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Unified Diff: Modules/_decimal/libmpdec/mpdecimal.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/mpdecimal.c Sat Mar 10 18:12:20 2012 +0100
@@ -0,0 +1,7555 @@
+/*
+ * 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 <stdlib.h>
+#include <string.h>
+#include <limits.h>
+#include <math.h>
+#include "basearith.h"
+#include "bits.h"
+#include "convolute.h"
+#include "crt.h"
+#include "errno.h"
+#include "memory.h"
+#include "typearith.h"
+#include "umodarith.h"
+
+#ifdef PPRO
+ #if defined(_MSC_VER)
+ #include <float.h>
+ #pragma fenv_access(on)
+ #elif !defined(__OpenBSD__) && !defined(__NetBSD__)
+ /* C99 */
+ #include <fenv.h>
+ #pragma STDC FENV_ACCESS ON
+ #endif
+#endif
+
+#if defined(__x86_64__) && defined(__GLIBC__) && !defined(__INTEL_COMPILER)
+ #define USE_80BIT_LONG_DOUBLE
+#endif
+
+#if defined(_MSC_VER)
+ #define ALWAYS_INLINE __forceinline
+#elif defined(LEGACY_COMPILER)
+ #define ALWAYS_INLINE
+ #undef inline
+ #define inline
+#else
+ #ifdef TEST_COVERAGE
+ #define ALWAYS_INLINE
+ #else
+ #define ALWAYS_INLINE inline __attribute__ ((always_inline))
+ #endif
+#endif
+
+
+#define MPD_NEWTONDIV_CUTOFF 1024L
+
+#define MPD_NEW_STATIC(name, flags, exp, digits, len) \
+ mpd_uint_t name##_data[MPD_MINALLOC_MAX]; \
+ mpd_t name = {flags|MPD_STATIC|MPD_STATIC_DATA, exp, digits, \
+ len, MPD_MINALLOC_MAX, name##_data}
+
+#define MPD_NEW_CONST(name, flags, exp, digits, len, alloc, initval) \
+ mpd_uint_t name##_data[alloc] = {initval}; \
+ mpd_t name = {flags|MPD_STATIC|MPD_CONST_DATA, exp, digits, \
+ len, alloc, name##_data}
+
+#define MPD_NEW_SHARED(name, a) \
+ mpd_t name = {(a->flags&~MPD_DATAFLAGS)|MPD_STATIC|MPD_SHARED_DATA, \
+ a->exp, a->digits, a->len, a->alloc, a->data}
+
+
+static mpd_uint_t data_one[1] = {1};
+static mpd_uint_t data_zero[1] = {0};
+static const mpd_t one = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_one};
+static const mpd_t minus_one = {MPD_NEG|MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1,
+ data_one};
+static const mpd_t zero = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_zero};
+
+static inline void _mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx,
+ uint32_t *status);
+static void _settriple(mpd_t *result, uint8_t sign, mpd_uint_t a,
+ mpd_ssize_t exp);
+static inline mpd_ssize_t _mpd_real_size(mpd_uint_t *data, mpd_ssize_t size);
+
+static void _mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status);
+static inline void _mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status);
+static void _mpd_qbarrett_divmod(mpd_t *q, mpd_t *r, const mpd_t *a,
+ const mpd_t *b, uint32_t *status);
+static inline void _mpd_qpow_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp,
+ uint8_t resultsign, const mpd_context_t *ctx, uint32_t *status);
+
+mpd_uint_t mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n);
+
+
+/******************************************************************************/
+/* Performance critical inline functions */
+/******************************************************************************/
+
+#ifdef CONFIG_64
+/* Digits in a word, primarily useful for the most significant word. */
+ALWAYS_INLINE int
+mpd_word_digits(mpd_uint_t word)
+{
+ if (word < mpd_pow10[9]) {
+ if (word < mpd_pow10[4]) {
+ if (word < mpd_pow10[2]) {
+ return (word < mpd_pow10[1]) ? 1 : 2;
+ }
+ return (word < mpd_pow10[3]) ? 3 : 4;
+ }
+ if (word < mpd_pow10[6]) {
+ return (word < mpd_pow10[5]) ? 5 : 6;
+ }
+ if (word < mpd_pow10[8]) {
+ return (word < mpd_pow10[7]) ? 7 : 8;
+ }
+ return 9;
+ }
+ if (word < mpd_pow10[14]) {
+ if (word < mpd_pow10[11]) {
+ return (word < mpd_pow10[10]) ? 10 : 11;
+ }
+ if (word < mpd_pow10[13]) {
+ return (word < mpd_pow10[12]) ? 12 : 13;
+ }
+ return 14;
+ }
+ if (word < mpd_pow10[18]) {
+ if (word < mpd_pow10[16]) {
+ return (word < mpd_pow10[15]) ? 15 : 16;
+ }
+ return (word < mpd_pow10[17]) ? 17 : 18;
+ }
+
+ return (word < mpd_pow10[19]) ? 19 : 20;
+}
+#else
+ALWAYS_INLINE int
+mpd_word_digits(mpd_uint_t word)
+{
+ if (word < mpd_pow10[4]) {
+ if (word < mpd_pow10[2]) {
+ return (word < mpd_pow10[1]) ? 1 : 2;
+ }
+ return (word < mpd_pow10[3]) ? 3 : 4;
+ }
+ if (word < mpd_pow10[6]) {
+ return (word < mpd_pow10[5]) ? 5 : 6;
+ }
+ if (word < mpd_pow10[8]) {
+ return (word < mpd_pow10[7]) ? 7 : 8;
+ }
+
+ return (word < mpd_pow10[9]) ? 9 : 10;
+}
+#endif
+
+
+/* Adjusted exponent */
+ALWAYS_INLINE mpd_ssize_t
+mpd_adjexp(const mpd_t *dec)
+{
+ return (dec->exp + dec->digits) - 1;
+}
+
+/* Etiny */
+ALWAYS_INLINE mpd_ssize_t
+mpd_etiny(const mpd_context_t *ctx)
+{
+ return ctx->emin - (ctx->prec - 1);
+}
+
+/* Etop: used for folding down in IEEE clamping */
+ALWAYS_INLINE mpd_ssize_t
+mpd_etop(const mpd_context_t *ctx)
+{
+ return ctx->emax - (ctx->prec - 1);
+}
+
+/* Most significant word */
+ALWAYS_INLINE mpd_uint_t
+mpd_msword(const mpd_t *dec)
+{
+ assert(dec->len > 0);
+ return dec->data[dec->len-1];
+}
+
+/* Most significant digit of a word */
+inline mpd_uint_t
+mpd_msd(mpd_uint_t word)
+{
+ int n;
+
+ n = mpd_word_digits(word);
+ return word / mpd_pow10[n-1];
+}
+
+/* Least significant digit of a word */
+ALWAYS_INLINE mpd_uint_t
+mpd_lsd(mpd_uint_t word)
+{
+ return word % 10;
+}
+
+/* Coefficient size needed to store 'digits' */
+ALWAYS_INLINE mpd_ssize_t
+mpd_digits_to_size(mpd_ssize_t digits)
+{
+ mpd_ssize_t q, r;
+
+ _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS);
+ return (r == 0) ? q : q+1;
+}
+
+/* Number of digits in the exponent. Not defined for MPD_SSIZE_MIN. */
+inline int
+mpd_exp_digits(mpd_ssize_t exp)
+{
+ exp = (exp < 0) ? -exp : exp;
+ return mpd_word_digits(exp);
+}
+
+/* Canonical */
+ALWAYS_INLINE int
+mpd_iscanonical(const mpd_t *dec UNUSED)
+{
+ return 1;
+}
+
+/* Finite */
+ALWAYS_INLINE int
+mpd_isfinite(const mpd_t *dec)
+{
+ return !(dec->flags & MPD_SPECIAL);
+}
+
+/* Infinite */
+ALWAYS_INLINE int
+mpd_isinfinite(const mpd_t *dec)
+{
+ return dec->flags & MPD_INF;
+}
+
+/* NaN */
+ALWAYS_INLINE int
+mpd_isnan(const mpd_t *dec)
+{
+ return dec->flags & (MPD_NAN|MPD_SNAN);
+}
+
+/* Negative */
+ALWAYS_INLINE int
+mpd_isnegative(const mpd_t *dec)
+{
+ return dec->flags & MPD_NEG;
+}
+
+/* Positive */
+ALWAYS_INLINE int
+mpd_ispositive(const mpd_t *dec)
+{
+ return !(dec->flags & MPD_NEG);
+}
+
+/* qNaN */
+ALWAYS_INLINE int
+mpd_isqnan(const mpd_t *dec)
+{
+ return dec->flags & MPD_NAN;
+}
+
+/* Signed */
+ALWAYS_INLINE int
+mpd_issigned(const mpd_t *dec)
+{
+ return dec->flags & MPD_NEG;
+}
+
+/* sNaN */
+ALWAYS_INLINE int
+mpd_issnan(const mpd_t *dec)
+{
+ return dec->flags & MPD_SNAN;
+}
+
+/* Special */
+ALWAYS_INLINE int
+mpd_isspecial(const mpd_t *dec)
+{
+ return dec->flags & MPD_SPECIAL;
+}
+
+/* Zero */
+ALWAYS_INLINE int
+mpd_iszero(const mpd_t *dec)
+{
+ return !mpd_isspecial(dec) && mpd_msword(dec) == 0;
+}
+
+/* Test for zero when specials have been ruled out already */
+ALWAYS_INLINE int
+mpd_iszerocoeff(const mpd_t *dec)
+{
+ return mpd_msword(dec) == 0;
+}
+
+/* Normal */
+inline int
+mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx)
+{
+ if (mpd_isspecial(dec)) return 0;
+ if (mpd_iszerocoeff(dec)) return 0;
+
+ return mpd_adjexp(dec) >= ctx->emin;
+}
+
+/* Subnormal */
+inline int
+mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx)
+{
+ if (mpd_isspecial(dec)) return 0;
+ if (mpd_iszerocoeff(dec)) return 0;
+
+ return mpd_adjexp(dec) < ctx->emin;
+}
+
+/* Odd word */
+ALWAYS_INLINE int
+mpd_isoddword(mpd_uint_t word)
+{
+ return word & 1;
+}
+
+/* Odd coefficient */
+ALWAYS_INLINE int
+mpd_isoddcoeff(const mpd_t *dec)
+{
+ return mpd_isoddword(dec->data[0]);
+}
+
+/* 0 if dec is positive, 1 if dec is negative */
+ALWAYS_INLINE uint8_t
+mpd_sign(const mpd_t *dec)
+{
+ return dec->flags & MPD_NEG;
+}
+
+/* 1 if dec is positive, -1 if dec is negative */
+ALWAYS_INLINE int
+mpd_arith_sign(const mpd_t *dec)
+{
+ return 1 - 2 * mpd_isnegative(dec);
+}
+
+/* Radix */
+ALWAYS_INLINE long
+mpd_radix(void)
+{
+ return 10;
+}
+
+/* Dynamic decimal */
+ALWAYS_INLINE int
+mpd_isdynamic(mpd_t *dec)
+{
+ return !(dec->flags & MPD_STATIC);
+}
+
+/* Static decimal */
+ALWAYS_INLINE int
+mpd_isstatic(mpd_t *dec)
+{
+ return dec->flags & MPD_STATIC;
+}
+
+/* Data of decimal is dynamic */
+ALWAYS_INLINE int
+mpd_isdynamic_data(mpd_t *dec)
+{
+ return !(dec->flags & MPD_DATAFLAGS);
+}
+
+/* Data of decimal is static */
+ALWAYS_INLINE int
+mpd_isstatic_data(mpd_t *dec)
+{
+ return dec->flags & MPD_STATIC_DATA;
+}
+
+/* Data of decimal is shared */
+ALWAYS_INLINE int
+mpd_isshared_data(mpd_t *dec)
+{
+ return dec->flags & MPD_SHARED_DATA;
+}
+
+/* Data of decimal is const */
+ALWAYS_INLINE int
+mpd_isconst_data(mpd_t *dec)
+{
+ return dec->flags & MPD_CONST_DATA;
+}
+
+
+/******************************************************************************/
+/* Inline memory handling */
+/******************************************************************************/
+
+/* Fill destination with zeros */
+ALWAYS_INLINE void
+mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len)
+{
+ mpd_size_t i;
+
+ for (i = 0; i < len; i++) {
+ dest[i] = 0;
+ }
+}
+
+/* Free a decimal */
+ALWAYS_INLINE void
+mpd_del(mpd_t *dec)
+{
+ if (mpd_isdynamic_data(dec)) {
+ mpd_free(dec->data);
+ }
+ if (mpd_isdynamic(dec)) {
+ mpd_free(dec);
+ }
+}
+
+/*
+ * Update the memory size for the coefficient. Existing data up to size is
+ * left untouched.
+ *
+ * Error handling: When relloc fails, result->data will still be a valid pointer
+ * to the old memory area of size result->len. If the requested size is less than
+ * result->len, we can continue normally, so we treat the failure as a soft error.
+ * If the requested size is greater than the old area, MPD_Malloc_error is
+ * set and the result will be a NaN.
+ */
+ALWAYS_INLINE int
+mpd_qresize(mpd_t *result, mpd_ssize_t size, uint32_t *status)
+{
+ assert(!mpd_isconst_data(result)); /* illegal operation for a const */
+ assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
+
+ if (mpd_isstatic_data(result)) {
+ if (size > result->alloc) {
+ return mpd_switch_to_dyn(result, size, status);
+ }
+ }
+ else if (size != result->alloc && size >= MPD_MINALLOC) {
+ return mpd_realloc_dyn(result, size, status);
+ }
+
+ return 1;
+}
+
+/* Same as mpd_qresize, but the complete coefficient (including the old
+ * memory area!) is initialized to zero. */
+ALWAYS_INLINE int
+mpd_qresize_zero(mpd_t *result, mpd_ssize_t size, uint32_t *status)
+{
+ assert(!mpd_isconst_data(result)); /* illegal operation for a const */
+ assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
+
+ if (mpd_isstatic_data(result)) {
+ if (size > result->alloc) {
+ return mpd_switch_to_dyn_zero(result, size, status);
+ }
+ }
+ else if (size != result->alloc && size >= MPD_MINALLOC) {
+ if (!mpd_realloc_dyn(result, size, status)) {
+ return 0;
+ }
+ }
+
+ mpd_uint_zero(result->data, size);
+
+ return 1;
+}
+
+/*
+ * Reduce memory size for the coefficient to MPD_MINALLOC. In theory,
+ * realloc may fail even when reducing the memory size. But in that case
+ * the old memory area is always big enough, so checking for MPD_Malloc_error
+ * is not imperative.
+ */
+ALWAYS_INLINE void
+mpd_minalloc(mpd_t *result)
+{
+ assert(!mpd_isconst_data(result)); /* illegal operation for a const */
+ assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
+
+ if (!mpd_isstatic_data(result) && result->alloc > MPD_MINALLOC) {
+ uint8_t err = 0;
+ result->data = mpd_realloc(result->data, MPD_MINALLOC,
+ sizeof *result->data, &err);
+ if (!err) {
+ result->alloc = MPD_MINALLOC;
+ }
+ }
+}
+
+int
+mpd_resize(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx)
+{
+ uint32_t status = 0;
+ if (!mpd_qresize(result, size, &status)) {
+ mpd_addstatus_raise(ctx, status);
+ return 0;
+ }
+ return 1;
+}
+
+int
+mpd_resize_zero(mpd_t *result, mpd_ssize_t size, mpd_context_t *ctx)
+{
+ uint32_t status = 0;
+ if (!mpd_qresize_zero(result, size, &status)) {
+ mpd_addstatus_raise(ctx, status);
+ return 0;
+ }
+ return 1;
+}
+
+
+/******************************************************************************/
+/* Set attributes of a decimal */
+/******************************************************************************/
+
+/* Set digits. result->len is assumed to be correct. */
+inline void
+mpd_setdigits(mpd_t *result)
+{
+ mpd_ssize_t wdigits = mpd_word_digits(mpd_msword(result));
+ result->digits = wdigits + (result->len-1) * MPD_RDIGITS;
+}
+
+/* Set sign */
+ALWAYS_INLINE void
+mpd_set_sign(mpd_t *result, uint8_t sign)
+{
+ result->flags &= ~MPD_NEG;
+ result->flags |= sign;
+}
+
+/* Copy sign from another decimal */
+ALWAYS_INLINE void
+mpd_signcpy(mpd_t *result, mpd_t *a)
+{
+ uint8_t sign = a->flags&MPD_NEG;
+
+ result->flags &= ~MPD_NEG;
+ result->flags |= sign;
+}
+
+/* Set infinity */
+ALWAYS_INLINE void
+mpd_set_infinity(mpd_t *result)
+{
+ result->flags &= ~MPD_SPECIAL;
+ result->flags |= MPD_INF;
+}
+
+/* Set qNaN */
+ALWAYS_INLINE void
+mpd_set_qnan(mpd_t *result)
+{
+ result->flags &= ~MPD_SPECIAL;
+ result->flags |= MPD_NAN;
+}
+
+/* Set sNaN */
+ALWAYS_INLINE void
+mpd_set_snan(mpd_t *result)
+{
+ result->flags &= ~MPD_SPECIAL;
+ result->flags |= MPD_SNAN;
+}
+
+/* Set to negative */
+ALWAYS_INLINE void
+mpd_set_negative(mpd_t *result)
+{
+ result->flags |= MPD_NEG;
+}
+
+/* Set to positive */
+ALWAYS_INLINE void
+mpd_set_positive(mpd_t *result)
+{
+ result->flags &= ~MPD_NEG;
+}
+
+/* Set to dynamic */
+ALWAYS_INLINE void
+mpd_set_dynamic(mpd_t *result)
+{
+ result->flags &= ~MPD_STATIC;
+}
+
+/* Set to static */
+ALWAYS_INLINE void
+mpd_set_static(mpd_t *result)
+{
+ result->flags |= MPD_STATIC;
+}
+
+/* Set data to dynamic */
+ALWAYS_INLINE void
+mpd_set_dynamic_data(mpd_t *result)
+{
+ result->flags &= ~MPD_DATAFLAGS;
+}
+
+/* Set data to static */
+ALWAYS_INLINE void
+mpd_set_static_data(mpd_t *result)
+{
+ result->flags &= ~MPD_DATAFLAGS;
+ result->flags |= MPD_STATIC_DATA;
+}
+
+/* Set data to shared */
+ALWAYS_INLINE void
+mpd_set_shared_data(mpd_t *result)
+{
+ result->flags &= ~MPD_DATAFLAGS;
+ result->flags |= MPD_SHARED_DATA;
+}
+
+/* Set data to const */
+ALWAYS_INLINE void
+mpd_set_const_data(mpd_t *result)
+{
+ result->flags &= ~MPD_DATAFLAGS;
+ result->flags |= MPD_CONST_DATA;
+}
+
+/* Clear flags, preserving memory attributes. */
+ALWAYS_INLINE void
+mpd_clear_flags(mpd_t *result)
+{
+ result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
+}
+
+/* Set flags, preserving memory attributes. */
+ALWAYS_INLINE void
+mpd_set_flags(mpd_t *result, uint8_t flags)
+{
+ result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
+ result->flags |= flags;
+}
+
+/* Copy flags, preserving memory attributes of result. */
+ALWAYS_INLINE void
+mpd_copy_flags(mpd_t *result, const mpd_t *a)
+{
+ uint8_t aflags = a->flags;
+ result->flags &= (MPD_STATIC|MPD_DATAFLAGS);
+ result->flags |= (aflags & ~(MPD_STATIC|MPD_DATAFLAGS));
+}
+
+/* Make a work context */
+static inline void
+mpd_workcontext(mpd_context_t *workctx, const mpd_context_t *ctx)
+{
+ workctx->prec = ctx->prec;
+ workctx->emax = ctx->emax;
+ workctx->emin = ctx->emin;
+ workctx->round = ctx->round;
+ workctx->traps = 0;
+ workctx->status= 0;
+ workctx->newtrap= 0;
+ workctx->clamp = ctx->clamp;
+ workctx->allcr = ctx->allcr;
+}
+
+
+/******************************************************************************/
+/* Getting and setting parts of decimals */
+/******************************************************************************/
+
+/* Flip the sign of a decimal */
+static inline void
+_mpd_negate(mpd_t *dec)
+{
+ dec->flags ^= MPD_NEG;
+}
+
+/* Set coefficient to zero */
+void
+mpd_zerocoeff(mpd_t *result)
+{
+ mpd_minalloc(result);
+ result->digits = 1;
+ result->len = 1;
+ result->data[0] = 0;
+}
+
+/* Set the coefficient to all nines. */
+void
+mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_ssize_t len, r;
+
+ _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS);
+ len = (r == 0) ? len : len+1;
+
+ if (!mpd_qresize(result, len, status)) {
+ return;
+ }
+
+ result->len = len;
+ result->digits = ctx->prec;
+
+ --len;
+ if (r > 0) {
+ result->data[len--] = mpd_pow10[r]-1;
+ }
+ for (; len >= 0; --len) {
+ result->data[len] = MPD_RADIX-1;
+ }
+}
+
+/*
+ * Cut off the most significant digits so that the rest fits in ctx->prec.
+ * Cannot fail.
+ */
+static void
+_mpd_cap(mpd_t *result, const mpd_context_t *ctx)
+{
+ uint32_t dummy;
+ mpd_ssize_t len, r;
+
+ if (result->len > 0 && result->digits > ctx->prec) {
+ _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS);
+ len = (r == 0) ? len : len+1;
+
+ if (r != 0) {
+ result->data[len-1] %= mpd_pow10[r];
+ }
+
+ len = _mpd_real_size(result->data, len);
+ /* resize to fewer words cannot fail */
+ mpd_qresize(result, len, &dummy);
+ result->len = len;
+ mpd_setdigits(result);
+ }
+ if (mpd_iszero(result)) {
+ _settriple(result, mpd_sign(result), 0, result->exp);
+ }
+}
+
+/*
+ * Cut off the most significant digits of a NaN payload so that the rest
+ * fits in ctx->prec - ctx->clamp. Cannot fail.
+ */
+static void
+_mpd_fix_nan(mpd_t *result, const mpd_context_t *ctx)
+{
+ uint32_t dummy;
+ mpd_ssize_t prec;
+ mpd_ssize_t len, r;
+
+ prec = ctx->prec - ctx->clamp;
+ if (result->len > 0 && result->digits > prec) {
+ if (prec == 0) {
+ mpd_minalloc(result);
+ result->len = result->digits = 0;
+ }
+ else {
+ _mpd_idiv_word(&len, &r, prec, MPD_RDIGITS);
+ len = (r == 0) ? len : len+1;
+
+ if (r != 0) {
+ result->data[len-1] %= mpd_pow10[r];
+ }
+
+ len = _mpd_real_size(result->data, len);
+ /* resize to fewer words cannot fail */
+ mpd_qresize(result, len, &dummy);
+ result->len = len;
+ mpd_setdigits(result);
+ if (mpd_iszerocoeff(result)) {
+ /* NaN0 is not a valid representation */
+ result->len = result->digits = 0;
+ }
+ }
+ }
+}
+
+/*
+ * Get n most significant digits from a decimal, where 0 < n <= MPD_UINT_DIGITS.
+ * Assumes MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for 32 and 64 bit
+ * machines.
+ *
+ * The result of the operation will be in lo. If the operation is impossible,
+ * hi will be nonzero. This is used to indicate an error.
