git.distorted.org.uk Git - u/mdw/catacomb/blob - mp-sqrt.c

   1 /* -*-c-*-
   2  *
   3  * $Id: mp-sqrt.c,v 1.4 2004/03/27 17:54:11 mdw Exp $
   4  *
   5  * Compute integer square roots
   6  *
   7  * (c) 2000 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: mp-sqrt.c,v $
  33  * Revision 1.4  2004/03/27 17:54:11  mdw
  34  * Standard curves and curve checking.
  35  *
  36  * Revision 1.3  2001/02/03 12:00:29  mdw
  37  * Now @mp_drop@ checks its argument is non-NULL before attempting to free
  38  * it.  Note that the macro version @MP_DROP@ doesn't do this.
  39  *
  40  * Revision 1.2  2000/10/08 12:02:21  mdw
  41  * Use @MP_EQ@ instead of @MP_CMP@.
  42  *
  43  * Revision 1.1  2000/06/22 19:01:44  mdw
  44  * Compute (approximations to) integer square roots.
  45  *
  46  */
  47
  48 /*----- Header files ------------------------------------------------------*/
  49
  50 #include "mp.h"
  51
  52 /*----- Main code ---------------------------------------------------------*/
  53
  54 /* --- @mp_sqrt@ --- *
  55  *
  56  * Arguments:   @mp *d@ = pointer to destination integer
  57  *              @mp *a@ = (nonnegative) integer to take square root of
  58  *
  59  * Returns:     The largest integer %$x$% such that %$x^2 \le a$%.
  60  *
  61  * Use:         Computes integer square roots.
  62  *
  63  *              The current implementation isn't very good: it uses the
  64  *              Newton-Raphson method to find an approximation to %$a$%.  If
  65  *              there's any demand for a better version, I'll write one.
  66  */
  67
  68 mp *mp_sqrt(mp *d, mp *a)
  69 {
  70   unsigned long z;
  71   mp *q = MP_NEW, *r = MP_NEW;
  72
  73   /* --- Sanity preservation --- */
  74
  75   assert(((void)"imaginary root in mp_sqrt", !(a->f & MP_NEG)));
  76
  77   /* --- Deal with trivial cases --- */
  78
  79   MP_SHRINK(a);
  80   if (a->v == a->vl) {
  81     mp_drop(d);
  82     return (MP_ZERO);
  83   }
  84
  85   /* --- Find an initial guess of about the right size --- */
  86
  87   z = mp_bits(a);
  88   z >>= 1;
  89   mp_copy(a);
  90   d = mp_lsr(d, a, z);
  91
  92   /* --- Main approximation --- *
  93    *
  94    * We use the Newton-Raphson recurrence relation
  95    *
  96    *   %$x_{i+1} = x_i - \frac{x_i^2 - a}{2 x_i}$%
  97    *
  98    * We inspect the term %$q = x^2 - a$% to see when to stop.  Increasing
  99    * %$x$% is pointless when %$-q < 2 x + 1$%.
 100    */
 101
 102   for (;;) {
 103     q = mp_sqr(q, d);
 104     q = mp_sub(q, q, a);
 105     if (q->v == q->vl)
 106       break;
 107     if (q->f & MP_NEG) {
 108       r = mp_lsl(r, d, 1);
 109       r->f |= MP_NEG;
 110       if (MP_CMP(q, <=, r))
 111         break;
 112     }
 113     mp_div(&r, &q, q, d);
 114     r = mp_lsr(r, r, 1);
 115     if (r->v == r->vl)
 116       d = mp_sub(d, d, MP_ONE);
 117     else
 118       d = mp_sub(d, d, r);
 119   }
 120
 121   /* --- Finished, at last --- */
 122
 123   mp_drop(a);
 124   mp_drop(q);
 125   mp_drop(r);
 126   return (d);
 127 }
 128
 129 /*----- Test rig ----------------------------------------------------------*/
 130
 131 #ifdef TEST_RIG
 132
 133 #include <mLib/testrig.h>
 134
 135 static int verify(dstr *v)
 136 {
 137   mp *a = *(mp **)v[0].buf;
 138   mp *qq = *(mp **)v[1].buf;
 139   mp *q = mp_sqrt(MP_NEW, a);
 140   int ok = 1;
 141
 142   if (!MP_EQ(q, qq)) {
 143     ok = 0;
 144     fputs("\n*** sqrt failed", stderr);
 145     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 10);
 146     fputs("\n*** result = ", stderr); mp_writefile(q, stderr, 10);
 147     fputs("\n*** expect = ", stderr); mp_writefile(qq, stderr, 10);
 148     fputc('\n', stderr);
 149   }
 150
 151   mp_drop(a);
 152   mp_drop(q);
 153   mp_drop(qq);
 154   assert(mparena_count(MPARENA_GLOBAL) == 0);
 155
 156   return (ok);
 157 }
 158
 159 static test_chunk tests[] = {
 160   { "sqrt", verify, { &type_mp, &type_mp, 0 } },
 161   { 0, 0, { 0 } },
 162 };
 163
 164 int main(int argc, char *argv[])
 165 {
 166   sub_init();
 167   test_run(argc, argv, tests, SRCDIR "/tests/mp");
 168   return (0);
 169 }
 170
 171 #endif
 172
 173 /*----- That's all, folks -------------------------------------------------*/