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

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