Line data    Source code

       1             : #include "tommath_private.h"
       2             : #ifdef BN_MP_ROOT_U32_C
       3             : /* LibTomMath, multiple-precision integer library -- Tom St Denis */
       4             : /* SPDX-License-Identifier: Unlicense */
       5             : 
       6             : /* find the n'th root of an integer
       7             :  *
       8             :  * Result found such that (c)**b <= a and (c+1)**b > a
       9             :  *
      10             :  * This algorithm uses Newton's approximation
      11             :  * x[i+1] = x[i] - f(x[i])/f'(x[i])
      12             :  * which will find the root in log(N) time where
      13             :  * each step involves a fair bit.
      14             :  */
      15           0 : mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c)
      16             : {
      17           0 :    mp_int t1, t2, t3, a_;
      18           0 :    mp_ord cmp;
      19           0 :    int    ilog2;
      20           0 :    mp_err err;
      21             : 
      22             :    /* input must be positive if b is even */
      23           0 :    if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
      24           0 :       return MP_VAL;
      25             :    }
      26           0 :    if (b == 0) {
      27           0 :       return MP_VAL;
      28             :    }
      29             : 
      30           0 :    if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) {
      31           0 :       return err;
      32             :    }
      33             : 
      34             :    /* if a is negative fudge the sign but keep track */
      35           0 :    a_ = *a;
      36           0 :    a_.sign = MP_ZPOS;
      37             : 
      38             :    /* Compute seed: 2^(log_2(n)/b + 2)*/
      39           0 :    ilog2 = mp_count_bits(a);
      40             : 
      41             :    /*
      42             :      If "b" is larger than INT_MAX it is also larger than
      43             :      log_2(n) because the bit-length of the "n" is measured
      44             :      with an int and hence the root is always < 2 (two).
      45             :    */
      46           0 :    if (b > (uint32_t)(INT_MAX/2)) {
      47           0 :       mp_set(c, 1uL);
      48           0 :       c->sign = a->sign;
      49           0 :       err = MP_OKAY;
      50           0 :       goto LBL_ERR;
      51             :    }
      52             : 
      53             :    /* "b" is smaller than INT_MAX, we can cast safely */
      54           0 :    if (ilog2 < (int)b) {
      55           0 :       mp_set(c, 1uL);
      56           0 :       c->sign = a->sign;
      57           0 :       err = MP_OKAY;
      58           0 :       goto LBL_ERR;
      59             :    }
      60           0 :    ilog2 =  ilog2 / ((int)b);
      61           0 :    if (ilog2 == 0) {
      62           0 :       mp_set(c, 1uL);
      63           0 :       c->sign = a->sign;
      64           0 :       err = MP_OKAY;
      65           0 :       goto LBL_ERR;
      66             :    }
      67             :    /* Start value must be larger than root */
      68           0 :    ilog2 += 2;
      69           0 :    if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY)                    goto LBL_ERR;
      70           0 :    do {
      71             :       /* t1 = t2 */
      72           0 :       if ((err = mp_copy(&t2, &t1)) != MP_OKAY)                   goto LBL_ERR;
      73             : 
      74             :       /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
      75             : 
      76             :       /* t3 = t1**(b-1) */
      77           0 :       if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY)       goto LBL_ERR;
      78             : 
      79             :       /* numerator */
      80             :       /* t2 = t1**b */
      81           0 :       if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY)               goto LBL_ERR;
      82             : 
      83             :       /* t2 = t1**b - a */
      84           0 :       if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY)               goto LBL_ERR;
      85             : 
      86             :       /* denominator */
      87             :       /* t3 = t1**(b-1) * b  */
      88           0 :       if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY)               goto LBL_ERR;
      89             : 
      90             :       /* t3 = (t1**b - a)/(b * t1**(b-1)) */
      91           0 :       if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY)         goto LBL_ERR;
      92             : 
      93           0 :       if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY)               goto LBL_ERR;
      94             : 
      95             :       /*
      96             :           Number of rounds is at most log_2(root). If it is more it
      97             :           got stuck, so break out of the loop and do the rest manually.
      98             :        */
      99           0 :       if (ilog2-- == 0) {
     100           0 :          break;
     101             :       }
     102           0 :    }  while (mp_cmp(&t1, &t2) != MP_EQ);
     103             : 
     104             :    /* result can be off by a few so check */
     105             :    /* Loop beneath can overshoot by one if found root is smaller than actual root */
     106           0 :    for (;;) {
     107           0 :       if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY)            goto LBL_ERR;
     108           0 :       cmp = mp_cmp(&t2, &a_);
     109           0 :       if (cmp == MP_EQ) {
     110           0 :          err = MP_OKAY;
     111           0 :          goto LBL_ERR;
     112             :       }
     113           0 :       if (cmp == MP_LT) {
     114           0 :          if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY)          goto LBL_ERR;
     115             :       } else {
     116           0 :          break;
     117             :       }
     118             :    }
     119             :    /* correct overshoot from above or from recurrence */
     120           0 :    for (;;) {
     121           0 :       if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY)            goto LBL_ERR;
     122           0 :       if (mp_cmp(&t2, &a_) == MP_GT) {
     123           0 :          if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY)          goto LBL_ERR;
     124             :       } else {
     125           0 :          break;
     126             :       }
     127             :    }
     128             : 
     129             :    /* set the result */
     130           0 :    mp_exch(&t1, c);
     131             : 
     132             :    /* set the sign of the result */
     133           0 :    c->sign = a->sign;
     134             : 
     135           0 :    err = MP_OKAY;
     136             : 
     137           0 : LBL_ERR:
     138           0 :    mp_clear_multi(&t1, &t2, &t3, NULL);
     139           0 :    return err;
     140             : }
     141             : 
     142             : #endif