3 * $Id: mp-sqrt.c,v 1.1 2000/06/22 19:01:44 mdw Exp $
5 * Compute integer square roots
7 * (c) 2000 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
33 * Revision 1.1 2000/06/22 19:01:44 mdw
34 * Compute (approximations to) integer square roots.
38 /*----- Header files ------------------------------------------------------*/
42 /*----- Main code ---------------------------------------------------------*/
44 /* --- @mp_sqrt@ --- *
46 * Arguments: @mp *d@ = pointer to destination integer
47 * @mp *a@ = (nonnegative) integer to take square root of
49 * Returns: The largest integer %$x$% such that %$x^2 \le a$%.
51 * Use: Computes integer square roots.
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.
58 mp *mp_sqrt(mp *d, mp *a)
61 mp *q = MP_NEW, *r = MP_NEW;
63 /* --- Sanity preservation --- */
65 assert(((void)"imaginary root in mp_sqrt", !(a->f & MP_NEG)));
67 /* --- Deal with trivial cases --- */
76 /* --- Find an initial guess of about the right size --- */
84 /* --- Main approximation --- *
86 * We use the Newton-Raphson recurrence relation
88 * %$x_{i+1} = x_i - \frac{x_i^2 - a}{2 x_i}$%
90 * We inspect the term %$q = x^2 - a$% to see when to stop. Increasing
91 * %$x$% is pointless when %$-q < 2 x + 1$%.
102 if (MP_CMP(q, <=, r))
105 mp_div(&r, &q, q, d);
108 d = mp_sub(d, d, MP_ONE);
113 /* --- Finished, at last --- */
121 /*----- Test rig ----------------------------------------------------------*/
125 #include <mLib/testrig.h>
127 static int verify(dstr *v)
129 mp *a = *(mp **)v[0].buf;
130 mp *qq = *(mp **)v[1].buf;
131 mp *q = mp_sqrt(MP_NEW, a);
134 if (MP_CMP(q, !=, qq)) {
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);
146 assert(mparena_count(MPARENA_GLOBAL) == 0);
151 static test_chunk tests[] = {
152 { "sqrt", verify, { &type_mp, &type_mp, 0 } },
156 int main(int argc, char *argv[])
159 test_run(argc, argv, tests, SRCDIR "/tests/mp");
165 /*----- That's all, folks -------------------------------------------------*/