| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mp-sqrt.c,v 1.3 2001/02/03 12:00:29 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 1.3 2001/02/03 12:00:29 mdw |
| 34 | * Now @mp_drop@ checks its argument is non-NULL before attempting to free |
| 35 | * it. Note that the macro version @MP_DROP@ doesn't do this. |
| 36 | * |
| 37 | * Revision 1.2 2000/10/08 12:02:21 mdw |
| 38 | * Use @MP_EQ@ instead of @MP_CMP@. |
| 39 | * |
| 40 | * Revision 1.1 2000/06/22 19:01:44 mdw |
| 41 | * Compute (approximations to) integer square roots. |
| 42 | * |
| 43 | */ |
| 44 | |
| 45 | /*----- Header files ------------------------------------------------------*/ |
| 46 | |
| 47 | #include "mp.h" |
| 48 | |
| 49 | /*----- Main code ---------------------------------------------------------*/ |
| 50 | |
| 51 | /* --- @mp_sqrt@ --- * |
| 52 | * |
| 53 | * Arguments: @mp *d@ = pointer to destination integer |
| 54 | * @mp *a@ = (nonnegative) integer to take square root of |
| 55 | * |
| 56 | * Returns: The largest integer %$x$% such that %$x^2 \le a$%. |
| 57 | * |
| 58 | * Use: Computes integer square roots. |
| 59 | * |
| 60 | * The current implementation isn't very good: it uses the |
| 61 | * Newton-Raphson method to find an approximation to %$a$%. If |
| 62 | * there's any demand for a better version, I'll write one. |
| 63 | */ |
| 64 | |
| 65 | mp *mp_sqrt(mp *d, mp *a) |
| 66 | { |
| 67 | unsigned long z; |
| 68 | mp *q = MP_NEW, *r = MP_NEW; |
| 69 | |
| 70 | /* --- Sanity preservation --- */ |
| 71 | |
| 72 | assert(((void)"imaginary root in mp_sqrt", !(a->f & MP_NEG))); |
| 73 | |
| 74 | /* --- Deal with trivial cases --- */ |
| 75 | |
| 76 | MP_SHRINK(a); |
| 77 | if (a->v == a->vl) { |
| 78 | mp_drop(d); |
| 79 | return (MP_ZERO); |
| 80 | } |
| 81 | |
| 82 | /* --- Find an initial guess of about the right size --- */ |
| 83 | |
| 84 | z = mp_bits(a); |
| 85 | z >>= 1; |
| 86 | mp_copy(a); |
| 87 | d = mp_lsr(d, a, z); |
| 88 | mp_drop(a); |
| 89 | |
| 90 | /* --- Main approximation --- * |
| 91 | * |
| 92 | * We use the Newton-Raphson recurrence relation |
| 93 | * |
| 94 | * %$x_{i+1} = x_i - \frac{x_i^2 - a}{2 x_i}$% |
| 95 | * |
| 96 | * We inspect the term %$q = x^2 - a$% to see when to stop. Increasing |
| 97 | * %$x$% is pointless when %$-q < 2 x + 1$%. |
| 98 | */ |
| 99 | |
| 100 | for (;;) { |
| 101 | q = mp_sqr(q, d); |
| 102 | q = mp_sub(q, q, a); |
| 103 | if (q->v == q->vl) |
| 104 | break; |
| 105 | if (q->f & MP_NEG) { |
| 106 | r = mp_lsl(r, d, 1); |
| 107 | r->f |= MP_NEG; |
| 108 | if (MP_CMP(q, <=, r)) |
| 109 | break; |
| 110 | } |
| 111 | mp_div(&r, &q, q, d); |
| 112 | r = mp_lsr(r, r, 1); |
| 113 | if (r->v == r->vl) |
| 114 | d = mp_sub(d, d, MP_ONE); |
| 115 | else |
| 116 | d = mp_sub(d, d, r); |
| 117 | } |
| 118 | |
| 119 | /* --- Finished, at last --- */ |
| 120 | |
| 121 | mp_drop(q); |
| 122 | mp_drop(r); |
| 123 | return (d); |
| 124 | } |
| 125 | |
| 126 | /*----- Test rig ----------------------------------------------------------*/ |
| 127 | |
| 128 | #ifdef TEST_RIG |
| 129 | |
| 130 | #include <mLib/testrig.h> |
| 131 | |
| 132 | static int verify(dstr *v) |
| 133 | { |
| 134 | mp *a = *(mp **)v[0].buf; |
| 135 | mp *qq = *(mp **)v[1].buf; |
| 136 | mp *q = mp_sqrt(MP_NEW, a); |
| 137 | int ok = 1; |
| 138 | |
| 139 | if (!MP_EQ(q, qq)) { |
| 140 | ok = 0; |
| 141 | fputs("\n*** sqrt failed", stderr); |
| 142 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
| 143 | fputs("\n*** result = ", stderr); mp_writefile(q, stderr, 10); |
| 144 | fputs("\n*** expect = ", stderr); mp_writefile(qq, stderr, 10); |
| 145 | fputc('\n', stderr); |
| 146 | } |
| 147 | |
| 148 | mp_drop(a); |
| 149 | mp_drop(q); |
| 150 | mp_drop(qq); |
| 151 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 152 | |
| 153 | return (ok); |
| 154 | } |
| 155 | |
| 156 | static test_chunk tests[] = { |
| 157 | { "sqrt", verify, { &type_mp, &type_mp, 0 } }, |
| 158 | { 0, 0, { 0 } }, |
| 159 | }; |
| 160 | |
| 161 | int main(int argc, char *argv[]) |
| 162 | { |
| 163 | sub_init(); |
| 164 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
| 165 | return (0); |
| 166 | } |
| 167 | |
| 168 | #endif |
| 169 | |
| 170 | /*----- That's all, folks -------------------------------------------------*/ |