| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: matrix.c,v 1.2 2000/07/02 15:22:07 mdw Exp $ |
| 4 | * |
| 5 | * Matrix arithmetic mod %$2^{24}$% |
| 6 | * |
| 7 | * (c) 2000 Mark Wooding |
| 8 | */ |
| 9 | |
| 10 | /*----- Licensing notice --------------------------------------------------* |
| 11 | * |
| 12 | * Copyright (c) 2000 Mark Wooding |
| 13 | * All rights reserved. |
| 14 | * |
| 15 | * Redistribution and use in source and binary forms, with or without |
| 16 | * modification, are permitted provided that the following conditions are |
| 17 | * met: |
| 18 | * |
| 19 | * 1. Redistributions of source code must retain the above copyright |
| 20 | * notice, this list of conditions and the following disclaimer. |
| 21 | * |
| 22 | * 2, Redistributions in binary form must reproduce the above copyright |
| 23 | * notice, this list of conditions and the following disclaimer in the |
| 24 | * documentation and/or other materials provided with the distribution. |
| 25 | * |
| 26 | * 3. The name of the authors may not be used to endorse or promote |
| 27 | * products derived from this software without specific prior written |
| 28 | * permission. |
| 29 | * |
| 30 | * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED |
| 31 | * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF |
| 32 | * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN |
| 33 | * NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, |
| 34 | * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| 35 | * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR |
| 36 | * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 37 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| 38 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN |
| 39 | * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| 40 | * POSSIBILITY OF SUCH DAMAGE. |
| 41 | * |
| 42 | * Instead of accepting the above terms, you may redistribute and/or modify |
| 43 | * this software under the terms of either the GNU General Public License, |
| 44 | * or the GNU Library General Public License, published by the Free |
| 45 | * Software Foundation; either version 2 of the License, or (at your |
| 46 | * option) any later version. |
| 47 | */ |
| 48 | |
| 49 | /*----- Revision history --------------------------------------------------* |
| 50 | * |
| 51 | * $Log: matrix.c,v $ |
| 52 | * Revision 1.2 2000/07/02 15:22:07 mdw |
| 53 | * Fix licence text. Change to matinv to mark inputs as constants. |
| 54 | * |
| 55 | * Revision 1.1 2000/05/21 11:28:30 mdw |
| 56 | * Initial check-in. |
| 57 | * |
| 58 | */ |
| 59 | |
| 60 | /*----- Header files ------------------------------------------------------*/ |
| 61 | |
| 62 | #include <assert.h> |
| 63 | #include <stdio.h> |
| 64 | #include <stdlib.h> |
| 65 | |
| 66 | #include "arith24.h" |
| 67 | #include "bits.h" |
| 68 | #include "matrix.h" |
| 69 | |
| 70 | /*----- Main code ---------------------------------------------------------*/ |
| 71 | |
| 72 | /* --- @matmul@ --- * |
| 73 | * |
| 74 | * Arguments: @uint24 *d@ = pointer to destination matrix |
| 75 | * @uint24 *a, *b@ = pointer to operand matrices |
| 76 | * @unsigned x, y, z@ = dimensions of the operand matrices |
| 77 | * |
| 78 | * Returns: --- |
| 79 | * |
| 80 | * Use: Performs matrix multiplication mod %$2^{24}$%. The matrix |
| 81 | * @d@ may not overlap either operand matrix. |
| 82 | */ |
| 83 | |
| 84 | void matmul(uint24 *d, const uint24 *a, const uint24 *b, |
| 85 | unsigned x, unsigned y, unsigned z) |
| 86 | { |
| 87 | unsigned i, j, k; |
| 88 | |
| 89 | for (i = 0; i < x; i++) { |
| 90 | const uint24 *bb = b; |
| 91 | for (j = 0; j < z; j++) { |
| 92 | uint24 n = 0; |
| 93 | for (k = 0; k < y; k++) |
| 94 | n += a[k] * bb[k * z]; |
| 95 | *d++ = U24(n); |
| 96 | bb++; |
| 97 | } |
| 98 | a += y; |
| 99 | } |
| 100 | } |
| 101 | |
| 102 | /* --- @matinv@ --- * |
| 103 | * |
| 104 | * Arguments: @uint24 *d@ = pointer to destination matrix |
| 105 | * @const uint24 *a@ = pointer to operand matrix |
| 106 | * @unsigned x, y@ = dimensions of operand matrix |
| 107 | * |
| 108 | * Returns: Zero if the matrix was successfully inverted, %$-1$% if the |
| 109 | * matrix is singular. |
| 110 | * |
| 111 | * Use: Computes the mod %$2^{24}$% inverse of a square matrix. |
| 112 | */ |
| 113 | |
| 114 | int matinv(uint24 *d, const uint24 *a, unsigned x, unsigned y) |
| 115 | { |
| 116 | unsigned i, j, k; |
| 117 | uint24 *aa; |
| 118 | uint32 *p, *q, *r, *s; |
| 119 | |
| 120 | assert(x == y); |
| 121 | |
| 122 | aa = malloc(sizeof(uint24) * x * y); |
| 123 | if (!aa) { |
| 124 | fprintf(stderr, "unable to allocate memory\n"); |
| 125 | exit(EXIT_FAILURE); |
| 126 | } |
| 127 | memcpy(aa, a, sizeof(uint24) * x * y); |
| 128 | |
| 129 | p = d; |
| 130 | for (i = 0; i < x; i++) { |
| 131 | for (j = 0; j < y; j++) |
| 132 | *p++ = i == j; |
| 133 | } |
| 134 | |
| 135 | for (i = 0; i < x; i++) { |
| 136 | uint24 c = inv24(aa[(x + 1) * i]); |
| 137 | if (!c) |
| 138 | goto fail; |
| 139 | r = aa + y * i; |
| 140 | s = d + y * i; |
| 141 | for (j = 0; j < y; j++) { |
| 142 | r[j] = U24(r[j] * c); |
| 143 | s[j] = U24(s[j] * c); |
| 144 | } |
| 145 | for (j = 0; j < x; j++) { |
| 146 | if (j == i) |
| 147 | continue; |
| 148 | p = aa + y * j; |
| 149 | q = d + y * j; |
| 150 | c = p[i]; |
| 151 | for (k = 0; k < y; k++) { |
| 152 | p[k] = U24(p[k] - c * r[k]); |
| 153 | q[k] = U24(q[k] - c * s[k]); |
| 154 | } |
| 155 | } |
| 156 | } |
| 157 | |
| 158 | free(aa); |
| 159 | return (0); |
| 160 | |
| 161 | fail: |
| 162 | free(aa); |
| 163 | return (-1); |
| 164 | } |
| 165 | |
| 166 | /*----- That's all, folks -------------------------------------------------*/ |