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Unified Diff: Modules/_decimal/libmpdec/fourstep.c

Issue 7652: Merge C version of decimal into py3k.
Patch Set: Created 7 years, 8 months ago
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Modules/_decimal/libmpdec/fourstep.c Sat Mar 10 18:12:20 2012 +0100
@@ -0,0 +1,255 @@
+/*
+ * Copyright (c) 2008-2010 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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