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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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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 | |
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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 | |
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57 | assert(!MP_NEGP(a)); |
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58 | |
59 | /* --- Deal with trivial cases --- */ |
60 | |
61 | MP_SHRINK(a); |
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62 | if (MP_ZEROP(a)) { |
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63 | mp_drop(d); |
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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); |
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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); |
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87 | if (MP_ZEROP(q)) |
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88 | break; |
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89 | if (MP_NEGP(q)) { |
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90 | r = mp_lsl(r, d, 1); |
91 | r->f |= MP_NEG; |
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92 | if (MP_CMP(q, >=, r)) |
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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 | |
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105 | mp_drop(a); |
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106 | mp_drop(q); |
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107 | mp_drop(r); |
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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 | |
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124 | if (!MP_EQ(q, qq)) { |
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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 -------------------------------------------------*/ |