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/*
* Copyright (c) 2008-2016 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;
}