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 /*----- Header files ------------------------------------------------------*/
34 /*----- Main code ---------------------------------------------------------*/
36 /* --- @mp_sqrt@ --- *
38 * Arguments: @mp *d@ = pointer to destination integer
39 * @mp *a@ = (nonnegative) integer to take square root of
41 * Returns: The largest integer %$x$% such that %$x^2 \le a$%.
43 * Use: Computes integer square roots.
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.
50 mp
*mp_sqrt(mp
*d
, mp
*a
)
53 mp
*q
= MP_NEW
, *r
= MP_NEW
;
55 /* --- Sanity preservation --- */
59 /* --- Deal with trivial cases --- */
67 /* --- Find an initial guess of about the right size --- */
74 /* --- Main approximation --- *
76 * We use the Newton-Raphson recurrence relation
78 * %$x_{i+1} = x_i - \frac{x_i^2 - a}{2 x_i}$%
80 * We inspect the term %$q = x^2 - a$% to see when to stop. Increasing
81 * %$x$% is pointless when %$-q < 2 x + 1$%.
98 d
= mp_sub(d
, d
, MP_ONE
);
103 /* --- Finished, at last --- */
111 /*----- Test rig ----------------------------------------------------------*/
115 #include <mLib/testrig.h>
117 static int verify(dstr
*v
)
119 mp
*a
= *(mp
**)v
[0].buf
;
120 mp
*qq
= *(mp
**)v
[1].buf
;
121 mp
*q
= mp_sqrt(MP_NEW
, a
);
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);
136 assert(mparena_count(MPARENA_GLOBAL
) == 0);
141 static test_chunk tests
[] = {
142 { "sqrt", verify
, { &type_mp
, &type_mp
, 0 } },
146 int main(int argc
, char *argv
[])
149 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mp");
155 /*----- That's all, folks -------------------------------------------------*/