+ */
+static inline void
+_mpd_get_msdigits(mpd_uint_t *hi, mpd_uint_t *lo, const mpd_t *dec,
+ unsigned int n)
+{
+ mpd_uint_t r, tmp;
+
+ assert(0 < n && n <= MPD_RDIGITS+1);
+
+ _mpd_div_word(&tmp, &r, dec->digits, MPD_RDIGITS);
+ r = (r == 0) ? MPD_RDIGITS : r; /* digits in the most significant word */
+
+ *hi = 0;
+ *lo = dec->data[dec->len-1];
+ if (n <= r) {
+ *lo /= mpd_pow10[r-n];
+ }
+ else if (dec->len > 1) {
+ /* at this point 1 <= r < n <= MPD_RDIGITS+1 */
+ _mpd_mul_words(hi, lo, *lo, mpd_pow10[n-r]);
+ tmp = dec->data[dec->len-2] / mpd_pow10[MPD_RDIGITS-(n-r)];
+ *lo = *lo + tmp;
+ if (*lo < tmp) (*hi)++;
+ }
+}
+
+
+/******************************************************************************/
+/* Gathering information about a decimal */
+/******************************************************************************/
+
+/* The real size of the coefficient without leading zero words. */
+static inline mpd_ssize_t
+_mpd_real_size(mpd_uint_t *data, mpd_ssize_t size)
+{
+ while (size > 1 && data[size-1] == 0) {
+ size--;
+ }
+
+ return size;
+}
+
+/* Return number of trailing zeros. No errors are possible. */
+mpd_ssize_t
+mpd_trail_zeros(const mpd_t *dec)
+{
+ mpd_uint_t word;
+ mpd_ssize_t i, tz = 0;
+
+ for (i=0; i < dec->len; ++i) {
+ if (dec->data[i] != 0) {
+ word = dec->data[i];
+ tz = i * MPD_RDIGITS;
+ while (word % 10 == 0) {
+ word /= 10;
+ tz++;
+ }
+ break;
+ }
+ }
+
+ return tz;
+}
+
+/* Integer: Undefined for specials */
+static int
+_mpd_isint(const mpd_t *dec)
+{
+ mpd_ssize_t tz;
+
+ if (mpd_iszerocoeff(dec)) {
+ return 1;
+ }
+
+ tz = mpd_trail_zeros(dec);
+ return (dec->exp + tz >= 0);
+}
+
+/* Integer */
+int
+mpd_isinteger(const mpd_t *dec)
+{
+ if (mpd_isspecial(dec)) {
+ return 0;
+ }
+ return _mpd_isint(dec);
+}
+
+/* Word is a power of 10 */
+static int
+mpd_word_ispow10(mpd_uint_t word)
+{
+ int n;
+
+ n = mpd_word_digits(word);
+ if (word == mpd_pow10[n-1]) {
+ return 1;
+ }
+
+ return 0;
+}
+
+/* Coefficient is a power of 10 */
+static int
+mpd_coeff_ispow10(const mpd_t *dec)
+{
+ if (mpd_word_ispow10(mpd_msword(dec))) {
+ if (_mpd_isallzero(dec->data, dec->len-1)) {
+ return 1;
+ }
+ }
+
+ return 0;
+}
+
+/* All digits of a word are nines */
+static int
+mpd_word_isallnine(mpd_uint_t word)
+{
+ int n;
+
+ n = mpd_word_digits(word);
+ if (word == mpd_pow10[n]-1) {
+ return 1;
+ }
+
+ return 0;
+}
+
+/* All digits of the coefficient are nines */
+static int
+mpd_coeff_isallnine(const mpd_t *dec)
+{
+ if (mpd_word_isallnine(mpd_msword(dec))) {
+ if (_mpd_isallnine(dec->data, dec->len-1)) {
+ return 1;
+ }
+ }
+
+ return 0;
+}
+
+/* Odd decimal: Undefined for non-integers! */
+int
+mpd_isodd(const mpd_t *dec)
+{
+ mpd_uint_t q, r;
+ assert(mpd_isinteger(dec));
+ if (mpd_iszerocoeff(dec)) return 0;
+ if (dec->exp < 0) {
+ _mpd_div_word(&q, &r, -dec->exp, MPD_RDIGITS);
+ q = dec->data[q] / mpd_pow10[r];
+ return mpd_isoddword(q);
+ }
+ return dec->exp == 0 && mpd_isoddword(dec->data[0]);
+}
+
+/* Even: Undefined for non-integers! */
+int
+mpd_iseven(const mpd_t *dec)
+{
+ return !mpd_isodd(dec);
+}
+
+/******************************************************************************/
+/* Getting and setting decimals */
+/******************************************************************************/
+
+/* Internal function: Set a static decimal from a triple, no error checking. */
+static void
+_ssettriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp)
+{
+ mpd_set_flags(result, sign);
+ result->exp = exp;
+ _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX);
+ result->len = (result->data[1] == 0) ? 1 : 2;
+ mpd_setdigits(result);
+}
+
+/* Internal function: Set a decimal from a triple, no error checking. */
+static void
+_settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp)
+{
+ mpd_minalloc(result);
+ mpd_set_flags(result, sign);
+ result->exp = exp;
+ _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX);
+ result->len = (result->data[1] == 0) ? 1 : 2;
+ mpd_setdigits(result);
+}
+
+/* Set a special number from a triple */
+void
+mpd_setspecial(mpd_t *result, uint8_t sign, uint8_t type)
+{
+ mpd_minalloc(result);
+ result->flags &= ~(MPD_NEG|MPD_SPECIAL);
+ result->flags |= (sign|type);
+ result->exp = result->digits = result->len = 0;
+}
+
+/* Set result of NaN with an error status */
+void
+mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status)
+{
+ mpd_minalloc(result);
+ mpd_set_qnan(result);
+ mpd_set_positive(result);
+ result->exp = result->digits = result->len = 0;
+ *status |= flags;
+}
+
+/* quietly set a static decimal from an mpd_ssize_t */
+void
+mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_uint_t u;
+ uint8_t sign = MPD_POS;
+
+ if (a < 0) {
+ if (a == MPD_SSIZE_MIN) {
+ u = (mpd_uint_t)MPD_SSIZE_MAX +
+ (-(MPD_SSIZE_MIN+MPD_SSIZE_MAX));
+ }
+ else {
+ u = -a;
+ }
+ sign = MPD_NEG;
+ }
+ else {
+ u = a;
+ }
+ _ssettriple(result, sign, u, 0);
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* quietly set a static decimal from an mpd_uint_t */
+void
+mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ _ssettriple(result, MPD_POS, a, 0);
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* quietly set a static decimal from an int32_t */
+void
+mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_qsset_ssize(result, a, ctx, status);
+}
+
+/* quietly set a static decimal from a uint32_t */
+void
+mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_qsset_uint(result, a, ctx, status);
+}
+
+#ifdef CONFIG_64
+/* quietly set a static decimal from an int64_t */
+void
+mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_qsset_ssize(result, a, ctx, status);
+}
+
+/* quietly set a static decimal from a uint64_t */
+void
+mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_qsset_uint(result, a, ctx, status);
+}
+#endif
+
+/* quietly set a decimal from an mpd_ssize_t */
+void
+mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_minalloc(result);
+ mpd_qsset_ssize(result, a, ctx, status);
+}
+
+/* quietly set a decimal from an mpd_uint_t */
+void
+mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ _settriple(result, MPD_POS, a, 0);
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* quietly set a decimal from an int32_t */
+void
+mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_qset_ssize(result, a, ctx, status);
+}
+
+/* quietly set a decimal from a uint32_t */
+void
+mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_qset_uint(result, a, ctx, status);
+}
+
+#if defined(CONFIG_32) && !defined(LEGACY_COMPILER)
+/* set a decimal from a uint64_t */
+static void
+_c32setu64(mpd_t *result, uint64_t u, uint8_t sign, uint32_t *status)
+{
+ mpd_uint_t w[3];
+ uint64_t q;
+ int i, len;
+
+ len = 0;
+ do {
+ q = u / MPD_RADIX;
+ w[len] = (mpd_uint_t)(u - q * MPD_RADIX);
+ u = q; len++;
+ } while (u != 0);
+
+ if (!mpd_qresize(result, len, status)) {
+ return;
+ }
+ for (i = 0; i < len; i++) {
+ result->data[i] = w[i];
+ }
+
+ mpd_set_sign(result, sign);
+ result->exp = 0;
+ result->len = len;
+ mpd_setdigits(result);
+}
+
+static void
+_c32_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ _c32setu64(result, a, MPD_POS, status);
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* set a decimal from an int64_t */
+static void
+_c32_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ uint64_t u;
+ uint8_t sign = MPD_POS;
+
+ if (a < 0) {
+ if (a == INT64_MIN) {
+ u = (uint64_t)INT64_MAX + (-(INT64_MIN+INT64_MAX));
+ }
+ else {
+ u = -a;
+ }
+ sign = MPD_NEG;
+ }
+ else {
+ u = a;
+ }
+ _c32setu64(result, u, sign, status);
+ mpd_qfinalize(result, ctx, status);
+}
+#endif /* CONFIG_32 && !LEGACY_COMPILER */
+
+#ifndef LEGACY_COMPILER
+/* quietly set a decimal from an int64_t */
+void
+mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+#ifdef CONFIG_64
+ mpd_qset_ssize(result, a, ctx, status);
+#else
+ _c32_qset_i64(result, a, ctx, status);
+#endif
+}
+
+/* quietly set a decimal from a uint64_t */
+void
+mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+#ifdef CONFIG_64
+ mpd_qset_uint(result, a, ctx, status);
+#else
+ _c32_qset_u64(result, a, ctx, status);
+#endif
+}
+#endif /* !LEGACY_COMPILER */
+
+
+/*
+ * Quietly get an mpd_uint_t from a decimal. Assumes
+ * MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for
+ * 32 and 64 bit machines.
+ *
+ * If the operation is impossible, MPD_Invalid_operation is set.
+ */
+static mpd_uint_t
+_mpd_qget_uint(int use_sign, const mpd_t *a, uint32_t *status)
+{
+ mpd_t tmp;
+ mpd_uint_t tmp_data[2];
+ mpd_uint_t lo, hi;
+
+ if (mpd_isspecial(a)) {
+ *status |= MPD_Invalid_operation;
+ return MPD_UINT_MAX;
+ }
+ if (mpd_iszero(a)) {
+ return 0;
+ }
+ if (use_sign && mpd_isnegative(a)) {
+ *status |= MPD_Invalid_operation;
+ return MPD_UINT_MAX;
+ }
+
+ if (a->digits+a->exp > MPD_RDIGITS+1) {
+ *status |= MPD_Invalid_operation;
+ return MPD_UINT_MAX;
+ }
+
+ if (a->exp < 0) {
+ if (!_mpd_isint(a)) {
+ *status |= MPD_Invalid_operation;
+ return MPD_UINT_MAX;
+ }
+ /* At this point a->digits+a->exp <= MPD_RDIGITS+1,
+ * so the shift fits. */
+ tmp.data = tmp_data;
+ tmp.flags = MPD_STATIC|MPD_CONST_DATA;
+ mpd_qsshiftr(&tmp, a, -a->exp);
+ tmp.exp = 0;
+ a = &tmp;
+ }
+
+ _mpd_get_msdigits(&hi, &lo, a, MPD_RDIGITS+1);
+ if (hi) {
+ *status |= MPD_Invalid_operation;
+ return MPD_UINT_MAX;
+ }
+
+ if (a->exp > 0) {
+ _mpd_mul_words(&hi, &lo, lo, mpd_pow10[a->exp]);
+ if (hi) {
+ *status |= MPD_Invalid_operation;
+ return MPD_UINT_MAX;
+ }
+ }
+
+ return lo;
+}
+
+/*
+ * Sets Invalid_operation for:
+ * - specials
+ * - negative numbers (except negative zero)
+ * - non-integers
+ * - overflow
+ */
+mpd_uint_t
+mpd_qget_uint(const mpd_t *a, uint32_t *status)
+{
+ return _mpd_qget_uint(1, a, status);
+}
+
+/* Same as above, but gets the absolute value, i.e. the sign is ignored. */
+mpd_uint_t
+mpd_qabs_uint(const mpd_t *a, uint32_t *status)
+{
+ return _mpd_qget_uint(0, a, status);
+}
+
+/* quietly get an mpd_ssize_t from a decimal */
+mpd_ssize_t
+mpd_qget_ssize(const mpd_t *a, uint32_t *status)
+{
+ mpd_uint_t u;
+ int isneg;
+
+ u = mpd_qabs_uint(a, status);
+ if (*status&MPD_Invalid_operation) {
+ return MPD_SSIZE_MAX;
+ }
+
+ isneg = mpd_isnegative(a);
+ if (u <= MPD_SSIZE_MAX) {
+ return isneg ? -((mpd_ssize_t)u) : (mpd_ssize_t)u;
+ }
+ else if (isneg && u-1 == MPD_SSIZE_MAX) {
+ return MPD_SSIZE_MIN;
+ }
+
+ *status |= MPD_Invalid_operation;
+ return MPD_SSIZE_MAX;
+}
+
+#ifdef CONFIG_64
+/* quietly get a uint64_t from a decimal */
+uint64_t
+mpd_qget_u64(const mpd_t *a, uint32_t *status)
+{
+ return mpd_qget_uint(a, status);
+}
+
+/* quietly get an int64_t from a decimal */
+int64_t
+mpd_qget_i64(const mpd_t *a, uint32_t *status)
+{
+ return mpd_qget_ssize(a, status);
+}
+#else
+/* quietly get a uint32_t from a decimal */
+uint32_t
+mpd_qget_u32(const mpd_t *a, uint32_t *status)
+{
+ return mpd_qget_uint(a, status);
+}
+
+/* quietly get an int32_t from a decimal */
+int32_t
+mpd_qget_i32(const mpd_t *a, uint32_t *status)
+{
+ return mpd_qget_ssize(a, status);
+}
+#endif
+
+
+/******************************************************************************/
+/* Filtering input of functions, finalizing output of functions */
+/******************************************************************************/
+
+/*
+ * Check if the operand is NaN, copy to result and return 1 if this is
+ * the case. Copying can fail since NaNs are allowed to have a payload that
+ * does not fit in MPD_MINALLOC.
+ */
+int
+mpd_qcheck_nan(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (mpd_isnan(a)) {
+ *status |= mpd_issnan(a) ? MPD_Invalid_operation : 0;
+ mpd_qcopy(result, a, status);
+ mpd_set_qnan(result);
+ _mpd_fix_nan(result, ctx);
+ return 1;
+ }
+ return 0;
+}
+
+/*
+ * Check if either operand is NaN, copy to result and return 1 if this
+ * is the case. Copying can fail since NaNs are allowed to have a payload
+ * that does not fit in MPD_MINALLOC.
+ */
+int
+mpd_qcheck_nans(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ if ((a->flags|b->flags)&(MPD_NAN|MPD_SNAN)) {
+ const mpd_t *choice = b;
+ if (mpd_issnan(a)) {
+ choice = a;
+ *status |= MPD_Invalid_operation;
+ }
+ else if (mpd_issnan(b)) {
+ *status |= MPD_Invalid_operation;
+ }
+ else if (mpd_isqnan(a)) {
+ choice = a;
+ }
+ mpd_qcopy(result, choice, status);
+ mpd_set_qnan(result);
+ _mpd_fix_nan(result, ctx);
+ return 1;
+ }
+ return 0;
+}
+
+/*
+ * Check if one of the operands is NaN, copy to result and return 1 if this
+ * is the case. Copying can fail since NaNs are allowed to have a payload
+ * that does not fit in MPD_MINALLOC.
+ */
+static int
+mpd_qcheck_3nans(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ if ((a->flags|b->flags|c->flags)&(MPD_NAN|MPD_SNAN)) {
+ const mpd_t *choice = c;
+ if (mpd_issnan(a)) {
+ choice = a;
+ *status |= MPD_Invalid_operation;
+ }
+ else if (mpd_issnan(b)) {
+ choice = b;
+ *status |= MPD_Invalid_operation;
+ }
+ else if (mpd_issnan(c)) {
+ *status |= MPD_Invalid_operation;
+ }
+ else if (mpd_isqnan(a)) {
+ choice = a;
+ }
+ else if (mpd_isqnan(b)) {
+ choice = b;
+ }
+ mpd_qcopy(result, choice, status);
+ mpd_set_qnan(result);
+ _mpd_fix_nan(result, ctx);
+ return 1;
+ }
+ return 0;
+}
+
+/* Check if rounding digit 'rnd' leads to an increment. */
+static inline int
+_mpd_rnd_incr(const mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx)
+{
+ int ld;
+
+ switch (ctx->round) {
+ case MPD_ROUND_DOWN: case MPD_ROUND_TRUNC:
+ return 0;
+ case MPD_ROUND_HALF_UP:
+ return (rnd >= 5);
+ case MPD_ROUND_HALF_EVEN:
+ return (rnd > 5) || ((rnd == 5) && mpd_isoddcoeff(dec));
+ case MPD_ROUND_CEILING:
+ return !(rnd == 0 || mpd_isnegative(dec));
+ case MPD_ROUND_FLOOR:
+ return !(rnd == 0 || mpd_ispositive(dec));
+ case MPD_ROUND_HALF_DOWN:
+ return (rnd > 5);
+ case MPD_ROUND_UP:
+ return !(rnd == 0);
+ case MPD_ROUND_05UP:
+ ld = (int)mpd_lsd(dec->data[0]);
+ return (!(rnd == 0) && (ld == 0 || ld == 5));
+ default:
+ /* Without a valid context, further results will be undefined. */
+ return 0; /* GCOV_NOT_REACHED */
+ }
+}
+
+/*
+ * Apply rounding to a decimal that has been right-shifted into a full
+ * precision decimal. If an increment leads to an overflow of the precision,
+ * adjust the coefficient and the exponent and check the new exponent for
+ * overflow.
+ */
+static inline void
+_mpd_apply_round(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (_mpd_rnd_incr(dec, rnd, ctx)) {
+ /* We have a number with exactly ctx->prec digits. The increment
+ * can only lead to an overflow if the decimal is all nines. In
+ * that case, the result is a power of ten with prec+1 digits.
+ *
+ * If the precision is a multiple of MPD_RDIGITS, this situation is
+ * detected by _mpd_baseincr returning a carry.
+ * If the precision is not a multiple of MPD_RDIGITS, we have to
+ * check if the result has one digit too many.
+ */
+ mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
+ if (carry) {
+ dec->data[dec->len-1] = mpd_pow10[MPD_RDIGITS-1];
+ dec->exp += 1;
+ _mpd_check_exp(dec, ctx, status);
+ return;
+ }
+ mpd_setdigits(dec);
+ if (dec->digits > ctx->prec) {
+ mpd_qshiftr_inplace(dec, 1);
+ dec->exp += 1;
+ dec->digits = ctx->prec;
+ _mpd_check_exp(dec, ctx, status);
+ }
+ }
+}
+
+/*
+ * Apply rounding to a decimal. Allow overflow of the precision.
+ */
+static inline void
+_mpd_apply_round_excess(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (_mpd_rnd_incr(dec, rnd, ctx)) {
+ mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
+ if (carry) {
+ if (!mpd_qresize(dec, dec->len+1, status)) {
+ return;
+ }
+ dec->data[dec->len] = 1;
+ dec->len += 1;
+ }
+ mpd_setdigits(dec);
+ }
+}
+
+/*
+ * Apply rounding to a decimal that has been right-shifted into a decimal
+ * with full precision or less. Return failure if an increment would
+ * overflow the precision.
+ */
+static inline int
+_mpd_apply_round_fit(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (_mpd_rnd_incr(dec, rnd, ctx)) {
+ mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len);
+ if (carry) {
+ if (!mpd_qresize(dec, dec->len+1, status)) {
+ return 0;
+ }
+ dec->data[dec->len] = 1;
+ dec->len += 1;
+ }
+ mpd_setdigits(dec);
+ if (dec->digits > ctx->prec) {
+ mpd_seterror(dec, MPD_Invalid_operation, status);
+ return 0;
+ }
+ }
+ return 1;
+}
+
+/* Check a normal number for overflow, underflow, clamping. If the operand
+ is modified, it will be zero, special or (sub)normal with a coefficient
+ that fits into the current context precision. */
+static inline void
+_mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_ssize_t adjexp, etiny, shift;
+ int rnd;
+
+ adjexp = mpd_adjexp(dec);
+ if (adjexp > ctx->emax) {
+
+ if (mpd_iszerocoeff(dec)) {
+ dec->exp = ctx->emax;
+ if (ctx->clamp) {
+ dec->exp -= (ctx->prec-1);
+ }
+ mpd_zerocoeff(dec);
+ *status |= MPD_Clamped;
+ return;
+ }
+
+ switch (ctx->round) {
+ case MPD_ROUND_HALF_UP: case MPD_ROUND_HALF_EVEN:
+ case MPD_ROUND_HALF_DOWN: case MPD_ROUND_UP:
+ case MPD_ROUND_TRUNC:
+ mpd_setspecial(dec, mpd_sign(dec), MPD_INF);
+ break;
+ case MPD_ROUND_DOWN: case MPD_ROUND_05UP:
+ mpd_qmaxcoeff(dec, ctx, status);
+ dec->exp = ctx->emax - ctx->prec + 1;
+ break;
+ case MPD_ROUND_CEILING:
+ if (mpd_isnegative(dec)) {
+ mpd_qmaxcoeff(dec, ctx, status);
+ dec->exp = ctx->emax - ctx->prec + 1;
+ }
+ else {
+ mpd_setspecial(dec, MPD_POS, MPD_INF);
+ }
+ break;
+ case MPD_ROUND_FLOOR:
+ if (mpd_ispositive(dec)) {
+ mpd_qmaxcoeff(dec, ctx, status);
+ dec->exp = ctx->emax - ctx->prec + 1;
+ }
+ else {
+ mpd_setspecial(dec, MPD_NEG, MPD_INF);
+ }
+ break;
+ default: /* debug */
+ abort(); /* GCOV_NOT_REACHED */
+ }
+
+ *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
+
+ } /* fold down */
+ else if (ctx->clamp && dec->exp > mpd_etop(ctx)) {
+ /* At this point adjexp=exp+digits-1 <= emax and exp > etop=emax-prec+1:
+ * (1) shift = exp -emax+prec-1 > 0
+ * (2) digits+shift = exp+digits-1 - emax + prec <= prec */
+ shift = dec->exp - mpd_etop(ctx);
+ if (!mpd_qshiftl(dec, dec, shift, status)) {
+ return;
+ }
+ dec->exp -= shift;
+ *status |= MPD_Clamped;
+ if (!mpd_iszerocoeff(dec) && adjexp < ctx->emin) {
+ /* Underflow is impossible, since exp < etiny=emin-prec+1
+ * and exp > etop=emax-prec+1 would imply emax < emin. */
+ *status |= MPD_Subnormal;
+ }
+ }
+ else if (adjexp < ctx->emin) {
+
+ etiny = mpd_etiny(ctx);
+
+ if (mpd_iszerocoeff(dec)) {
+ if (dec->exp < etiny) {
+ dec->exp = etiny;
+ mpd_zerocoeff(dec);
+ *status |= MPD_Clamped;
+ }
+ return;
+ }
+
+ *status |= MPD_Subnormal;
+ if (dec->exp < etiny) {
+ /* At this point adjexp=exp+digits-1 < emin and exp < etiny=emin-prec+1:
+ * (1) shift = emin-prec+1 - exp > 0
+ * (2) digits-shift = exp+digits-1 - emin + prec < prec */
+ shift = etiny - dec->exp;
+ rnd = (int)mpd_qshiftr_inplace(dec, shift);
+ dec->exp = etiny;
+ /* We always have a spare digit in case of an increment. */
+ _mpd_apply_round_excess(dec, rnd, ctx, status);
+ *status |= MPD_Rounded;
+ if (rnd) {
+ *status |= (MPD_Inexact|MPD_Underflow);
+ if (mpd_iszerocoeff(dec)) {
+ mpd_zerocoeff(dec);
+ *status |= MPD_Clamped;
+ }
+ }
+ }
+ /* Case exp >= etiny=emin-prec+1:
+ * (1) adjexp=exp+digits-1 < emin
+ * (2) digits < emin-exp+1 <= prec */
+ }
+}
+
+/* Transcendental functions do not always set Underflow reliably,
+ * since they only use as much precision as is necessary for correct
+ * rounding. If a result like 1.0000000000e-101 is finalized, there
+ * is no rounding digit that would trigger Underflow. But we can
+ * assume Inexact, so a short check suffices. */
+static inline void
+mpd_check_underflow(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
+{
+ if (mpd_adjexp(dec) < ctx->emin && !mpd_iszero(dec) &&
+ dec->exp < mpd_etiny(ctx)) {
+ *status |= MPD_Underflow;
+ }
+}
+
+/* Check if a normal number must be rounded after the exponent has been checked. */
+static inline void
+_mpd_check_round(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_uint_t rnd;
+ mpd_ssize_t shift;
+
+ /* must handle specials: _mpd_check_exp() can produce infinities or NaNs */
+ if (mpd_isspecial(dec)) {
+ return;
+ }
+
+ if (dec->digits > ctx->prec) {
+ shift = dec->digits - ctx->prec;
+ rnd = mpd_qshiftr_inplace(dec, shift);
+ dec->exp += shift;
+ _mpd_apply_round(dec, rnd, ctx, status);
+ *status |= MPD_Rounded;
+ if (rnd) {
+ *status |= MPD_Inexact;
+ }
+ }
+}
+
+/* Finalize all operations. */
+void
+mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status)
+{
+ if (mpd_isspecial(result)) {
+ if (mpd_isnan(result)) {
+ _mpd_fix_nan(result, ctx);
+ }
+ return;
+ }
+
+ _mpd_check_exp(result, ctx, status);
+ _mpd_check_round(result, ctx, status);
+}
+
+
+/******************************************************************************/
+/* Copying */
+/******************************************************************************/
+
+/* Internal function: Copy a decimal, share data with src: USE WITH CARE! */
+static inline void
+_mpd_copy_shared(mpd_t *dest, const mpd_t *src)
+{
+ dest->flags = src->flags;
+ dest->exp = src->exp;
+ dest->digits = src->digits;
+ dest->len = src->len;
+ dest->alloc = src->alloc;
+ dest->data = src->data;
+
+ mpd_set_shared_data(dest);
+}
+
+/*
+ * Copy a decimal. In case of an error, status is set to MPD_Malloc_error.
+ */
+int
+mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status)
+{
+ if (result == a) return 1;
+
+ if (!mpd_qresize(result, a->len, status)) {
+ return 0;
+ }
+
+ mpd_copy_flags(result, a);
+ result->exp = a->exp;
+ result->digits = a->digits;
+ result->len = a->len;
+ memcpy(result->data, a->data, a->len * (sizeof *result->data));
+
+ return 1;
+}
+
+/*
+ * Copy to a decimal with a static buffer. The caller has to make sure that
+ * the buffer is big enough. Cannot fail.
+ */
+static void
+mpd_qcopy_static(mpd_t *result, const mpd_t *a)
+{
+ if (result == a) return;
+
+ memcpy(result->data, a->data, a->len * (sizeof *result->data));
+
+ mpd_copy_flags(result, a);
+ result->exp = a->exp;
+ result->digits = a->digits;
+ result->len = a->len;
+}
+
+/*
+ * Return a newly allocated copy of the operand. In case of an error,
+ * status is set to MPD_Malloc_error and the return value is NULL.
+ */
+mpd_t *
+mpd_qncopy(const mpd_t *a)
+{
+ mpd_t *result;
+
+ if ((result = mpd_qnew_size(a->len)) == NULL) {
+ return NULL;
+ }
+ memcpy(result->data, a->data, a->len * (sizeof *result->data));
+ mpd_copy_flags(result, a);
+ result->exp = a->exp;
+ result->digits = a->digits;
+ result->len = a->len;
+
+ return result;
+}
+
+/*
+ * Copy a decimal and set the sign to positive. In case of an error, the
+ * status is set to MPD_Malloc_error.
+ */
+int
+mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status)
+{
+ if (!mpd_qcopy(result, a, status)) {
+ return 0;
+ }
+ mpd_set_positive(result);
+ return 1;
+}
+
+/*
+ * Copy a decimal and negate the sign. In case of an error, the
+ * status is set to MPD_Malloc_error.
+ */
+int
+mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status)
+{
+ if (!mpd_qcopy(result, a, status)) {
+ return 0;
+ }
+ _mpd_negate(result);
+ return 1;
+}
+
+/*
+ * Copy a decimal, setting the sign of the first operand to the sign of the
+ * second operand. In case of an error, the status is set to MPD_Malloc_error.
