kc3-lang/libtommath/mp_root_u32.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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• mp_root_u32.c

• #include "tommath_private.h"
  #ifdef MP_ROOT_U32_C
  /* LibTomMath, multiple-precision integer library -- Tom St Denis */
  /* SPDX-License-Identifier: Unlicense */
  
  /* find the n'th root of an integer
   *
   * Result found such that (c)**b <= a and (c+1)**b > a
   *
   * This algorithm uses Newton's approximation
   * x[i+1] = x[i] - f(x[i])/f'(x[i])
   * which will find the root in log(N) time where
   * each step involves a fair bit.
   */
  mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c)
  {
     mp_int t1, t2, t3, a_;
     mp_ord cmp;
     int    ilog2;
     mp_err err;
  
     /* input must be positive if b is even */
     if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
        return MP_VAL;
     }
  
     if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) {
        return err;
     }
  
     /* if a is negative fudge the sign but keep track */
     a_ = *a;
     a_.sign = MP_ZPOS;
  
     /* Compute seed: 2^(log_2(n)/b + 2)*/
     ilog2 = mp_count_bits(a);
  
     /*
       If "b" is larger than INT_MAX it is also larger than
       log_2(n) because the bit-length of the "n" is measured
       with an int and hence the root is always < 2 (two).
     */
     if (b > (uint32_t)(INT_MAX/2)) {
        mp_set(c, 1uL);
        c->sign = a->sign;
        err = MP_OKAY;
        goto LBL_ERR;
     }
  
     /* "b" is smaller than INT_MAX, we can cast safely */
     if (ilog2 < (int)b) {
        mp_set(c, 1uL);
        c->sign = a->sign;
        err = MP_OKAY;
        goto LBL_ERR;
     }
     ilog2 =  ilog2 / ((int)b);
     if (ilog2 == 0) {
        mp_set(c, 1uL);
        c->sign = a->sign;
        err = MP_OKAY;
        goto LBL_ERR;
     }
     /* Start value must be larger than root */
     ilog2 += 2;
     if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY)                    goto LBL_ERR;
     do {
        /* t1 = t2 */
        if ((err = mp_copy(&t2, &t1)) != MP_OKAY)                   goto LBL_ERR;
  
        /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
  
        /* t3 = t1**(b-1) */
        if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY)       goto LBL_ERR;
  
        /* numerator */
        /* t2 = t1**b */
        if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY)               goto LBL_ERR;
  
        /* t2 = t1**b - a */
        if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY)               goto LBL_ERR;
  
        /* denominator */
        /* t3 = t1**(b-1) * b  */
        if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY)               goto LBL_ERR;
  
        /* t3 = (t1**b - a)/(b * t1**(b-1)) */
        if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY)         goto LBL_ERR;
  
        if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY)               goto LBL_ERR;
  
        /*
            Number of rounds is at most log_2(root). If it is more it
            got stuck, so break out of the loop and do the rest manually.
         */
        if (ilog2-- == 0) {
           break;
        }
     }  while (mp_cmp(&t1, &t2) != MP_EQ);
  
     /* result can be off by a few so check */
     /* Loop beneath can overshoot by one if found root is smaller than actual root */
     for (;;) {
        if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY)            goto LBL_ERR;
        cmp = mp_cmp(&t2, &a_);
        if (cmp == MP_EQ) {
           err = MP_OKAY;
           goto LBL_ERR;
        }
        if (cmp == MP_LT) {
           if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY)          goto LBL_ERR;
        } else {
           break;
        }
     }
     /* correct overshoot from above or from recurrence */
     for (;;) {
        if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY)            goto LBL_ERR;
        if (mp_cmp(&t2, &a_) == MP_GT) {
           if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY)          goto LBL_ERR;
        } else {
           break;
        }
     }
  
     /* set the result */
     mp_exch(&t1, c);
  
     /* set the sign of the result */
     c->sign = a->sign;
  
     err = MP_OKAY;
  
  LBL_ERR:
     mp_clear_multi(&t1, &t2, &t3, NULL);
     return err;
  }
  
  #endif
  

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