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257 lines
6.4 KiB
C
257 lines
6.4 KiB
C
/*
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* Copyright (c) 2008-2012 Stefan Krah. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include "mpdecimal.h"
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#include <assert.h>
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#include "numbertheory.h"
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#include "sixstep.h"
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#include "transpose.h"
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#include "umodarith.h"
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#include "fourstep.h"
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/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
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form 3 * 2**n (See literature/matrix-transform.txt). */
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#ifndef PPRO
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static inline void
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std_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3,
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mpd_uint_t w3table[3], mpd_uint_t umod)
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{
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mpd_uint_t r1, r2;
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mpd_uint_t w;
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mpd_uint_t s, tmp;
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/* k = 0 -> w = 1 */
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s = *x1;
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s = addmod(s, *x2, umod);
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s = addmod(s, *x3, umod);
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r1 = s;
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/* k = 1 */
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s = *x1;
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w = w3table[1];
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tmp = MULMOD(*x2, w);
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s = addmod(s, tmp, umod);
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w = w3table[2];
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tmp = MULMOD(*x3, w);
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s = addmod(s, tmp, umod);
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r2 = s;
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/* k = 2 */
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s = *x1;
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w = w3table[2];
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tmp = MULMOD(*x2, w);
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s = addmod(s, tmp, umod);
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w = w3table[1];
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tmp = MULMOD(*x3, w);
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s = addmod(s, tmp, umod);
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*x3 = s;
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*x2 = r2;
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*x1 = r1;
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}
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#else /* PPRO */
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static inline void
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ppro_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_uint_t w3table[3],
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mpd_uint_t umod, double *dmod, uint32_t dinvmod[3])
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{
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mpd_uint_t r1, r2;
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mpd_uint_t w;
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mpd_uint_t s, tmp;
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/* k = 0 -> w = 1 */
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s = *x1;
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s = addmod(s, *x2, umod);
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s = addmod(s, *x3, umod);
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r1 = s;
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/* k = 1 */
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s = *x1;
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w = w3table[1];
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tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
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s = addmod(s, tmp, umod);
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w = w3table[2];
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tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
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s = addmod(s, tmp, umod);
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r2 = s;
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/* k = 2 */
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s = *x1;
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w = w3table[2];
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tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
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s = addmod(s, tmp, umod);
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w = w3table[1];
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tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
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s = addmod(s, tmp, umod);
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*x3 = s;
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*x2 = r2;
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*x1 = r1;
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}
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#endif
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/* forward transform, sign = -1; transform length = 3 * 2**n */
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int
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four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
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{
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mpd_size_t R = 3; /* number of rows */
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mpd_size_t C = n / 3; /* number of columns */
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mpd_uint_t w3table[3];
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mpd_uint_t kernel, w0, w1, wstep;
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mpd_uint_t *s, *p0, *p1, *p2;
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mpd_uint_t umod;
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#ifdef PPRO
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double dmod;
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uint32_t dinvmod[3];
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#endif
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mpd_size_t i, k;
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assert(n >= 48);
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assert(n <= 3*MPD_MAXTRANSFORM_2N);
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/* Length R transform on the columns. */
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SETMODULUS(modnum);
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_mpd_init_w3table(w3table, -1, modnum);
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for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
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SIZE3_NTT(p0, p1, p2, w3table);
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}
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/* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
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kernel = _mpd_getkernel(n, -1, modnum);
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for (i = 1; i < R; i++) {
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w0 = 1; /* r**(i*0): initial value for k=0 */
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w1 = POWMOD(kernel, i); /* r**(i*1): initial value for k=1 */
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wstep = MULMOD(w1, w1); /* r**(2*i) */
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for (k = 0; k < C-1; k += 2) {
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mpd_uint_t x0 = a[i*C+k];
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mpd_uint_t x1 = a[i*C+k+1];
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MULMOD2(&x0, w0, &x1, w1);
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MULMOD2C(&w0, &w1, wstep); /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */
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a[i*C+k] = x0;
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a[i*C+k+1] = x1;
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}
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}
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/* Length C transform on the rows. */
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for (s = a; s < a+n; s += C) {
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if (!six_step_fnt(s, C, modnum)) {
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return 0;
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}
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}
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#if 0
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/* An unordered transform is sufficient for convolution. */
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/* Transpose the matrix. */
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transpose_3xpow2(a, R, C);
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#endif
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return 1;
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}
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/* backward transform, sign = 1; transform length = 3 * 2**n */
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int
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inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
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{
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mpd_size_t R = 3; /* number of rows */
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mpd_size_t C = n / 3; /* number of columns */
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mpd_uint_t w3table[3];
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mpd_uint_t kernel, w0, w1, wstep;
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mpd_uint_t *s, *p0, *p1, *p2;
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mpd_uint_t umod;
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#ifdef PPRO
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double dmod;
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uint32_t dinvmod[3];
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#endif
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mpd_size_t i, k;
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assert(n >= 48);
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assert(n <= 3*MPD_MAXTRANSFORM_2N);
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#if 0
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/* An unordered transform is sufficient for convolution. */
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/* Transpose the matrix, producing an R*C matrix. */
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transpose_3xpow2(a, C, R);
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#endif
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/* Length C transform on the rows. */
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for (s = a; s < a+n; s += C) {
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if (!inv_six_step_fnt(s, C, modnum)) {
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return 0;
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}
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}
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/* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
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SETMODULUS(modnum);
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kernel = _mpd_getkernel(n, 1, modnum);
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for (i = 1; i < R; i++) {
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w0 = 1;
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w1 = POWMOD(kernel, i);
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wstep = MULMOD(w1, w1);
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for (k = 0; k < C; k += 2) {
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mpd_uint_t x0 = a[i*C+k];
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mpd_uint_t x1 = a[i*C+k+1];
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MULMOD2(&x0, w0, &x1, w1);
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MULMOD2C(&w0, &w1, wstep);
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a[i*C+k] = x0;
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a[i*C+k+1] = x1;
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}
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}
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/* Length R transform on the columns. */
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_mpd_init_w3table(w3table, 1, modnum);
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for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
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SIZE3_NTT(p0, p1, p2, w3table);
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}
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return 1;
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}
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