+ */
+int
+mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status)
+{
+ uint8_t sign_b = mpd_sign(b); /* result may equal b! */
+
+ if (!mpd_qcopy(result, a, status)) {
+ return 0;
+ }
+ mpd_set_sign(result, sign_b);
+ return 1;
+}
+
+
+/******************************************************************************/
+/* Comparisons */
+/******************************************************************************/
+
+/*
+ * For all functions that compare two operands and return an int the usual
+ * convention applies to the return value:
+ *
+ * -1 if op1 < op2
+ * 0 if op1 == op2
+ * 1 if op1 > op2
+ *
+ * INT_MAX for error
+ */
+
+
+/* Convenience macro. If a and b are not equal, return from the calling
+ * function with the correct comparison value. */
+#define CMP_EQUAL_OR_RETURN(a, b) \
+ if (a != b) { \
+ if (a < b) { \
+ return -1; \
+ } \
+ return 1; \
+ }
+
+/*
+ * Compare the data of big and small. This function does the equivalent
+ * of first shifting small to the left and then comparing the data of
+ * big and small, except that no allocation for the left shift is needed.
+ */
+static int
+_mpd_basecmp(mpd_uint_t *big, mpd_uint_t *small, mpd_size_t n, mpd_size_t m,
+ mpd_size_t shift)
+{
+#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__)
+ /* spurious uninitialized warnings */
+ mpd_uint_t l=l, lprev=lprev, h=h;
+#else
+ mpd_uint_t l, lprev, h;
+#endif
+ mpd_uint_t q, r;
+ mpd_uint_t ph, x;
+
+ assert(m > 0 && n >= m && shift > 0);
+
+ _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS);
+
+ if (r != 0) {
+
+ ph = mpd_pow10[r];
+
+ --m; --n;
+ _mpd_divmod_pow10(&h, &lprev, small[m--], MPD_RDIGITS-r);
+ if (h != 0) {
+ CMP_EQUAL_OR_RETURN(big[n], h)
+ --n;
+ }
+ for (; m != MPD_SIZE_MAX; m--,n--) {
+ _mpd_divmod_pow10(&h, &l, small[m], MPD_RDIGITS-r);
+ x = ph * lprev + h;
+ CMP_EQUAL_OR_RETURN(big[n], x)
+ lprev = l;
+ }
+ x = ph * lprev;
+ CMP_EQUAL_OR_RETURN(big[q], x)
+ }
+ else {
+ while (--m != MPD_SIZE_MAX) {
+ CMP_EQUAL_OR_RETURN(big[m+q], small[m])
+ }
+ }
+
+ return !_mpd_isallzero(big, q);
+}
+
+/* Compare two decimals with the same adjusted exponent. */
+static int
+_mpd_cmp_same_adjexp(const mpd_t *a, const mpd_t *b)
+{
+ mpd_ssize_t shift, i;
+
+ if (a->exp != b->exp) {
+ /* Cannot wrap: a->exp + a->digits = b->exp + b->digits, so
+ * a->exp - b->exp = b->digits - a->digits. */
+ shift = a->exp - b->exp;
+ if (shift > 0) {
+ return -1 * _mpd_basecmp(b->data, a->data, b->len, a->len, shift);
+ }
+ else {
+ return _mpd_basecmp(a->data, b->data, a->len, b->len, -shift);
+ }
+ }
+
+ /*
+ * At this point adjexp(a) == adjexp(b) and a->exp == b->exp,
+ * so a->digits == b->digits, therefore a->len == b->len.
+ */
+ for (i = a->len-1; i >= 0; --i) {
+ CMP_EQUAL_OR_RETURN(a->data[i], b->data[i])
+ }
+
+ return 0;
+}
+
+/* Compare two numerical values. */
+static int
+_mpd_cmp(const mpd_t *a, const mpd_t *b)
+{
+ mpd_ssize_t adjexp_a, adjexp_b;
+
+ /* equal pointers */
+ if (a == b) {
+ return 0;
+ }
+
+ /* infinities */
+ if (mpd_isinfinite(a)) {
+ if (mpd_isinfinite(b)) {
+ return mpd_isnegative(b) - mpd_isnegative(a);
+ }
+ return mpd_arith_sign(a);
+ }
+ if (mpd_isinfinite(b)) {
+ return -mpd_arith_sign(b);
+ }
+
+ /* zeros */
+ if (mpd_iszerocoeff(a)) {
+ if (mpd_iszerocoeff(b)) {
+ return 0;
+ }
+ return -mpd_arith_sign(b);
+ }
+ if (mpd_iszerocoeff(b)) {
+ return mpd_arith_sign(a);
+ }
+
+ /* different signs */
+ if (mpd_sign(a) != mpd_sign(b)) {
+ return mpd_sign(b) - mpd_sign(a);
+ }
+
+ /* different adjusted exponents */
+ adjexp_a = mpd_adjexp(a);
+ adjexp_b = mpd_adjexp(b);
+ if (adjexp_a != adjexp_b) {
+ if (adjexp_a < adjexp_b) {
+ return -1 * mpd_arith_sign(a);
+ }
+ return mpd_arith_sign(a);
+ }
+
+ /* same adjusted exponents */
+ return _mpd_cmp_same_adjexp(a, b) * mpd_arith_sign(a);
+}
+
+/* Compare the absolutes of two numerical values. */
+static int
+_mpd_cmp_abs(const mpd_t *a, const mpd_t *b)
+{
+ mpd_ssize_t adjexp_a, adjexp_b;
+
+ /* equal pointers */
+ if (a == b) {
+ return 0;
+ }
+
+ /* infinities */
+ if (mpd_isinfinite(a)) {
+ if (mpd_isinfinite(b)) {
+ return 0;
+ }
+ return 1;
+ }
+ if (mpd_isinfinite(b)) {
+ return -1;
+ }
+
+ /* zeros */
+ if (mpd_iszerocoeff(a)) {
+ if (mpd_iszerocoeff(b)) {
+ return 0;
+ }
+ return -1;
+ }
+ if (mpd_iszerocoeff(b)) {
+ return 1;
+ }
+
+ /* different adjusted exponents */
+ adjexp_a = mpd_adjexp(a);
+ adjexp_b = mpd_adjexp(b);
+ if (adjexp_a != adjexp_b) {
+ if (adjexp_a < adjexp_b) {
+ return -1;
+ }
+ return 1;
+ }
+
+ /* same adjusted exponents */
+ return _mpd_cmp_same_adjexp(a, b);
+}
+
+/* Compare two values and return an integer result. */
+int
+mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status)
+{
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_isnan(a) || mpd_isnan(b)) {
+ *status |= MPD_Invalid_operation;
+ return INT_MAX;
+ }
+ }
+
+ return _mpd_cmp(a, b);
+}
+
+/*
+ * Compare a and b, convert the the usual integer result to a decimal and
+ * store it in 'result'. For convenience, the integer result of the comparison
+ * is returned. Comparisons involving NaNs return NaN/INT_MAX.
+ */
+int
+mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ int c;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return INT_MAX;
+ }
+ }
+
+ c = _mpd_cmp(a, b);
+ _settriple(result, (c < 0), (c != 0), 0);
+ return c;
+}
+
+/* Same as mpd_compare(), but signal for all NaNs, i.e. also for quiet NaNs. */
+int
+mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ int c;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ *status |= MPD_Invalid_operation;
+ return INT_MAX;
+ }
+ }
+
+ c = _mpd_cmp(a, b);
+ _settriple(result, (c < 0), (c != 0), 0);
+ return c;
+}
+
+/* Compare the operands using a total order. */
+int
+mpd_cmp_total(const mpd_t *a, const mpd_t *b)
+{
+ mpd_t aa, bb;
+ int nan_a, nan_b;
+ int c;
+
+ if (mpd_sign(a) != mpd_sign(b)) {
+ return mpd_sign(b) - mpd_sign(a);
+ }
+
+
+ if (mpd_isnan(a)) {
+ c = 1;
+ if (mpd_isnan(b)) {
+ nan_a = (mpd_isqnan(a)) ? 1 : 0;
+ nan_b = (mpd_isqnan(b)) ? 1 : 0;
+ if (nan_b == nan_a) {
+ if (a->len > 0 && b->len > 0) {
+ _mpd_copy_shared(&aa, a);
+ _mpd_copy_shared(&bb, b);
+ aa.exp = bb.exp = 0;
+ /* compare payload */
+ c = _mpd_cmp_abs(&aa, &bb);
+ }
+ else {
+ c = (a->len > 0) - (b->len > 0);
+ }
+ }
+ else {
+ c = nan_a - nan_b;
+ }
+ }
+ }
+ else if (mpd_isnan(b)) {
+ c = -1;
+ }
+ else {
+ c = _mpd_cmp_abs(a, b);
+ if (c == 0 && a->exp != b->exp) {
+ c = (a->exp < b->exp) ? -1 : 1;
+ }
+ }
+
+ return c * mpd_arith_sign(a);
+}
+
+/*
+ * Compare a and b according to a total order, convert the usual integer result
+ * to a decimal and store it in 'result'. For convenience, the integer result
+ * of the comparison is returned.
+ */
+int
+mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b)
+{
+ int c;
+
+ c = mpd_cmp_total(a, b);
+ _settriple(result, (c < 0), (c != 0), 0);
+ return c;
+}
+
+/* Compare the magnitude of the operands using a total order. */
+int
+mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b)
+{
+ mpd_t aa, bb;
+
+ _mpd_copy_shared(&aa, a);
+ _mpd_copy_shared(&bb, b);
+
+ mpd_set_positive(&aa);
+ mpd_set_positive(&bb);
+
+ return mpd_cmp_total(&aa, &bb);
+}
+
+/*
+ * Compare the magnitude of a and b according to a total order, convert the
+ * the usual integer result to a decimal and store it in 'result'.
+ * For convenience, the integer result of the comparison is returned.
+ */
+int
+mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b)
+{
+ int c;
+
+ c = mpd_cmp_total_mag(a, b);
+ _settriple(result, (c < 0), (c != 0), 0);
+ return c;
+}
+
+/* Determine an ordering for operands that are numerically equal. */
+static inline int
+_mpd_cmp_numequal(const mpd_t *a, const mpd_t *b)
+{
+ int sign_a, sign_b;
+ int c;
+
+ sign_a = mpd_sign(a);
+ sign_b = mpd_sign(b);
+ if (sign_a != sign_b) {
+ c = sign_b - sign_a;
+ }
+ else {
+ c = (a->exp < b->exp) ? -1 : 1;
+ c *= mpd_arith_sign(a);
+ }
+
+ return c;
+}
+
+
+/******************************************************************************/
+/* Shifting the coefficient */
+/******************************************************************************/
+
+/*
+ * Shift the coefficient of the operand to the left, no check for specials.
+ * Both operands may be the same pointer. If the result length has to be
+ * increased, mpd_qresize() might fail with MPD_Malloc_error.
+ */
+int
+mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status)
+{
+ mpd_ssize_t size;
+
+ assert(n >= 0);
+
+ if (mpd_iszerocoeff(a) || n == 0) {
+ return mpd_qcopy(result, a, status);
+ }
+
+ size = mpd_digits_to_size(a->digits+n);
+ if (!mpd_qresize(result, size, status)) {
+ return 0; /* result is NaN */
+ }
+
+ _mpd_baseshiftl(result->data, a->data, size, a->len, n);
+
+ mpd_copy_flags(result, a);
+ result->len = size;
+ result->exp = a->exp;
+ result->digits = a->digits+n;
+
+ return 1;
+}
+
+/* Determine the rounding indicator if all digits of the coefficient are shifted
+ * out of the picture. */
+static mpd_uint_t
+_mpd_get_rnd(const mpd_uint_t *data, mpd_ssize_t len, int use_msd)
+{
+ mpd_uint_t rnd = 0, rest = 0, word;
+
+ word = data[len-1];
+ /* special treatment for the most significant digit if shift == digits */
+ if (use_msd) {
+ _mpd_divmod_pow10(&rnd, &rest, word, mpd_word_digits(word)-1);
+ if (len > 1 && rest == 0) {
+ rest = !_mpd_isallzero(data, len-1);
+ }
+ }
+ else {
+ rest = !_mpd_isallzero(data, len);
+ }
+
+ return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd;
+}
+
+/*
+ * Same as mpd_qshiftr(), but 'result' is a static array. It is the
+ * caller's responsibility to make sure that the array is big enough.
+ * The function cannot fail.
+ */
+mpd_uint_t
+mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n)
+{
+ mpd_uint_t rnd;
+ mpd_ssize_t size;
+
+ assert(n >= 0);
+
+ if (mpd_iszerocoeff(a) || n == 0) {
+ mpd_qcopy_static(result, a);
+ return 0;
+ }
+
+ if (n >= a->digits) {
+ rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits));
+ mpd_zerocoeff(result);
+ result->digits = 1;
+ size = 1;
+ }
+ else {
+ result->digits = a->digits-n;
+ size = mpd_digits_to_size(result->digits);
+ rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
+ }
+
+ mpd_copy_flags(result, a);
+ result->exp = a->exp;
+ result->len = size;
+
+ return rnd;
+}
+
+/*
+ * Inplace shift of the coefficient to the right, no check for specials.
+ * Returns the rounding indicator for mpd_rnd_incr().
+ * The function cannot fail.
+ */
+mpd_uint_t
+mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n)
+{
+ uint32_t dummy;
+ mpd_uint_t rnd;
+ mpd_ssize_t size;
+
+ assert(n >= 0);
+
+ if (mpd_iszerocoeff(result) || n == 0) {
+ return 0;
+ }
+
+ if (n >= result->digits) {
+ rnd = _mpd_get_rnd(result->data, result->len, (n==result->digits));
+ mpd_zerocoeff(result);
+ result->digits = 1;
+ size = 1;
+ }
+ else {
+ rnd = _mpd_baseshiftr(result->data, result->data, result->len, n);
+ result->digits -= n;
+ size = mpd_digits_to_size(result->digits);
+ /* reducing the size cannot fail */
+ mpd_qresize(result, size, &dummy);
+ }
+
+ result->len = size;
+
+ return rnd;
+}
+
+/*
+ * Shift the coefficient of the operand to the right, no check for specials.
+ * Both operands may be the same pointer. Returns the rounding indicator to
+ * be used by mpd_rnd_incr(). If the result length has to be increased,
+ * mpd_qcopy() or mpd_qresize() might fail with MPD_Malloc_error. In those
+ * cases, MPD_UINT_MAX is returned.
+ */
+mpd_uint_t
+mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status)
+{
+ mpd_uint_t rnd;
+ mpd_ssize_t size;
+
+ assert(n >= 0);
+
+ if (mpd_iszerocoeff(a) || n == 0) {
+ if (!mpd_qcopy(result, a, status)) {
+ return MPD_UINT_MAX;
+ }
+ return 0;
+ }
+
+ if (n >= a->digits) {
+ rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits));
+ mpd_zerocoeff(result);
+ result->digits = 1;
+ size = 1;
+ }
+ else {
+ result->digits = a->digits-n;
+ size = mpd_digits_to_size(result->digits);
+ if (result == a) {
+ rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
+ /* reducing the size cannot fail */
+ mpd_qresize(result, size, status);
+ }
+ else {
+ if (!mpd_qresize(result, size, status)) {
+ return MPD_UINT_MAX;
+ }
+ rnd = _mpd_baseshiftr(result->data, a->data, a->len, n);
+ }
+ }
+
+ mpd_copy_flags(result, a);
+ result->exp = a->exp;
+ result->len = size;
+
+ return rnd;
+}
+
+
+/******************************************************************************/
+/* Miscellaneous operations */
+/******************************************************************************/
+
+/* Logical And */
+void
+mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ const mpd_t *big = a, *small = b;
+ mpd_uint_t x, y, z, xbit, ybit;
+ int k, mswdigits;
+ mpd_ssize_t i;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b) ||
+ mpd_isnegative(a) || mpd_isnegative(b) ||
+ a->exp != 0 || b->exp != 0) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (b->digits > a->digits) {
+ big = b;
+ small = a;
+ }
+ if (!mpd_qresize(result, big->len, status)) {
+ return;
+ }
+
+
+ /* full words */
+ for (i = 0; i < small->len-1; i++) {
+ x = small->data[i];
+ y = big->data[i];
+ z = 0;
+ for (k = 0; k < MPD_RDIGITS; k++) {
+ xbit = x % 10;
+ x /= 10;
+ ybit = y % 10;
+ y /= 10;
+ if (xbit > 1 || ybit > 1) {
+ goto invalid_operation;
+ }
+ z += (xbit&ybit) ? mpd_pow10[k] : 0;
+ }
+ result->data[i] = z;
+ }
+ /* most significant word of small */
+ x = small->data[i];
+ y = big->data[i];
+ z = 0;
+ mswdigits = mpd_word_digits(x);
+ for (k = 0; k < mswdigits; k++) {
+ xbit = x % 10;
+ x /= 10;
+ ybit = y % 10;
+ y /= 10;
+ if (xbit > 1 || ybit > 1) {
+ goto invalid_operation;
+ }
+ z += (xbit&ybit) ? mpd_pow10[k] : 0;
+ }
+ result->data[i++] = z;
+
+ /* scan the rest of y for digit > 1 */
+ for (; k < MPD_RDIGITS; k++) {
+ ybit = y % 10;
+ y /= 10;
+ if (ybit > 1) {
+ goto invalid_operation;
+ }
+ }
+ /* scan the rest of big for digit > 1 */
+ for (; i < big->len; i++) {
+ y = big->data[i];
+ for (k = 0; k < MPD_RDIGITS; k++) {
+ ybit = y % 10;
+ y /= 10;
+ if (ybit > 1) {
+ goto invalid_operation;
+ }
+ }
+ }
+
+ mpd_clear_flags(result);
+ result->exp = 0;
+ result->len = _mpd_real_size(result->data, small->len);
+ mpd_qresize(result, result->len, status);
+ mpd_setdigits(result);
+ _mpd_cap(result, ctx);
+ return;
+
+invalid_operation:
+ mpd_seterror(result, MPD_Invalid_operation, status);
+}
+
+/* Class of an operand. Returns a pointer to the constant name. */
+const char *
+mpd_class(const mpd_t *a, const mpd_context_t *ctx)
+{
+ if (mpd_isnan(a)) {
+ if (mpd_isqnan(a))
+ return "NaN";
+ else
+ return "sNaN";
+ }
+ else if (mpd_ispositive(a)) {
+ if (mpd_isinfinite(a))
+ return "+Infinity";
+ else if (mpd_iszero(a))
+ return "+Zero";
+ else if (mpd_isnormal(a, ctx))
+ return "+Normal";
+ else
+ return "+Subnormal";
+ }
+ else {
+ if (mpd_isinfinite(a))
+ return "-Infinity";
+ else if (mpd_iszero(a))
+ return "-Zero";
+ else if (mpd_isnormal(a, ctx))
+ return "-Normal";
+ else
+ return "-Subnormal";
+ }
+}
+
+/* Logical Xor */
+void
+mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_uint_t x, z, xbit;
+ mpd_ssize_t i, digits, len;
+ mpd_ssize_t q, r;
+ int k;
+
+ if (mpd_isspecial(a) || mpd_isnegative(a) || a->exp != 0) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ digits = (a->digits < ctx->prec) ? ctx->prec : a->digits;
+ _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS);
+ len = (r == 0) ? q : q+1;
+ if (!mpd_qresize(result, len, status)) {
+ return;
+ }
+
+ for (i = 0; i < len; i++) {
+ x = (i < a->len) ? a->data[i] : 0;
+ z = 0;
+ for (k = 0; k < MPD_RDIGITS; k++) {
+ xbit = x % 10;
+ x /= 10;
+ if (xbit > 1) {
+ goto invalid_operation;
+ }
+ z += !xbit ? mpd_pow10[k] : 0;
+ }
+ result->data[i] = z;
+ }
+
+ mpd_clear_flags(result);
+ result->exp = 0;
+ result->len = _mpd_real_size(result->data, len);
+ mpd_qresize(result, result->len, status);
+ mpd_setdigits(result);
+ _mpd_cap(result, ctx);
+ return;
+
+invalid_operation:
+ mpd_seterror(result, MPD_Invalid_operation, status);
+}
+
+/* Exponent of the magnitude of the most significant digit of the operand. */
+void
+mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ mpd_setspecial(result, MPD_POS, MPD_INF);
+ }
+ else if (mpd_iszerocoeff(a)) {
+ mpd_setspecial(result, MPD_NEG, MPD_INF);
+ *status |= MPD_Division_by_zero;
+ }
+ else {
+ mpd_qset_ssize(result, mpd_adjexp(a), ctx, status);
+ }
+}
+
+/* Logical Or */
+void
+mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ const mpd_t *big = a, *small = b;
+ mpd_uint_t x, y, z, xbit, ybit;
+ int k, mswdigits;
+ mpd_ssize_t i;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b) ||
+ mpd_isnegative(a) || mpd_isnegative(b) ||
+ a->exp != 0 || b->exp != 0) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (b->digits > a->digits) {
+ big = b;
+ small = a;
+ }
+ if (!mpd_qresize(result, big->len, status)) {
+ return;
+ }
+
+
+ /* full words */
+ for (i = 0; i < small->len-1; i++) {
+ x = small->data[i];
+ y = big->data[i];
+ z = 0;
+ for (k = 0; k < MPD_RDIGITS; k++) {
+ xbit = x % 10;
+ x /= 10;
+ ybit = y % 10;
+ y /= 10;
+ if (xbit > 1 || ybit > 1) {
+ goto invalid_operation;
+ }
+ z += (xbit|ybit) ? mpd_pow10[k] : 0;
+ }
+ result->data[i] = z;
+ }
+ /* most significant word of small */
+ x = small->data[i];
+ y = big->data[i];
+ z = 0;
+ mswdigits = mpd_word_digits(x);
+ for (k = 0; k < mswdigits; k++) {
+ xbit = x % 10;
+ x /= 10;
+ ybit = y % 10;
+ y /= 10;
+ if (xbit > 1 || ybit > 1) {
+ goto invalid_operation;
+ }
+ z += (xbit|ybit) ? mpd_pow10[k] : 0;
+ }
+
+ /* scan and copy the rest of y for digit > 1 */
+ for (; k < MPD_RDIGITS; k++) {
+ ybit = y % 10;
+ y /= 10;
+ if (ybit > 1) {
+ goto invalid_operation;
+ }
+ z += ybit*mpd_pow10[k];
+ }
+ result->data[i++] = z;
+ /* scan and copy the rest of big for digit > 1 */
+ for (; i < big->len; i++) {
+ y = big->data[i];
+ for (k = 0; k < MPD_RDIGITS; k++) {
+ ybit = y % 10;
+ y /= 10;
+ if (ybit > 1) {
+ goto invalid_operation;
+ }
+ }
+ result->data[i] = big->data[i];
+ }
+
+ mpd_clear_flags(result);
+ result->exp = 0;
+ result->len = _mpd_real_size(result->data, big->len);
+ mpd_qresize(result, result->len, status);
+ mpd_setdigits(result);
+ _mpd_cap(result, ctx);
+ return;
+
+invalid_operation:
+ mpd_seterror(result, MPD_Invalid_operation, status);
+}
+
+/*
+ * Rotate the coefficient of a by b->data digits. b must be an integer with
+ * exponent 0.
+ */
+void
+mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ MPD_NEW_STATIC(tmp,0,0,0,0);
+ MPD_NEW_STATIC(big,0,0,0,0);
+ MPD_NEW_STATIC(small,0,0,0,0);
+ mpd_ssize_t n, lshift, rshift;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ }
+ if (b->exp != 0 || mpd_isinfinite(b)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ n = mpd_qget_ssize(b, &workstatus);
+ if (workstatus&MPD_Invalid_operation) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (n > ctx->prec || n < -ctx->prec) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ mpd_qcopy(result, a, status);
+ return;
+ }
+
+ if (n >= 0) {
+ lshift = n;
+ rshift = ctx->prec-n;
+ }
+ else {
+ lshift = ctx->prec+n;
+ rshift = -n;
+ }
+
+ if (a->digits > ctx->prec) {
+ if (!mpd_qcopy(&tmp, a, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ goto finish;
+ }
+ _mpd_cap(&tmp, ctx);
+ a = &tmp;
+ }
+
+ if (!mpd_qshiftl(&big, a, lshift, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ goto finish;
+ }
+ _mpd_cap(&big, ctx);
+
+ if (mpd_qshiftr(&small, a, rshift, status) == MPD_UINT_MAX) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ goto finish;
+ }
+ _mpd_qadd(result, &big, &small, ctx, status);
+
+
+finish:
+ mpd_del(&tmp);
+ mpd_del(&big);
+ mpd_del(&small);
+}
+
+/*
+ * b must be an integer with exponent 0 and in the range +-2*(emax + prec).
+ * XXX: In my opinion +-(2*emax + prec) would be more sensible.
+ * The result is a with the value of b added to its exponent.
+ */
+void
+mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_uint_t n, maxjump;
+#ifndef LEGACY_COMPILER
+ int64_t exp;
+#else
+ mpd_uint_t x;
+ int x_sign, n_sign;
+ mpd_ssize_t exp;
+#endif
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ }
+ if (b->exp != 0 || mpd_isinfinite(b)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ n = mpd_qabs_uint(b, &workstatus);
+ /* the spec demands this */
+ maxjump = 2 * (mpd_uint_t)(ctx->emax + ctx->prec);
+
+ if (n > maxjump || workstatus&MPD_Invalid_operation) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ mpd_qcopy(result, a, status);
+ return;
+ }
+
+#ifndef LEGACY_COMPILER
+ exp = a->exp + (int64_t)n * mpd_arith_sign(b);
+ exp = (exp > MPD_EXP_INF) ? MPD_EXP_INF : exp;
+ exp = (exp < MPD_EXP_CLAMP) ? MPD_EXP_CLAMP : exp;
+#else
+ x = (a->exp < 0) ? -a->exp : a->exp;
+ x_sign = (a->exp < 0) ? 1 : 0;
+ n_sign = mpd_isnegative(b) ? 1 : 0;
+
+ if (x_sign == n_sign) {
+ x = x + n;
+ if (x < n) x = MPD_UINT_MAX;
+ }
+ else {
+ x_sign = (x >= n) ? x_sign : n_sign;
+ x = (x >= n) ? x - n : n - x;
+ }
+ if (!x_sign && x > MPD_EXP_INF) x = MPD_EXP_INF;
+ if (x_sign && x > -MPD_EXP_CLAMP) x = -MPD_EXP_CLAMP;
+ exp = x_sign ? -((mpd_ssize_t)x) : (mpd_ssize_t)x;
+#endif
+
+ mpd_qcopy(result, a, status);
+ result->exp = (mpd_ssize_t)exp;
+
+ mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * Shift the coefficient by n digits, positive n is a left shift. In the case
+ * of a left shift, the result is decapitated to fit the context precision. If
+ * you don't want that, use mpd_shiftl().
