8b327dd75c
Change-Id: I0e807118e6a2196d2f2858ed195782a90572a2e9 Reviewed-on: https://gerrit.libreoffice.org/c/core/+/158303 Tested-by: Jenkins Reviewed-by: Mike Kaganski <mike.kaganski@collabora.com>
772 lines
28 KiB
C++
772 lines
28 KiB
C++
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
|
|
/*
|
|
* This file is part of the LibreOffice project.
|
|
*
|
|
* This Source Code Form is subject to the terms of the Mozilla Public
|
|
* License, v. 2.0. If a copy of the MPL was not distributed with this
|
|
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
|
*
|
|
* This file incorporates work covered by the following license notice:
|
|
*
|
|
* Licensed to the Apache Software Foundation (ASF) under one or more
|
|
* contributor license agreements. See the NOTICE file distributed
|
|
* with this work for additional information regarding copyright
|
|
* ownership. The ASF licenses this file to you under the Apache
|
|
* License, Version 2.0 (the "License"); you may not use this file
|
|
* except in compliance with the License. You may obtain a copy of
|
|
* the License at http://www.apache.org/licenses/LICENSE-2.0 .
|
|
*/
|
|
|
|
#include <rtl/math.h>
|
|
|
|
#include <osl/diagnose.h>
|
|
#include <rtl/character.hxx>
|
|
#include <rtl/math.hxx>
|
|
|
|
#include <algorithm>
|
|
#include <cassert>
|
|
#include <cfenv>
|
|
#include <cmath>
|
|
#include <float.h>
|
|
#include <limits>
|
|
#include <memory>
|
|
#include <stdlib.h>
|
|
|
|
#include "strtmpl.hxx"
|
|
|
|
#include <dtoa.h>
|
|
|
|
constexpr int minExp = -323, maxExp = 308;
|
|
constexpr double n10s[] = {
|
|
1e-323, 1e-322, 1e-321, 1e-320, 1e-319, 1e-318, 1e-317, 1e-316, 1e-315, 1e-314, 1e-313, 1e-312,
|
|
1e-311, 1e-310, 1e-309, 1e-308, 1e-307, 1e-306, 1e-305, 1e-304, 1e-303, 1e-302, 1e-301, 1e-300,
|
|
1e-299, 1e-298, 1e-297, 1e-296, 1e-295, 1e-294, 1e-293, 1e-292, 1e-291, 1e-290, 1e-289, 1e-288,
|
|
1e-287, 1e-286, 1e-285, 1e-284, 1e-283, 1e-282, 1e-281, 1e-280, 1e-279, 1e-278, 1e-277, 1e-276,
|
|
1e-275, 1e-274, 1e-273, 1e-272, 1e-271, 1e-270, 1e-269, 1e-268, 1e-267, 1e-266, 1e-265, 1e-264,
|
|
1e-263, 1e-262, 1e-261, 1e-260, 1e-259, 1e-258, 1e-257, 1e-256, 1e-255, 1e-254, 1e-253, 1e-252,
|
|
1e-251, 1e-250, 1e-249, 1e-248, 1e-247, 1e-246, 1e-245, 1e-244, 1e-243, 1e-242, 1e-241, 1e-240,
|
|
1e-239, 1e-238, 1e-237, 1e-236, 1e-235, 1e-234, 1e-233, 1e-232, 1e-231, 1e-230, 1e-229, 1e-228,
|
|
1e-227, 1e-226, 1e-225, 1e-224, 1e-223, 1e-222, 1e-221, 1e-220, 1e-219, 1e-218, 1e-217, 1e-216,
|
|
1e-215, 1e-214, 1e-213, 1e-212, 1e-211, 1e-210, 1e-209, 1e-208, 1e-207, 1e-206, 1e-205, 1e-204,
|
|
1e-203, 1e-202, 1e-201, 1e-200, 1e-199, 1e-198, 1e-197, 1e-196, 1e-195, 1e-194, 1e-193, 1e-192,
|
|
1e-191, 1e-190, 1e-189, 1e-188, 1e-187, 1e-186, 1e-185, 1e-184, 1e-183, 1e-182, 1e-181, 1e-180,
|
|
1e-179, 1e-178, 1e-177, 1e-176, 1e-175, 1e-174, 1e-173, 1e-172, 1e-171, 1e-170, 1e-169, 1e-168,
|
|
1e-167, 1e-166, 1e-165, 1e-164, 1e-163, 1e-162, 1e-161, 1e-160, 1e-159, 1e-158, 1e-157, 1e-156,
|
|
1e-155, 1e-154, 1e-153, 1e-152, 1e-151, 1e-150, 1e-149, 1e-148, 1e-147, 1e-146, 1e-145, 1e-144,
|
|
1e-143, 1e-142, 1e-141, 1e-140, 1e-139, 1e-138, 1e-137, 1e-136, 1e-135, 1e-134, 1e-133, 1e-132,
|
|
1e-131, 1e-130, 1e-129, 1e-128, 1e-127, 1e-126, 1e-125, 1e-124, 1e-123, 1e-122, 1e-121, 1e-120,
|
|
1e-119, 1e-118, 1e-117, 1e-116, 1e-115, 1e-114, 1e-113, 1e-112, 1e-111, 1e-110, 1e-109, 1e-108,
|
|
1e-107, 1e-106, 1e-105, 1e-104, 1e-103, 1e-102, 1e-101, 1e-100, 1e-99, 1e-98, 1e-97, 1e-96,
