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

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