+ */
+void
+mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ mpd_qcopy(result, a, status);
+ return;
+ }
+
+ if (n >= 0 && n <= ctx->prec) {
+ mpd_qshiftl(result, a, n, status);
+ _mpd_cap(result, ctx);
+ }
+ else if (n < 0 && n >= -ctx->prec) {
+ if (!mpd_qcopy(result, a, status)) {
+ return;
+ }
+ _mpd_cap(result, ctx);
+ mpd_qshiftr_inplace(result, -n);
+ }
+ else {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ }
+}
+
+/*
+ * Same as mpd_shiftn(), but the shift is specified by the decimal b, which
+ * must be an integer with a zero exponent. Infinities remain infinities.
+ */
+void
+mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_ssize_t n;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ }
+ if (b->exp != 0 || mpd_isinfinite(b)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ n = mpd_qget_ssize(b, &workstatus);
+ if (workstatus&MPD_Invalid_operation) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (n > ctx->prec || n < -ctx->prec) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ mpd_qcopy(result, a, status);
+ return;
+ }
+
+ if (n >= 0) {
+ mpd_qshiftl(result, a, n, status);
+ _mpd_cap(result, ctx);
+ }
+ else {
+ if (!mpd_qcopy(result, a, status)) {
+ return;
+ }
+ _mpd_cap(result, ctx);
+ mpd_qshiftr_inplace(result, -n);
+ }
+}
+
+/* Logical Xor */
+void
+mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ const mpd_t *big = a, *small = b;
+ mpd_uint_t x, y, z, xbit, ybit;
+ int k, mswdigits;
+ mpd_ssize_t i;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b) ||
+ mpd_isnegative(a) || mpd_isnegative(b) ||
+ a->exp != 0 || b->exp != 0) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (b->digits > a->digits) {
+ big = b;
+ small = a;
+ }
+ if (!mpd_qresize(result, big->len, status)) {
+ return;
+ }
+
+
+ /* full words */
+ for (i = 0; i < small->len-1; i++) {
+ x = small->data[i];
+ y = big->data[i];
+ z = 0;
+ for (k = 0; k < MPD_RDIGITS; k++) {
+ xbit = x % 10;
+ x /= 10;
+ ybit = y % 10;
+ y /= 10;
+ if (xbit > 1 || ybit > 1) {
+ goto invalid_operation;
+ }
+ z += (xbit^ybit) ? mpd_pow10[k] : 0;
+ }
+ result->data[i] = z;
+ }
+ /* most significant word of small */
+ x = small->data[i];
+ y = big->data[i];
+ z = 0;
+ mswdigits = mpd_word_digits(x);
+ for (k = 0; k < mswdigits; k++) {
+ xbit = x % 10;
+ x /= 10;
+ ybit = y % 10;
+ y /= 10;
+ if (xbit > 1 || ybit > 1) {
+ goto invalid_operation;
+ }
+ z += (xbit^ybit) ? mpd_pow10[k] : 0;
+ }
+
+ /* scan and copy the rest of y for digit > 1 */
+ for (; k < MPD_RDIGITS; k++) {
+ ybit = y % 10;
+ y /= 10;
+ if (ybit > 1) {
+ goto invalid_operation;
+ }
+ z += ybit*mpd_pow10[k];
+ }
+ result->data[i++] = z;
+ /* scan and copy the rest of big for digit > 1 */
+ for (; i < big->len; i++) {
+ y = big->data[i];
+ for (k = 0; k < MPD_RDIGITS; k++) {
+ ybit = y % 10;
+ y /= 10;
+ if (ybit > 1) {
+ goto invalid_operation;
+ }
+ }
+ result->data[i] = big->data[i];
+ }
+
+ mpd_clear_flags(result);
+ result->exp = 0;
+ result->len = _mpd_real_size(result->data, big->len);
+ mpd_qresize(result, result->len, status);
+ mpd_setdigits(result);
+ _mpd_cap(result, ctx);
+ return;
+
+invalid_operation:
+ mpd_seterror(result, MPD_Invalid_operation, status);
+}
+
+
+/******************************************************************************/
+/* Arithmetic operations */
+/******************************************************************************/
+
+/*
+ * The absolute value of a. If a is negative, the result is the same
+ * as the result of the minus operation. Otherwise, the result is the
+ * result of the plus operation.
+ */
+void
+mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ }
+
+ if (mpd_isnegative(a)) {
+ mpd_qminus(result, a, ctx, status);
+ }
+ else {
+ mpd_qplus(result, a, ctx, status);
+ }
+
+ mpd_qfinalize(result, ctx, status);
+}
+
+static inline void
+_mpd_ptrswap(mpd_t **a, mpd_t **b)
+{
+ mpd_t *t = *a;
+ *a = *b;
+ *b = t;
+}
+
+/* Add or subtract infinities. */
+static void
+_mpd_qaddsub_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b,
+ uint32_t *status)
+{
+ if (mpd_isinfinite(a)) {
+ if (mpd_sign(a) != sign_b && mpd_isinfinite(b)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ }
+ else {
+ mpd_setspecial(result, mpd_sign(a), MPD_INF);
+ }
+ return;
+ }
+ assert(mpd_isinfinite(b));
+ mpd_setspecial(result, sign_b, MPD_INF);
+}
+
+/* Add or subtract non-special numbers. */
+static void
+_mpd_qaddsub(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_t *big, *small;
+ MPD_NEW_STATIC(big_aligned,0,0,0,0);
+ MPD_NEW_CONST(tiny,0,0,0,1,1,1);
+ mpd_uint_t carry;
+ mpd_ssize_t newsize, shift;
+ mpd_ssize_t exp, i;
+ int swap = 0;
+
+
+ /* compare exponents */
+ big = (mpd_t *)a; small = (mpd_t *)b;
+ if (big->exp != small->exp) {
+ if (small->exp > big->exp) {
+ _mpd_ptrswap(&big, &small);
+ swap++;
+ }
+ if (!mpd_iszerocoeff(big)) {
+ /* Test for adjexp(small) + big->digits < adjexp(big), if big-digits > prec
+ * Test for adjexp(small) + prec + 1 < adjexp(big), if big-digits <= prec
+ * If true, the magnitudes of the numbers are so far apart that one can as
+ * well add or subtract 1*10**big->exp. */
+ exp = big->exp - 1;
+ exp += (big->digits > ctx->prec) ? 0 : big->digits-ctx->prec-1;
+ if (mpd_adjexp(small) < exp) {
+ mpd_copy_flags(&tiny, small);
+ tiny.exp = exp;
+ tiny.digits = 1;
+ tiny.len = 1;
+ tiny.data[0] = mpd_iszerocoeff(small) ? 0 : 1;
+ small = &tiny;
+ }
+ /* this cannot wrap: the difference is positive and <= maxprec+1 */
+ shift = big->exp - small->exp;
+ if (!mpd_qshiftl(&big_aligned, big, shift, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ goto finish;
+ }
+ big = &big_aligned;
+ }
+ }
+ result->exp = small->exp;
+
+
+ /* compare length of coefficients */
+ if (big->len < small->len) {
+ _mpd_ptrswap(&big, &small);
+ swap++;
+ }
+
+ newsize = big->len;
+ if (!mpd_qresize(result, newsize, status)) {
+ goto finish;
+ }
+
+ if (mpd_sign(a) == sign_b) {
+
+ carry = _mpd_baseadd(result->data, big->data, small->data,
+ big->len, small->len);
+
+ if (carry) {
+ newsize = big->len + 1;
+ if (!mpd_qresize(result, newsize, status)) {
+ goto finish;
+ }
+ result->data[newsize-1] = carry;
+ }
+
+ result->len = newsize;
+ mpd_set_flags(result, sign_b);
+ }
+ else {
+ if (big->len == small->len) {
+ for (i=big->len-1; i >= 0; --i) {
+ if (big->data[i] != small->data[i]) {
+ if (big->data[i] < small->data[i]) {
+ _mpd_ptrswap(&big, &small);
+ swap++;
+ }
+ break;
+ }
+ }
+ }
+
+ _mpd_basesub(result->data, big->data, small->data,
+ big->len, small->len);
+ newsize = _mpd_real_size(result->data, big->len);
+ /* resize to smaller cannot fail */
+ (void)mpd_qresize(result, newsize, status);
+
+ result->len = newsize;
+ sign_b = (swap & 1) ? sign_b : mpd_sign(a);
+ mpd_set_flags(result, sign_b);
+
+ if (mpd_iszerocoeff(result)) {
+ mpd_set_positive(result);
+ if (ctx->round == MPD_ROUND_FLOOR) {
+ mpd_set_negative(result);
+ }
+ }
+ }
+
+ mpd_setdigits(result);
+
+finish:
+ mpd_del(&big_aligned);
+}
+
+/* Add a and b. No specials, no finalizing. */
+static void
+_mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status);
+}
+
+/* Subtract b from a. No specials, no finalizing. */
+static void
+_mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status);
+}
+
+/* Add a and b. */
+void
+mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ _mpd_qaddsub_inf(result, a, b, mpd_sign(b), status);
+ return;
+ }
+
+ _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status);
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* Subtract b from a. */
+void
+mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ _mpd_qaddsub_inf(result, a, b, !mpd_sign(b), status);
+ return;
+ }
+
+ _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status);
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* Add decimal and mpd_ssize_t. */
+void
+mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(bb,0,0,0,0);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_qsset_ssize(&bb, b, &maxcontext, status);
+ mpd_qadd(result, a, &bb, ctx, status);
+ mpd_del(&bb);
+}
+
+/* Add decimal and mpd_uint_t. */
+void
+mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(bb,0,0,0,0);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_qsset_uint(&bb, b, &maxcontext, status);
+ mpd_qadd(result, a, &bb, ctx, status);
+ mpd_del(&bb);
+}
+
+/* Subtract mpd_ssize_t from decimal. */
+void
+mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(bb,0,0,0,0);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_qsset_ssize(&bb, b, &maxcontext, status);
+ mpd_qsub(result, a, &bb, ctx, status);
+ mpd_del(&bb);
+}
+
+/* Subtract mpd_uint_t from decimal. */
+void
+mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(bb,0,0,0,0);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_qsset_uint(&bb, b, &maxcontext, status);
+ mpd_qsub(result, a, &bb, ctx, status);
+ mpd_del(&bb);
+}
+
+/* Add decimal and int32_t. */
+void
+mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qadd_ssize(result, a, b, ctx, status);
+}
+
+/* Add decimal and uint32_t. */
+void
+mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qadd_uint(result, a, b, ctx, status);
+}
+
+#ifdef CONFIG_64
+/* Add decimal and int64_t. */
+void
+mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qadd_ssize(result, a, b, ctx, status);
+}
+
+/* Add decimal and uint64_t. */
+void
+mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qadd_uint(result, a, b, ctx, status);
+}
+#endif
+
+/* Subtract int32_t from decimal. */
+void
+mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qsub_ssize(result, a, b, ctx, status);
+}
+
+/* Subtract uint32_t from decimal. */
+void
+mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qsub_uint(result, a, b, ctx, status);
+}
+
+#ifdef CONFIG_64
+/* Subtract int64_t from decimal. */
+void
+mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qsub_ssize(result, a, b, ctx, status);
+}
+
+/* Subtract uint64_t from decimal. */
+void
+mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qsub_uint(result, a, b, ctx, status);
+}
+#endif
+
+
+/* Divide infinities. */
+static void
+_mpd_qdiv_inf(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ if (mpd_isinfinite(a)) {
+ if (mpd_isinfinite(b)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
+ return;
+ }
+ assert(mpd_isinfinite(b));
+ _settriple(result, mpd_sign(a)^mpd_sign(b), 0, mpd_etiny(ctx));
+ *status |= MPD_Clamped;
+}
+
+enum {NO_IDEAL_EXP, SET_IDEAL_EXP};
+/* Divide a by b. */
+static void
+_mpd_qdiv(int action, mpd_t *q, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ MPD_NEW_STATIC(aligned,0,0,0,0);
+ mpd_uint_t ld;
+ mpd_ssize_t shift, exp, tz;
+ mpd_ssize_t newsize;
+ mpd_ssize_t ideal_exp;
+ mpd_uint_t rem;
+ uint8_t sign_a = mpd_sign(a);
+ uint8_t sign_b = mpd_sign(b);
+
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+ return;
+ }
+ _mpd_qdiv_inf(q, a, b, ctx, status);
+ return;
+ }
+ if (mpd_iszerocoeff(b)) {
+ if (mpd_iszerocoeff(a)) {
+ mpd_seterror(q, MPD_Division_undefined, status);
+ }
+ else {
+ mpd_setspecial(q, sign_a^sign_b, MPD_INF);
+ *status |= MPD_Division_by_zero;
+ }
+ return;
+ }
+ if (mpd_iszerocoeff(a)) {
+ exp = a->exp - b->exp;
+ _settriple(q, sign_a^sign_b, 0, exp);
+ mpd_qfinalize(q, ctx, status);
+ return;
+ }
+
+ shift = (b->digits - a->digits) + ctx->prec + 1;
+ ideal_exp = a->exp - b->exp;
+ exp = ideal_exp - shift;
+ if (shift > 0) {
+ if (!mpd_qshiftl(&aligned, a, shift, status)) {
+ mpd_seterror(q, MPD_Malloc_error, status);
+ goto finish;
+ }
+ a = &aligned;
+ }
+ else if (shift < 0) {
+ shift = -shift;
+ if (!mpd_qshiftl(&aligned, b, shift, status)) {
+ mpd_seterror(q, MPD_Malloc_error, status);
+ goto finish;
+ }
+ b = &aligned;
+ }
+
+
+ newsize = a->len - b->len + 1;
+ if ((q != b && q != a) || (q == b && newsize > b->len)) {
+ if (!mpd_qresize(q, newsize, status)) {
+ mpd_seterror(q, MPD_Malloc_error, status);
+ goto finish;
+ }
+ }
+
+
+ if (b->len == 1) {
+ rem = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]);
+ }
+ else if (a->len < 2*MPD_NEWTONDIV_CUTOFF &&
+ b->len < MPD_NEWTONDIV_CUTOFF) {
+ int ret = _mpd_basedivmod(q->data, NULL, a->data, b->data,
+ a->len, b->len);
+ if (ret < 0) {
+ mpd_seterror(q, MPD_Malloc_error, status);
+ goto finish;
+ }
+ rem = ret;
+ }
+ else {
+ MPD_NEW_STATIC(r,0,0,0,0);
+ _mpd_qbarrett_divmod(q, &r, a, b, status);
+ if (mpd_isspecial(q) || mpd_isspecial(&r)) {
+ mpd_del(&r);
+ goto finish;
+ }
+ rem = !mpd_iszerocoeff(&r);
+ mpd_del(&r);
+ newsize = q->len;
+ }
+
+ newsize = _mpd_real_size(q->data, newsize);
+ /* resize to smaller cannot fail */
+ mpd_qresize(q, newsize, status);
+ q->len = newsize;
+ mpd_setdigits(q);
+
+ shift = ideal_exp - exp;
+ if (rem) {
+ ld = mpd_lsd(q->data[0]);
+ if (ld == 0 || ld == 5) {
+ q->data[0] += 1;
+ }
+ }
+ else if (action == SET_IDEAL_EXP && shift > 0) {
+ tz = mpd_trail_zeros(q);
+ shift = (tz > shift) ? shift : tz;
+ mpd_qshiftr_inplace(q, shift);
+ exp += shift;
+ }
+
+ mpd_set_flags(q, sign_a^sign_b);
+ q->exp = exp;
+
+
+finish:
+ mpd_del(&aligned);
+ mpd_qfinalize(q, ctx, status);
+}
+
+/* Divide a by b. */
+void
+mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ _mpd_qdiv(SET_IDEAL_EXP, q, a, b, ctx, status);
+}
+
+/* Internal function. */
+static void
+_mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ MPD_NEW_STATIC(aligned,0,0,0,0);
+ mpd_ssize_t qsize, rsize;
+ mpd_ssize_t ideal_exp, expdiff, shift;
+ uint8_t sign_a = mpd_sign(a);
+ uint8_t sign_ab = mpd_sign(a)^mpd_sign(b);
+
+
+ ideal_exp = (a->exp > b->exp) ? b->exp : a->exp;
+ if (mpd_iszerocoeff(a)) {
+ if (!mpd_qcopy(r, a, status)) {
+ goto nanresult; /* GCOV_NOT_REACHED */
+ }
+ r->exp = ideal_exp;
+ _settriple(q, sign_ab, 0, 0);
+ return;
+ }
+
+ expdiff = mpd_adjexp(a) - mpd_adjexp(b);
+ if (expdiff < 0) {
+ if (a->exp > b->exp) {
+ /* positive and less than b->digits - a->digits */
+ shift = a->exp - b->exp;
+ if (!mpd_qshiftl(r, a, shift, status)) {
+ goto nanresult;
+ }
+ r->exp = ideal_exp;
+ }
+ else {
+ if (!mpd_qcopy(r, a, status)) {
+ goto nanresult;
+ }
+ }
+ _settriple(q, sign_ab, 0, 0);
+ return;
+ }
+ if (expdiff > ctx->prec) {
+ *status |= MPD_Division_impossible;
+ goto nanresult;
+ }
+
+
+ /*
+ * At this point we have:
+ * (1) 0 <= a->exp + a->digits - b->exp - b->digits <= prec
+ * (2) a->exp - b->exp >= b->digits - a->digits
+ * (3) a->exp - b->exp <= prec + b->digits - a->digits
+ */
+ if (a->exp != b->exp) {
+ shift = a->exp - b->exp;
+ if (shift > 0) {
+ /* by (3), after the shift a->digits <= prec + b->digits */
+ if (!mpd_qshiftl(&aligned, a, shift, status)) {
+ goto nanresult;
+ }
+ a = &aligned;
+ }
+ else {
+ shift = -shift;
+ /* by (2), after the shift b->digits <= a->digits */
+ if (!mpd_qshiftl(&aligned, b, shift, status)) {
+ goto nanresult;
+ }
+ b = &aligned;
+ }
+ }
+
+
+ qsize = a->len - b->len + 1;
+ if (!(q == a && qsize < a->len) && !(q == b && qsize < b->len)) {
+ if (!mpd_qresize(q, qsize, status)) {
+ goto nanresult;
+ }
+ }
+
+ rsize = b->len;
+ if (!(r == a && rsize < a->len)) {
+ if (!mpd_qresize(r, rsize, status)) {
+ goto nanresult;
+ }
+ }
+
+ if (b->len == 1) {
+ if (a->len == 1) {
+ _mpd_div_word(&q->data[0], &r->data[0], a->data[0], b->data[0]);
+ }
+ else {
+ r->data[0] = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]);
+ }
+ }
+ else if (a->len < 2*MPD_NEWTONDIV_CUTOFF &&
+ b->len < MPD_NEWTONDIV_CUTOFF) {
+ int ret;
+ ret = _mpd_basedivmod(q->data, r->data, a->data, b->data,
+ a->len, b->len);
+ if (ret == -1) {
+ *status |= MPD_Malloc_error;
+ goto nanresult;
+ }
+ }
+ else {
+ _mpd_qbarrett_divmod(q, r, a, b, status);
+ if (mpd_isspecial(q) || mpd_isspecial(r)) {
+ goto nanresult;
+ }
+ if (mpd_isinfinite(q) || q->digits > ctx->prec) {
+ *status |= MPD_Division_impossible;
+ goto nanresult;
+ }
+ qsize = q->len;
+ rsize = r->len;
+ }
+
+ qsize = _mpd_real_size(q->data, qsize);
+ /* resize to smaller cannot fail */
+ mpd_qresize(q, qsize, status);
+ q->len = qsize;
+ mpd_setdigits(q);
+ mpd_set_flags(q, sign_ab);
+ q->exp = 0;
+ if (q->digits > ctx->prec) {
+ *status |= MPD_Division_impossible;
+ goto nanresult;
+ }
+
+ rsize = _mpd_real_size(r->data, rsize);
+ /* resize to smaller cannot fail */
+ mpd_qresize(r, rsize, status);
+ r->len = rsize;
+ mpd_setdigits(r);
+ mpd_set_flags(r, sign_a);
+ r->exp = ideal_exp;
+
+out:
+ mpd_del(&aligned);
+ return;
+
+nanresult:
+ mpd_setspecial(q, MPD_POS, MPD_NAN);
+ mpd_setspecial(r, MPD_POS, MPD_NAN);
+ goto out;
+}
+
+/* Integer division with remainder. */
+void
+mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint8_t sign = mpd_sign(a)^mpd_sign(b);
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+ mpd_qcopy(r, q, status);
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ if (mpd_isinfinite(b)) {
+ mpd_setspecial(q, MPD_POS, MPD_NAN);
+ }
+ else {
+ mpd_setspecial(q, sign, MPD_INF);
+ }
+ mpd_setspecial(r, MPD_POS, MPD_NAN);
+ *status |= MPD_Invalid_operation;
+ return;
+ }
+ if (mpd_isinfinite(b)) {
+ if (!mpd_qcopy(r, a, status)) {
+ mpd_seterror(q, MPD_Malloc_error, status);
+ return;
+ }
+ mpd_qfinalize(r, ctx, status);
+ _settriple(q, sign, 0, 0);
+ return;
+ }
+ /* debug */
+ abort(); /* GCOV_NOT_REACHED */
+ }
+ if (mpd_iszerocoeff(b)) {
+ if (mpd_iszerocoeff(a)) {
+ mpd_setspecial(q, MPD_POS, MPD_NAN);
+ mpd_setspecial(r, MPD_POS, MPD_NAN);
+ *status |= MPD_Division_undefined;
+ }
+ else {
+ mpd_setspecial(q, sign, MPD_INF);
+ mpd_setspecial(r, MPD_POS, MPD_NAN);
+ *status |= (MPD_Division_by_zero|MPD_Invalid_operation);
+ }
+ return;
+ }
+
+ _mpd_qdivmod(q, r, a, b, ctx, status);
+ mpd_qfinalize(q, ctx, status);
+ mpd_qfinalize(r, ctx, status);
+}
+
+void
+mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ MPD_NEW_STATIC(r,0,0,0,0);
+ uint8_t sign = mpd_sign(a)^mpd_sign(b);
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(q, a, b, ctx, status)) {
+ return;
+ }
+ if (mpd_isinfinite(a) && mpd_isinfinite(b)) {
+ mpd_seterror(q, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ mpd_setspecial(q, sign, MPD_INF);
+ return;
+ }
+ if (mpd_isinfinite(b)) {
+ _settriple(q, sign, 0, 0);
+ return;
+ }
+ /* debug */
+ abort(); /* GCOV_NOT_REACHED */
+ }
+ if (mpd_iszerocoeff(b)) {
+ if (mpd_iszerocoeff(a)) {
+ mpd_seterror(q, MPD_Division_undefined, status);
+ }
+ else {
+ mpd_setspecial(q, sign, MPD_INF);
+ *status |= MPD_Division_by_zero;
+ }
+ return;
+ }
+
+
+ _mpd_qdivmod(q, &r, a, b, ctx, status);
+ mpd_del(&r);
+ mpd_qfinalize(q, ctx, status);
+}
+
+/* Divide decimal by mpd_ssize_t. */
+void
+mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(bb,0,0,0,0);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_qsset_ssize(&bb, b, &maxcontext, status);
+ mpd_qdiv(result, a, &bb, ctx, status);
+ mpd_del(&bb);
+}
+
+/* Divide decimal by mpd_uint_t. */
+void
+mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(bb,0,0,0,0);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_qsset_uint(&bb, b, &maxcontext, status);
+ mpd_qdiv(result, a, &bb, ctx, status);
+ mpd_del(&bb);
+}
+
+/* Divide decimal by int32_t. */
+void
+mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qdiv_ssize(result, a, b, ctx, status);
+}
+
+/* Divide decimal by uint32_t. */
+void
+mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qdiv_uint(result, a, b, ctx, status);
+}
+
+#ifdef CONFIG_64
+/* Divide decimal by int64_t. */
+void
+mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qdiv_ssize(result, a, b, ctx, status);
+}
+
+/* Divide decimal by uint64_t. */
+void
+mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qdiv_uint(result, a, b, ctx, status);
+}
+#endif
+
+#if defined(_MSC_VER)
+ /* conversion from 'double' to 'mpd_ssize_t', possible loss of data */
+ #pragma warning(disable:4244)
+#endif
+/*
+ * Get the number of iterations for the Horner scheme in _mpd_qexp().
+ */
+static inline mpd_ssize_t
+_mpd_get_exp_iterations(const mpd_t *a, mpd_ssize_t prec)
+{
+ mpd_uint_t dummy;
+ mpd_uint_t msdigits;
+ double f;
+
+ /* 9 is MPD_RDIGITS for 32 bit platforms */
+ _mpd_get_msdigits(&dummy, &msdigits, a, 9);
+ f = ((double)msdigits + 1) / mpd_pow10[mpd_word_digits(msdigits)];
+
+#ifdef CONFIG_64
+ #ifdef USE_80BIT_LONG_DOUBLE
+ return ceill((1.435*(long double)prec - 1.182)
+ / log10l((long double)prec/f));
+ #else
+ /* prec > floor((1ULL<<53) / 1.435) */
+ if (prec > 6276793905742851LL) {
+ return MPD_SSIZE_MAX;
+ }
+ return ceil((1.435*(double)prec - 1.182) / log10((double)prec/f));
+ #endif
+#else /* CONFIG_32 */
+ return ceil((1.435*(double)prec - 1.182) / log10((double)prec/f));
+ #if defined(_MSC_VER)
+ #pragma warning(default:4244)
+ #endif
+#endif
+}
+
+/*
+ * Internal function, specials have been dealt with.
