Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 1 | /* |
| 2 | * Copyright (c) 2008-2012 Stefan Krah. All rights reserved. |
| 3 | * |
| 4 | * Redistribution and use in source and binary forms, with or without |
| 5 | * modification, are permitted provided that the following conditions |
| 6 | * are met: |
| 7 | * |
| 8 | * 1. Redistributions of source code must retain the above copyright |
| 9 | * notice, this list of conditions and the following disclaimer. |
| 10 | * |
| 11 | * 2. Redistributions in binary form must reproduce the above copyright |
| 12 | * notice, this list of conditions and the following disclaimer in the |
| 13 | * documentation and/or other materials provided with the distribution. |
| 14 | * |
| 15 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND |
| 16 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 17 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 18 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| 19 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| 20 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| 21 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 22 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| 23 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| 24 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| 25 | * SUCH DAMAGE. |
| 26 | */ |
| 27 | |
| 28 | |
| 29 | #include "mpdecimal.h" |
| 30 | #include <stdio.h> |
| 31 | #include "bits.h" |
| 32 | #include "constants.h" |
| 33 | #include "fnt.h" |
| 34 | #include "fourstep.h" |
| 35 | #include "numbertheory.h" |
| 36 | #include "sixstep.h" |
| 37 | #include "umodarith.h" |
| 38 | #include "convolute.h" |
| 39 | |
| 40 | |
| 41 | /* Bignum: Fast convolution using the Number Theoretic Transform. Used for |
| 42 | the multiplication of very large coefficients. */ |
| 43 | |
| 44 | |
| 45 | /* Convolute the data in c1 and c2. Result is in c1. */ |
| 46 | int |
| 47 | fnt_convolute(mpd_uint_t *c1, mpd_uint_t *c2, mpd_size_t n, int modnum) |
| 48 | { |
| 49 | int (*fnt)(mpd_uint_t *, mpd_size_t, int); |
| 50 | int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int); |
| 51 | #ifdef PPRO |
| 52 | double dmod; |
| 53 | uint32_t dinvmod[3]; |
| 54 | #endif |
| 55 | mpd_uint_t n_inv, umod; |
| 56 | mpd_size_t i; |
| 57 | |
| 58 | |
| 59 | SETMODULUS(modnum); |
| 60 | n_inv = POWMOD(n, (umod-2)); |
| 61 | |
| 62 | if (ispower2(n)) { |
| 63 | if (n > SIX_STEP_THRESHOLD) { |
| 64 | fnt = six_step_fnt; |
| 65 | inv_fnt = inv_six_step_fnt; |
| 66 | } |
| 67 | else { |
| 68 | fnt = std_fnt; |
| 69 | inv_fnt = std_inv_fnt; |
| 70 | } |
| 71 | } |
| 72 | else { |
| 73 | fnt = four_step_fnt; |
| 74 | inv_fnt = inv_four_step_fnt; |
| 75 | } |
| 76 | |
| 77 | if (!fnt(c1, n, modnum)) { |
| 78 | return 0; |
| 79 | } |
| 80 | if (!fnt(c2, n, modnum)) { |
| 81 | return 0; |
| 82 | } |
| 83 | for (i = 0; i < n-1; i += 2) { |
| 84 | mpd_uint_t x0 = c1[i]; |
| 85 | mpd_uint_t y0 = c2[i]; |
| 86 | mpd_uint_t x1 = c1[i+1]; |
| 87 | mpd_uint_t y1 = c2[i+1]; |
| 88 | MULMOD2(&x0, y0, &x1, y1); |
| 89 | c1[i] = x0; |
| 90 | c1[i+1] = x1; |
| 91 | } |
| 92 | |
| 93 | if (!inv_fnt(c1, n, modnum)) { |
| 94 | return 0; |
| 95 | } |
| 96 | for (i = 0; i < n-3; i += 4) { |
| 97 | mpd_uint_t x0 = c1[i]; |
| 98 | mpd_uint_t x1 = c1[i+1]; |
| 99 | mpd_uint_t x2 = c1[i+2]; |
| 100 | mpd_uint_t x3 = c1[i+3]; |
| 101 | MULMOD2C(&x0, &x1, n_inv); |
| 102 | MULMOD2C(&x2, &x3, n_inv); |
| 103 | c1[i] = x0; |
| 104 | c1[i+1] = x1; |
| 105 | c1[i+2] = x2; |
| 106 | c1[i+3] = x3; |
| 107 | } |
| 108 | |
| 109 | return 1; |
| 110 | } |
| 111 | |
| 112 | /* Autoconvolute the data in c1. Result is in c1. */ |
| 113 | int |
| 114 | fnt_autoconvolute(mpd_uint_t *c1, mpd_size_t n, int modnum) |
| 115 | { |
| 116 | int (*fnt)(mpd_uint_t *, mpd_size_t, int); |
| 117 | int (*inv_fnt)(mpd_uint_t *, mpd_size_t, int); |
| 118 | #ifdef PPRO |
| 119 | double dmod; |
| 120 | uint32_t dinvmod[3]; |
| 121 | #endif |
| 122 | mpd_uint_t n_inv, umod; |
| 123 | mpd_size_t i; |
| 124 | |
| 125 | |
| 126 | SETMODULUS(modnum); |
| 127 | n_inv = POWMOD(n, (umod-2)); |
| 128 | |
| 129 | if (ispower2(n)) { |
| 130 | if (n > SIX_STEP_THRESHOLD) { |
| 131 | fnt = six_step_fnt; |
| 132 | inv_fnt = inv_six_step_fnt; |
| 133 | } |
| 134 | else { |
| 135 | fnt = std_fnt; |
| 136 | inv_fnt = std_inv_fnt; |
| 137 | } |
| 138 | } |
| 139 | else { |
| 140 | fnt = four_step_fnt; |
| 141 | inv_fnt = inv_four_step_fnt; |
| 142 | } |
| 143 | |
| 144 | if (!fnt(c1, n, modnum)) { |
| 145 | return 0; |
| 146 | } |
| 147 | for (i = 0; i < n-1; i += 2) { |
| 148 | mpd_uint_t x0 = c1[i]; |
| 149 | mpd_uint_t x1 = c1[i+1]; |
| 150 | MULMOD2(&x0, x0, &x1, x1); |
| 151 | c1[i] = x0; |
| 152 | c1[i+1] = x1; |
| 153 | } |
| 154 | |
| 155 | if (!inv_fnt(c1, n, modnum)) { |
| 156 | return 0; |
| 157 | } |
| 158 | for (i = 0; i < n-3; i += 4) { |
| 159 | mpd_uint_t x0 = c1[i]; |
| 160 | mpd_uint_t x1 = c1[i+1]; |
| 161 | mpd_uint_t x2 = c1[i+2]; |
| 162 | mpd_uint_t x3 = c1[i+3]; |
| 163 | MULMOD2C(&x0, &x1, n_inv); |
| 164 | MULMOD2C(&x2, &x3, n_inv); |
| 165 | c1[i] = x0; |
| 166 | c1[i+1] = x1; |
| 167 | c1[i+2] = x2; |
| 168 | c1[i+3] = x3; |
| 169 | } |
| 170 | |
| 171 | return 1; |
| 172 | } |
| 173 | |
| 174 | |