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Unified Diff: Modules/_decimal/libmpdec/typearith.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/typearith.h Sat Mar 10 18:12:20 2012 +0100
@@ -0,0 +1,669 @@
+/*
+ * 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 TYPEARITH_H
+#define TYPEARITH_H
+
+
+#include "mpdecimal.h"
+
+
+/*****************************************************************************/
+/* Low level native arithmetic on basic types */
+/*****************************************************************************/
+
+
+/** ------------------------------------------------------------
+ ** Double width multiplication and division
+ ** ------------------------------------------------------------
+ */
+
+#if defined(CONFIG_64)
+#if defined(ANSI)
+#if defined(HAVE_UINT128_T)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+ __uint128_t hl;
+
+ hl = (__uint128_t)a * b;
+
+ *hi = hl >> 64;
+ *lo = (mpd_uint_t)hl;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+ mpd_uint_t d)
+{
+ __uint128_t hl;
+
+ hl = ((__uint128_t)hi<<64) + lo;
+ *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */
+ *r = (mpd_uint_t)(hl - (__uint128_t)(*q) * d);
+}
+#else
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+ uint32_t w[4], carry;
+ uint32_t ah, al, bh, bl;
+ uint64_t hl;
+
+ ah = (uint32_t)(a>>32); al = (uint32_t)a;
+ bh = (uint32_t)(b>>32); bl = (uint32_t)b;
+
+ hl = (uint64_t)al * bl;
+ w[0] = (uint32_t)hl;
+ carry = (uint32_t)(hl>>32);
+
+ hl = (uint64_t)ah * bl + carry;
+ w[1] = (uint32_t)hl;
+ w[2] = (uint32_t)(hl>>32);
+
+ hl = (uint64_t)al * bh + w[1];
+ w[1] = (uint32_t)hl;
+ carry = (uint32_t)(hl>>32);
+
+ hl = ((uint64_t)ah * bh + w[2]) + carry;
+ w[2] = (uint32_t)hl;
+ w[3] = (uint32_t)(hl>>32);
+
+ *hi = ((uint64_t)w[3]<<32) + w[2];
+ *lo = ((uint64_t)w[1]<<32) + w[0];
+}
+
+/*
+ * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt
+ * http://www.hackersdelight.org/permissions.htm:
+ * "You are free to use, copy, and distribute any of the code on this web
+ * site, whether modified by you or not. You need not give attribution."
+ *
+ * Slightly modified, comments are mine.
+ */
+static inline int
+nlz(uint64_t x)
+{
+ int n;
+
+ if (x == 0) return(64);
+
+ n = 0;
+ if (x <= 0x00000000FFFFFFFF) {n = n +32; x = x <<32;}
+ if (x <= 0x0000FFFFFFFFFFFF) {n = n +16; x = x <<16;}
+ if (x <= 0x00FFFFFFFFFFFFFF) {n = n + 8; x = x << 8;}
+ if (x <= 0x0FFFFFFFFFFFFFFF) {n = n + 4; x = x << 4;}
+ if (x <= 0x3FFFFFFFFFFFFFFF) {n = n + 2; x = x << 2;}
+ if (x <= 0x7FFFFFFFFFFFFFFF) {n = n + 1;}
+
+ return n;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0,
+ mpd_uint_t v)
+{
+ const mpd_uint_t b = 4294967296;
+ mpd_uint_t un1, un0,
+ vn1, vn0,
+ q1, q0,
+ un32, un21, un10,
+ rhat, t;
+ int s;
+
+ assert(u1 < v);
+
+ s = nlz(v);
+ v = v << s;
+ vn1 = v >> 32;
+ vn0 = v & 0xFFFFFFFF;
+
+ t = (s == 0) ? 0 : u0 >> (64 - s);
+ un32 = (u1 << s) | t;
+ un10 = u0 << s;
+
+ un1 = un10 >> 32;
+ un0 = un10 & 0xFFFFFFFF;
+
+ q1 = un32 / vn1;
+ rhat = un32 - q1*vn1;
+again1:
+ if (q1 >= b || q1*vn0 > b*rhat + un1) {
+ q1 = q1 - 1;
+ rhat = rhat + vn1;
+ if (rhat < b) goto again1;
+ }
+
+ /*
+ * Before again1 we had:
+ * (1) q1*vn1 + rhat = un32
+ * (2) q1*vn1*b + rhat*b + un1 = un32*b + un1
+ *
+ * The statements inside the if-clause do not change the value
+ * of the left-hand side of (2), and the loop is only exited
+ * if q1*vn0 <= rhat*b + un1, so:
+ *
+ * (3) q1*vn1*b + q1*vn0 <= un32*b + un1
+ * (4) q1*v <= un32*b + un1
+ * (5) 0 <= un32*b + un1 - q1*v
+ *
+ * By (5) we are certain that the possible add-back step from
+ * Knuth's algorithm D is never required.
