kc3-lang/libtommath/bn_mp_n_root_ex.c

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• Hash : 4534056c
  Author :
  Date : 2019-05-13T00:22:18
  

  use enums mp_err, mp_ord, mp_bool, mp_sign * MP_USE_ENUMS enables enums * Wc++-compat catches some implicit conversions if MP_USE_ENUMS is defined * 100% backwards compatible API/ABI if MP_USE_ENUMS is not defined

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• bn_mp_n_root_ex.c

• #include "tommath_private.h"
  #ifdef BN_MP_N_ROOT_EX_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_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
  {
     mp_int t1, t2, t3, a_;
     int    cmp;
     int    ilog2;
     mp_err res;
  
     /* input must be positive if b is even */
     if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
        return MP_VAL;
     }
  
     if ((res = mp_init(&t1)) != MP_OKAY) {
        return res;
     }
  
     if ((res = mp_init(&t2)) != MP_OKAY) {
        goto LBL_T1;
     }
  
     if ((res = mp_init(&t3)) != MP_OKAY) {
        goto LBL_T2;
     }
  
     /* 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);
  
     /*
        GCC and clang do not understand the sizeof tests and complain,
        icc (the Intel compiler) seems to understand, at least it doesn't complain.
        2 of 3 say these macros are necessary, so there they are.
     */
  #if ( !(defined MP_8BIT) && !(defined MP_16BIT) )
     /*
         The type of mp_digit might be larger than an int.
         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 (sizeof(mp_digit) >= sizeof(int)) {
        if (b > (mp_digit)(INT_MAX/2)) {
           mp_set(c, 1uL);
           c->sign = a->sign;
           res = MP_OKAY;
           goto LBL_T3;
        }
     }
  #endif
     /* "b" is smaller than INT_MAX, we can cast safely */
     if (ilog2 < (int)b) {
        mp_set(c, 1uL);
        c->sign = a->sign;
        res = MP_OKAY;
        goto LBL_T3;
     }
     ilog2 =  ilog2 / ((int)b);
     if (ilog2 == 0) {
        mp_set(c, 1uL);
        c->sign = a->sign;
        res = MP_OKAY;
        goto LBL_T3;
     }
     /* Start value must be larger than root */
     ilog2 += 2;
     if ((res = mp_2expt(&t2,ilog2)) != MP_OKAY) {
        goto LBL_T3;
     }
     do {
        /* t1 = t2 */
        if ((res = mp_copy(&t2, &t1)) != MP_OKAY) {
           goto LBL_T3;
        }
  
        /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
  
        /* t3 = t1**(b-1) */
        if ((res = mp_expt_d_ex(&t1, b - 1u, &t3, fast)) != MP_OKAY) {
           goto LBL_T3;
        }
        /* numerator */
        /* t2 = t1**b */
        if ((res = mp_mul(&t3, &t1, &t2)) != MP_OKAY) {
           goto LBL_T3;
        }
  
        /* t2 = t1**b - a */
        if ((res = mp_sub(&t2, &a_, &t2)) != MP_OKAY) {
           goto LBL_T3;
        }
  
        /* denominator */
        /* t3 = t1**(b-1) * b  */
        if ((res = mp_mul_d(&t3, b, &t3)) != MP_OKAY) {
           goto LBL_T3;
        }
  
        /* t3 = (t1**b - a)/(b * t1**(b-1)) */
        if ((res = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) {
           goto LBL_T3;
        }
  
        if ((res = mp_sub(&t1, &t3, &t2)) != MP_OKAY) {
           goto LBL_T3;
        }
        /*
            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 ((res = mp_expt_d_ex(&t1, b, &t2, fast)) != MP_OKAY) {
           goto LBL_T3;
        }
        cmp = mp_cmp(&t2, &a_);
        if (cmp == MP_EQ) {
           res = MP_OKAY;
           goto LBL_T3;
        }
        if (cmp == MP_LT) {
           if ((res = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) {
              goto LBL_T3;
           }
        } else {
           break;
        }
     }
     /* correct overshoot from above or from recurrence */
     for (;;) {
        if ((res = mp_expt_d_ex(&t1, b, &t2, fast)) != MP_OKAY) {
           goto LBL_T3;
        }
        if (mp_cmp(&t2, &a_) == MP_GT) {
           if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) {
              goto LBL_T3;
           }
        } else {
           break;
        }
     }
  
     /* set the result */
     mp_exch(&t1, c);
  
     /* set the sign of the result */
     c->sign = a->sign;
  
     res = MP_OKAY;
  
  LBL_T3:
     mp_clear(&t3);
  LBL_T2:
     mp_clear(&t2);
  LBL_T1:
     mp_clear(&t1);
     return res;
  }
  #endif
  

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