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Unified Diff: Modules/_decimal/libmpdec/basearith.h

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/basearith.h Sat Mar 10 18:12:20 2012 +0100
@@ -0,0 +1,213 @@
+/*
+ * 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.
+ */
+
+
+#ifndef BASEARITH_H
+#define BASEARITH_H
+
+
+#include "mpdecimal.h"
+#include <stdio.h>
+#include "typearith.h"
+
+
+mpd_uint_t _mpd_baseadd(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+ mpd_size_t m, mpd_size_t n);
+void _mpd_baseaddto(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
+mpd_uint_t _mpd_shortadd(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v);
+mpd_uint_t _mpd_shortadd_b(mpd_uint_t *w, mpd_size_t m, mpd_uint_t v,
+ mpd_uint_t b);
+mpd_uint_t _mpd_baseincr(mpd_uint_t *u, mpd_size_t n);
+void _mpd_basesub(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+ mpd_size_t m, mpd_size_t n);
+void _mpd_basesubfrom(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n);
+void _mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
+ mpd_size_t m, mpd_size_t n);
+void _mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+ mpd_uint_t v);
+void _mpd_shortmul_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+ mpd_uint_t v, mpd_uint_t b);
+mpd_uint_t _mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+ mpd_uint_t v);
+mpd_uint_t _mpd_shortdiv_b(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n,
+ mpd_uint_t v, mpd_uint_t b);
+int _mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r, const mpd_uint_t *uconst,
+ const mpd_uint_t *vconst, mpd_size_t nplusm, mpd_size_t n);
+void _mpd_baseshiftl(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t n,
+ mpd_size_t m, mpd_size_t shift);
+mpd_uint_t _mpd_baseshiftr(mpd_uint_t *dest, mpd_uint_t *src, mpd_size_t slen,
+ mpd_size_t shift);
+
+
+
+#ifdef CONFIG_64
+extern const mpd_uint_t mprime_rdx;
+
+/*
+ * Algorithm from: Division by Invariant Integers using Multiplication,
+ * T. Granlund and P. L. Montgomery, Proceedings of the SIGPLAN '94
+ * Conference on Programming Language Design and Implementation.
+ *
+ * http://gmplib.org/~tege/divcnst-pldi94.pdf
+ *
+ * Variables from the paper and their translations (See section 8):
+ *
+ * N := 64
+ * d := MPD_RADIX
+ * l := 64
+ * m' := floor((2**(64+64) - 1)/MPD_RADIX) - 2**64
+ *
+ * Since N-l == 0:
+ *
+ * dnorm := d
+ * n2 := hi
+ * n10 := lo
+ *
+ * ACL2 proof: mpd-div-words-r-correct
+ */
+static inline void
+_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
+{
+ mpd_uint_t n_adj, h, l, t;
+ mpd_uint_t n1_neg;
+
+ /* n1_neg = if lo >= 2**63 then MPD_UINT_MAX else 0 */
+ n1_neg = (lo & (1ULL<<63)) ? MPD_UINT_MAX : 0;
+ /* n_adj = if lo >= 2**63 then lo+MPD_RADIX else lo */
+ n_adj = lo + (n1_neg & MPD_RADIX);
+
+ /* (h, l) = if lo >= 2**63 then m'*(hi+1) else m'*hi */
+ _mpd_mul_words(&h, &l, mprime_rdx, hi-n1_neg);
+ l = l + n_adj;
+ if (l < n_adj) h++;
+ t = h + hi;
+ /* At this point t == qest, with q == qest or q == qest+1:
+ * 1) 0 <= 2**64*hi + lo - qest*MPD_RADIX < 2*MPD_RADIX
+ */
+
+ /* t = 2**64-1 - qest = 2**64 - (qest+1) */
+ t = MPD_UINT_MAX - t;
+
+ /* (h, l) = 2**64*MPD_RADIX - (qest+1)*MPD_RADIX */
+ _mpd_mul_words(&h, &l, t, MPD_RADIX);
+ l = l + lo;
+ if (l < lo) h++;
+ h += hi;
+ h -= MPD_RADIX;
+ /* (h, l) = 2**64*hi + lo - (qest+1)*MPD_RADIX (mod 2**128)
+ * Case q == qest+1:
+ * a) h == 0, l == r
+ * b) q := h - t == qest+1
+ * c) r := l
+ * Case q == qest:
+ * a) h == MPD_UINT_MAX, l == 2**64-(MPD_RADIX-r)
+ * b) q := h - t == qest
+ * c) r := l + MPD_RADIX = r
+ */
+
+ *q = (h - t);
+ *r = l + (MPD_RADIX & h);
+}
+#else
+static inline void
+_mpd_div_words_r(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo)
+{
+ _mpd_div_words(q, r, hi, lo, MPD_RADIX);
+}
+#endif
+
+
+/* Multiply two single base MPD_RADIX words, store result in array w[2]. */
+static inline void
+_mpd_singlemul(mpd_uint_t w[2], mpd_uint_t u, mpd_uint_t v)
+{
+ mpd_uint_t hi, lo;
+
+ _mpd_mul_words(&hi, &lo, u, v);
+ _mpd_div_words_r(&w[1], &w[0], hi, lo);
+}
+
+/* Multiply u (len 2) and v (len m, 1 <= m <= 2). */
+static inline void
+_mpd_mul_2_le2(mpd_uint_t w[4], mpd_uint_t u[2], mpd_uint_t v[2], mpd_ssize_t m)
+{
+ mpd_uint_t hi, lo;
+
+ _mpd_mul_words(&hi, &lo, u[0], v[0]);
+ _mpd_div_words_r(&w[1], &w[0], hi, lo);
+
+ _mpd_mul_words(&hi, &lo, u[1], v[0]);
+ lo = w[1] + lo;
+ if (lo < w[1]) hi++;
+ _mpd_div_words_r(&w[2], &w[1], hi, lo);
+ if (m == 1) return;
+
+ _mpd_mul_words(&hi, &lo, u[0], v[1]);
+ lo = w[1] + lo;
+ if (lo < w[1]) hi++;
+ _mpd_div_words_r(&w[3], &w[1], hi, lo);
+
+ _mpd_mul_words(&hi, &lo, u[1], v[1]);
+ lo = w[2] + lo;
+ if (lo < w[2]) hi++;
+ lo = w[3] + lo;
+ if (lo < w[3]) hi++;
+ _mpd_div_words_r(&w[3], &w[2], hi, lo);
+}
+
+
+/*
+ * Test if all words from data[len-1] to data[0] are zero. If len is 0, nothing
+ * is tested and the coefficient is regarded as "all zero".
+ */
+static inline int
+_mpd_isallzero(const mpd_uint_t *data, mpd_ssize_t len)
+{
+ while (--len >= 0) {
+ if (data[len] != 0) return 0;
+ }
+ return 1;
+}
+
+/*
+ * Test if all full words from data[len-1] to data[0] are MPD_RADIX-1
+ * (all nines). Return true if len == 0.
+ */
+static inline int
+_mpd_isallnine(const mpd_uint_t *data, mpd_ssize_t len)
+{
+ while (--len >= 0) {
+ if (data[len] != MPD_RADIX-1) return 0;
+ }
+ return 1;
+}
+
+
+#endif /* BASEARITH_H */
+
+
+
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