+ *
+ * Since the final quotient is less than 2**64, the following
+ * must be true:
+ *
+ * (6) un32*b + un1 - q1*v <= UINT64_MAX
+ *
+ * This means that in the following line, the high words
+ * of un32*b and q1*v can be discarded without any effect
+ * on the result.
+ */
+ un21 = un32*b + un1 - q1*v;
+
+ q0 = un21 / vn1;
+ rhat = un21 - q0*vn1;
+again2:
+ if (q0 >= b || q0*vn0 > b*rhat + un0) {
+ q0 = q0 - 1;
+ rhat = rhat + vn1;
+ if (rhat < b) goto again2;
+ }
+
+ *q = q1*b + q0;
+ *r = (un21*b + un0 - q0*v) >> s;
+}
+#endif
+
+/* END ANSI */
+#elif defined(ASM)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+ mpd_uint_t h, l;
+
+ asm ( "mulq %3\n\t"
+ : "=d" (h), "=a" (l)
+ : "%a" (a), "rm" (b)
+ : "cc"
+ );
+
+ *hi = h;
+ *lo = l;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+ mpd_uint_t d)
+{
+ mpd_uint_t qq, rr;
+
+ asm ( "divq %4\n\t"
+ : "=a" (qq), "=d" (rr)
+ : "a" (lo), "d" (hi), "rm" (d)
+ : "cc"
+ );
+
+ *q = qq;
+ *r = rr;
+}
+/* END GCC ASM */
+#elif defined(MASM)
+#include <intrin.h>
+#pragma intrinsic(_umul128)
+
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+ *lo = _umul128(a, b, hi);
+}
+
+void _mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+ mpd_uint_t d);
+
+/* END MASM (_MSC_VER) */
+#else
+ #error "need platform specific 128 bit multiplication and division"
+#endif
+
+#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d
+static inline void
+_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp)
+{
+ assert(exp <= 19);
+
+ if (exp <= 9) {
+ if (exp <= 4) {
+ switch (exp) {
+ case 0: *q = v; *r = 0; break;
+ case 1: DIVMOD(q, r, v, 10UL); break;
+ case 2: DIVMOD(q, r, v, 100UL); break;
+ case 3: DIVMOD(q, r, v, 1000UL); break;
+ case 4: DIVMOD(q, r, v, 10000UL); break;
+ }
+ }
+ else {
+ switch (exp) {
+ case 5: DIVMOD(q, r, v, 100000UL); break;
+ case 6: DIVMOD(q, r, v, 1000000UL); break;
+ case 7: DIVMOD(q, r, v, 10000000UL); break;
+ case 8: DIVMOD(q, r, v, 100000000UL); break;
+ case 9: DIVMOD(q, r, v, 1000000000UL); break;
+ }
+ }
+ }
+ else {
+ if (exp <= 14) {
+ switch (exp) {
+ case 10: DIVMOD(q, r, v, 10000000000ULL); break;
+ case 11: DIVMOD(q, r, v, 100000000000ULL); break;
+ case 12: DIVMOD(q, r, v, 1000000000000ULL); break;
+ case 13: DIVMOD(q, r, v, 10000000000000ULL); break;
+ case 14: DIVMOD(q, r, v, 100000000000000ULL); break;
+ }
+ }
+ else {
+ switch (exp) {
+ case 15: DIVMOD(q, r, v, 1000000000000000ULL); break;
+ case 16: DIVMOD(q, r, v, 10000000000000000ULL); break;
+ case 17: DIVMOD(q, r, v, 100000000000000000ULL); break;
+ case 18: DIVMOD(q, r, v, 1000000000000000000ULL); break;
+ case 19: DIVMOD(q, r, v, 10000000000000000000ULL); break; /* GCOV_NOT_REACHED */
+ }
+ }
+ }
+}
+
+/* END CONFIG_64 */
+#elif defined(CONFIG_32)
+#if defined(ANSI)
