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cpython/Modules/_decimal/libmpdec/fourstep.c

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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 <assert.h>
#include "numbertheory.h"
#include "sixstep.h"
#include "transpose.h"
#include "umodarith.h"
#include "fourstep.h"
/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
form 3 * 2**n (See literature/matrix-transform.txt). */
#ifndef PPRO
static inline void
std_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3,
mpd_uint_t w3table[3], mpd_uint_t umod)
{
mpd_uint_t r1, r2;
mpd_uint_t w;
mpd_uint_t s, tmp;
/* k = 0 -> w = 1 */
s = *x1;
s = addmod(s, *x2, umod);
s = addmod(s, *x3, umod);
r1 = s;
/* k = 1 */
s = *x1;
w = w3table[1];
tmp = MULMOD(*x2, w);
s = addmod(s, tmp, umod);
w = w3table[2];
tmp = MULMOD(*x3, w);
s = addmod(s, tmp, umod);
r2 = s;
/* k = 2 */
s = *x1;
w = w3table[2];
tmp = MULMOD(*x2, w);
s = addmod(s, tmp, umod);
w = w3table[1];
tmp = MULMOD(*x3, w);
s = addmod(s, tmp, umod);
*x3 = s;
*x2 = r2;
*x1 = r1;
}
#else /* PPRO */
static inline void
ppro_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_uint_t w3table[3],
mpd_uint_t umod, double *dmod, uint32_t dinvmod[3])
{
mpd_uint_t r1, r2;
mpd_uint_t w;
mpd_uint_t s, tmp;
/* k = 0 -> w = 1 */
s = *x1;
s = addmod(s, *x2, umod);
s = addmod(s, *x3, umod);
r1 = s;
/* k = 1 */
s = *x1;
w = w3table[1];
tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
s = addmod(s, tmp, umod);
w = w3table[2];
tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
s = addmod(s, tmp, umod);
r2 = s;
/* k = 2 */
s = *x1;
w = w3table[2];
tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
s = addmod(s, tmp, umod);
w = w3table[1];
tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
s = addmod(s, tmp, umod);
*x3 = s;
*x2 = r2;
*x1 = r1;
}
#endif
/* forward transform, sign = -1; transform length = 3 * 2**n */
int
four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{
mpd_size_t R = 3; /* number of rows */
mpd_size_t C = n / 3; /* number of columns */
mpd_uint_t w3table[3];
mpd_uint_t kernel, w0, w1, wstep;
mpd_uint_t *s, *p0, *p1, *p2;
mpd_uint_t umod;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
mpd_size_t i, k;
assert(n >= 48);
assert(n <= 3*MPD_MAXTRANSFORM_2N);
/* Length R transform on the columns. */
SETMODULUS(modnum);
_mpd_init_w3table(w3table, -1, modnum);
for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
SIZE3_NTT(p0, p1, p2, w3table);
}
/* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
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-1; 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. */
for (s = a; s < a+n; s += C) {
if (!six_step_fnt(s, C, modnum)) {
return 0;
}
}
#if 0
/* An unordered transform is sufficient for convolution. */
/* Transpose the matrix. */
transpose_3xpow2(a, R, C);
#endif
return 1;
}
/* backward transform, sign = 1; transform length = 3 * 2**n */
int
inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{
mpd_size_t R = 3; /* number of rows */
mpd_size_t C = n / 3; /* number of columns */
mpd_uint_t w3table[3];
mpd_uint_t kernel, w0, w1, wstep;
mpd_uint_t *s, *p0, *p1, *p2;
mpd_uint_t umod;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
mpd_size_t i, k;
assert(n >= 48);
assert(n <= 3*MPD_MAXTRANSFORM_2N);
#if 0
/* An unordered transform is sufficient for convolution. */
/* Transpose the matrix, producing an R*C matrix. */
transpose_3xpow2(a, C, R);
#endif
/* Length C transform on the rows. */
for (s = a; s < a+n; s += C) {
if (!inv_six_step_fnt(s, C, modnum)) {
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;
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;
}
}
/* Length R transform on the columns. */
_mpd_init_w3table(w3table, 1, modnum);
for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
SIZE3_NTT(p0, p1, p2, w3table);
}
return 1;
}
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