mirror of https://github.com/python/cpython.git
174 lines
4.4 KiB
C
174 lines
4.4 KiB
C
/*
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* Copyright (c) 2008-2020 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 "bits.h"
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#include "constants.h"
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#include "difradix2.h"
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#include "numbertheory.h"
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#include "umodarith.h"
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/* Bignum: The actual transform routine (decimation in frequency). */
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/*
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* Generate index pairs (x, bitreverse(x)) and carry out the permutation.
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* n must be a power of two.
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* Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational",
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* Chapter 1.14.4. [http://www.jjj.de/fxt/]
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*/
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static inline void
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bitreverse_permute(mpd_uint_t a[], mpd_size_t n)
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{
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mpd_size_t x = 0;
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mpd_size_t r = 0;
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mpd_uint_t t;
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do { /* Invariant: r = bitreverse(x) */
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if (r > x) {
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t = a[x];
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a[x] = a[r];
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a[r] = t;
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}
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/* Flip trailing consecutive 1 bits and the first zero bit
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* that absorbs a possible carry. */
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x += 1;
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/* Mirror the operation on r: Flip n_trailing_zeros(x)+1
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high bits of r. */
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r ^= (n - (n >> (mpd_bsf(x)+1)));
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/* The loop invariant is preserved. */
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} while (x < n);
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}
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/* Fast Number Theoretic Transform, decimation in frequency. */
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void
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fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams)
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{
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mpd_uint_t *wtable = tparams->wtable;
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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_uint_t u0, u1, v0, v1;
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mpd_uint_t w, w0, w1, wstep;
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mpd_size_t m, mhalf;
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mpd_size_t j, r;
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assert(ispower2(n));
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assert(n >= 4);
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SETMODULUS(tparams->modnum);
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/* m == n */
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mhalf = n / 2;
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for (j = 0; j < mhalf; j += 2) {
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w0 = wtable[j];
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w1 = wtable[j+1];
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u0 = a[j];
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v0 = a[j+mhalf];
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u1 = a[j+1];
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v1 = a[j+1+mhalf];
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a[j] = addmod(u0, v0, umod);
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v0 = submod(u0, v0, umod);
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a[j+1] = addmod(u1, v1, umod);
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v1 = submod(u1, v1, umod);
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MULMOD2(&v0, w0, &v1, w1);
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a[j+mhalf] = v0;
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a[j+1+mhalf] = v1;
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}
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wstep = 2;
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for (m = n/2; m >= 2; m>>=1, wstep<<=1) {
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mhalf = m / 2;
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/* j == 0 */
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for (r = 0; r < n; r += 2*m) {
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u0 = a[r];
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v0 = a[r+mhalf];
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u1 = a[m+r];
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v1 = a[m+r+mhalf];
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a[r] = addmod(u0, v0, umod);
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v0 = submod(u0, v0, umod);
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a[m+r] = addmod(u1, v1, umod);
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v1 = submod(u1, v1, umod);
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a[r+mhalf] = v0;
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a[m+r+mhalf] = v1;
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}
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for (j = 1; j < mhalf; j++) {
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w = wtable[j*wstep];
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for (r = 0; r < n; r += 2*m) {
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u0 = a[r+j];
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v0 = a[r+j+mhalf];
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u1 = a[m+r+j];
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v1 = a[m+r+j+mhalf];
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a[r+j] = addmod(u0, v0, umod);
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v0 = submod(u0, v0, umod);
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a[m+r+j] = addmod(u1, v1, umod);
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v1 = submod(u1, v1, umod);
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MULMOD2C(&v0, &v1, w);
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a[r+j+mhalf] = v0;
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a[m+r+j+mhalf] = v1;
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}
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}
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}
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bitreverse_permute(a, n);
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}
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