+#if !defined(LEGACY_COMPILER)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+ mpd_uuint_t hl;
+
+ hl = (mpd_uuint_t)a * b;
+
+ *hi = hl >> 32;
+ *lo = (mpd_uint_t)hl;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+ mpd_uint_t d)
+{
+ mpd_uuint_t hl;
+
+ hl = ((mpd_uuint_t)hi<<32) + lo;
+ *q = (mpd_uint_t)(hl / d); /* quotient is known to fit */
+ *r = (mpd_uint_t)(hl - (mpd_uuint_t)(*q) * d);
+}
+/* END ANSI + uint64_t */
+#else
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+ uint16_t w[4], carry;
+ uint16_t ah, al, bh, bl;
+ uint32_t hl;
+
+ ah = (uint16_t)(a>>16); al = (uint16_t)a;
+ bh = (uint16_t)(b>>16); bl = (uint16_t)b;
+
+ hl = (uint32_t)al * bl;
+ w[0] = (uint16_t)hl;
+ carry = (uint16_t)(hl>>16);
+
+ hl = (uint32_t)ah * bl + carry;
+ w[1] = (uint16_t)hl;
+ w[2] = (uint16_t)(hl>>16);
+
+ hl = (uint32_t)al * bh + w[1];
+ w[1] = (uint16_t)hl;
+ carry = (uint16_t)(hl>>16);
+
+ hl = ((uint32_t)ah * bh + w[2]) + carry;
+ w[2] = (uint16_t)hl;
+ w[3] = (uint16_t)(hl>>16);
+
+ *hi = ((uint32_t)w[3]<<16) + w[2];
+ *lo = ((uint32_t)w[1]<<16) + w[0];
+}
+
+/*
+ * By Henry S. Warren: http://www.hackersdelight.org/HDcode/divlu.c.txt
+ * http://www.hackersdelight.org/permissions.htm:
+ * "You are free to use, copy, and distribute any of the code on this web
+ * site, whether modified by you or not. You need not give attribution."
+ *
+ * Slightly modified, comments are mine.
+ */
+static inline int
+nlz(uint32_t x)
+{
+ int n;
+
+ if (x == 0) return(32);
+
+ n = 0;
+ if (x <= 0x0000FFFF) {n = n +16; x = x <<16;}
+ if (x <= 0x00FFFFFF) {n = n + 8; x = x << 8;}
+ if (x <= 0x0FFFFFFF) {n = n + 4; x = x << 4;}
+ if (x <= 0x3FFFFFFF) {n = n + 2; x = x << 2;}
+ if (x <= 0x7FFFFFFF) {n = n + 1;}
+
+ return n;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t u1, mpd_uint_t u0,
+ mpd_uint_t v)
+{
+ const mpd_uint_t b = 65536;
+ mpd_uint_t un1, un0,
+ vn1, vn0,
+ q1, q0,
+ un32, un21, un10,
+ rhat, t;
+ int s;
+
+ assert(u1 < v);
+
+ s = nlz(v);
+ v = v << s;
+ vn1 = v >> 16;
+ vn0 = v & 0xFFFF;
+
+ t = (s == 0) ? 0 : u0 >> (32 - s);
+ un32 = (u1 << s) | t;
+ un10 = u0 << s;
+
+ un1 = un10 >> 16;
+ un0 = un10 & 0xFFFF;
+
+ q1 = un32 / vn1;
+ rhat = un32 - q1*vn1;
+again1:
+ if (q1 >= b || q1*vn0 > b*rhat + un1) {
+ q1 = q1 - 1;
+ rhat = rhat + vn1;
+ if (rhat < b) goto again1;
+ }
+
+ /*
+ * Before again1 we had:
+ * (1) q1*vn1 + rhat = un32
+ * (2) q1*vn1*b + rhat*b + un1 = un32*b + un1
+ *
+ * The statements inside the if-clause do not change the value
+ * of the left-hand side of (2), and the loop is only exited
+ * if q1*vn0 <= rhat*b + un1, so:
+ *
+ * (3) q1*vn1*b + q1*vn0 <= un32*b + un1
+ * (4) q1*v <= un32*b + un1
+ * (5) 0 <= un32*b + un1 - q1*v
+ *
+ * By (5) we are certain that the possible add-back step from
+ * Knuth's algorithm D is never required.
