text: #include "tommath_private.h"
  #ifdef S_MP_LOG_C
  /* LibTomMath, multiple-precision integer library -- Tom St Denis */
  /* SPDX-License-Identifier: Unlicense */
  
  mp_err s_mp_log(const mp_int *a, mp_digit base, int *c)
  {
     mp_err err;
     int high, low;
     mp_int bracket_low, bracket_high, bracket_mid, t, bi_base;
  
     mp_ord cmp = mp_cmp_d(a, base);
     if ((cmp == MP_LT) || (cmp == MP_EQ)) {
        *c = cmp == MP_EQ;
        return MP_OKAY;
     }
  
     if ((err =
             mp_init_multi(&bracket_low, &bracket_high,
                           &bracket_mid, &t, &bi_base, NULL)) != MP_OKAY) {
        return err;
     }
  
     low = 0;
     mp_set(&bracket_low, 1uL);
     high = 1;
  
     mp_set(&bracket_high, base);
  
     /*
         A kind of Giant-step/baby-step algorithm.
         Idea shamelessly stolen from https://programmingpraxis.com/2010/05/07/integer-logarithms/2/
         The effect is asymptotic, hence needs benchmarks to test if the Giant-step should be skipped
         for small n.
      */
     while (mp_cmp(&bracket_high, a) == MP_LT) {
        low = high;
        if ((err = mp_copy(&bracket_high, &bracket_low)) != MP_OKAY) {
           goto LBL_END;
        }
        high <<= 1;
        if ((err = mp_sqr(&bracket_high, &bracket_high)) != MP_OKAY) {
           goto LBL_END;
        }
     }
     mp_set(&bi_base, base);
  
     while ((high - low) > 1) {
        int mid = (high + low) >> 1;
  
        if ((err = mp_expt_n(&bi_base, mid - low, &t)) != MP_OKAY) {
           goto LBL_END;
        }
        if ((err = mp_mul(&bracket_low, &t, &bracket_mid)) != MP_OKAY) {
           goto LBL_END;
        }
        cmp = mp_cmp(a, &bracket_mid);
        if (cmp == MP_LT) {
           high = mid;
           mp_exch(&bracket_mid, &bracket_high);
        }
        if (cmp == MP_GT) {
           low = mid;
           mp_exch(&bracket_mid, &bracket_low);
        }
        if (cmp == MP_EQ) {
           *c = mid;
           goto LBL_END;
        }
     }
  
     *c = (mp_cmp(&bracket_high, a) == MP_EQ) ? high : low;
  
  LBL_END:
     mp_clear_multi(&bracket_low, &bracket_high, &bracket_mid,
                    &t, &bi_base, NULL);
     return err;
  }
  
  
  #endif
  