* The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
 * SPDX-License-Identifier: Unlicense
 */

#ifndef NO_FLOATING_POINT
#include <math.h>
#endif

/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(const mp_int *arg, mp_int *ret)
{
   int res;
   mp_int t1, t2;
   int i, j, k;
#ifndef NO_FLOATING_POINT
   volatile double d;
   mp_digit dig;
#endif

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

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

   i = (arg->used / 2) - 1;
   j = 2 * i;
   if ((res = mp_init_size(&t1, i+2)) != MP_OKAY) {
   if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
      return res;
   }

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

   for (k = 0; k < i; ++k) {
      t1.dp[k] = (mp_digit) 0;
   }

   /* First approx. (not very bad for large arg) */
#ifndef NO_FLOATING_POINT

   /* Estimate the square root using the hardware floating point unit. */

   d = 0.0;
   for (k = arg->used-1; k >= j; --k) {
      d = ldexp(d, DIGIT_BIT) + (double)(arg->dp[k]);
   }

   /*
    * At this point, d is the nearest floating point number to the most
    * significant 1 or 2 mp_digits of arg. Extract its square root.
    */

   d = sqrt(d);

   /* dig is the most significant mp_digit of the square root */

   dig = (mp_digit) ldexp(d, -DIGIT_BIT);

   /*
    * If the most significant digit is nonzero, find the next digit down
    * by subtracting DIGIT_BIT times thie most significant digit.
    * Subtract one from the result so that our initial estimate is always
    * low.
    */

   if (dig) {
      t1.used = i+2;
   mp_rshd(&t1, t1.used/2);
      d -= ldexp((double) dig, DIGIT_BIT);
      if (d >= 1.0) {
         t1.dp[i+1] = dig;
         t1.dp[i] = ((mp_digit) d) - 1;
      } else {
         t1.dp[i+1] = dig-1;
         t1.dp[i] = MP_DIGIT_MAX;
      }
   } else {
      t1.used = i+1;
      t1.dp[i] = ((mp_digit) d) - 1;
   }

#else

   /* Estimate the square root as having 1 in the most significant place. */

   t1.used = i + 2;
   t1.dp[i+1] = (mp_digit) 1;
   t1.dp[i] = (mp_digit) 0;

#endif

   /* 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;