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/*
* Copyright (c) 2008-2016 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 "mpalloc.h"
#include "typearith.h"
#include "umodarith.h"
#ifdef PPRO
#if defined(_MSC_VER)
#include <float.h>
#pragma float_control(precise, on)
#pragma fenv_access(on)
#elif !defined(__OpenBSD__) && !defined(__NetBSD__)
/* C99 */
#include <fenv.h>
#pragma STDC FENV_ACCESS ON
#endif
#endif
/* Disable warning that is part of -Wextra since gcc 7.0. */
#if defined(__GNUC__) && !defined(__INTEL_COMPILER) && __GNUC__ >= 7
#pragma GCC diagnostic ignored "-Wimplicit-fallthrough"
#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 int _mpd_cmp_abs(const mpd_t *a, const mpd_t *b);
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_base_ndivmod(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, const mpd_t *base,
mpd_uint_t exp, uint8_t resultsign,
const mpd_context_t *ctx, uint32_t *status);
static mpd_uint_t mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n);
/******************************************************************************/
/* Version */
/******************************************************************************/
const char *
mpd_version(void)
{
return MPD_VERSION;
}
/******************************************************************************/
/* 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(const mpd_t *dec)
{
return !(dec->flags & MPD_STATIC);
}
/* Static decimal */
ALWAYS_INLINE int
mpd_isstatic(const mpd_t *dec)
{
return dec->flags & MPD_STATIC;
}
/* Data of decimal is dynamic */
ALWAYS_INLINE int
mpd_isdynamic_data(const mpd_t *dec)
{
return !(dec->flags & MPD_DATAFLAGS);
}
/* Data of decimal is static */
ALWAYS_INLINE int
mpd_isstatic_data(const mpd_t *dec)
{
return dec->flags & MPD_STATIC_DATA;
}
/* Data of decimal is shared */
ALWAYS_INLINE int
mpd_isshared_data(const mpd_t *dec)
{
return dec->flags & MPD_SHARED_DATA;
}
/* Data of decimal is const */
ALWAYS_INLINE int
mpd_isconst_data(const 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);
}
}
/*
* Resize the coefficient. Existing data up to 'nwords' is left untouched.
* Return 1 on success, 0 otherwise.
*
* Input invariant: MPD_MINALLOC <= result->alloc.
*
* Case nwords == result->alloc:
* 'result' is unchanged. Return 1.
*
* Case nwords > result->alloc:
* Case realloc success:
* The value of 'result' does not change. Return 1.
* Case realloc failure:
* 'result' is NaN, status is updated with MPD_Malloc_error. Return 0.
*
* Case nwords < result->alloc:
* Case is_static_data or realloc failure [1]:
* 'result' is unchanged. Return 1.
* Case realloc success:
* The value of result is undefined (expected). Return 1.
*
*
* [1] In that case the old (now oversized) area is still valid.
*/
ALWAYS_INLINE int
mpd_qresize(mpd_t *result, mpd_ssize_t nwords, uint32_t *status)
{
assert(!mpd_isconst_data(result)); /* illegal operation for a const */
assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
assert(MPD_MINALLOC <= result->alloc);
nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords;
if (nwords == result->alloc) {
return 1;
}
if (mpd_isstatic_data(result)) {
if (nwords > result->alloc) {
return mpd_switch_to_dyn(result, nwords, status);
}
return 1;
}
return mpd_realloc_dyn(result, nwords, status);
}
/* 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 nwords, uint32_t *status)
{
assert(!mpd_isconst_data(result)); /* illegal operation for a const */
assert(!mpd_isshared_data(result)); /* illegal operation for a shared */
assert(MPD_MINALLOC <= result->alloc);
nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords;
if (nwords != result->alloc) {
if (mpd_isstatic_data(result)) {
if (nwords > result->alloc) {
return mpd_switch_to_dyn_zero(result, nwords, status);
}
}
else if (!mpd_realloc_dyn(result, nwords, status)) {
return 0;
}
}
mpd_uint_zero(result->data, nwords);
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 nwords, mpd_context_t *ctx)
{
uint32_t status = 0;
if (!mpd_qresize(result, nwords, &status)) {
mpd_addstatus_raise(ctx, status);
return 0;
}
return 1;
}
int
mpd_resize_zero(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx)
{
uint32_t status = 0;
if (!mpd_qresize_zero(result, nwords, &status)) {
mpd_addstatus_raise(ctx, status);
return 0;
}
return 1;
}
/******************************************************************************/
/* Set attributes of a decimal */
/******************************************************************************/
/* Set digits. Assumption: result->len is initialized and > 0. */
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, const 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));
}
/* Initialize a workcontext from ctx. Set traps, flags and newtrap to 0. */
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! */
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