+ *
+ * Since the final quotient is less than 2**32, the following
+ * must be true:
+ *
+ * (6) un32*b + un1 - q1*v <= UINT32_MAX
+ *
+ * This means that in the following line, the high words
+ * of un32*b and q1*v can be discarded without any effect
+ * on the result.
+ */
+ un21 = un32*b + un1 - q1*v;
+
+ q0 = un21 / vn1;
+ rhat = un21 - q0*vn1;
+again2:
+ if (q0 >= b || q0*vn0 > b*rhat + un0) {
+ q0 = q0 - 1;
+ rhat = rhat + vn1;
+ if (rhat < b) goto again2;
+ }
+
+ *q = q1*b + q0;
+ *r = (un21*b + un0 - q0*v) >> s;
+}
+#endif /* END ANSI + LEGACY_COMPILER */
+
+/* END ANSI */
+#elif defined(ASM)
+static inline void
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+ mpd_uint_t h, l;
+
+ asm ( "mull %3\n\t"
+ : "=d" (h), "=a" (l)
+ : "%a" (a), "rm" (b)
+ : "cc"
+ );
+
+ *hi = h;
+ *lo = l;
+}
+
+static inline void
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+ mpd_uint_t d)
+{
+ mpd_uint_t qq, rr;
+
+ asm ( "divl %4\n\t"
+ : "=a" (qq), "=d" (rr)
+ : "a" (lo), "d" (hi), "rm" (d)
+ : "cc"
+ );
+
+ *q = qq;
+ *r = rr;
+}
+/* END GCC ASM */
+#elif defined(MASM)
+static inline void __cdecl
+_mpd_mul_words(mpd_uint_t *hi, mpd_uint_t *lo, mpd_uint_t a, mpd_uint_t b)
+{
+ mpd_uint_t h, l;
+
+ __asm {
+ mov eax, a
+ mul b
+ mov h, edx
+ mov l, eax
+ }
+
+ *hi = h;
+ *lo = l;
+}
+
+static inline void __cdecl
+_mpd_div_words(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t hi, mpd_uint_t lo,
+ mpd_uint_t d)
+{
+ mpd_uint_t qq, rr;
+
+ __asm {
+ mov eax, lo
+ mov edx, hi
+ div d
+ mov qq, eax
+ mov rr, edx
+ }
+
+ *q = qq;
+ *r = rr;
+}
+/* END MASM (_MSC_VER) */
+#else
+ #error "need platform specific 64 bit multiplication and division"
+#endif
+
+#define DIVMOD(q, r, v, d) *q = v / d; *r = v - *q * d
+static inline void
+_mpd_divmod_pow10(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t exp)
+{
+ assert(exp <= 9);
+
+ if (exp <= 4) {
+ switch (exp) {
+ case 0: *q = v; *r = 0; break;
+ case 1: DIVMOD(q, r, v, 10UL); break;
+ case 2: DIVMOD(q, r, v, 100UL); break;
+ case 3: DIVMOD(q, r, v, 1000UL); break;
+ case 4: DIVMOD(q, r, v, 10000UL); break;
+ }
+ }
+ else {
+ switch (exp) {
+ case 5: DIVMOD(q, r, v, 100000UL); break;
+ case 6: DIVMOD(q, r, v, 1000000UL); break;
+ case 7: DIVMOD(q, r, v, 10000000UL); break;
+ case 8: DIVMOD(q, r, v, 100000000UL); break;
+ case 9: DIVMOD(q, r, v, 1000000000UL); break; /* GCOV_NOT_REACHED */
+ }
+ }
+}
+/* END CONFIG_32 */
+
+/* NO CONFIG */
+#else