+ *
+ * The algorithm is from Hull&Abrham, Variable Precision Exponential Function,
+ * ACM Transactions on Mathematical Software, Vol. 12, No. 2, June 1986.
+ *
+ * Main differences:
+ *
+ * - The number of iterations for the Horner scheme is calculated using the
+ * C log10() function.
+ *
+ * - The analysis for early abortion has been adapted for the mpd_t
+ * ranges.
+ */
+static void
+_mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx;
+ MPD_NEW_STATIC(tmp,0,0,0,0);
+ MPD_NEW_STATIC(sum,0,0,0,0);
+ MPD_NEW_CONST(word,0,0,0,1,1,1);
+ mpd_ssize_t j, n, t;
+
+ assert(!mpd_isspecial(a));
+
+ /*
+ * We are calculating e^x = e^(r*10^t) = (e^r)^(10^t), where r < 1 and t >= 0.
+ *
+ * If t > 0, we have:
+ *
+ * (1) 0.1 <= r < 1, so e^r >= e^0.1. Overflow in the final power operation
+ * will occur when (e^0.1)^(10^t) > 10^(emax+1). If we consider MAX_EMAX,
+ * this will happen for t > 10 (32 bit) or (t > 19) (64 bit).
+ *
+ * (2) -1 < r <= -0.1, so e^r > e^-1. Underflow in the final power operation
+ * will occur when (e^-1)^(10^t) < 10^(etiny-1). If we consider MIN_ETINY,
+ * this will also happen for t > 10 (32 bit) or (t > 19) (64 bit).
+ */
+#if defined(CONFIG_64)
+ #define MPD_EXP_MAX_T 19
+#elif defined(CONFIG_32)
+ #define MPD_EXP_MAX_T 10
+#endif
+ t = a->digits + a->exp;
+ t = (t > 0) ? t : 0;
+ if (t > MPD_EXP_MAX_T) {
+ if (mpd_ispositive(a)) {
+ mpd_setspecial(result, MPD_POS, MPD_INF);
+ *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
+ }
+ else {
+ _settriple(result, MPD_POS, 0, mpd_etiny(ctx));
+ *status |= (MPD_Inexact|MPD_Rounded|MPD_Subnormal|
+ MPD_Underflow|MPD_Clamped);
+ }
+ return;
+ }
+
+ mpd_maxcontext(&workctx);
+ workctx.prec = ctx->prec + t + 2;
+ workctx.prec = (workctx.prec < 9) ? 9 : workctx.prec;
+ workctx.round = MPD_ROUND_HALF_EVEN;
+
+ if ((n = _mpd_get_exp_iterations(a, workctx.prec)) == MPD_SSIZE_MAX) {
+ mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_UNLIKELY */
+ goto finish; /* GCOV_UNLIKELY */
+ }
+
+ if (!mpd_qcopy(result, a, status)) {
+ goto finish;
+ }
+ result->exp -= t;
+
+ _settriple(&sum, MPD_POS, 1, 0);
+
+ for (j = n-1; j >= 1; j--) {
+ word.data[0] = j;
+ mpd_setdigits(&word);
+ mpd_qdiv(&tmp, result, &word, &workctx, &workctx.status);
+ mpd_qmul(&sum, &sum, &tmp, &workctx, &workctx.status);
+ mpd_qadd(&sum, &sum, &one, &workctx, &workctx.status);
+ }
+
+#ifdef CONFIG_64
+ _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status);
+#else
+ if (t <= MPD_MAX_POW10) {
+ _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status);
+ }
+ else {
+ t -= MPD_MAX_POW10;
+ _mpd_qpow_uint(&tmp, &sum, mpd_pow10[MPD_MAX_POW10], MPD_POS,
+ &workctx, status);
+ _mpd_qpow_uint(result, &tmp, mpd_pow10[t], MPD_POS, &workctx, status);
+ }
+#endif
+
+
+finish:
+ mpd_del(&tmp);
+ mpd_del(&sum);
+ *status |= (workctx.status&MPD_Errors);
+ *status |= (MPD_Inexact|MPD_Rounded);
+}
+
+/* exp(a) */
+void
+mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx;
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ _settriple(result, MPD_POS, 0, 0);
+ }
+ else {
+ mpd_setspecial(result, MPD_POS, MPD_INF);
+ }
+ return;
+ }
+ if (mpd_iszerocoeff(a)) {
+ _settriple(result, MPD_POS, 1, 0);
+ return;
+ }
+
+ workctx = *ctx;
+ workctx.round = MPD_ROUND_HALF_EVEN;
+
+ if (ctx->allcr) {
+ MPD_NEW_STATIC(t1, 0,0,0,0);
+ MPD_NEW_STATIC(t2, 0,0,0,0);
+ MPD_NEW_STATIC(ulp, 0,0,0,0);
+ MPD_NEW_STATIC(aa, 0,0,0,0);
+ mpd_ssize_t prec;
+
+ if (result == a) {
+ if (!mpd_qcopy(&aa, a, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+ a = &aa;
+ }
+
+ workctx.clamp = 0;
+ prec = ctx->prec + 3;
+ while (1) {
+ workctx.prec = prec;
+ _mpd_qexp(result, a, &workctx, status);
+ _ssettriple(&ulp, MPD_POS, 1,
+ result->exp + result->digits-workctx.prec-1);
+
+ workctx.prec = ctx->prec;
+ mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
+ mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
+ if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
+ mpd_qcmp(&t1, &t2, status) == 0) {
+ workctx.clamp = ctx->clamp;
+ mpd_check_underflow(result, &workctx, status);
+ mpd_qfinalize(result, &workctx, status);
+ break;
+ }
+ prec += MPD_RDIGITS;
+ }
+ mpd_del(&t1);
+ mpd_del(&t2);
+ mpd_del(&ulp);
+ mpd_del(&aa);
+ }
+ else {
+ _mpd_qexp(result, a, &workctx, status);
+ mpd_check_underflow(result, &workctx, status);
+ mpd_qfinalize(result, &workctx, status);
+ }
+}
+
+/* Fused multiply-add: (a * b) + c, with a single final rounding. */
+void
+mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_t *cc = (mpd_t *)c;
+
+ if (result == c) {
+ if ((cc = mpd_qncopy(c)) == NULL) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+ }
+
+ _mpd_qmul(result, a, b, ctx, &workstatus);
+ if (!(workstatus&MPD_Invalid_operation)) {
+ mpd_qadd(result, result, cc, ctx, &workstatus);
+ }
+
+ if (cc != c) mpd_del(cc);
+ *status |= workstatus;
+}
+
+static inline int
+ln_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], mpd_ssize_t maxprec,
+ mpd_ssize_t initprec)
+{
+ mpd_ssize_t k;
+ int i;
+
+ assert(maxprec >= 2 && initprec >= 2);
+ if (maxprec <= initprec) return -1;
+
+ i = 0; k = maxprec;
+ do {
+ k = (k+2) / 2;
+ klist[i++] = k;
+ } while (k > initprec);
+
+ return i-1;
+}
+
+/* Two word initial approximations for ln(10) */
+#ifdef CONFIG_64
+#if MPD_RDIGITS != 19
+ #error "mpdecimal.c: MPD_RDIGITS must be 19."
+#endif
+static mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = {
+ 179914546843642076, 2302585092994045684
+};
+static mpd_uint_t mpd_ln10_init[2] = {
+ 179914546843642076, 2302585092994045684
+};
+#else
+#if MPD_RDIGITS != 9
+ #error "mpdecimal.c: MPD_RDIGITS must be 9."
+#endif
+static mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = {299404568, 230258509};
+static mpd_uint_t mpd_ln10_init[2] = {299404568, 230258509};
+#endif
+/* mpd_ln10 is cached in order to speed up computations */
+mpd_t mpd_ln10 = {MPD_STATIC|MPD_STATIC_DATA, -(2*MPD_RDIGITS-1),
+ 2*MPD_RDIGITS, 2, MPD_MINALLOC_MAX, mpd_ln10_data};
+
+static void
+mpd_reset_ln10(void)
+{
+ if (mpd_isdynamic_data(&mpd_ln10)) {
+ mpd_free(mpd_ln10.data);
+ }
+ mpd_ln10.data = mpd_ln10_data;
+ mpd_ln10_data[0] = mpd_ln10_init[0];
+ mpd_ln10_data[1] = mpd_ln10_init[1];
+ mpd_ln10.flags = MPD_STATIC|MPD_STATIC_DATA;
+ mpd_ln10.exp = -(2*MPD_RDIGITS-1);
+ mpd_ln10.digits = 2*MPD_RDIGITS;
+ mpd_ln10.len = 2;
+ mpd_ln10.alloc = MPD_MINALLOC_MAX;
+}
+
+/*
+ * Initializes or updates mpd_ln10. If mpd_ln10 is cached and has exactly the
+ * requested precision, the function returns. If the cached precision is greater
+ * than the requested precision, mpd_ln10 is shifted to the requested precision.
+ *
+ * The function can fail with MPD_Malloc_error.
+ */
+void
+mpd_update_ln10(mpd_ssize_t maxprec, uint32_t *status)
+{
+ mpd_context_t varcontext, maxcontext;
+ MPD_NEW_STATIC(tmp, 0,0,0,0);
+ MPD_NEW_CONST(static10, 0,0,2,1,1,10);
+ mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
+ int i;
+
+ if (mpd_isspecial(&mpd_ln10)) {
+ mpd_reset_ln10();
+ }
+
+ if (mpd_ln10.digits > maxprec) {
+ /* shift to smaller cannot fail */
+ mpd_qshiftr_inplace(&mpd_ln10, mpd_ln10.digits-maxprec);
+ mpd_ln10.exp = -(mpd_ln10.digits-1);
+ return;
+ }
+ else if (mpd_ln10.digits == maxprec) {
+ return;
+ }
+
+ mpd_maxcontext(&maxcontext);
+ mpd_maxcontext(&varcontext);
+ varcontext.round = MPD_ROUND_TRUNC;
+
+ i = ln_schedule_prec(klist, maxprec+2, mpd_ln10.digits);
+ for (; i >= 0; i--) {
+ varcontext.prec = 2*klist[i]+3;
+ mpd_ln10.flags ^= MPD_NEG;
+ _mpd_qexp(&tmp, &mpd_ln10, &varcontext, status);
+ mpd_ln10.flags ^= MPD_NEG;
+ mpd_qmul(&tmp, &static10, &tmp, &varcontext, status);
+ mpd_qsub(&tmp, &tmp, &one, &maxcontext, status);
+ mpd_qadd(&mpd_ln10, &mpd_ln10, &tmp, &maxcontext, status);
+ if (mpd_isspecial(&mpd_ln10)) {
+ break;
+ }
+ }
+
+ mpd_del(&tmp);
+ varcontext.prec = maxprec;
+ varcontext.round = MPD_ROUND_HALF_EVEN;
+ mpd_qfinalize(&mpd_ln10, &varcontext, status);
+}
+
+/* Initial approximations for the ln() iteration */
+static const uint16_t lnapprox[900] = {
+ /* index 0 - 400: log((i+100)/100) * 1000 */
+ 0, 10, 20, 30, 39, 49, 58, 68, 77, 86, 95, 104, 113, 122, 131, 140, 148, 157,
+ 166, 174, 182, 191, 199, 207, 215, 223, 231, 239, 247, 255, 262, 270, 278,
+ 285, 293, 300, 308, 315, 322, 329, 336, 344, 351, 358, 365, 372, 378, 385,
+ 392, 399, 406, 412, 419, 425, 432, 438, 445, 451, 457, 464, 470, 476, 482,
+ 489, 495, 501, 507, 513, 519, 525, 531, 536, 542, 548, 554, 560, 565, 571,
+ 577, 582, 588, 593, 599, 604, 610, 615, 621, 626, 631, 637, 642, 647, 652,
+ 658, 663, 668, 673, 678, 683, 688, 693, 698, 703, 708, 713, 718, 723, 728,
+ 732, 737, 742, 747, 751, 756, 761, 766, 770, 775, 779, 784, 788, 793, 798,
+ 802, 806, 811, 815, 820, 824, 829, 833, 837, 842, 846, 850, 854, 859, 863,
+ 867, 871, 876, 880, 884, 888, 892, 896, 900, 904, 908, 912, 916, 920, 924,
+ 928, 932, 936, 940, 944, 948, 952, 956, 959, 963, 967, 971, 975, 978, 982,
+ 986, 990, 993, 997, 1001, 1004, 1008, 1012, 1015, 1019, 1022, 1026, 1030,
+ 1033, 1037, 1040, 1044, 1047, 1051, 1054, 1058, 1061, 1065, 1068, 1072, 1075,
+ 1078, 1082, 1085, 1089, 1092, 1095, 1099, 1102, 1105, 1109, 1112, 1115, 1118,
+ 1122, 1125, 1128, 1131, 1135, 1138, 1141, 1144, 1147, 1151, 1154, 1157, 1160,
+ 1163, 1166, 1169, 1172, 1176, 1179, 1182, 1185, 1188, 1191, 1194, 1197, 1200,
+ 1203, 1206, 1209, 1212, 1215, 1218, 1221, 1224, 1227, 1230, 1233, 1235, 1238,
+ 1241, 1244, 1247, 1250, 1253, 1256, 1258, 1261, 1264, 1267, 1270, 1273, 1275,
+ 1278, 1281, 1284, 1286, 1289, 1292, 1295, 1297, 1300, 1303, 1306, 1308, 1311,
+ 1314, 1316, 1319, 1322, 1324, 1327, 1330, 1332, 1335, 1338, 1340, 1343, 1345,
+ 1348, 1351, 1353, 1356, 1358, 1361, 1364, 1366, 1369, 1371, 1374, 1376, 1379,
+ 1381, 1384, 1386, 1389, 1391, 1394, 1396, 1399, 1401, 1404, 1406, 1409, 1411,
+ 1413, 1416, 1418, 1421, 1423, 1426, 1428, 1430, 1433, 1435, 1437, 1440, 1442,
+ 1445, 1447, 1449, 1452, 1454, 1456, 1459, 1461, 1463, 1466, 1468, 1470, 1472,
+ 1475, 1477, 1479, 1482, 1484, 1486, 1488, 1491, 1493, 1495, 1497, 1500, 1502,
+ 1504, 1506, 1509, 1511, 1513, 1515, 1517, 1520, 1522, 1524, 1526, 1528, 1530,
+ 1533, 1535, 1537, 1539, 1541, 1543, 1545, 1548, 1550, 1552, 1554, 1556, 1558,
+ 1560, 1562, 1564, 1567, 1569, 1571, 1573, 1575, 1577, 1579, 1581, 1583, 1585,
+ 1587, 1589, 1591, 1593, 1595, 1597, 1599, 1601, 1603, 1605, 1607, 1609,
+ /* index 401 - 899: -log((i+100)/1000) * 1000 */
+ 691, 689, 687, 685, 683, 681, 679, 677, 675, 673, 671, 669, 668, 666, 664,
+ 662, 660, 658, 656, 654, 652, 650, 648, 646, 644, 642, 641, 639, 637, 635,
+ 633, 631, 629, 627, 626, 624, 622, 620, 618, 616, 614, 612, 611, 609, 607,
+ 605, 603, 602, 600, 598, 596, 594, 592, 591, 589, 587, 585, 583, 582, 580,
+ 578, 576, 574, 573, 571, 569, 567, 566, 564, 562, 560, 559, 557, 555, 553,
+ 552, 550, 548, 546, 545, 543, 541, 540, 538, 536, 534, 533, 531, 529, 528,
+ 526, 524, 523, 521, 519, 518, 516, 514, 512, 511, 509, 508, 506, 504, 502,
+ 501, 499, 498, 496, 494, 493, 491, 489, 488, 486, 484, 483, 481, 480, 478,
+ 476, 475, 473, 472, 470, 468, 467, 465, 464, 462, 460, 459, 457, 456, 454,
+ 453, 451, 449, 448, 446, 445, 443, 442, 440, 438, 437, 435, 434, 432, 431,
+ 429, 428, 426, 425, 423, 422, 420, 419, 417, 416, 414, 412, 411, 410, 408,
+ 406, 405, 404, 402, 400, 399, 398, 396, 394, 393, 392, 390, 389, 387, 386,
+ 384, 383, 381, 380, 378, 377, 375, 374, 372, 371, 370, 368, 367, 365, 364,
+ 362, 361, 360, 358, 357, 355, 354, 352, 351, 350, 348, 347, 345, 344, 342,
+ 341, 340, 338, 337, 336, 334, 333, 331, 330, 328, 327, 326, 324, 323, 322,
+ 320, 319, 318, 316, 315, 313, 312, 311, 309, 308, 306, 305, 304, 302, 301,
+ 300, 298, 297, 296, 294, 293, 292, 290, 289, 288, 286, 285, 284, 282, 281,
+ 280, 278, 277, 276, 274, 273, 272, 270, 269, 268, 267, 265, 264, 263, 261,
+ 260, 259, 258, 256, 255, 254, 252, 251, 250, 248, 247, 246, 245, 243, 242,
+ 241, 240, 238, 237, 236, 234, 233, 232, 231, 229, 228, 227, 226, 224, 223,
+ 222, 221, 219, 218, 217, 216, 214, 213, 212, 211, 210, 208, 207, 206, 205,
+ 203, 202, 201, 200, 198, 197, 196, 195, 194, 192, 191, 190, 189, 188, 186,
+ 185, 184, 183, 182, 180, 179, 178, 177, 176, 174, 173, 172, 171, 170, 168,
+ 167, 166, 165, 164, 162, 161, 160, 159, 158, 157, 156, 154, 153, 152, 151,
+ 150, 148, 147, 146, 145, 144, 143, 142, 140, 139, 138, 137, 136, 135, 134,
+ 132, 131, 130, 129, 128, 127, 126, 124, 123, 122, 121, 120, 119, 118, 116,
+ 115, 114, 113, 112, 111, 110, 109, 108, 106, 105, 104, 103, 102, 101, 100,
+ 99, 98, 97, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 84, 83, 82, 81, 80, 79,
+ 78, 77, 76, 75, 74, 73, 72, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59,
+ 58, 57, 56, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39,
+ 38, 37, 36, 35, 34, 33, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19,
+ 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
+};
+
+/* Internal ln() function that does not check for specials, zero or one. */
+static void
+_mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t varcontext, maxcontext;
+ mpd_t *z = (mpd_t *) result;
+ MPD_NEW_STATIC(v,0,0,0,0);
+ MPD_NEW_STATIC(vtmp,0,0,0,0);
+ MPD_NEW_STATIC(tmp,0,0,0,0);
+ mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
+ mpd_ssize_t maxprec, shift, t;
+ mpd_ssize_t a_digits, a_exp;
+ mpd_uint_t dummy, x;
+ int i;
+
+ assert(!mpd_isspecial(a) && !mpd_iszerocoeff(a));
+
+ /*
+ * We are calculating ln(a) = ln(v * 10^t) = ln(v) + t*ln(10),
+ * where 0.5 < v <= 5.
+ */
+ if (!mpd_qcopy(&v, a, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ goto finish;
+ }
+
+ /* Initial approximation: we have at least one non-zero digit */
+ _mpd_get_msdigits(&dummy, &x, &v, 3);
+ if (x < 10) x *= 10;
+ if (x < 100) x *= 10;
+ x -= 100;
+
+ /* a may equal z */
+ a_digits = a->digits;
+ a_exp = a->exp;
+
+ mpd_minalloc(z);
+ mpd_clear_flags(z);
+ z->data[0] = lnapprox[x];
+ z->len = 1;
+ z->exp = -3;
+ mpd_setdigits(z);
+
+ if (x <= 400) {
+ v.exp = -(a_digits - 1);
+ t = a_exp + a_digits - 1;
+ }
+ else {
+ v.exp = -a_digits;
+ t = a_exp + a_digits;
+ mpd_set_negative(z);
+ }
+
+ mpd_maxcontext(&maxcontext);
+ mpd_maxcontext(&varcontext);
+ varcontext.round = MPD_ROUND_TRUNC;
+
+ maxprec = ctx->prec + 2;
+ if (x <= 10 || x >= 805) {
+ /* v is close to 1: Estimate the magnitude of the logarithm.
+ * If v = 1 or ln(v) will underflow, skip the loop. Otherwise,
+ * adjust the precision upwards in order to obtain a sufficient
+ * number of significant digits.
+ *
+ * 1) x/(1+x) < ln(1+x) < x, for x > -1, x != 0
+ *
+ * 2) (v-1)/v < ln(v) < v-1
+ */
+ mpd_t *lower = &tmp;
+ mpd_t *upper = &vtmp;
+ int cmp = _mpd_cmp(&v, &one);
+
+ varcontext.round = MPD_ROUND_CEILING;
+ varcontext.prec = maxprec;
+ mpd_qsub(upper, &v, &one, &varcontext, &varcontext.status);
+ varcontext.round = MPD_ROUND_FLOOR;
+ mpd_qdiv(lower, upper, &v, &varcontext, &varcontext.status);
+ varcontext.round = MPD_ROUND_TRUNC;
+
+ if (cmp < 0) {
+ _mpd_ptrswap(&upper, &lower);
+ }
+ if (mpd_adjexp(upper) < mpd_etiny(ctx)) {
+ _settriple(z, (cmp<0), 1, mpd_etiny(ctx)-1);
+ goto postloop;
+ }
+ if (mpd_adjexp(lower) < 0) {
+ maxprec = maxprec - mpd_adjexp(lower);
+ }
+ }
+
+ i = ln_schedule_prec(klist, maxprec, 2);
+ for (; i >= 0; i--) {
+ varcontext.prec = 2*klist[i]+3;
+ z->flags ^= MPD_NEG;
+ _mpd_qexp(&tmp, z, &varcontext, status);
+ z->flags ^= MPD_NEG;
+
+ if (v.digits > varcontext.prec) {
+ shift = v.digits - varcontext.prec;
+ mpd_qshiftr(&vtmp, &v, shift, status);
+ vtmp.exp += shift;
+ mpd_qmul(&tmp, &vtmp, &tmp, &varcontext, status);
+ }
+ else {
+ mpd_qmul(&tmp, &v, &tmp, &varcontext, status);
+ }
+
+ mpd_qsub(&tmp, &tmp, &one, &maxcontext, status);
+ mpd_qadd(z, z, &tmp, &maxcontext, status);
+ if (mpd_isspecial(z)) {
+ break;
+ }
+ }
+
+postloop:
+ mpd_update_ln10(maxprec+2, status);
+ mpd_qmul_ssize(&tmp, &mpd_ln10, t, &maxcontext, status);
+ varcontext.prec = maxprec+2;
+ mpd_qadd(result, &tmp, z, &varcontext, status);
+
+
+finish:
+ mpd_del(&v);
+ mpd_del(&vtmp);
+ mpd_del(&tmp);
+}
+
+/* ln(a) */
+void
+mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx;
+ mpd_ssize_t adjexp, t;
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ mpd_setspecial(result, MPD_POS, MPD_INF);
+ return;
+ }
+ if (mpd_iszerocoeff(a)) {
+ mpd_setspecial(result, MPD_NEG, MPD_INF);
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (_mpd_cmp(a, &one) == 0) {
+ _settriple(result, MPD_POS, 0, 0);
+ return;
+ }
+ /* Check if the result will overflow.
+ *
+ * 1) adjexp(a) + 1 > log10(a) >= adjexp(a)
+ *
+ * 2) |log10(a)| >= adjexp(a), if adjexp(a) >= 0
+ * |log10(a)| > -adjexp(a)-1, if adjexp(a) < 0
+ *
+ * 3) |log(a)| > 2*|log10(a)|
+ */
+ adjexp = mpd_adjexp(a);
+ t = (adjexp < 0) ? -adjexp-1 : adjexp;
+ t *= 2;
+ if (mpd_exp_digits(t)-1 > ctx->emax) {
+ *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
+ mpd_setspecial(result, (adjexp<0), MPD_INF);
+ return;
+ }
+
+ workctx = *ctx;
+ workctx.round = MPD_ROUND_HALF_EVEN;
+
+ if (ctx->allcr) {
+ MPD_NEW_STATIC(t1, 0,0,0,0);
+ MPD_NEW_STATIC(t2, 0,0,0,0);
+ MPD_NEW_STATIC(ulp, 0,0,0,0);
+ MPD_NEW_STATIC(aa, 0,0,0,0);
+ mpd_ssize_t prec;
+
+ if (result == a) {
+ if (!mpd_qcopy(&aa, a, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+ a = &aa;
+ }
+
+ workctx.clamp = 0;
+ prec = ctx->prec + 3;
+ while (1) {
+ workctx.prec = prec;
+ _mpd_qln(result, a, &workctx, status);
+ _ssettriple(&ulp, MPD_POS, 1,
+ result->exp + result->digits-workctx.prec-1);
+
+ workctx.prec = ctx->prec;
+ mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
+ mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
+ if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
+ mpd_qcmp(&t1, &t2, status) == 0) {
+ workctx.clamp = ctx->clamp;
+ mpd_check_underflow(result, &workctx, status);
+ mpd_qfinalize(result, &workctx, status);
+ break;
+ }
+ prec += MPD_RDIGITS;
+ }
+ mpd_del(&t1);
+ mpd_del(&t2);
+ mpd_del(&ulp);
+ mpd_del(&aa);
+ }
+ else {
+ _mpd_qln(result, a, &workctx, status);
+ mpd_check_underflow(result, &workctx, status);
+ mpd_qfinalize(result, &workctx, status);
+ }
+}
+
+/* Internal log10() function that does not check for specials, zero, ... */
+static void
+_mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx;
+
+ mpd_maxcontext(&workctx);
+ workctx.prec = ctx->prec + 3;
+ _mpd_qln(result, a, &workctx, status);
+ mpd_update_ln10(workctx.prec, status);
+
+ workctx = *ctx;
+ workctx.round = MPD_ROUND_HALF_EVEN;
+ _mpd_qdiv(NO_IDEAL_EXP, result, result, &mpd_ln10, &workctx, status);
+}
+
+/* log10(a) */
+void
+mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx;
+ mpd_ssize_t adjexp, t;
+
+ workctx = *ctx;
+ workctx.round = MPD_ROUND_HALF_EVEN;
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ mpd_setspecial(result, MPD_POS, MPD_INF);
+ return;
+ }
+ if (mpd_iszerocoeff(a)) {
+ mpd_setspecial(result, MPD_NEG, MPD_INF);
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_coeff_ispow10(a)) {
+ uint8_t sign = 0;
+ adjexp = mpd_adjexp(a);
+ if (adjexp < 0) {
+ sign = 1;
+ adjexp = -adjexp;
+ }
+ _settriple(result, sign, adjexp, 0);
+ mpd_qfinalize(result, &workctx, status);
+ return;
+ }
+ /* Check if the result will overflow.
