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 <stdlib.h> |
| 32 | #include <assert.h> |
| 33 | #include "bits.h" |
| 34 | #include "difradix2.h" |
| 35 | #include "numbertheory.h" |
| 36 | #include "transpose.h" |
| 37 | #include "umodarith.h" |
| 38 | #include "sixstep.h" |
| 39 | |
| 40 | |
| 41 | /* Bignum: Cache efficient Matrix Fourier Transform for arrays of the |
| 42 | form 2**n (See literature/six-step.txt). */ |
| 43 | |
| 44 | |
| 45 | /* forward transform with sign = -1 */ |
| 46 | int |
| 47 | six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) |
| 48 | { |
| 49 | struct fnt_params *tparams; |
| 50 | mpd_size_t log2n, C, R; |
| 51 | mpd_uint_t kernel; |
| 52 | mpd_uint_t umod; |
| 53 | #ifdef PPRO |
| 54 | double dmod; |
| 55 | uint32_t dinvmod[3]; |
| 56 | #endif |
| 57 | mpd_uint_t *x, w0, w1, wstep; |
| 58 | mpd_size_t i, k; |
| 59 | |
| 60 | |
| 61 | assert(ispower2(n)); |
| 62 | assert(n >= 16); |
| 63 | assert(n <= MPD_MAXTRANSFORM_2N); |
| 64 | |
| 65 | log2n = mpd_bsr(n); |
| 66 | C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */ |
| 67 | R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */ |
| 68 | |
| 69 | |
| 70 | /* Transpose the matrix. */ |
| 71 | if (!transpose_pow2(a, R, C)) { |
| 72 | return 0; |
| 73 | } |
| 74 | |
| 75 | /* Length R transform on the rows. */ |
| 76 | if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) { |
| 77 | return 0; |
| 78 | } |
| 79 | for (x = a; x < a+n; x += R) { |
| 80 | fnt_dif2(x, R, tparams); |
| 81 | } |
| 82 | |
| 83 | /* Transpose the matrix. */ |
| 84 | if (!transpose_pow2(a, C, R)) { |
| 85 | mpd_free(tparams); |
| 86 | return 0; |
| 87 | } |
| 88 | |
| 89 | /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ |
| 90 | SETMODULUS(modnum); |
| 91 | kernel = _mpd_getkernel(n, -1, modnum); |
| 92 | for (i = 1; i < R; i++) { |
| 93 | w0 = 1; /* r**(i*0): initial value for k=0 */ |
| 94 | w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */ |
| 95 | wstep = MULMOD(w1, w1); /* r**(2*i) */ |
| 96 | for (k = 0; k < C; k += 2) { |
| 97 | mpd_uint_t x0 = a[i*C+k]; |
| 98 | mpd_uint_t x1 = a[i*C+k+1]; |
| 99 | MULMOD2(&x0, w0, &x1, w1); |
| 100 | MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */ |
| 101 | a[i*C+k] = x0; |
| 102 | a[i*C+k+1] = x1; |
| 103 | } |
| 104 | } |
| 105 | |
| 106 | /* Length C transform on the rows. */ |
| 107 | if (C != R) { |
| 108 | mpd_free(tparams); |
| 109 | if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) { |
| 110 | return 0; |
| 111 | } |
| 112 | } |
| 113 | for (x = a; x < a+n; x += C) { |
| 114 | fnt_dif2(x, C, tparams); |
| 115 | } |
| 116 | mpd_free(tparams); |
| 117 | |
Stefan Krah | c64150b | 2012-03-23 16:34:41 +0100 | [diff] [blame^] | 118 | #if 0 |
| 119 | /* An unordered transform is sufficient for convolution. */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 120 | /* Transpose the matrix. */ |
| 121 | if (!transpose_pow2(a, R, C)) { |
| 122 | return 0; |
| 123 | } |
| 124 | #endif |
| 125 | |
| 126 | return 1; |
| 127 | } |
| 128 | |
| 129 | |
| 130 | /* reverse transform, sign = 1 */ |
| 131 | int |
| 132 | inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) |
| 133 | { |
| 134 | struct fnt_params *tparams; |
| 135 | mpd_size_t log2n, C, R; |
| 136 | mpd_uint_t kernel; |
| 137 | mpd_uint_t umod; |
| 138 | #ifdef PPRO |
| 139 | double dmod; |
| 140 | uint32_t dinvmod[3]; |
| 141 | #endif |
| 142 | mpd_uint_t *x, w0, w1, wstep; |
| 143 | mpd_size_t i, k; |
| 144 | |
| 145 | |
| 146 | assert(ispower2(n)); |
| 147 | assert(n >= 16); |
| 148 | assert(n <= MPD_MAXTRANSFORM_2N); |
| 149 | |
| 150 | log2n = mpd_bsr(n); |
| 151 | C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */ |
| 152 | R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */ |
| 153 | |
| 154 | |
Stefan Krah | c64150b | 2012-03-23 16:34:41 +0100 | [diff] [blame^] | 155 | #if 0 |
| 156 | /* An unordered transform is sufficient for convolution. */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 157 | /* Transpose the matrix, producing an R*C matrix. */ |
| 158 | if (!transpose_pow2(a, C, R)) { |
| 159 | return 0; |
| 160 | } |
| 161 | #endif |
| 162 | |
| 163 | /* Length C transform on the rows. */ |
| 164 | if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) { |
| 165 | return 0; |
| 166 | } |
| 167 | for (x = a; x < a+n; x += C) { |
| 168 | fnt_dif2(x, C, tparams); |
| 169 | } |
| 170 | |
| 171 | /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ |
| 172 | SETMODULUS(modnum); |
| 173 | kernel = _mpd_getkernel(n, 1, modnum); |
| 174 | for (i = 1; i < R; i++) { |
| 175 | w0 = 1; |
| 176 | w1 = POWMOD(kernel, i); |
| 177 | wstep = MULMOD(w1, w1); |
| 178 | for (k = 0; k < C; k += 2) { |
| 179 | mpd_uint_t x0 = a[i*C+k]; |
| 180 | mpd_uint_t x1 = a[i*C+k+1]; |
| 181 | MULMOD2(&x0, w0, &x1, w1); |
| 182 | MULMOD2C(&w0, &w1, wstep); |
| 183 | a[i*C+k] = x0; |
| 184 | a[i*C+k+1] = x1; |
| 185 | } |
| 186 | } |
| 187 | |
| 188 | /* Transpose the matrix. */ |
| 189 | if (!transpose_pow2(a, R, C)) { |
| 190 | mpd_free(tparams); |
| 191 | return 0; |
| 192 | } |
| 193 | |
| 194 | /* Length R transform on the rows. */ |
| 195 | if (R != C) { |
| 196 | mpd_free(tparams); |
| 197 | if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) { |
| 198 | return 0; |
| 199 | } |
| 200 | } |
| 201 | for (x = a; x < a+n; x += R) { |
| 202 | fnt_dif2(x, R, tparams); |
| 203 | } |
| 204 | mpd_free(tparams); |
| 205 | |
| 206 | /* Transpose the matrix. */ |
| 207 | if (!transpose_pow2(a, C, R)) { |
| 208 | return 0; |
| 209 | } |
| 210 | |
| 211 | return 1; |
| 212 | } |
| 213 | |
| 214 | |