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

   1 /* -*-c-*-
   2  *
   3  * $Id: mp-sqrt.c,v 1.2 2000/10/08 12:02:21 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 1.2  2000/10/08 12:02:21  mdw
  34  * Use @MP_EQ@ instead of @MP_CMP@.
  35  *
  36  * Revision 1.1  2000/06/22 19:01:44  mdw
  37  * Compute (approximations to) integer square roots.
  38  *
  39  */
  40
  41 /*----- Header files ------------------------------------------------------*/
  42
  43 #include "mp.h"
  44
  45 /*----- Main code ---------------------------------------------------------*/
  46
  47 /* --- @mp_sqrt@ --- *
  48  *
  49  * Arguments:   @mp *d@ = pointer to destination integer
  50  *              @mp *a@ = (nonnegative) integer to take square root of
  51  *
  52  * Returns:     The largest integer %$x$% such that %$x^2 \le a$%.
  53  *
  54  * Use:         Computes integer square roots.
  55  *
  56  *              The current implementation isn't very good: it uses the
  57  *              Newton-Raphson method to find an approximation to %$a$%.  If
  58  *              there's any demand for a better version, I'll write one.
  59  */
  60
  61 mp *mp_sqrt(mp *d, mp *a)
  62 {
  63   unsigned long z;
  64   mp *q = MP_NEW, *r = MP_NEW;
  65
  66   /* --- Sanity preservation --- */
  67
  68   assert(((void)"imaginary root in mp_sqrt", !(a->f & MP_NEG)));
  69
  70   /* --- Deal with trivial cases --- */
  71
  72   MP_SHRINK(a);
  73   if (a->v == a->vl) {
  74     if (d)
  75       mp_drop(d);
  76     return (MP_ZERO);
  77   }
  78
  79   /* --- Find an initial guess of about the right size --- */
  80
  81   z = mp_bits(a);
  82   z >>= 1;
  83   mp_copy(a);
  84   d = mp_lsr(d, a, z);
  85   mp_drop(a);
  86
  87   /* --- Main approximation --- *
  88    *
  89    * We use the Newton-Raphson recurrence relation
  90    *
  91    *   %$x_{i+1} = x_i - \frac{x_i^2 - a}{2 x_i}$%
  92    *
  93    * We inspect the term %$q = x^2 - a$% to see when to stop.  Increasing
  94    * %$x$% is pointless when %$-q < 2 x + 1$%.
  95    */
  96
  97   for (;;) {
  98     q = mp_sqr(q, d);
  99     q = mp_sub(q, q, a);
 100     if (q->v == q->vl)
 101       break;
 102     if (q->f & MP_NEG) {
 103       r = mp_lsl(r, d, 1);
 104       r->f |= MP_NEG;
 105       if (MP_CMP(q, <=, r))
 106         break;
 107     }
 108     mp_div(&r, &q, q, d);
 109     r = mp_lsr(r, r, 1);
 110     if (r->v == r->vl)
 111       d = mp_sub(d, d, MP_ONE);
 112     else
 113       d = mp_sub(d, d, r);
 114   }
 115
 116   /* --- Finished, at last --- */
 117
 118   mp_drop(q);
 119   if (r)
 120     mp_drop(r);
 121   return (d);
 122 }
 123
 124 /*----- Test rig ----------------------------------------------------------*/
 125
 126 #ifdef TEST_RIG
 127
 128 #include <mLib/testrig.h>
 129
 130 static int verify(dstr *v)
 131 {
 132   mp *a = *(mp **)v[0].buf;
 133   mp *qq = *(mp **)v[1].buf;
 134   mp *q = mp_sqrt(MP_NEW, a);
 135   int ok = 1;
 136
 137   if (!MP_EQ(q, qq)) {
 138     ok = 0;
 139     fputs("\n*** sqrt failed", stderr);
 140     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 10);
 141     fputs("\n*** result = ", stderr); mp_writefile(q, stderr, 10);
 142     fputs("\n*** expect = ", stderr); mp_writefile(qq, stderr, 10);
 143     fputc('\n', stderr);
 144   }
 145
 146   mp_drop(a);
 147   mp_drop(q);
 148   mp_drop(qq);
 149   assert(mparena_count(MPARENA_GLOBAL) == 0);
 150
 151   return (ok);
 152 }
 153
 154 static test_chunk tests[] = {
 155   { "sqrt", verify, { &type_mp, &type_mp, 0 } },
 156   { 0, 0, { 0 } },
 157 };
 158
 159 int main(int argc, char *argv[])
 160 {
 161   sub_init();
 162   test_run(argc, argv, tests, SRCDIR "/tests/mp");
 163   return (0);
 164 }
 165
 166 #endif
 167
 168 /*----- That's all, folks -------------------------------------------------*/