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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 <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);
}