174 lines
4.4 KiB
C
174 lines
4.4 KiB
C
/*
|
|
* 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 <assert.h>
|
|
#include "bits.h"
|
|
#include "numbertheory.h"
|
|
#include "umodarith.h"
|
|
#include "difradix2.h"
|
|
|
|
|
|
/* Bignum: The actual transform routine (decimation in frequency). */
|
|
|
|
|
|
/*
|
|
* Generate index pairs (x, bitreverse(x)) and carry out the permutation.
|
|
* n must be a power of two.
|
|
* Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational",
|
|
* Chapter 1.14.4. [http://www.jjj.de/fxt/]
|
|
*/
|
|
static inline void
|
|
bitreverse_permute(mpd_uint_t a[], mpd_size_t n)
|
|
{
|
|
mpd_size_t x = 0;
|
|
mpd_size_t r = 0;
|
|
mpd_uint_t t;
|
|
|
|
do { /* Invariant: r = bitreverse(x) */
|
|
if (r > x) {
|
|
t = a[x];
|
|
a[x] = a[r];
|
|
a[r] = t;
|
|
}
|
|
/* Flip trailing consecutive 1 bits and the first zero bit
|
|
* that absorbs a possible carry. */
|
|
x += 1;
|
|
/* Mirror the operation on r: Flip n_trailing_zeros(x)+1
|
|
high bits of r. */
|
|
r ^= (n - (n >> (mpd_bsf(x)+1)));
|
|
/* The loop invariant is preserved. */
|
|
} while (x < n);
|
|
}
|
|
|
|
|
|
/* Fast Number Theoretic Transform, decimation in frequency. */
|
|
void
|
|
fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams)
|
|
{
|
|
mpd_uint_t *wtable = tparams->wtable;
|
|
mpd_uint_t umod;
|
|
#ifdef PPRO
|
|
double dmod;
|
|
uint32_t dinvmod[3];
|
|
#endif
|
|
mpd_uint_t u0, u1, v0, v1;
|
|
mpd_uint_t w, w0, w1, wstep;
|
|
mpd_size_t m, mhalf;
|
|
mpd_size_t j, r;
|
|
|
|
|
|
assert(ispower2(n));
|
|
assert(n >= 4);
|
|
|
|
SETMODULUS(tparams->modnum);
|
|
|
|
/* m == n */
|
|
mhalf = n / 2;
|
|
for (j = 0; j < mhalf; j += 2) {
|
|
|
|
w0 = wtable[j];
|
|
w1 = wtable[j+1];
|
|
|
|
u0 = a[j];
|
|
v0 = a[j+mhalf];
|
|
|
|
u1 = a[j+1];
|
|
v1 = a[j+1+mhalf];
|
|
|
|
a[j] = addmod(u0, v0, umod);
|
|
v0 = submod(u0, v0, umod);
|
|
|
|
a[j+1] = addmod(u1, v1, umod);
|
|
v1 = submod(u1, v1, umod);
|
|
|
|
MULMOD2(&v0, w0, &v1, w1);
|
|
|
|
a[j+mhalf] = v0;
|
|
a[j+1+mhalf] = v1;
|
|
|
|
}
|
|
|
|
wstep = 2;
|
|
for (m = n/2; m >= 2; m>>=1, wstep<<=1) {
|
|
|
|
mhalf = m / 2;
|
|
|
|
/* j == 0 */
|
|
for (r = 0; r < n; r += 2*m) {
|
|
|
|
u0 = a[r];
|
|
v0 = a[r+mhalf];
|
|
|
|
u1 = a[m+r];
|
|
v1 = a[m+r+mhalf];
|
|
|
|
a[r] = addmod(u0, v0, umod);
|
|
v0 = submod(u0, v0, umod);
|
|
|
|
a[m+r] = addmod(u1, v1, umod);
|
|
v1 = submod(u1, v1, umod);
|
|
|
|
a[r+mhalf] = v0;
|
|
a[m+r+mhalf] = v1;
|
|
}
|
|
|
|
for (j = 1; j < mhalf; j++) {
|
|
|
|
w = wtable[j*wstep];
|
|
|
|
for (r = 0; r < n; r += 2*m) {
|
|
|
|
u0 = a[r+j];
|
|
v0 = a[r+j+mhalf];
|
|
|
|
u1 = a[m+r+j];
|
|
v1 = a[m+r+j+mhalf];
|
|
|
|
a[r+j] = addmod(u0, v0, umod);
|
|
v0 = submod(u0, v0, umod);
|
|
|
|
a[m+r+j] = addmod(u1, v1, umod);
|
|
v1 = submod(u1, v1, umod);
|
|
|
|
MULMOD2C(&v0, &v1, w);
|
|
|
|
a[r+j+mhalf] = v0;
|
|
a[m+r+j+mhalf] = v1;
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
bitreverse_permute(a, n);
|
|
}
|
|
|
|
|