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

   1 /* -*-c-*-
   2  *
   3  * $Id$
   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 /*----- Header files ------------------------------------------------------*/
  31
  32 #include "mp.h"
  33
  34 /*----- Main code ---------------------------------------------------------*/
  35
  36 /* --- @mp_sqrt@ --- *
  37  *
  38  * Arguments:   @mp *d@ = pointer to destination integer
  39  *              @mp *a@ = (nonnegative) integer to take square root of
  40  *
  41  * Returns:     The largest integer %$x$% such that %$x^2 \le a$%.
  42  *
  43  * Use:         Computes integer square roots.
  44  *
  45  *              The current implementation isn't very good: it uses the
  46  *              Newton-Raphson method to find an approximation to %$a$%.  If
  47  *              there's any demand for a better version, I'll write one.
  48  */
  49
  50 mp *mp_sqrt(mp *d, mp *a)
  51 {
  52   unsigned long z;
  53   mp *q = MP_NEW, *r = MP_NEW;
  54
  55   /* --- Sanity preservation --- */
  56
  57   assert(!MP_NEGP(a));
  58
  59   /* --- Deal with trivial cases --- */
  60
  61   MP_SHRINK(a);
  62   if (MP_ZEROP(a)) {
  63     mp_drop(d);
  64     return (MP_ZERO);
  65   }
  66
  67   /* --- Find an initial guess of about the right size --- */
  68
  69   z = mp_bits(a);
  70   z >>= 1;
  71   mp_copy(a);
  72   d = mp_lsr(d, a, z);
  73
  74   /* --- Main approximation --- *
  75    *
  76    * We use the Newton-Raphson recurrence relation
  77    *
  78    *   %$x_{i+1} = x_i - \frac{x_i^2 - a}{2 x_i}$%
  79    *
  80    * We inspect the term %$q = x^2 - a$% to see when to stop.  Increasing
  81    * %$x$% is pointless when %$-q < 2 x + 1$%.
  82    */
  83
  84   for (;;) {
  85     q = mp_sqr(q, d);
  86     q = mp_sub(q, q, a);
  87     if (MP_ZEROP(q))
  88       break;
  89     if (MP_NEGP(q)) {
  90       r = mp_lsl(r, d, 1);
  91       r->f |= MP_NEG;
  92       if (MP_CMP(q, >=, r))
  93         break;
  94     }
  95     mp_div(&r, &q, q, d);
  96     r = mp_lsr(r, r, 1);
  97     if (r->v == r->vl)
  98       d = mp_sub(d, d, MP_ONE);
  99     else
 100       d = mp_sub(d, d, r);
 101   }
 102
 103   /* --- Finished, at last --- */
 104
 105   mp_drop(a);
 106   mp_drop(q);
 107   mp_drop(r);
 108   return (d);
 109 }
 110
 111 /*----- Test rig ----------------------------------------------------------*/
 112
 113 #ifdef TEST_RIG
 114
 115 #include <mLib/testrig.h>
 116
 117 static int verify(dstr *v)
 118 {
 119   mp *a = *(mp **)v[0].buf;
 120   mp *qq = *(mp **)v[1].buf;
 121   mp *q = mp_sqrt(MP_NEW, a);
 122   int ok = 1;
 123
 124   if (!MP_EQ(q, qq)) {
 125     ok = 0;
 126     fputs("\n*** sqrt failed", stderr);
 127     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 10);
 128     fputs("\n*** result = ", stderr); mp_writefile(q, stderr, 10);
 129     fputs("\n*** expect = ", stderr); mp_writefile(qq, stderr, 10);
 130     fputc('\n', stderr);
 131   }
 132
 133   mp_drop(a);
 134   mp_drop(q);
 135   mp_drop(qq);
 136   assert(mparena_count(MPARENA_GLOBAL) == 0);
 137
 138   return (ok);
 139 }
 140
 141 static test_chunk tests[] = {
 142   { "sqrt", verify, { &type_mp, &type_mp, 0 } },
 143   { 0, 0, { 0 } },
 144 };
 145
 146 int main(int argc, char *argv[])
 147 {
 148   sub_init();
 149   test_run(argc, argv, tests, SRCDIR "/tests/mp");
 150   return (0);
 151 }
 152
 153 #endif
 154
 155 /*----- That's all, folks -------------------------------------------------*/