tommath/bn_mp_sqrt.c

#include <tommath_private.h>
#ifdef BN_MP_SQRT_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
 */

/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
{
  int res;
  mp_int t1, t2;

  /* must be positive */
  if (arg->sign == MP_NEG) {
    return MP_VAL;
  }

  /* easy out */
  if (mp_iszero(arg) == MP_YES) {
    mp_zero(ret);
    return MP_OKAY;
  }

  if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
    return res;
  }

  if ((res = mp_init(&t2)) != MP_OKAY) {
    goto E2;
  }

  /* First approx. (not very bad for large arg) */
  mp_rshd(&t1, t1.used/2);

  /* t1 > 0  */
  if ((res = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
    goto E1;
  }
  if ((res = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
    goto E1;
  }
  if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) {
    goto E1;
  }
  /* And now t1 > sqrt(arg) */
  do {
    if ((res = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
      goto E1;
    }
    if ((res = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
      goto E1;
    }
    if ((res = mp_div_2(&t1, &t1)) != MP_OKAY) {
      goto E1;
    }
    /* t1 >= sqrt(arg) >= t2 at this point */
  } while (mp_cmp_mag(&t1, &t2) == MP_GT);

  mp_exch(&t1, ret);

E1: mp_clear(&t2);
E2: mp_clear(&t1);
  return res;
}

#endif

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