+ *
+ * 1) adjexp(a) + 1 > log10(a) >= adjexp(a)
+ *
+ * 2) |log10(a)| >= adjexp(a), if adjexp(a) >= 0
+ * |log10(a)| > -adjexp(a)-1, if adjexp(a) < 0
+ */
+ adjexp = mpd_adjexp(a);
+ t = (adjexp < 0) ? -adjexp-1 : adjexp;
+ if (mpd_exp_digits(t)-1 > ctx->emax) {
+ *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded;
+ mpd_setspecial(result, (adjexp<0), MPD_INF);
+ return;
+ }
+
+ if (ctx->allcr) {
+ MPD_NEW_STATIC(t1, 0,0,0,0);
+ MPD_NEW_STATIC(t2, 0,0,0,0);
+ MPD_NEW_STATIC(ulp, 0,0,0,0);
+ MPD_NEW_STATIC(aa, 0,0,0,0);
+ mpd_ssize_t prec;
+
+ if (result == a) {
+ if (!mpd_qcopy(&aa, a, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+ a = &aa;
+ }
+
+ workctx.clamp = 0;
+ prec = ctx->prec + 3;
+ while (1) {
+ workctx.prec = prec;
+ _mpd_qlog10(result, a, &workctx, status);
+ _ssettriple(&ulp, MPD_POS, 1,
+ result->exp + result->digits-workctx.prec-1);
+
+ workctx.prec = ctx->prec;
+ mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status);
+ mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status);
+ if (mpd_isspecial(result) || mpd_iszerocoeff(result) ||
+ mpd_qcmp(&t1, &t2, status) == 0) {
+ workctx.clamp = ctx->clamp;
+ mpd_check_underflow(result, &workctx, status);
+ mpd_qfinalize(result, &workctx, status);
+ break;
+ }
+ prec += MPD_RDIGITS;
+ }
+ mpd_del(&t1);
+ mpd_del(&t2);
+ mpd_del(&ulp);
+ mpd_del(&aa);
+ }
+ else {
+ _mpd_qlog10(result, a, &workctx, status);
+ mpd_check_underflow(result, &workctx, status);
+ }
+}
+
+/*
+ * Maximum of the two operands. Attention: If one operand is a quiet NaN and the
+ * other is numeric, the numeric operand is returned. This may not be what one
+ * expects.
+ */
+void
+mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ int c;
+
+ if (mpd_isqnan(a) && !mpd_isnan(b)) {
+ mpd_qcopy(result, b, status);
+ }
+ else if (mpd_isqnan(b) && !mpd_isnan(a)) {
+ mpd_qcopy(result, a, status);
+ }
+ else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ else {
+ c = _mpd_cmp(a, b);
+ if (c == 0) {
+ c = _mpd_cmp_numequal(a, b);
+ }
+
+ if (c < 0) {
+ mpd_qcopy(result, b, status);
+ }
+ else {
+ mpd_qcopy(result, a, status);
+ }
+ }
+
+ mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * Maximum magnitude: Same as mpd_max(), but compares the operands with their
+ * sign ignored.
+ */
+void
+mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ int c;
+
+ if (mpd_isqnan(a) && !mpd_isnan(b)) {
+ mpd_qcopy(result, b, status);
+ }
+ else if (mpd_isqnan(b) && !mpd_isnan(a)) {
+ mpd_qcopy(result, a, status);
+ }
+ else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ else {
+ c = _mpd_cmp_abs(a, b);
+ if (c == 0) {
+ c = _mpd_cmp_numequal(a, b);
+ }
+
+ if (c < 0) {
+ mpd_qcopy(result, b, status);
+ }
+ else {
+ mpd_qcopy(result, a, status);
+ }
+ }
+
+ mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * Minimum of the two operands. Attention: If one operand is a quiet NaN and the
+ * other is numeric, the numeric operand is returned. This may not be what one
+ * expects.
+ */
+void
+mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ int c;
+
+ if (mpd_isqnan(a) && !mpd_isnan(b)) {
+ mpd_qcopy(result, b, status);
+ }
+ else if (mpd_isqnan(b) && !mpd_isnan(a)) {
+ mpd_qcopy(result, a, status);
+ }
+ else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ else {
+ c = _mpd_cmp(a, b);
+ if (c == 0) {
+ c = _mpd_cmp_numequal(a, b);
+ }
+
+ if (c < 0) {
+ mpd_qcopy(result, a, status);
+ }
+ else {
+ mpd_qcopy(result, b, status);
+ }
+ }
+
+ mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * Minimum magnitude: Same as mpd_min(), but compares the operands with their
+ * sign ignored.
+ */
+void
+mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ int c;
+
+ if (mpd_isqnan(a) && !mpd_isnan(b)) {
+ mpd_qcopy(result, b, status);
+ }
+ else if (mpd_isqnan(b) && !mpd_isnan(a)) {
+ mpd_qcopy(result, a, status);
+ }
+ else if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ else {
+ c = _mpd_cmp_abs(a, b);
+ if (c == 0) {
+ c = _mpd_cmp_numequal(a, b);
+ }
+
+ if (c < 0) {
+ mpd_qcopy(result, a, status);
+ }
+ else {
+ mpd_qcopy(result, b, status);
+ }
+ }
+
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* Minimum space needed for the result array in _karatsuba_rec(). */
+static inline mpd_size_t
+_kmul_resultsize(mpd_size_t la, mpd_size_t lb)
+{
+ mpd_size_t n, m;
+
+ n = add_size_t(la, lb);
+ n = add_size_t(n, 1);
+
+ m = (la+1)/2 + 1;
+ m = mul_size_t(m, 3);
+
+ return (m > n) ? m : n;
+}
+
+/* Work space needed in _karatsuba_rec(). lim >= 4 */
+static inline mpd_size_t
+_kmul_worksize(mpd_size_t n, mpd_size_t lim)
+{
+ mpd_size_t m;
+
+ if (n <= lim) {
+ return 0;
+ }
+
+ m = (n+1)/2 + 1;
+
+ return add_size_t(mul_size_t(m, 2), _kmul_worksize(m, lim));
+}
+
+
+#define MPD_KARATSUBA_BASECASE 16 /* must be >= 4 */
+
+/*
+ * Add the product of a and b to c.
+ * c must be _kmul_resultsize(la, lb) in size.
+ * w is used as a work array and must be _kmul_worksize(a, lim) in size.
+ * Roman E. Maeder, Storage Allocation for the Karatsuba Integer Multiplication
+ * Algorithm. In "Design and implementation of symbolic computation systems",
+ * Springer, 1993, ISBN 354057235X, 9783540572350.
+ */
+static void
+_karatsuba_rec(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b,
+ mpd_uint_t *w, mpd_size_t la, mpd_size_t lb)
+{
+ mpd_size_t m, lt;
+
+ assert (la >= lb && lb > 0);
+
+ if (la <= MPD_KARATSUBA_BASECASE) {
+ _mpd_basemul(c, a, b, la, lb);
+ return;
+ }
+
+ m = (la+1)/2; // ceil(la/2)
+
+ /* lb <= m < la */
+ if (lb <= m) {
+
+ /* lb can now be larger than la-m */
+ if (lb > la-m) {
+ lt = lb + lb + 1; // space needed for result array
+ mpd_uint_zero(w, lt); // clear result array
+ _karatsuba_rec(w, b, a+m, w+lt, lb, la-m); // b*ah
+ }
+ else {
+ lt = (la-m) + (la-m) + 1; // space needed for result array
+ mpd_uint_zero(w, lt); // clear result array
+ _karatsuba_rec(w, a+m, b, w+lt, la-m, lb); // ah*b
+ }
+ _mpd_baseaddto(c+m, w, (la-m)+lb); // add ah*b*B**m
+
+ lt = m + m + 1; // space needed for the result array
+ mpd_uint_zero(w, lt); // clear result array
+ _karatsuba_rec(w, a, b, w+lt, m, lb); // al*b
+ _mpd_baseaddto(c, w, m+lb); // add al*b
+
+ return;
+ }
+
+ /* la >= lb > m */
+ memcpy(w, a, m * sizeof *w);
+ w[m] = 0;
+ _mpd_baseaddto(w, a+m, la-m);
+
+ memcpy(w+(m+1), b, m * sizeof *w);
+ w[m+1+m] = 0;
+ _mpd_baseaddto(w+(m+1), b+m, lb-m);
+
+ _karatsuba_rec(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1);
+
+ lt = (la-m) + (la-m) + 1;
+ mpd_uint_zero(w, lt);
+
+ _karatsuba_rec(w, a+m, b+m, w+lt, la-m, lb-m);
+
+ _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m));
+ _mpd_basesubfrom(c+m, w, (la-m) + (lb-m));
+
+ lt = m + m + 1;
+ mpd_uint_zero(w, lt);
+
+ _karatsuba_rec(w, a, b, w+lt, m, m);
+ _mpd_baseaddto(c, w, m+m);
+ _mpd_basesubfrom(c+m, w, m+m);
+
+ return;
+}
+
+/*
+ * Multiply u and v, using Karatsuba multiplication. Returns a pointer
+ * to the result or NULL in case of failure (malloc error).
+ * Conditions: ulen >= vlen, ulen >= 4
+ */
+mpd_uint_t *
+_mpd_kmul(const mpd_uint_t *u, const mpd_uint_t *v,
+ mpd_size_t ulen, mpd_size_t vlen,
+ mpd_size_t *rsize)
+{
+ mpd_uint_t *result = NULL, *w = NULL;
+ mpd_size_t m;
+
+ assert(ulen >= 4);
+ assert(ulen >= vlen);
+
+ *rsize = _kmul_resultsize(ulen, vlen);
+ if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) {
+ return NULL;
+ }
+
+ m = _kmul_worksize(ulen, MPD_KARATSUBA_BASECASE);
+ if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) {
+ mpd_free(result);
+ return NULL;
+ }
+
+ _karatsuba_rec(result, u, v, w, ulen, vlen);
+
+
+ if (w) mpd_free(w);
+ return result;
+}
+
+
+/* Determine the minimum length for the number theoretic transform. */
+static inline mpd_size_t
+_mpd_get_transform_len(mpd_size_t rsize)
+{
+ mpd_size_t log2rsize;
+ mpd_size_t x, step;
+
+ assert(rsize >= 4);
+ log2rsize = mpd_bsr(rsize);
+
+ if (rsize <= 1024) {
+ x = ((mpd_size_t)1)<<log2rsize;
+ return (rsize == x) ? x : x<<1;
+ }
+ else if (rsize <= MPD_MAXTRANSFORM_2N) {
+ x = ((mpd_size_t)1)<<log2rsize;
+ if (rsize == x) return x;
+ step = x>>1;
+ x += step;
+ return (rsize <= x) ? x : x + step;
+ }
+ else if (rsize <= MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2) {
+ return MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2;
+ }
+ else if (rsize <= 3*MPD_MAXTRANSFORM_2N) {
+ return 3*MPD_MAXTRANSFORM_2N;
+ }
+ else {
+ return MPD_SIZE_MAX;
+ }
+}
+
+#ifdef PPRO
+#ifndef _MSC_VER
+static inline unsigned short
+_mpd_get_control87(void)
+{
+ unsigned short cw;
+
+ __asm__ __volatile__ ("fnstcw %0" : "=m" (cw));
+ return cw;
+}
+
+static inline void
+_mpd_set_control87(unsigned short cw)
+{
+ __asm__ __volatile__ ("fldcw %0" : : "m" (cw));
+}
+#endif
+
+unsigned int
+mpd_set_fenv(void)
+{
+ unsigned int cw;
+#ifdef _MSC_VER
+ cw = _control87(0, 0);
+ _control87((_RC_CHOP|_PC_64), (_MCW_RC|_MCW_PC));
+#else
+ cw = _mpd_get_control87();
+ _mpd_set_control87(cw|0x780);
+#endif
+ return cw;
+}
+
+void
+mpd_restore_fenv(unsigned int cw)
+{
+#ifdef _MSC_VER
+ _control87(cw, (_MCW_RC|_MCW_PC));
+#else
+ _mpd_set_control87((unsigned short)cw);
+#endif
+}
+#endif /* PPRO */
+
+/*
+ * Multiply u and v, using the fast number theoretic transform. Returns
+ * a pointer to the result or NULL in case of failure (malloc error).
+ */
+mpd_uint_t *
+_mpd_fntmul(const mpd_uint_t *u, const mpd_uint_t *v,
+ mpd_size_t ulen, mpd_size_t vlen,
+ mpd_size_t *rsize)
+{
+ mpd_uint_t *c1 = NULL, *c2 = NULL, *c3 = NULL, *vtmp = NULL;
+ mpd_size_t n;
+
+#ifdef PPRO
+ unsigned int cw;
+ cw = mpd_set_fenv();
+#endif
+
+ *rsize = add_size_t(ulen, vlen);
+ if ((n = _mpd_get_transform_len(*rsize)) == MPD_SIZE_MAX) {
+ goto malloc_error;
+ }
+
+ if ((c1 = mpd_calloc(sizeof *c1, n)) == NULL) {
+ goto malloc_error;
+ }
+ if ((c2 = mpd_calloc(sizeof *c2, n)) == NULL) {
+ goto malloc_error;
+ }
+ if ((c3 = mpd_calloc(sizeof *c3, n)) == NULL) {
+ goto malloc_error;
+ }
+
+ memcpy(c1, u, ulen * (sizeof *c1));
+ memcpy(c2, u, ulen * (sizeof *c2));
+ memcpy(c3, u, ulen * (sizeof *c3));
+
+ if (u == v) {
+ if (!fnt_autoconvolute(c1, n, P1) ||
+ !fnt_autoconvolute(c2, n, P2) ||
+ !fnt_autoconvolute(c3, n, P3)) {
+ goto malloc_error;
+ }
+ }
+ else {
+ if ((vtmp = mpd_calloc(sizeof *vtmp, n)) == NULL) {
+ goto malloc_error;
+ }
+
+ memcpy(vtmp, v, vlen * (sizeof *vtmp));
+ if (!fnt_convolute(c1, vtmp, n, P1)) {
+ mpd_free(vtmp);
+ goto malloc_error;
+ }
+
+ memcpy(vtmp, v, vlen * (sizeof *vtmp));
+ mpd_uint_zero(vtmp+vlen, n-vlen);
+ if (!fnt_convolute(c2, vtmp, n, P2)) {
+ mpd_free(vtmp);
+ goto malloc_error;
+ }
+
+ memcpy(vtmp, v, vlen * (sizeof *vtmp));
+ mpd_uint_zero(vtmp+vlen, n-vlen);
+ if (!fnt_convolute(c3, vtmp, n, P3)) {
+ mpd_free(vtmp);
+ goto malloc_error;
+ }
+
+ mpd_free(vtmp);
+ }
+
+ crt3(c1, c2, c3, *rsize);
+
+out:
+#ifdef PPRO
+ mpd_restore_fenv(cw);
+#endif
+ if (c2) mpd_free(c2);
+ if (c3) mpd_free(c3);
+ return c1;
+
+malloc_error:
+ if (c1) mpd_free(c1);
+ c1 = NULL;
+ goto out;
+}
+
+
+/*
+ * Karatsuba multiplication with FNT/basemul as the base case.
+ */
+static int
+_karatsuba_rec_fnt(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b,
+ mpd_uint_t *w, mpd_size_t la, mpd_size_t lb)
+{
+ mpd_size_t m, lt;
+
+ assert (la >= lb && lb > 0);
+
+ if (la <= 3*(MPD_MAXTRANSFORM_2N/2)) {
+
+ if (lb <= 192) {
+ _mpd_basemul(c, b, a, lb, la);
+ }
+ else {
+ mpd_uint_t *result;
+ mpd_size_t dummy;
+
+ if ((result = _mpd_fntmul(a, b, la, lb, &dummy)) == NULL) {
+ return 0;
+ }
+ memcpy(c, result, (la+lb) * (sizeof *result));
+ mpd_free(result);
+ }
+ return 1;
+ }
+
+ m = (la+1)/2; // ceil(la/2)
+
+ /* lb <= m < la */
+ if (lb <= m) {
+
+ /* lb can now be larger than la-m */
+ if (lb > la-m) {
+ lt = lb + lb + 1; // space needed for result array
+ mpd_uint_zero(w, lt); // clear result array
+ if (!_karatsuba_rec_fnt(w, b, a+m, w+lt, lb, la-m)) { // b*ah
+ return 0; /* GCOV_UNLIKELY */
+ }
+ }
+ else {
+ lt = (la-m) + (la-m) + 1; // space needed for result array
+ mpd_uint_zero(w, lt); // clear result array
+ if (!_karatsuba_rec_fnt(w, a+m, b, w+lt, la-m, lb)) { // ah*b
+ return 0; /* GCOV_UNLIKELY */
+ }
+ }
+ _mpd_baseaddto(c+m, w, (la-m)+lb); // add ah*b*B**m
+
+ lt = m + m + 1; // space needed for the result array
+ mpd_uint_zero(w, lt); // clear result array
+ if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, lb)) { // al*b
+ return 0; /* GCOV_UNLIKELY */
+ }
+ _mpd_baseaddto(c, w, m+lb); // add al*b
+
+ return 1;
+ }
+
+ /* la >= lb > m */
+ memcpy(w, a, m * sizeof *w);
+ w[m] = 0;
+ _mpd_baseaddto(w, a+m, la-m);
+
+ memcpy(w+(m+1), b, m * sizeof *w);
+ w[m+1+m] = 0;
+ _mpd_baseaddto(w+(m+1), b+m, lb-m);
+
+ if (!_karatsuba_rec_fnt(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1)) {
+ return 0; /* GCOV_UNLIKELY */
+ }
+
+ lt = (la-m) + (la-m) + 1;
+ mpd_uint_zero(w, lt);
+
+ if (!_karatsuba_rec_fnt(w, a+m, b+m, w+lt, la-m, lb-m)) {
+ return 0; /* GCOV_UNLIKELY */
+ }
+
+ _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m));
+ _mpd_basesubfrom(c+m, w, (la-m) + (lb-m));
+
+ lt = m + m + 1;
+ mpd_uint_zero(w, lt);
+
+ if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, m)) {
+ return 0; /* GCOV_UNLIKELY */
+ }
+ _mpd_baseaddto(c, w, m+m);
+ _mpd_basesubfrom(c+m, w, m+m);
+
+ return 1;
+}
+
+/*
+ * Multiply u and v, using Karatsuba multiplication with the FNT as the
+ * base case. Returns a pointer to the result or NULL in case of failure
+ * (malloc error). Conditions: ulen >= vlen, ulen >= 4.
+ */
+mpd_uint_t *
+_mpd_kmul_fnt(const mpd_uint_t *u, const mpd_uint_t *v,
+ mpd_size_t ulen, mpd_size_t vlen,
+ mpd_size_t *rsize)
+{
+ mpd_uint_t *result = NULL, *w = NULL;
+ mpd_size_t m;
+
+ assert(ulen >= 4);
+ assert(ulen >= vlen);
+
+ *rsize = _kmul_resultsize(ulen, vlen);
+ if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) {
+ return NULL;
+ }
+
+ m = _kmul_worksize(ulen, 3*(MPD_MAXTRANSFORM_2N/2));
+ if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) {
+ mpd_free(result); /* GCOV_UNLIKELY */
+ return NULL; /* GCOV_UNLIKELY */
+ }
+
+ if (!_karatsuba_rec_fnt(result, u, v, w, ulen, vlen)) {
+ mpd_free(result);
+ result = NULL;
+ }
+
+
+ if (w) mpd_free(w);
+ return result;
+}
+
+
+/* Deal with the special cases of multiplying infinities. */
+static void
+_mpd_qmul_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status)
+{
+ if (mpd_isinfinite(a)) {
+ if (mpd_iszero(b)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ }
+ else {
+ mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
+ }
+ return;
+ }
+ assert(mpd_isinfinite(b));
+ if (mpd_iszero(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ }
+ else {
+ mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF);
+ }
+}
+
+/*
+ * Internal function: Multiply a and b. _mpd_qmul deals with specials but
+ * does NOT finalize the result. This is for use in mpd_fma().
+ */
+static inline void
+_mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_t *big = (mpd_t *)a, *small = (mpd_t *)b;
+ mpd_uint_t *rdata = NULL;
+ mpd_uint_t rbuf[MPD_MINALLOC_MAX];
+ mpd_size_t rsize, i;
+
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ _mpd_qmul_inf(result, a, b, status);
+ return;
+ }
+
+ if (small->len > big->len) {
+ _mpd_ptrswap(&big, &small);
+ }
+
+ rsize = big->len + small->len;
+
+ if (big->len == 1) {
+ _mpd_singlemul(result->data, big->data[0], small->data[0]);
+ goto finish;
+ }
+ if (rsize <= (mpd_size_t)MPD_MINALLOC_MAX) {
+ if (big->len == 2) {
+ _mpd_mul_2_le2(rbuf, big->data, small->data, small->len);
+ }
+ else {
+ mpd_uint_zero(rbuf, rsize);
+ if (small->len == 1) {
+ _mpd_shortmul(rbuf, big->data, big->len, small->data[0]);
+ }
+ else {
+ _mpd_basemul(rbuf, small->data, big->data, small->len, big->len);
+ }
+ }
+ if (!mpd_qresize(result, rsize, status)) {
+ return;
+ }
+ for(i = 0; i < rsize; i++) {
+ result->data[i] = rbuf[i];
+ }
+ goto finish;
+ }
+
+
+ if (small->len == 1) {
+ if ((rdata = mpd_calloc(rsize, sizeof *rdata)) == NULL) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+ _mpd_shortmul(rdata, big->data, big->len, small->data[0]);
+ }
+ else if (rsize <= 1024) {
+ rdata = _mpd_kmul(big->data, small->data, big->len, small->len, &rsize);
+ if (rdata == NULL) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+ }
+ else if (rsize <= 3*MPD_MAXTRANSFORM_2N) {
+ rdata = _mpd_fntmul(big->data, small->data, big->len, small->len, &rsize);
+ if (rdata == NULL) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+ }
+ else {
+ rdata = _mpd_kmul_fnt(big->data, small->data, big->len, small->len, &rsize);
+ if (rdata == NULL) {
+ mpd_seterror(result, MPD_Malloc_error, status); /* GCOV_UNLIKELY */
+ return; /* GCOV_UNLIKELY */
+ }
+ }
+
+ if (mpd_isdynamic_data(result)) {
+ mpd_free(result->data);
+ }
+ result->data = rdata;
+ result->alloc = rsize;
+ mpd_set_dynamic_data(result);
+
+
+finish:
+ mpd_set_flags(result, mpd_sign(a)^mpd_sign(b));
+ result->exp = big->exp + small->exp;
+ result->len = _mpd_real_size(result->data, rsize);
+ /* resize to smaller cannot fail */
+ mpd_qresize(result, result->len, status);
+ mpd_setdigits(result);
+}
+
+/* Multiply a and b. */
+void
+mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ _mpd_qmul(result, a, b, ctx, status);
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* Multiply decimal and mpd_ssize_t. */
+void
+mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(bb,0,0,0,0);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_qsset_ssize(&bb, b, &maxcontext, status);
+ mpd_qmul(result, a, &bb, ctx, status);
+ mpd_del(&bb);
+}
+
+/* Multiply decimal and mpd_uint_t. */
+void
+mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(bb,0,0,0,0);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_qsset_uint(&bb, b, &maxcontext, status);
+ mpd_qmul(result, a, &bb, ctx, status);
+ mpd_del(&bb);
+}
+
+void
+mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qmul_ssize(result, a, b, ctx, status);
+}
+
+void
+mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qmul_uint(result, a, b, ctx, status);
+}
+
+#ifdef CONFIG_64
+void
+mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qmul_ssize(result, a, b, ctx, status);
+}
+
+void
+mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_qmul_uint(result, a, b, ctx, status);
+}
+#endif
+
+/* Like the minus operator. */
+void
+mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ }
+
+ if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) {
+ mpd_qcopy_abs(result, a, status);
+ }
+ else {
+ mpd_qcopy_negate(result, a, status);
+ }
+
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* Like the plus operator. */
+void
+mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ }
+
+ if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) {
+ mpd_qcopy_abs(result, a, status);
+ }
+ else {
+ mpd_qcopy(result, a, status);
+ }
+
+ mpd_qfinalize(result, ctx, status);
+}
+
+/* The largest representable number that is smaller than the operand. */
+void
+mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx; /* function context */
+ MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1);
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ if (mpd_isnegative(a)) {
+ mpd_qcopy(result, a, status);
+ return;
+ }
+ else {
+ mpd_clear_flags(result);
+ mpd_qmaxcoeff(result, ctx, status);
+ if (mpd_isnan(result)) {
+ return;
+ }
+ result->exp = ctx->emax - ctx->prec + 1;
+ return;
+ }
+ }
+ /* debug */
+ abort(); /* GCOV_NOT_REACHED */
+ }
+
+ mpd_workcontext(&workctx, ctx);
+ workctx.round = MPD_ROUND_FLOOR;
+
+ if (!mpd_qcopy(result, a, status)) {
+ return;
+ }
+
+ mpd_qfinalize(result, &workctx, &workctx.status);
+ if (workctx.status&(MPD_Inexact|MPD_Errors)) {
+ *status |= (workctx.status&MPD_Errors);
+ return;
+ }
+
+ workctx.status = 0;
+ mpd_qsub(result, a, &tiny, &workctx, &workctx.status);
+ *status |= (workctx.status&MPD_Errors);
+}
+
+/* The smallest representable number that is larger than the operand. */
+void
+mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx;
+ MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1);
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ if (mpd_ispositive(a)) {
+ mpd_qcopy(result, a, status);
+ }
+ else {
+ mpd_clear_flags(result);
+ mpd_qmaxcoeff(result, ctx, status);
+ if (mpd_isnan(result)) {
+ return;
+ }
+ mpd_set_flags(result, MPD_NEG);
+ result->exp = mpd_etop(ctx);
+ }
+ return;
+ }
+ }
+
+ mpd_workcontext(&workctx, ctx);
+ workctx.round = MPD_ROUND_CEILING;
+
+ if (!mpd_qcopy(result, a, status)) {
+ return;
+ }
+
+ mpd_qfinalize(result, &workctx, &workctx.status);
+ if (workctx.status & (MPD_Inexact|MPD_Errors)) {
+ *status |= (workctx.status&MPD_Errors);
+ return;
+ }
+
+ workctx.status = 0;
+ mpd_qadd(result, a, &tiny, &workctx, &workctx.status);
+ *status |= (workctx.status&MPD_Errors);
+}
+
+/*
+ * The number closest to the first operand that is in the direction towards
+ * the second operand.