+ #error "define CONFIG_64 or CONFIG_32"
+#endif /* CONFIG */
+
+
+static inline void
+_mpd_div_word(mpd_uint_t *q, mpd_uint_t *r, mpd_uint_t v, mpd_uint_t d)
+{
+ *q = v / d;
+ *r = v - *q * d;
+}
+
+static inline void
+_mpd_idiv_word(mpd_ssize_t *q, mpd_ssize_t *r, mpd_ssize_t v, mpd_ssize_t d)
+{
+ *q = v / d;
+ *r = v - *q * d;
+}
+
+
+/** ------------------------------------------------------------
+ ** Arithmetic with overflow checking
+ ** ------------------------------------------------------------
+ */
+
+/* The following macros do call exit() in case of an overflow.
+ If the library is used correctly (i.e. with valid context
+ parameters), such overflows cannot occur. The macros are used
+ as sanity checks in a couple of strategic places and should
+ be viewed as a handwritten version of gcc's -ftrapv option. */
+
+static inline mpd_size_t
+add_size_t(mpd_size_t a, mpd_size_t b)
+{
+ if (a > MPD_SIZE_MAX - b) {
+ mpd_err_fatal("add_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+ }
+ return a + b;
+}
+
+static inline mpd_size_t
+sub_size_t(mpd_size_t a, mpd_size_t b)
+{
+ if (b > a) {
+ mpd_err_fatal("sub_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+ }
+ return a - b;
+}
+
+#if MPD_SIZE_MAX != MPD_UINT_MAX
+ #error "adapt mul_size_t() and mulmod_size_t()"
+#endif
+
+static inline mpd_size_t
+mul_size_t(mpd_size_t a, mpd_size_t b)
+{
+ mpd_uint_t hi, lo;
+
+ _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
+ if (hi) {
+ mpd_err_fatal("mul_size_t(): overflow: check the context"); /* GCOV_NOT_REACHED */
+ }
+ return lo;
+}
+
+static inline mpd_size_t
+add_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow)
+{
+ mpd_size_t ret;
+
+ *overflow = 0;
+ ret = a + b;
+ if (ret < a) *overflow = 1;
+ return ret;
+}
+
+static inline mpd_size_t
+mul_size_t_overflow(mpd_size_t a, mpd_size_t b, mpd_size_t *overflow)
+{
+ mpd_uint_t lo;
+
+ _mpd_mul_words((mpd_uint_t *)overflow, &lo, (mpd_uint_t)a,
+ (mpd_uint_t)b);
+ return lo;
+}
+
+static inline mpd_ssize_t
+mod_mpd_ssize_t(mpd_ssize_t a, mpd_ssize_t m)
+{
+ mpd_ssize_t r = a % m;
+ return (r < 0) ? r + m : r;
+}
+
+static inline mpd_size_t
+mulmod_size_t(mpd_size_t a, mpd_size_t b, mpd_size_t m)
+{
+ mpd_uint_t hi, lo;
+ mpd_uint_t q, r;
+
+ _mpd_mul_words(&hi, &lo, (mpd_uint_t)a, (mpd_uint_t)b);
+ _mpd_div_words(&q, &r, hi, lo, (mpd_uint_t)m);
+
+ return r;
+}
+
+
+#endif /* TYPEARITH_H */
+
+
+
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