1 /*
2 * Copyright (c) 2008-2020 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
31 #include <assert.h>
32 #include <stdio.h>
33
34 #include "bits.h"
35 #include "constants.h"
36 #include "difradix2.h"
37 #include "numbertheory.h"
38 #include "sixstep.h"
39 #include "transpose.h"
40 #include "umodarith.h"
41
42
43 /* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
44 form 2**n (See literature/six-step.txt). */
45
46
47 /* forward transform with sign = -1 */
48 int
49 six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
50 {
51 struct fnt_params *tparams;
52 mpd_size_t log2n, C, R;
53 mpd_uint_t kernel;
54 mpd_uint_t umod;
55 #ifdef PPRO
56 double dmod;
57 uint32_t dinvmod[3];
58 #endif
59 mpd_uint_t *x, w0, w1, wstep;
60 mpd_size_t i, k;
61
62
63 assert(ispower2(n));
64 assert(n >= 16);
65 assert(n <= MPD_MAXTRANSFORM_2N);
66
67 log2n = mpd_bsr(n);
68 C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */
69 R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */
70
71
72 /* Transpose the matrix. */
73 if (!transpose_pow2(a, R, C)) {
74 return 0;
75 }
76
77 /* Length R transform on the rows. */
78 if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) {
79 return 0;
80 }
81 for (x = a; x < a+n; x += R) {
82 fnt_dif2(x, R, tparams);
83 }
84
85 /* Transpose the matrix. */
86 if (!transpose_pow2(a, C, R)) {
87 mpd_free(tparams);
88 return 0;
89 }
90
91 /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
92 SETMODULUS(modnum);
93 kernel = _mpd_getkernel(n, -1, modnum);
94 for (i = 1; i < R; i++) {
95 w0 = 1; /* r**(i*0): initial value for k=0 */
96 w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */
97 wstep = MULMOD(w1, w1); /* r**(2*i) */
98 for (k = 0; k < C; k += 2) {
99 mpd_uint_t x0 = a[i*C+k];
100 mpd_uint_t x1 = a[i*C+k+1];
101 MULMOD2(&x0, w0, &x1, w1);
102 MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */
103 a[i*C+k] = x0;
104 a[i*C+k+1] = x1;
105 }
106 }
107
108 /* Length C transform on the rows. */
109 if (C != R) {
110 mpd_free(tparams);
111 if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) {
112 return 0;
113 }
114 }
115 for (x = a; x < a+n; x += C) {
116 fnt_dif2(x, C, tparams);
117 }
118 mpd_free(tparams);
119
120 #if 0
121 /* An unordered transform is sufficient for convolution. */
122 /* Transpose the matrix. */
123 if (!transpose_pow2(a, R, C)) {
124 return 0;
125 }
126 #endif
127
128 return 1;
129 }
130
131
132 /* reverse transform, sign = 1 */
133 int
134 inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
135 {
136 struct fnt_params *tparams;
137 mpd_size_t log2n, C, R;
138 mpd_uint_t kernel;
139 mpd_uint_t umod;
140 #ifdef PPRO
141 double dmod;
142 uint32_t dinvmod[3];
143 #endif
144 mpd_uint_t *x, w0, w1, wstep;
145 mpd_size_t i, k;
146
147
148 assert(ispower2(n));
149 assert(n >= 16);
150 assert(n <= MPD_MAXTRANSFORM_2N);
151
152 log2n = mpd_bsr(n);
153 C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */
154 R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */
155
156
157 #if 0
158 /* An unordered transform is sufficient for convolution. */
159 /* Transpose the matrix, producing an R*C matrix. */
160 if (!transpose_pow2(a, C, R)) {
161 return 0;
162 }
163 #endif
164
165 /* Length C transform on the rows. */
166 if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) {
167 return 0;
168 }
169 for (x = a; x < a+n; x += C) {
170 fnt_dif2(x, C, tparams);
171 }
172
173 /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
174 SETMODULUS(modnum);
175 kernel = _mpd_getkernel(n, 1, modnum);
176 for (i = 1; i < R; i++) {
177 w0 = 1;
178 w1 = POWMOD(kernel, i);
179 wstep = MULMOD(w1, w1);
180 for (k = 0; k < C; k += 2) {
181 mpd_uint_t x0 = a[i*C+k];
182 mpd_uint_t x1 = a[i*C+k+1];
183 MULMOD2(&x0, w0, &x1, w1);
184 MULMOD2C(&w0, &w1, wstep);
185 a[i*C+k] = x0;
186 a[i*C+k+1] = x1;
187 }
188 }
189
190 /* Transpose the matrix. */
191 if (!transpose_pow2(a, R, C)) {
192 mpd_free(tparams);
193 return 0;
194 }
195
196 /* Length R transform on the rows. */
197 if (R != C) {
198 mpd_free(tparams);
199 if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) {
200 return 0;
201 }
202 }
203 for (x = a; x < a+n; x += R) {
204 fnt_dif2(x, R, tparams);
205 }
206 mpd_free(tparams);
207
208 /* Transpose the matrix. */
209 if (!transpose_pow2(a, C, R)) {
210 return 0;
211 }
212
213 return 1;
214 }