+ */
+void
+mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ int c;
+
+ if (mpd_isnan(a) || mpd_isnan(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status))
+ return;
+ }
+
+ c = _mpd_cmp(a, b);
+ if (c == 0) {
+ mpd_qcopy_sign(result, a, b, status);
+ return;
+ }
+
+ if (c < 0) {
+ mpd_qnext_plus(result, a, ctx, status);
+ }
+ else {
+ mpd_qnext_minus(result, a, ctx, status);
+ }
+
+ if (mpd_isinfinite(result)) {
+ *status |= (MPD_Overflow|MPD_Rounded|MPD_Inexact);
+ }
+ else if (mpd_adjexp(result) < ctx->emin) {
+ *status |= (MPD_Underflow|MPD_Subnormal|MPD_Rounded|MPD_Inexact);
+ if (mpd_iszero(result)) {
+ *status |= MPD_Clamped;
+ }
+ }
+}
+
+/*
+ * Internal function: Integer power with mpd_uint_t exponent, base is modified!
+ * Function can fail with MPD_Malloc_error.
+ */
+static inline void
+_mpd_qpow_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp, uint8_t resultsign,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_uint_t n;
+
+ if (exp == 0) {
+ _settriple(result, resultsign, 1, 0); /* GCOV_NOT_REACHED */
+ return; /* GCOV_NOT_REACHED */
+ }
+
+ if (!mpd_qcopy(result, base, status)) {
+ return;
+ }
+
+ n = mpd_bits[mpd_bsr(exp)];
+ while (n >>= 1) {
+ mpd_qmul(result, result, result, ctx, &workstatus);
+ if (exp & n) {
+ mpd_qmul(result, result, base, ctx, &workstatus);
+ }
+ if (workstatus & (MPD_Overflow|MPD_Clamped)) {
+ break;
+ }
+ }
+
+ *status |= workstatus;
+ mpd_set_sign(result, resultsign);
+}
+
+/*
+ * Internal function: Integer power with mpd_t exponent, tbase and texp
+ * are modified!! Function can fail with MPD_Malloc_error.
+ */
+static inline void
+_mpd_qpow_mpd(mpd_t *result, mpd_t *tbase, mpd_t *texp, uint8_t resultsign,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_context_t maxctx;
+ MPD_NEW_CONST(two,0,0,1,1,1,2);
+
+
+ mpd_maxcontext(&maxctx);
+
+ /* resize to smaller cannot fail */
+ mpd_qcopy(result, &one, status);
+
+ while (!mpd_iszero(texp)) {
+ if (mpd_isodd(texp)) {
+ mpd_qmul(result, result, tbase, ctx, &workstatus);
+ *status |= workstatus;
+ if (workstatus & (MPD_Overflow|MPD_Clamped)) {
+ break;
+ }
+ }
+ mpd_qmul(tbase, tbase, tbase, ctx, &workstatus);
+ mpd_qdivint(texp, texp, &two, &maxctx, &workstatus);
+ if (mpd_isnan(tbase) || mpd_isnan(texp)) {
+ mpd_seterror(result, workstatus&MPD_Errors, status);
+ return;
+ }
+ }
+ mpd_set_sign(result, resultsign);
+}
+
+/*
+ * The power function for integer exponents.
+ */
+static void
+_mpd_qpow_int(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+ uint8_t resultsign,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t workctx;
+ MPD_NEW_STATIC(tbase,0,0,0,0);
+ MPD_NEW_STATIC(texp,0,0,0,0);
+ mpd_ssize_t n;
+
+
+ mpd_workcontext(&workctx, ctx);
+ workctx.prec += (exp->digits + exp->exp + 2);
+ workctx.round = MPD_ROUND_HALF_EVEN;
+ workctx.clamp = 0;
+ if (mpd_isnegative(exp)) {
+ mpd_qdiv(&tbase, &one, base, &workctx, status);
+ if (*status&MPD_Errors) {
+ mpd_setspecial(result, MPD_POS, MPD_NAN);
+ goto finish;
+ }
+ }
+ else {
+ if (!mpd_qcopy(&tbase, base, status)) {
+ mpd_setspecial(result, MPD_POS, MPD_NAN);
+ goto finish;
+ }
+ }
+
+ n = mpd_qabs_uint(exp, &workctx.status);
+ if (workctx.status&MPD_Invalid_operation) {
+ if (!mpd_qcopy(&texp, exp, status)) {
+ mpd_setspecial(result, MPD_POS, MPD_NAN); /* GCOV_UNLIKELY */
+ goto finish; /* GCOV_UNLIKELY */
+ }
+ _mpd_qpow_mpd(result, &tbase, &texp, resultsign, &workctx, status);
+ }
+ else {
+ _mpd_qpow_uint(result, &tbase, n, resultsign, &workctx, status);
+ }
+
+ if (mpd_isinfinite(result)) {
+ /* for ROUND_DOWN, ROUND_FLOOR, etc. */
+ _settriple(result, resultsign, 1, MPD_EXP_INF);
+ }
+
+finish:
+ mpd_del(&tbase);
+ mpd_del(&texp);
+ mpd_qfinalize(result, ctx, status);
+}
+
+/*
+ * This is an internal function that does not check for NaNs.
+ */
+static int
+_qcheck_pow_one_inf(mpd_t *result, const mpd_t *base, uint8_t resultsign,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_ssize_t shift;
+ int cmp;
+
+ if ((cmp = _mpd_cmp(base, &one)) == 0) {
+ shift = ctx->prec-1;
+ mpd_qshiftl(result, &one, shift, status);
+ result->exp = -shift;
+ mpd_set_flags(result, resultsign);
+ *status |= (MPD_Inexact|MPD_Rounded);
+ }
+
+ return cmp;
+}
+
+/*
+ * If base equals one, calculate the correct power of one result.
+ * Otherwise, result is undefined. Return the value of the comparison
+ * against 1.
+ *
+ * This is an internal function that does not check for specials.
+ */
+static int
+_qcheck_pow_one(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+ uint8_t resultsign,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_ssize_t shift;
+ int cmp;
+
+ if ((cmp = _mpd_cmp_abs(base, &one)) == 0) {
+ if (_mpd_isint(exp)) {
+ if (mpd_isnegative(exp)) {
+ _settriple(result, resultsign, 1, 0);
+ return 0;
+ }
+ /* 1.000**3 = 1.000000000 */
+ mpd_qmul_ssize(result, exp, -base->exp, ctx, &workstatus);
+ if (workstatus&MPD_Errors) {
+ *status |= (workstatus&MPD_Errors);
+ return 0;
+ }
+ /* digits-1 after exponentiation */
+ shift = mpd_qget_ssize(result, &workstatus);
+ /* shift is MPD_SSIZE_MAX if result is too large */
+ if (shift > ctx->prec-1) {
+ shift = ctx->prec-1;
+ *status |= MPD_Rounded;
+ }
+ }
+ else if (mpd_ispositive(base)) {
+ shift = ctx->prec-1;
+ *status |= (MPD_Inexact|MPD_Rounded);
+ }
+ else {
+ return -2; /* GCOV_NOT_REACHED */
+ }
+ if (!mpd_qshiftl(result, &one, shift, status)) {
+ return 0;
+ }
+ result->exp = -shift;
+ mpd_set_flags(result, resultsign);
+ }
+
+ return cmp;
+}
+
+/*
+ * Detect certain over/underflow of x**y.
+ * ACL2 proof: pow_bounds.lisp.
+ *
+ * Symbols:
+ *
+ * e: EXP_INF or EXP_CLAMP
+ * x: base
+ * y: exponent
+ *
+ * omega(e) = log10(abs(e))
+ * zeta(x) = log10(abs(log10(x)))
+ * theta(y) = log10(abs(y))
+ *
+ * Upper and lower bounds:
+ *
+ * ub_omega(e) = ceil(log10(abs(e)))
+ * lb_theta(y) = floor(log10(abs(y)))
+ *
+ * | floor(log10(floor(abs(log10(x))))) if x < 1/10 or x >= 10
+ * lb_zeta(x) = | floor(log10(abs(x-1)/10)) if 1/10 <= x < 1
+ * | floor(log10(abs((x-1)/100))) if 1 < x < 10
+ *
+ * ub_omega(e) and lb_theta(y) are obviously upper and lower bounds
+ * for omega(e) and theta(y).
+ *
+ * lb_zeta is a lower bound for zeta(x):
+ *
+ * x < 1/10 or x >= 10:
+ *
+ * abs(log10(x)) >= 1, so the outer log10 is well defined. Since log10
+ * is strictly increasing, the end result is a lower bound.
+ *
+ * 1/10 <= x < 1:
+ *
+ * We use: log10(x) <= (x-1)/log(10)
+ * abs(log10(x)) >= abs(x-1)/log(10)
+ * abs(log10(x)) >= abs(x-1)/10
+ *
+ * 1 < x < 10:
+ *
+ * We use: (x-1)/(x*log(10)) < log10(x)
+ * abs((x-1)/100) < abs(log10(x))
+ *
+ * XXX: abs((x-1)/10) would work, need ACL2 proof.
+ *
+ *
+ * Let (0 < x < 1 and y < 0) or (x > 1 and y > 0). (H1)
+ * Let ub_omega(exp_inf) < lb_zeta(x) + lb_theta(y) (H2)
+ *
+ * Then:
+ * log10(abs(exp_inf)) < log10(abs(log10(x))) + log10(abs(y)). (1)
+ * exp_inf < log10(x) * y (2)
+ * 10**exp_inf < x**y (3)
+ *
+ * Let (0 < x < 1 and y > 0) or (x > 1 and y < 0). (H3)
+ * Let ub_omega(exp_clamp) < lb_zeta(x) + lb_theta(y) (H4)
+ *
+ * Then:
+ * log10(abs(exp_clamp)) < log10(abs(log10(x))) + log10(abs(y)). (4)
+ * log10(x) * y < exp_clamp (5)
+ * x**y < 10**exp_clamp (6)
+ *
+ */
+static mpd_ssize_t
+_lower_bound_zeta(const mpd_t *x, uint32_t *status)
+{
+ mpd_context_t maxctx;
+ MPD_NEW_STATIC(scratch,0,0,0,0);
+ mpd_ssize_t t, u;
+
+ t = mpd_adjexp(x);
+ if (t > 0) {
+ /* x >= 10 -> floor(log10(floor(abs(log10(x))))) */
+ return mpd_exp_digits(t) - 1;
+ }
+ else if (t < -1) {
+ /* x < 1/10 -> floor(log10(floor(abs(log10(x))))) */
+ return mpd_exp_digits(t+1) - 1;
+ }
+ else {
+ mpd_maxcontext(&maxctx);
+ mpd_qsub(&scratch, x, &one, &maxctx, status);
+ if (mpd_isspecial(&scratch)) {
+ mpd_del(&scratch);
+ return MPD_SSIZE_MAX;
+ }
+ u = mpd_adjexp(&scratch);
+ mpd_del(&scratch);
+
+ /* t == -1, 1/10 <= x < 1 -> floor(log10(abs(x-1)/10))
+ * t == 0, 1 < x < 10 -> floor(log10(abs(x-1)/100)) */
+ return (t == 0) ? u-2 : u-1;
+ }
+}
+
+/*
+ * Detect cases of certain overflow/underflow in the power function.
+ * Assumptions: x != 1, y != 0. The proof above is for positive x.
+ * If x is negative and y is an odd integer, x**y == -(abs(x)**y),
+ * so the analysis does not change.
+ */
+static int
+_qcheck_pow_bounds(mpd_t *result, const mpd_t *x, const mpd_t *y,
+ uint8_t resultsign,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ MPD_NEW_SHARED(abs_x, x);
+ mpd_ssize_t ub_omega, lb_zeta, lb_theta;
+ uint8_t sign;
+
+ mpd_set_positive(&abs_x);
+
+ lb_theta = mpd_adjexp(y);
+ lb_zeta = _lower_bound_zeta(&abs_x, status);
+ if (lb_zeta == MPD_SSIZE_MAX) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return 1;
+ }
+
+ sign = (mpd_adjexp(&abs_x) < 0) ^ mpd_sign(y);
+ if (sign == 0) {
+ /* (0 < |x| < 1 and y < 0) or (|x| > 1 and y > 0) */
+ ub_omega = mpd_exp_digits(ctx->emax);
+ if (ub_omega < lb_zeta + lb_theta) {
+ _settriple(result, resultsign, 1, MPD_EXP_INF);
+ mpd_qfinalize(result, ctx, status);
+ return 1;
+ }
+ }
+ else {
+ /* (0 < |x| < 1 and y > 0) or (|x| > 1 and y < 0). */
+ ub_omega = mpd_exp_digits(mpd_etiny(ctx));
+ if (ub_omega < lb_zeta + lb_theta) {
+ _settriple(result, resultsign, 1, mpd_etiny(ctx)-1);
+ mpd_qfinalize(result, ctx, status);
+ return 1;
+ }
+ }
+
+ return 0;
+}
+
+/*
+ * TODO: Implement algorithm for computing exact powers from decimal.py.
+ * In order to prevent infinite loops, this has to be called before
+ * using Ziv's strategy for correct rounding.
+ */
+/*
+static int
+_mpd_qpow_exact(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ return 0;
+}
+*/
+
+/* The power function for real exponents */
+static void
+_mpd_qpow_real(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t workctx;
+ MPD_NEW_STATIC(texp,0,0,0,0);
+
+ if (!mpd_qcopy(&texp, exp, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+
+ mpd_maxcontext(&workctx);
+ workctx.prec = (base->digits > ctx->prec) ? base->digits : ctx->prec;
+ workctx.prec += (4 + MPD_EXPDIGITS);
+ workctx.round = MPD_ROUND_HALF_EVEN;
+ workctx.allcr = ctx->allcr;
+
+ mpd_qln(result, base, &workctx, &workctx.status);
+ mpd_qmul(result, result, &texp, &workctx, &workctx.status);
+ mpd_qexp(result, result, &workctx, status);
+
+ mpd_del(&texp);
+ *status |= (workctx.status&MPD_Errors);
+ *status |= (MPD_Inexact|MPD_Rounded);
+}
+
+/* The power function: base**exp */
+void
+mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint8_t resultsign = 0;
+ int intexp = 0;
+ int cmp;
+
+ if (mpd_isspecial(base) || mpd_isspecial(exp)) {
+ if (mpd_qcheck_nans(result, base, exp, ctx, status)) {
+ return;
+ }
+ }
+ if (mpd_isinteger(exp)) {
+ intexp = 1;
+ resultsign = mpd_isnegative(base) && mpd_isodd(exp);
+ }
+
+ if (mpd_iszero(base)) {
+ if (mpd_iszero(exp)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ }
+ else if (mpd_isnegative(exp)) {
+ mpd_setspecial(result, resultsign, MPD_INF);
+ }
+ else {
+ _settriple(result, resultsign, 0, 0);
+ }
+ return;
+ }
+ if (mpd_isnegative(base)) {
+ if (!intexp || mpd_isinfinite(exp)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ }
+ if (mpd_isinfinite(exp)) {
+ /* power of one */
+ cmp = _qcheck_pow_one_inf(result, base, resultsign, ctx, status);
+ if (cmp == 0) {
+ return;
+ }
+ else {
+ cmp *= mpd_arith_sign(exp);
+ if (cmp < 0) {
+ _settriple(result, resultsign, 0, 0);
+ }
+ else {
+ mpd_setspecial(result, resultsign, MPD_INF);
+ }
+ }
+ return;
+ }
+ if (mpd_isinfinite(base)) {
+ if (mpd_iszero(exp)) {
+ _settriple(result, resultsign, 1, 0);
+ }
+ else if (mpd_isnegative(exp)) {
+ _settriple(result, resultsign, 0, 0);
+ }
+ else {
+ mpd_setspecial(result, resultsign, MPD_INF);
+ }
+ return;
+ }
+ if (mpd_iszero(exp)) {
+ _settriple(result, resultsign, 1, 0);
+ return;
+ }
+ if (_qcheck_pow_one(result, base, exp, resultsign, ctx, status) == 0) {
+ return;
+ }
+ if (_qcheck_pow_bounds(result, base, exp, resultsign, ctx, status)) {
+ return;
+ }
+
+ if (intexp) {
+ _mpd_qpow_int(result, base, exp, resultsign, ctx, status);
+ }
+ else {
+ _mpd_qpow_real(result, base, exp, ctx, status);
+ if (!mpd_isspecial(result) && _mpd_cmp(result, &one) == 0) {
+ mpd_ssize_t shift = ctx->prec-1;
+ mpd_qshiftl(result, &one, shift, status);
+ result->exp = -shift;
+ }
+ if (mpd_isinfinite(result)) {
+ /* for ROUND_DOWN, ROUND_FLOOR, etc. */
+ _settriple(result, MPD_POS, 1, MPD_EXP_INF);
+ }
+ mpd_qfinalize(result, ctx, status);
+ }
+}
+
+/*
+ * Internal function: Integer powmod with mpd_uint_t exponent, base is modified!
+ * Function can fail with MPD_Malloc_error.
+ */
+static inline void
+_mpd_qpowmod_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp,
+ mpd_t *mod, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+
+ mpd_maxcontext(&maxcontext);
+
+ /* resize to smaller cannot fail */
+ mpd_qcopy(result, &one, status);
+
+ while (exp > 0) {
+ if (exp & 1) {
+ mpd_qmul(result, result, base, &maxcontext, status);
+ mpd_qrem(result, result, mod, &maxcontext, status);
+ }
+ mpd_qmul(base, base, base, &maxcontext, status);
+ mpd_qrem(base, base, mod, &maxcontext, status);
+ exp >>= 1;
+ }
+}
+
+/* The powmod function: (base**exp) % mod */
+void
+mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp,
+ const mpd_t *mod,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxcontext;
+ MPD_NEW_STATIC(tbase,0,0,0,0);
+ MPD_NEW_STATIC(texp,0,0,0,0);
+ MPD_NEW_STATIC(tmod,0,0,0,0);
+ MPD_NEW_STATIC(tmp,0,0,0,0);
+ MPD_NEW_CONST(two,0,0,1,1,1,2);
+ mpd_ssize_t tbase_exp, texp_exp;
+ mpd_ssize_t i;
+ mpd_t t;
+ mpd_uint_t r;
+ uint8_t sign;
+
+
+ if (mpd_isspecial(base) || mpd_isspecial(exp) || mpd_isspecial(mod)) {
+ if (mpd_qcheck_3nans(result, base, exp, mod, ctx, status)) {
+ return;
+ }
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+
+ if (!_mpd_isint(base) || !_mpd_isint(exp) || !_mpd_isint(mod)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_iszerocoeff(mod)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mod->digits+mod->exp > ctx->prec) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ sign = (mpd_isnegative(base)) && (mpd_isodd(exp));
+ if (mpd_iszerocoeff(exp)) {
+ if (mpd_iszerocoeff(base)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ r = (_mpd_cmp_abs(mod, &one)==0) ? 0 : 1;
+ _settriple(result, sign, r, 0);
+ return;
+ }
+ if (mpd_isnegative(exp)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_iszerocoeff(base)) {
+ _settriple(result, sign, 0, 0);
+ return;
+ }
+
+ if (!mpd_qcopy(&tmod, mod, status)) {
+ goto mpd_errors;
+ }
+ mpd_set_positive(&tmod);
+
+ mpd_maxcontext(&maxcontext);
+
+ mpd_qround_to_int(&tbase, base, &maxcontext, status);
+ mpd_qround_to_int(&texp, exp, &maxcontext, status);
+ mpd_qround_to_int(&tmod, &tmod, &maxcontext, status);
+
+ tbase_exp = tbase.exp;
+ tbase.exp = 0;
+ texp_exp = texp.exp;
+ texp.exp = 0;
+
+ /* base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo */
+ mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
+ _settriple(result, MPD_POS, 1, tbase_exp);
+ mpd_qrem(result, result, &tmod, &maxcontext, status);
+ mpd_qmul(&tbase, &tbase, result, &maxcontext, status);
+ mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
+ if (mpd_isspecial(&tbase) ||
+ mpd_isspecial(&texp) ||
+ mpd_isspecial(&tmod)) {
+ goto mpd_errors;
+ }
+
+ for (i = 0; i < texp_exp; i++) {
+ _mpd_qpowmod_uint(&tmp, &tbase, 10, &tmod, status);
+ t = tmp;
+ tmp = tbase;
+ tbase = t;
+ }
+ if (mpd_isspecial(&tbase)) {
+ goto mpd_errors; /* GCOV_UNLIKELY */
+ }
+
+ /* resize to smaller cannot fail */
+ mpd_qcopy(result, &one, status);
+ while (mpd_isfinite(&texp) && !mpd_iszero(&texp)) {
+ if (mpd_isodd(&texp)) {
+ mpd_qmul(result, result, &tbase, &maxcontext, status);
+ mpd_qrem(result, result, &tmod, &maxcontext, status);
+ }
+ mpd_qmul(&tbase, &tbase, &tbase, &maxcontext, status);
+ mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status);
+ mpd_qdivint(&texp, &texp, &two, &maxcontext, status);
+ }
+ if (mpd_isspecial(&texp) || mpd_isspecial(&tbase) ||
+ mpd_isspecial(&tmod) || mpd_isspecial(result)) {
+ /* MPD_Malloc_error */
+ goto mpd_errors;
+ }
+ else {
+ mpd_set_sign(result, sign);
+ }
+
+out:
+ mpd_del(&tbase);
+ mpd_del(&texp);
+ mpd_del(&tmod);
+ mpd_del(&tmp);
+ mpd_qfinalize(result, ctx, status);
+ return;
+
+mpd_errors:
+ mpd_setspecial(result, MPD_POS, MPD_NAN);
+ goto out;
+}
+
+void
+mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_ssize_t b_exp = b->exp;
+ mpd_ssize_t expdiff, shift;
+ mpd_uint_t rnd;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(result, a, b, ctx, status)) {
+ return;
+ }
+ if (mpd_isinfinite(a) && mpd_isinfinite(b)) {
+ mpd_qcopy(result, a, status);
+ return;
+ }
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ if (b->exp > ctx->emax || b->exp < mpd_etiny(ctx)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ if (mpd_iszero(a)) {
+ _settriple(result, mpd_sign(a), 0, b->exp);
+ mpd_qfinalize(result, ctx, status);
+ return;
+ }
+
+
+ expdiff = a->exp - b->exp;
+ if (a->digits + expdiff > ctx->prec) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ if (expdiff >= 0) {
+ shift = expdiff;
+ if (!mpd_qshiftl(result, a, shift, status)) {
+ return;
+ }
+ result->exp = b_exp;
+ }
+ else {
+ /* At this point expdiff < 0 and a->digits+expdiff <= prec,
+ * so the shift before an increment will fit in prec. */
+ shift = -expdiff;
+ rnd = mpd_qshiftr(result, a, shift, status);
+ if (rnd == MPD_UINT_MAX) {
+ return;
+ }
+ result->exp = b_exp;
+ if (!_mpd_apply_round_fit(result, rnd, ctx, status)) {
+ return;
+ }
+ workstatus |= MPD_Rounded;
+ if (rnd) {
+ workstatus |= MPD_Inexact;
+ }
+ }
+
+ if (mpd_adjexp(result) > ctx->emax ||
+ mpd_adjexp(result) < mpd_etiny(ctx)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ *status |= workstatus;
+ mpd_qfinalize(result, ctx, status);
+}
+
+void
+mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_ssize_t shift, maxexp, maxshift;
+ uint8_t sign_a = mpd_sign(a);
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ mpd_qcopy(result, a, status);
+ return;
+ }
+
+ if (!mpd_qcopy(result, a, status)) {
+ return;
+ }
+ mpd_qfinalize(result, ctx, status);
+ if (mpd_isspecial(result)) {
+ return;
+ }
+ if (mpd_iszero(result)) {
+ _settriple(result, sign_a, 0, 0);
+ return;
+ }
+
+ shift = mpd_trail_zeros(result);
+ maxexp = (ctx->clamp) ? mpd_etop(ctx) : ctx->emax;
+ /* After the finalizing above result->exp <= maxexp. */
+ maxshift = maxexp - result->exp;
+ shift = (shift > maxshift) ? maxshift : shift;
+
+ mpd_qshiftr_inplace(result, shift);
+ result->exp += shift;
+}
+
+void
+mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ MPD_NEW_STATIC(q,0,0,0,0);
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(r, a, b, ctx, status)) {
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ mpd_seterror(r, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_isinfinite(b)) {
+ mpd_qcopy(r, a, status);
+ mpd_qfinalize(r, ctx, status);
+ return;
+ }
+ /* debug */
+ abort(); /* GCOV_NOT_REACHED */
+ }
+ if (mpd_iszerocoeff(b)) {
+ if (mpd_iszerocoeff(a)) {
+ mpd_seterror(r, MPD_Division_undefined, status);
+ }
+ else {
+ mpd_seterror(r, MPD_Invalid_operation, status);
+ }
+ return;
+ }
+
+ _mpd_qdivmod(&q, r, a, b, ctx, status);
+ mpd_del(&q);
+ mpd_qfinalize(r, ctx, status);
+}
+
+void
+mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t workctx;
+ MPD_NEW_STATIC(btmp,0,0,0,0);
+ MPD_NEW_STATIC(q,0,0,0,0);
+ mpd_ssize_t expdiff, floordigits;
+ int cmp, isodd, allnine;
+
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ if (mpd_qcheck_nans(r, a, b, ctx, status)) {
+ return;
+ }
+ if (mpd_isinfinite(a)) {
+ mpd_seterror(r, MPD_Invalid_operation, status);
+ return;
+ }
+ if (mpd_isinfinite(b)) {
+ mpd_qcopy(r, a, status);
+ mpd_qfinalize(r, ctx, status);
+ return;
+ }
+ /* debug */
+ abort(); /* GCOV_NOT_REACHED */
+ }
+ if (mpd_iszerocoeff(b)) {
+ if (mpd_iszerocoeff(a)) {
+ mpd_seterror(r, MPD_Division_undefined, status);
+ }
+ else {
+ mpd_seterror(r, MPD_Invalid_operation, status);
+ }
+ return;
+ }
+
+ if (r == b) {
+ if (!mpd_qcopy(&btmp, b, status)) {
+ mpd_seterror(r, MPD_Malloc_error, status);
+ return;
+ }
+ b = &btmp;
+ }
+
+ workctx = *ctx;
+ workctx.prec = a->digits;
+ workctx.prec = (workctx.prec > ctx->prec) ? workctx.prec : ctx->prec;
+
+ _mpd_qdivmod(&q, r, a, b, &workctx, status);
+ if (mpd_isnan(&q) || mpd_isnan(r) || q.digits > ctx->prec) {
+ mpd_seterror(r, MPD_Division_impossible, status);
+ goto finish;
+ }
+ if (mpd_iszerocoeff(r)) {
+ goto finish;
+ }
+
+ /* Deal with cases like rmnx078:
+ * remaindernear 999999999.5 1 -> NaN Division_impossible */
+ expdiff = mpd_adjexp(b) - mpd_adjexp(r);
+ if (-1 <= expdiff && expdiff <= 1) {
+
+ mpd_qtrunc(&q, &q, &workctx, &workctx.status);
+ allnine = mpd_coeff_isallnine(&q);
+ floordigits = q.digits;
+ isodd = mpd_isodd(&q);
+
+ mpd_maxcontext(&workctx);
+ if (mpd_sign(a) == mpd_sign(b)) {
+ _mpd_qsub(&q, r, b, &workctx, &workctx.status);
+ if (workctx.status&MPD_Errors) {
+ mpd_seterror(r, workctx.status&MPD_Errors, status);
+ goto finish;
+ }
+ }
+ else {
+ _mpd_qadd(&q, r, b, &workctx, &workctx.status);
+ if (workctx.status&MPD_Errors) {
+ mpd_seterror(r, workctx.status&MPD_Errors, status);
+ goto finish;
+ }
+ }
+
+ cmp = mpd_cmp_total_mag(&q, r);
+ if (cmp < 0 || (cmp == 0 && isodd)) {
+ if (allnine && floordigits == ctx->prec) {
+ mpd_seterror(r, MPD_Division_impossible, status);
+ goto finish;
+ }
+ mpd_qcopy(r, &q, status);
+ *status &= ~MPD_Rounded;
+ }
+ }
+
+
+finish:
+ mpd_del(&btmp);
+ mpd_del(&q);
+ mpd_qfinalize(r, ctx, status);
+}
+
+ALWAYS_INLINE void
+_mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_ssize_t expdiff, shift;
+ mpd_uint_t rnd;
+
+ if (mpd_isspecial(a)) {
+ mpd_qcopy(result, a, status);
+ return;
+ }
+
+ if (mpd_iszero(a)) {
+ _settriple(result, mpd_sign(a), 0, exp);
+ return;
+ }
+
+ expdiff = a->exp - exp;
+ if (expdiff >= 0) {
+ shift = expdiff;
+ if (a->digits + shift > MPD_MAX_PREC+1) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ if (!mpd_qshiftl(result, a, shift, status)) {
+ return;
+ }
+ result->exp = exp;
+ }
+ else {
+ shift = -expdiff;
+ rnd = mpd_qshiftr(result, a, shift, status);
+ if (rnd == MPD_UINT_MAX) {
+ return;
+ }
+ result->exp = exp;
+ _mpd_apply_round_excess(result, rnd, ctx, status);
+ *status |= MPD_Rounded;
+ if (rnd) {
+ *status |= MPD_Inexact;
+ }
+ }
+
+ if (mpd_issubnormal(result, ctx)) {
+ *status |= MPD_Subnormal;
+ }
+}
+
+/*
+ * Rescale a number so that it has exponent 'exp'. Does not regard context
+ * precision, emax, emin, but uses the rounding mode. Special numbers are
+ * quietly copied. Restrictions:
+ *
+ * MPD_MIN_ETINY <= exp <= MPD_MAX_EMAX+1
+ * result->digits <= MPD_MAX_PREC+1
+ */
+void
+mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ _mpd_qrescale(result, a, exp, ctx, status);
+}
+
+/*
+ * Same as mpd_qrescale, but with relaxed restrictions. The result of this
+ * function should only be used for formatting a number and never as input
+ * for other operations.
