Line data    Source code

       1             : #include <tommath.h>
       2             : #ifdef BN_MP_N_ROOT_C
       3             : /* LibTomMath, multiple-precision integer library -- Tom St Denis
       4             :  *
       5             :  * LibTomMath is a library that provides multiple-precision
       6             :  * integer arithmetic as well as number theoretic functionality.
       7             :  *
       8             :  * The library was designed directly after the MPI library by
       9             :  * Michael Fromberger but has been written from scratch with
      10             :  * additional optimizations in place.
      11             :  *
      12             :  * The library is free for all purposes without any express
      13             :  * guarantee it works.
      14             :  *
      15             :  * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
      16             :  */
      17             : 
      18             : /* find the n'th root of an integer
      19             :  *
      20             :  * Result found such that (c)**b <= a and (c+1)**b > a
      21             :  *
      22             :  * This algorithm uses Newton's approximation
      23             :  * x[i+1] = x[i] - f(x[i])/f'(x[i])
      24             :  * which will find the root in log(N) time where
      25             :  * each step involves a fair bit.  This is not meant to
      26             :  * find huge roots [square and cube, etc].
      27             :  */
      28           0 : int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
      29             : {
      30             :   mp_int  t1, t2, t3;
      31             :   int     res, neg;
      32             : 
      33             :   /* input must be positive if b is even */
      34           0 :   if ((b & 1) == 0 && a->sign == MP_NEG) {
      35           0 :     return MP_VAL;
      36             :   }
      37             : 
      38           0 :   if ((res = mp_init (&t1)) != MP_OKAY) {
      39           0 :     return res;
      40             :   }
      41             : 
      42           0 :   if ((res = mp_init (&t2)) != MP_OKAY) {
      43           0 :     goto LBL_T1;
      44             :   }
      45             : 
      46           0 :   if ((res = mp_init (&t3)) != MP_OKAY) {
      47           0 :     goto LBL_T2;
      48             :   }
      49             : 
      50             :   /* if a is negative fudge the sign but keep track */
      51           0 :   neg     = a->sign;
      52           0 :   a->sign = MP_ZPOS;
      53             : 
      54             :   /* t2 = 2 */
      55           0 :   mp_set (&t2, 2);
      56             : 
      57             :   do {
      58             :     /* t1 = t2 */
      59           0 :     if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
      60           0 :       goto LBL_T3;
      61             :     }
      62             : 
      63             :     /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
      64             : 
      65             :     /* t3 = t1**(b-1) */
      66           0 :     if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
      67           0 :       goto LBL_T3;
      68             :     }
      69             : 
      70             :     /* numerator */
      71             :     /* t2 = t1**b */
      72           0 :     if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
      73           0 :       goto LBL_T3;
      74             :     }
      75             : 
      76             :     /* t2 = t1**b - a */
      77           0 :     if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
      78           0 :       goto LBL_T3;
      79             :     }
      80             : 
      81             :     /* denominator */
      82             :     /* t3 = t1**(b-1) * b  */
      83           0 :     if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
      84           0 :       goto LBL_T3;
      85             :     }
      86             : 
      87             :     /* t3 = (t1**b - a)/(b * t1**(b-1)) */
      88           0 :     if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
      89           0 :       goto LBL_T3;
      90             :     }
      91             : 
      92           0 :     if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
      93           0 :       goto LBL_T3;
      94             :     }
      95           0 :   }  while (mp_cmp (&t1, &t2) != MP_EQ);
      96             : 
      97             :   /* result can be off by a few so check */
      98             :   for (;;) {
      99           0 :     if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
     100           0 :       goto LBL_T3;
     101             :     }
     102             : 
     103           0 :     if (mp_cmp (&t2, a) == MP_GT) {
     104           0 :       if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
     105           0 :          goto LBL_T3;
     106             :       }
     107             :     } else {
     108           0 :       break;
     109             :     }
     110             :   }
     111             : 
     112             :   /* reset the sign of a first */
     113           0 :   a->sign = neg;
     114             : 
     115             :   /* set the result */
     116           0 :   mp_exch (&t1, c);
     117             : 
     118             :   /* set the sign of the result */
     119           0 :   c->sign = neg;
     120             : 
     121           0 :   res = MP_OKAY;
     122             : 
     123           0 : LBL_T3:mp_clear (&t3);
     124           0 : LBL_T2:mp_clear (&t2);
     125           0 : LBL_T1:mp_clear (&t1);
     126           0 :   return res;
     127             : }
     128             : #endif
     129             : 
     130             : /* $Source: /cvs/libtom/libtommath/bn_mp_n_root.c,v $ */
     131             : /* $Revision: 1.4 $ */
     132             : /* $Date: 2006/12/28 01:25:13 $ */