| /* |
| * Copyright (c) 2008-2012 Stefan Krah. All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| */ |
| |
| |
| #include "mpdecimal.h" |
| #include <stdio.h> |
| #include <stdlib.h> |
| #include <assert.h> |
| #include "bits.h" |
| #include "difradix2.h" |
| #include "numbertheory.h" |
| #include "transpose.h" |
| #include "umodarith.h" |
| #include "sixstep.h" |
| |
| |
| /* Bignum: Cache efficient Matrix Fourier Transform for arrays of the |
| form 2**n (See literature/six-step.txt). */ |
| |
| |
| /* forward transform with sign = -1 */ |
| int |
| six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) |
| { |
| struct fnt_params *tparams; |
| mpd_size_t log2n, C, R; |
| mpd_uint_t kernel; |
| mpd_uint_t umod; |
| #ifdef PPRO |
| double dmod; |
| uint32_t dinvmod[3]; |
| #endif |
| mpd_uint_t *x, w0, w1, wstep; |
| mpd_size_t i, k; |
| |
| |
| assert(ispower2(n)); |
| assert(n >= 16); |
| assert(n <= MPD_MAXTRANSFORM_2N); |
| |
| log2n = mpd_bsr(n); |
| C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */ |
| R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */ |
| |
| |
| /* Transpose the matrix. */ |
| if (!transpose_pow2(a, R, C)) { |
| return 0; |
| } |
| |
| /* Length R transform on the rows. */ |
| if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) { |
| return 0; |
| } |
| for (x = a; x < a+n; x += R) { |
| fnt_dif2(x, R, tparams); |
| } |
| |
| /* Transpose the matrix. */ |
| if (!transpose_pow2(a, C, R)) { |
| mpd_free(tparams); |
| return 0; |
| } |
| |
| /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ |
| SETMODULUS(modnum); |
| kernel = _mpd_getkernel(n, -1, modnum); |
| for (i = 1; i < R; i++) { |
| w0 = 1; /* r**(i*0): initial value for k=0 */ |
| w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */ |
| wstep = MULMOD(w1, w1); /* r**(2*i) */ |
| for (k = 0; k < C; k += 2) { |
| mpd_uint_t x0 = a[i*C+k]; |
| mpd_uint_t x1 = a[i*C+k+1]; |
| MULMOD2(&x0, w0, &x1, w1); |
| MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */ |
| a[i*C+k] = x0; |
| a[i*C+k+1] = x1; |
| } |
| } |
| |
| /* Length C transform on the rows. */ |
| if (C != R) { |
| mpd_free(tparams); |
| if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) { |
| return 0; |
| } |
| } |
| for (x = a; x < a+n; x += C) { |
| fnt_dif2(x, C, tparams); |
| } |
| mpd_free(tparams); |
| |
| #if 0 /* An unordered transform is sufficient for convolution. */ |
| /* Transpose the matrix. */ |
| if (!transpose_pow2(a, R, C)) { |
| return 0; |
| } |
| #endif |
| |
| return 1; |
| } |
| |
| |
| /* reverse transform, sign = 1 */ |
| int |
| inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum) |
| { |
| struct fnt_params *tparams; |
| mpd_size_t log2n, C, R; |
| mpd_uint_t kernel; |
| mpd_uint_t umod; |
| #ifdef PPRO |
| double dmod; |
| uint32_t dinvmod[3]; |
| #endif |
| mpd_uint_t *x, w0, w1, wstep; |
| mpd_size_t i, k; |
| |
| |
| assert(ispower2(n)); |
| assert(n >= 16); |
| assert(n <= MPD_MAXTRANSFORM_2N); |
| |
| log2n = mpd_bsr(n); |
| C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */ |
| R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */ |
| |
| |
| #if 0 /* An unordered transform is sufficient for convolution. */ |
| /* Transpose the matrix, producing an R*C matrix. */ |
| if (!transpose_pow2(a, C, R)) { |
| return 0; |
| } |
| #endif |
| |
| /* Length C transform on the rows. */ |
| if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) { |
| return 0; |
| } |
| for (x = a; x < a+n; x += C) { |
| fnt_dif2(x, C, tparams); |
| } |
| |
| /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */ |
| SETMODULUS(modnum); |
| kernel = _mpd_getkernel(n, 1, modnum); |
| for (i = 1; i < R; i++) { |
| w0 = 1; |
| w1 = POWMOD(kernel, i); |
| wstep = MULMOD(w1, w1); |
| for (k = 0; k < C; k += 2) { |
| mpd_uint_t x0 = a[i*C+k]; |
| mpd_uint_t x1 = a[i*C+k+1]; |
| MULMOD2(&x0, w0, &x1, w1); |
| MULMOD2C(&w0, &w1, wstep); |
| a[i*C+k] = x0; |
| a[i*C+k+1] = x1; |
| } |
| } |
| |
| /* Transpose the matrix. */ |
| if (!transpose_pow2(a, R, C)) { |
| mpd_free(tparams); |
| return 0; |
| } |
| |
| /* Length R transform on the rows. */ |
| if (R != C) { |
| mpd_free(tparams); |
| if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) { |
| return 0; |
| } |
| } |
| for (x = a; x < a+n; x += R) { |
| fnt_dif2(x, R, tparams); |
| } |
| mpd_free(tparams); |
| |
| /* Transpose the matrix. */ |
| if (!transpose_pow2(a, C, R)) { |
| return 0; |
| } |
| |
| return 1; |
| } |
| |
| |