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

Issue 7652: Merge C version of decimal into py3k.
Patch Set: Created 7 years, 3 months ago
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Modules/_decimal/libmpdec/crt.c Sat Mar 10 18:12:20 2012 +0100
@@ -0,0 +1,179 @@
+/*
+ * 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 <stdio.h>
+#include <assert.h>
+#include "numbertheory.h"
+#include "umodarith.h"
+#include "crt.h"
+
+
+/* Bignum: Chinese Remainder Theorem, extends the maximum transform length. */
+
+
+/* Multiply P1P2 by v, store result in w. */
+static inline void
+_crt_mulP1P2_3(mpd_uint_t w[3], mpd_uint_t v)
+{
+ mpd_uint_t hi1, hi2, lo;
+
+ _mpd_mul_words(&hi1, &lo, LH_P1P2, v);
+ w[0] = lo;
+
+ _mpd_mul_words(&hi2, &lo, UH_P1P2, v);
+ lo = hi1 + lo;
+ if (lo < hi1) hi2++;
+
+ w[1] = lo;
+ w[2] = hi2;
+}
+
+/* Add 3 words from v to w. The result is known to fit in w. */
+static inline void
+_crt_add3(mpd_uint_t w[3], mpd_uint_t v[3])
+{
+ mpd_uint_t carry;
+ mpd_uint_t s;
+
+ s = w[0] + v[0];
+ carry = (s < w[0]);
+ w[0] = s;
+
+ s = w[1] + (v[1] + carry);
+ carry = (s < w[1]);
+ w[1] = s;
+
+ w[2] = w[2] + (v[2] + carry);
+}
+
+/* Divide 3 words in u by v, store result in w, return remainder. */
+static inline mpd_uint_t
+_crt_div3(mpd_uint_t *w, const mpd_uint_t *u, mpd_uint_t v)
+{
+ mpd_uint_t r1 = u[2];
+ mpd_uint_t r2;
+
+ if (r1 < v) {
+ w[2] = 0;
+ }
+ else {
+ _mpd_div_word(&w[2], &r1, u[2], v); /* GCOV_NOT_REACHED */
+ }
+
+ _mpd_div_words(&w[1], &r2, r1, u[1], v);
+ _mpd_div_words(&w[0], &r1, r2, u[0], v);
+
+ return r1;
+}
+
+
+/*
+ * Chinese Remainder Theorem:
+ * Algorithm from Joerg Arndt, "Matters Computational",
+ * Chapter 37.4.1 [http://www.jjj.de/fxt/]
+ *
+ * See also Knuth, TAOCP, Volume 2, 4.3.2, exercise 7.
+ */
+
+/*
+ * CRT with carry: x1, x2, x3 contain numbers modulo p1, p2, p3. For each
+ * triple of members of the arrays, find the unique z modulo p1*p2*p3, with
+ * zmax = p1*p2*p3 - 1.
+ *
+ * In each iteration of the loop, split z into result[i] = z % MPD_RADIX
+ * and carry = z / MPD_RADIX. Let N be the size of carry[] and cmax the
+ * maximum carry.
+ *
+ * Limits for the 32-bit build:
+ *
+ * N = 2**96
+ * cmax = 7711435591312380274
+ *
+ * Limits for the 64 bit build:
+ *
+ * N = 2**192
+ * cmax = 627710135393475385904124401220046371710
+ *
+ * The following statements hold for both versions:
+ *
+ * 1) cmax + zmax < N, so the addition does not overflow.
+ *
+ * 2) (cmax + zmax) / MPD_RADIX == cmax.
+ *
+ * 3) If c <= cmax, then c_next = (c + zmax) / MPD_RADIX <= cmax.
+ */
+void
+crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize)
+{
+ mpd_uint_t p1 = mpd_moduli[P1];
+ mpd_uint_t umod;
+#ifdef PPRO
+ double dmod;
+ uint32_t dinvmod[3];
+#endif
+ mpd_uint_t a1, a2, a3;
+ mpd_uint_t s;
+ mpd_uint_t z[3], t[3];
+ mpd_uint_t carry[3] = {0,0,0};
+ mpd_uint_t hi, lo;
+ mpd_size_t i;
+
+ for (i = 0; i < rsize; i++) {
+
+ a1 = x1[i];
+ a2 = x2[i];
+ a3 = x3[i];
+
+ SETMODULUS(P2);
+ s = ext_submod(a2, a1, umod);
+ s = MULMOD(s, INV_P1_MOD_P2);
+
+ _mpd_mul_words(&hi, &lo, s, p1);
+ lo = lo + a1;
+ if (lo < a1) hi++;
+
+ SETMODULUS(P3);
+ s = dw_submod(a3, hi, lo, umod);
+ s = MULMOD(s, INV_P1P2_MOD_P3);
+
+ z[0] = lo;
+ z[1] = hi;
+ z[2] = 0;
+
+ _crt_mulP1P2_3(t, s);
+ _crt_add3(z, t);
+ _crt_add3(carry, z);
+
+ x1[i] = _crt_div3(carry, carry, MPD_RADIX);
+ }
+
+ assert(carry[0] == 0 && carry[1] == 0 && carry[2] == 0);
+}
+
+
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