+ *
+ * MPD_MIN_ETINY-MPD_MAX_PREC <= exp <= MPD_MAX_EMAX+1
+ * result->digits <= MPD_MAX_PREC+1
+ */
+void
+mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY-MPD_MAX_PREC) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ _mpd_qrescale(result, a, exp, ctx, status);
+}
+
+/* Round to an integer according to 'action' and ctx->round. */
+enum {TO_INT_EXACT, TO_INT_SILENT, TO_INT_TRUNC};
+static void
+_mpd_qround_to_integral(int action, mpd_t *result, const mpd_t *a,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_uint_t rnd;
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ mpd_qcopy(result, a, status);
+ return;
+ }
+ if (a->exp >= 0) {
+ mpd_qcopy(result, a, status);
+ return;
+ }
+ if (mpd_iszerocoeff(a)) {
+ _settriple(result, mpd_sign(a), 0, 0);
+ return;
+ }
+
+ rnd = mpd_qshiftr(result, a, -a->exp, status);
+ if (rnd == MPD_UINT_MAX) {
+ return;
+ }
+ result->exp = 0;
+
+ if (action == TO_INT_EXACT || action == TO_INT_SILENT) {
+ _mpd_apply_round_excess(result, rnd, ctx, status);
+ if (action == TO_INT_EXACT) {
+ *status |= MPD_Rounded;
+ if (rnd) {
+ *status |= MPD_Inexact;
+ }
+ }
+ }
+}
+
+void
+mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ (void)_mpd_qround_to_integral(TO_INT_EXACT, result, a, ctx, status);
+}
+
+void
+mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, ctx, status);
+}
+
+void
+mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ (void)_mpd_qround_to_integral(TO_INT_TRUNC, result, a, ctx, status);
+}
+
+void
+mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx = *ctx;
+ workctx.round = MPD_ROUND_FLOOR;
+ (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a,
+ &workctx, status);
+}
+
+void
+mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t workctx = *ctx;
+ workctx.round = MPD_ROUND_CEILING;
+ (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a,
+ &workctx, status);
+}
+
+int
+mpd_same_quantum(const mpd_t *a, const mpd_t *b)
+{
+ if (mpd_isspecial(a) || mpd_isspecial(b)) {
+ return ((mpd_isnan(a) && mpd_isnan(b)) ||
+ (mpd_isinfinite(a) && mpd_isinfinite(b)));
+ }
+
+ return a->exp == b->exp;
+}
+
+/* Schedule the increase in precision for the Newton iteration. */
+static inline int
+recpr_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2],
+ mpd_ssize_t maxprec, mpd_ssize_t initprec)
+{
+ mpd_ssize_t k;
+ int i;
+
+ assert(maxprec > 0 && initprec > 0);
+ if (maxprec <= initprec) return -1;
+
+ i = 0; k = maxprec;
+ do {
+ k = (k+1) / 2;
+ klist[i++] = k;
+ } while (k > initprec);
+
+ return i-1;
+}
+
+/*
+ * Initial approximation for the reciprocal. Result has MPD_RDIGITS-2
+ * significant digits.
+ */
+static void
+_mpd_qreciprocal_approx(mpd_t *z, const mpd_t *v, uint32_t *status)
+{
+ mpd_uint_t p10data[2] = {0, mpd_pow10[MPD_RDIGITS-2]}; /* 10**(2*MPD_RDIGITS-2) */
+ mpd_uint_t dummy, word;
+ int n;
+
+ _mpd_get_msdigits(&dummy, &word, v, MPD_RDIGITS);
+ n = mpd_word_digits(word);
+ word *= mpd_pow10[MPD_RDIGITS-n];
+
+ mpd_qresize(z, 2, status);
+ (void)_mpd_shortdiv(z->data, p10data, 2, word);
+
+ mpd_clear_flags(z);
+ z->exp = -(v->exp + v->digits) - (MPD_RDIGITS-2);
+ z->len = (z->data[1] == 0) ? 1 : 2;
+ mpd_setdigits(z);
+}
+
+/* Reciprocal, calculated with Newton's Method */
+static void
+_mpd_qreciprocal(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ mpd_context_t varcontext, maxcontext;
+ mpd_t *z = result; /* current approximation */
+ mpd_t *v; /* a, normalized to a number between 0.1 and 1 */
+ MPD_NEW_SHARED(vtmp, a); /* by default v will share data with a */
+ MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */
+ MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */
+ MPD_NEW_CONST(two,0,0,1,1,1,2); /* const 2 */
+ mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
+ mpd_ssize_t adj, maxprec, initprec;
+ uint8_t sign = mpd_sign(a);
+ int i;
+
+ v = &vtmp;
+ if (result == a) {
+ if ((v = mpd_qncopy(a)) == NULL) { /* GCOV_NOT_REACHED */
+ mpd_seterror(result, MPD_Malloc_error, status); /* GCOV_NOT_REACHED */
+ goto finish; /* GCOV_NOT_REACHED */
+ }
+ }
+
+ mpd_clear_flags(v);
+ adj = v->digits + v->exp;
+ v->exp = -v->digits;
+
+ /* initial approximation */
+ _mpd_qreciprocal_approx(z, v, status);
+
+ mpd_maxcontext(&varcontext);
+ mpd_maxcontext(&maxcontext);
+ varcontext.round = MPD_ROUND_TRUNC;
+ maxcontext.round = MPD_ROUND_TRUNC;
+
+ maxprec = (v->digits > ctx->prec) ? v->digits : ctx->prec;
+ maxprec += 2;
+ initprec = MPD_RDIGITS-3;
+
+ i = recpr_schedule_prec(klist, maxprec, initprec);
+ for (; i >= 0; i--) {
+ mpd_qmul(&s, z, z, &maxcontext, status);
+ varcontext.prec = 2*klist[i] + 5;
+ if (v->digits > varcontext.prec) {
+ mpd_qshiftr(&t, v, v->digits-varcontext.prec, status);
+ t.exp = -varcontext.prec;
+ mpd_qmul(&t, &t, &s, &varcontext, status);
+ }
+ else {
+ mpd_qmul(&t, v, &s, &varcontext, status);
+ }
+ mpd_qmul(&s, z, &two, &maxcontext, status);
+ mpd_qsub(z, &s, &t, &maxcontext, status);
+ }
+
+ if (!mpd_isspecial(z)) {
+ z->exp -= adj;
+ mpd_set_flags(z, sign);
+ }
+
+finish:
+ mpd_del(&s);
+ mpd_del(&t);
+ if (v != &vtmp) mpd_del(v);
+ mpd_qfinalize(z, ctx, status);
+}
+
+/*
+ * Integer division with remainder of the coefficients: coeff(a) / coeff(b).
+ * This function is for large numbers where it is faster to divide by
+ * multiplying the dividend by the reciprocal of the divisor.
+ * The inexact result is fixed by a small loop, which should not take
+ * more than 2 iterations.
+ */
+static void
+_mpd_qbarrett_divmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b,
+ uint32_t *status)
+{
+ mpd_context_t workctx;
+ mpd_t *qq = q, *rr = r;
+ mpd_t aa, bb;
+ int k;
+
+ mpd_maxcontext(&workctx);
+ _mpd_copy_shared(&aa, a);
+ _mpd_copy_shared(&bb, b);
+
+ mpd_set_positive(&aa);
+ mpd_set_positive(&bb);
+ aa.exp = 0;
+ bb.exp = 0;
+
+ if (q == a || q == b) {
+ if ((qq = mpd_qnew()) == NULL) {
+ *status |= MPD_Malloc_error;
+ goto nanresult;
+ }
+ }
+ if (r == a || r == b) {
+ if ((rr = mpd_qnew()) == NULL) {
+ *status |= MPD_Malloc_error;
+ goto nanresult;
+ }
+ }
+
+ /* maximum length of q + 3 digits */
+ workctx.prec = aa.digits - bb.digits + 1 + 3;
+ /* we get the reciprocal with precision maxlen(q) + 3 */
+ _mpd_qreciprocal(rr, &bb, &workctx, &workctx.status);
+
+ mpd_qmul(qq, &aa, rr, &workctx, &workctx.status);
+ mpd_qtrunc(qq, qq, &workctx, &workctx.status);
+
+ workctx.prec = aa.digits + 3;
+ /* get the remainder */
+ mpd_qmul(rr, &bb, qq, &workctx, &workctx.status);
+ mpd_qsub(rr, &aa, rr, &workctx, &workctx.status);
+
+ /* Fix the result. Algorithm from: Karl Hasselstrom, Fast Division of Large Integers */
+ for (k = 0;; k++) {
+ if (mpd_isspecial(rr)) {
+ *status |= (workctx.status&MPD_Errors);
+ goto nanresult;
+ }
+ if (k > 2) {
+ mpd_err_warn("_mpd_barrett_divmod: k > 2 in correcting loop"); /* GCOV_NOT_REACHED */
+ abort(); /* GCOV_NOT_REACHED */
+ }
+ else if (_mpd_cmp(&zero, rr) == 1) {
+ mpd_qadd(rr, rr, &bb, &workctx, &workctx.status);
+ mpd_qadd(qq, qq, &minus_one, &workctx, &workctx.status);
+ }
+ else if (_mpd_cmp(rr, &bb) == -1) {
+ break;
+ }
+ else {
+ mpd_qsub(rr, rr, &bb, &workctx, &workctx.status);
+ mpd_qadd(qq, qq, &one, &workctx, &workctx.status);
+ }
+ }
+
+ if (qq != q) {
+ if (!mpd_qcopy(q, qq, status)) {
+ goto nanresult; /* GCOV_UNLIKELY */
+ }
+ mpd_del(qq);
+ }
+ if (rr != r) {
+ if (!mpd_qcopy(r, rr, status)) {
+ goto nanresult; /* GCOV_UNLIKELY */
+ }
+ mpd_del(rr);
+ }
+
+ *status |= (workctx.status&MPD_Errors);
+ return;
+
+
+nanresult:
+ if (qq && qq != q) mpd_del(qq);
+ if (rr && rr != r) mpd_del(rr);
+ mpd_setspecial(q, MPD_POS, MPD_NAN);
+ mpd_setspecial(r, MPD_POS, MPD_NAN);
+}
+
+static inline int
+invroot_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2],
+ mpd_ssize_t maxprec, mpd_ssize_t initprec)
+{
+ mpd_ssize_t k;
+ int i;
+
+ assert(maxprec >= 3 && initprec >= 3);
+ if (maxprec <= initprec) return -1;
+
+ i = 0; k = maxprec;
+ do {
+ k = (k+3) / 2;
+ klist[i++] = k;
+ } while (k > initprec);
+
+ return i-1;
+}
+
+/*
+ * Initial approximation for the inverse square root.
+ *
+ * Input:
+ * v := 7 or 8 decimal digits with an implicit exponent of 10**-6,
+ * representing a number 1 <= x < 100.
+ *
+ * Output:
+ * An approximation to 1/sqrt(v)
+ */
+static inline void
+_invroot_init_approx(mpd_t *z, mpd_uint_t v)
+{
+ mpd_uint_t lo = 1000;
+ mpd_uint_t hi = 10000;
+ mpd_uint_t a, sq;
+
+ assert(v >= lo*lo && v < (hi+1)*(hi+1));
+
+ for(;;) {
+ a = (lo + hi) / 2;
+ sq = a * a;
+ if (v >= sq) {
+ if (v < sq + 2*a + 1) {
+ break;
+ }
+ lo = a + 1;
+ }
+ else {
+ hi = a - 1;
+ }
+ }
+
+ /* At this point a/1000 is an approximation to sqrt(v). */
+ mpd_minalloc(z);
+ mpd_clear_flags(z);
+ z->data[0] = 1000000000UL / a;
+ z->len = 1;
+ z->exp = -6;
+ mpd_setdigits(z);
+}
+
+static void
+_mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_context_t varcontext, maxcontext;
+ mpd_t *z = result; /* current approximation */
+ mpd_t *v; /* a, normalized to a number between 1 and 100 */
+ MPD_NEW_SHARED(vtmp, a); /* by default v will share data with a */
+ MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */
+ MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */
+ MPD_NEW_CONST(one_half,0,-1,1,1,1,5);
+ MPD_NEW_CONST(three,0,0,1,1,1,3);
+ mpd_ssize_t klist[MPD_MAX_PREC_LOG2];
+ mpd_ssize_t ideal_exp, shift;
+ mpd_ssize_t adj, tz;
+ mpd_ssize_t maxprec, fracdigits;
+ mpd_uint_t x, dummy;
+ int i, n;
+
+
+ ideal_exp = -(a->exp - (a->exp & 1)) / 2;
+
+ v = &vtmp;
+ if (result == a) {
+ if ((v = mpd_qncopy(a)) == NULL) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ return;
+ }
+ }
+
+ /* normalize a to 1 <= v < 100 */
+ if ((v->digits+v->exp) & 1) {
+ fracdigits = v->digits - 1;
+ v->exp = -fracdigits;
+ n = (v->digits > 7) ? 7 : (int)v->digits;
+ _mpd_get_msdigits(&dummy, &x, v, n);
+ if (n < 7) {
+ x *= mpd_pow10[7-n];
+ }
+ }
+ else {
+ fracdigits = v->digits - 2;
+ v->exp = -fracdigits;
+ n = (v->digits > 8) ? 8 : (int)v->digits;
+ _mpd_get_msdigits(&dummy, &x, v, n);
+ if (n < 8) {
+ x *= mpd_pow10[8-n];
+ }
+ }
+ adj = (a->exp-v->exp) / 2;
+
+ /* initial approximation */
+ _invroot_init_approx(z, x);
+
+ mpd_maxcontext(&maxcontext);
+ mpd_maxcontext(&varcontext);
+ varcontext.round = MPD_ROUND_TRUNC;
+ maxprec = ctx->prec + 2;
+
+ i = invroot_schedule_prec(klist, maxprec, 3);
+ for (; i >= 0; i--) {
+ varcontext.prec = 2*klist[i]+2;
+ mpd_qmul(&s, z, z, &maxcontext, &workstatus);
+ if (v->digits > varcontext.prec) {
+ shift = v->digits - varcontext.prec;
+ mpd_qshiftr(&t, v, shift, &workstatus);
+ t.exp += shift;
+ mpd_qmul(&t, &t, &s, &varcontext, &workstatus);
+ }
+ else {
+ mpd_qmul(&t, v, &s, &varcontext, &workstatus);
+ }
+ mpd_qsub(&t, &three, &t, &maxcontext, &workstatus);
+ mpd_qmul(z, z, &t, &varcontext, &workstatus);
+ mpd_qmul(z, z, &one_half, &maxcontext, &workstatus);
+ }
+
+ z->exp -= adj;
+
+ tz = mpd_trail_zeros(result);
+ shift = ideal_exp - result->exp;
+ shift = (tz > shift) ? shift : tz;
+ if (shift > 0) {
+ mpd_qshiftr_inplace(result, shift);
+ result->exp += shift;
+ }
+
+
+ mpd_del(&s);
+ mpd_del(&t);
+ if (v != &vtmp) mpd_del(v);
+ *status |= (workstatus&MPD_Errors);
+ varcontext = *ctx;
+ varcontext.round = MPD_ROUND_HALF_EVEN;
+ mpd_qfinalize(result, &varcontext, status);
+}
+
+void
+mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ /* positive infinity */
+ _settriple(result, MPD_POS, 0, mpd_etiny(ctx));
+ *status |= MPD_Clamped;
+ return;
+ }
+ if (mpd_iszero(a)) {
+ mpd_setspecial(result, mpd_sign(a), MPD_INF);
+ *status |= MPD_Division_by_zero;
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ _mpd_qinvroot(result, a, ctx, status);
+}
+
+/*
+ * Ensure correct rounding. Algorithm after Hull & Abrham, "Properly Rounded
+ * Variable Precision Square Root", ACM Transactions on Mathematical Software,
+ * Vol. 11, No. 3.
+ */
+static void
+_mpd_fix_sqrt(mpd_t *result, const mpd_t *a, mpd_t *tmp,
+ const mpd_context_t *ctx, uint32_t *status)
+{
+ mpd_context_t maxctx;
+ MPD_NEW_CONST(u,0,0,1,1,1,5);
+
+ mpd_maxcontext(&maxctx);
+ u.exp = u.digits - ctx->prec + result->exp - 1;
+
+ _mpd_qsub(tmp, result, &u, &maxctx, status);
+ if (*status&MPD_Errors) goto nanresult;
+
+ _mpd_qmul(tmp, tmp, tmp, &maxctx, status);
+ if (*status&MPD_Errors) goto nanresult;
+
+ if (_mpd_cmp(tmp, a) == 1) {
+ u.exp += 1;
+ u.data[0] = 1;
+ _mpd_qsub(result, result, &u, &maxctx, status);
+ }
+ else {
+ _mpd_qadd(tmp, result, &u, &maxctx, status);
+ if (*status&MPD_Errors) goto nanresult;
+
+ _mpd_qmul(tmp, tmp, tmp, &maxctx, status);
+ if (*status&MPD_Errors) goto nanresult;
+
+ if (_mpd_cmp(tmp, a) == -1) {
+ u.exp += 1;
+ u.data[0] = 1;
+ _mpd_qadd(result, result, &u, &maxctx, status);
+ }
+ }
+
+ return;
+
+nanresult:
+ mpd_setspecial(result, MPD_POS, MPD_NAN);
+}
+
+void
+mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx,
+ uint32_t *status)
+{
+ uint32_t workstatus = 0;
+ mpd_context_t varcontext;
+ mpd_t *z = result; /* current approximation */
+ MPD_NEW_STATIC(v,0,0,0,0); /* a, normalized to a number between 1 and 10 */
+ MPD_NEW_STATIC(vtmp,0,0,0,0);
+ MPD_NEW_STATIC(tmp,0,0,0,0);
+ mpd_ssize_t ideal_exp, shift;
+ mpd_ssize_t target_prec, fracdigits;
+ mpd_ssize_t a_exp, a_digits;
+ mpd_ssize_t adj, tz;
+ mpd_uint_t dummy, t;
+ int exact = 0;
+
+
+ varcontext = *ctx;
+ varcontext.round = MPD_ROUND_HALF_EVEN;
+ ideal_exp = (a->exp - (a->exp & 1)) / 2;
+
+ if (mpd_isspecial(a)) {
+ if (mpd_qcheck_nan(result, a, ctx, status)) {
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+ mpd_setspecial(result, MPD_POS, MPD_INF);
+ return;
+ }
+ if (mpd_iszero(a)) {
+ _settriple(result, mpd_sign(a), 0, ideal_exp);
+ mpd_qfinalize(result, ctx, status);
+ return;
+ }
+ if (mpd_isnegative(a)) {
+ mpd_seterror(result, MPD_Invalid_operation, status);
+ return;
+ }
+
+ if (!mpd_qcopy(&v, a, status)) {
+ mpd_seterror(result, MPD_Malloc_error, status);
+ goto finish;
+ }
+
+ a_exp = a->exp;
+ a_digits = a->digits;
+
+ /* normalize a to 1 <= v < 100 */
+ if ((v.digits+v.exp) & 1) {
+ fracdigits = v.digits - 1;
+ v.exp = -fracdigits;
+ _mpd_get_msdigits(&dummy, &t, &v, 3);
+ t = t < 100 ? t*10 : t;
+ t = t < 100 ? t*10 : t;
+ }
+ else {
+ fracdigits = v.digits - 2;
+ v.exp = -fracdigits;
+ _mpd_get_msdigits(&dummy, &t, &v, 4);
+ t = t < 1000 ? t*10 : t;
+ t = t < 1000 ? t*10 : t;
+ t = t < 1000 ? t*10 : t;
+ }
+ adj = (a_exp-v.exp) / 2;
+
+
+ /* use excess digits */
+ target_prec = (a_digits > ctx->prec) ? a_digits : ctx->prec;
+ target_prec += 2;
+ varcontext.prec = target_prec + 3;
+
+ /* invroot is much faster for large numbers */
+ _mpd_qinvroot(&tmp, &v, &varcontext, &workstatus);
+
+ varcontext.prec = target_prec;
+ _mpd_qdiv(NO_IDEAL_EXP, z, &one, &tmp, &varcontext, &workstatus);
+
+
+ tz = mpd_trail_zeros(result);
+ if ((result->digits-tz)*2-1 <= v.digits) {
+ _mpd_qmul(&tmp, result, result, &varcontext, &workstatus);
+ if (workstatus&MPD_Errors) {
+ mpd_seterror(result, workstatus&MPD_Errors, status);
+ goto finish;
+ }
+ exact = (_mpd_cmp(&tmp, &v) == 0);
+ }
+ *status |= (workstatus&MPD_Errors);