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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 -------------------------------------------------*/ |