t1, &x1x1, b) != MP_OKAY)
    goto X1X1;           /* t1 = x0x0 + t1 + x1x1 */

  err = MP_OKAY;

X1X1:
  mp_clear(&x1x1);
X0X0:
  mp_clear(&x0x0);
T2:
  mp_clear(&t2);
T1:
  mp_clear(&t1);
X1:
  mp_clear(&x1);
X0:
  mp_clear(&x0);
ERR:
  return err;
}
#endif

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