|
|
1e-95, 1e-94, 1e-93, 1e-92, 1e-91, 1e-90, 1e-89, 1e-88, 1e-87, 1e-86, 1e-85, 1e-84,
|
|
1e-83, 1e-82, 1e-81, 1e-80, 1e-79, 1e-78, 1e-77, 1e-76, 1e-75, 1e-74, 1e-73, 1e-72,
|
|
1e-71, 1e-70, 1e-69, 1e-68, 1e-67, 1e-66, 1e-65, 1e-64, 1e-63, 1e-62, 1e-61, 1e-60,
|
|
1e-59, 1e-58, 1e-57, 1e-56, 1e-55, 1e-54, 1e-53, 1e-52, 1e-51, 1e-50, 1e-49, 1e-48,
|
|
1e-47, 1e-46, 1e-45, 1e-44, 1e-43, 1e-42, 1e-41, 1e-40, 1e-39, 1e-38, 1e-37, 1e-36,
|
|
1e-35, 1e-34, 1e-33, 1e-32, 1e-31, 1e-30, 1e-29, 1e-28, 1e-27, 1e-26, 1e-25, 1e-24,
|
|
1e-23, 1e-22, 1e-21, 1e-20, 1e-19, 1e-18, 1e-17, 1e-16, 1e-15, 1e-14, 1e-13, 1e-12,
|
|
1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1e0,
|
|
1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12,
|
|
1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22, 1e23, 1e24,
|
|
1e25, 1e26, 1e27, 1e28, 1e29, 1e30, 1e31, 1e32, 1e33, 1e34, 1e35, 1e36,
|
|
1e37, 1e38, 1e39, 1e40, 1e41, 1e42, 1e43, 1e44, 1e45, 1e46, 1e47, 1e48,
|
|
1e49, 1e50, 1e51, 1e52, 1e53, 1e54, 1e55, 1e56, 1e57, 1e58, 1e59, 1e60,
|
|
1e61, 1e62, 1e63, 1e64, 1e65, 1e66, 1e67, 1e68, 1e69, 1e70, 1e71, 1e72,
|
|
1e73, 1e74, 1e75, 1e76, 1e77, 1e78, 1e79, 1e80, 1e81, 1e82, 1e83, 1e84,
|
|
1e85, 1e86, 1e87, 1e88, 1e89, 1e90, 1e91, 1e92, 1e93, 1e94, 1e95, 1e96,
|
|
1e97, 1e98, 1e99, 1e100, 1e101, 1e102, 1e103, 1e104, 1e105, 1e106, 1e107, 1e108,
|
|
1e109, 1e110, 1e111, 1e112, 1e113, 1e114, 1e115, 1e116, 1e117, 1e118, 1e119, 1e120,
|
|
1e121, 1e122, 1e123, 1e124, 1e125, 1e126, 1e127, 1e128, 1e129, 1e130, 1e131, 1e132,
|
|
1e133, 1e134, 1e135, 1e136, 1e137, 1e138, 1e139, 1e140, 1e141, 1e142, 1e143, 1e144,
|
|
1e145, 1e146, 1e147, 1e148, 1e149, 1e150, 1e151, 1e152, 1e153, 1e154, 1e155, 1e156,
|
|
1e157, 1e158, 1e159, 1e160, 1e161, 1e162, 1e163, 1e164, 1e165, 1e166, 1e167, 1e168,
|
|
1e169, 1e170, 1e171, 1e172, 1e173, 1e174, 1e175, 1e176, 1e177, 1e178, 1e179, 1e180,
|
|
1e181, 1e182, 1e183, 1e184, 1e185, 1e186, 1e187, 1e188, 1e189, 1e190, 1e191, 1e192,
|
|
1e193, 1e194, 1e195, 1e196, 1e197, 1e198, 1e199, 1e200, 1e201, 1e202, 1e203, 1e204,
|
|
1e205, 1e206, 1e207, 1e208, 1e209, 1e210, 1e211, 1e212, 1e213, 1e214, 1e215, 1e216,
|
|
1e217, 1e218, 1e219, 1e220, 1e221, 1e222, 1e223, 1e224, 1e225, 1e226, 1e227, 1e228,
|
|
1e229, 1e230, 1e231, 1e232, 1e233, 1e234, 1e235, 1e236, 1e237, 1e238, 1e239, 1e240,
|
|
1e241, 1e242, 1e243, 1e244, 1e245, 1e246, 1e247, 1e248, 1e249, 1e250, 1e251, 1e252,
|
|
1e253, 1e254, 1e255, 1e256, 1e257, 1e258, 1e259, 1e260, 1e261, 1e262, 1e263, 1e264,
|
|
1e265, 1e266, 1e267, 1e268, 1e269, 1e270, 1e271, 1e272, 1e273, 1e274, 1e275, 1e276,
|
|
1e277, 1e278, 1e279, 1e280, 1e281, 1e282, 1e283, 1e284, 1e285, 1e286, 1e287, 1e288,
|
|
1e289, 1e290, 1e291, 1e292, 1e293, 1e294, 1e295, 1e296, 1e297, 1e298, 1e299, 1e300,
|
|
1e301, 1e302, 1e303, 1e304, 1e305, 1e306, 1e307, 1e308,
|
|
};
|
|
static_assert(SAL_N_ELEMENTS(n10s) == maxExp - minExp + 1);
|
|
|
|
// return pow(10.0,nExp) optimized for exponents in the interval [-323,308] (i.e., incl. denormals)
|
|
static double getN10Exp(int nExp)
|
|
{
|
|
if (nExp < minExp || nExp > maxExp)
|
|
return pow(10.0, static_cast<double>(nExp)); // will return 0 or INF with IEEE 754
|
|
return n10s[nExp - minExp];
|
|
}
|
|
|
|
namespace
|
|
{
|
|
/** If value (passed as absolute value) is an integer representable as double,
|
|
which we handle explicitly at some places.
|
|
*/
|
|
bool isRepresentableInteger(double fAbsValue)
|
|
{
|
|
static_assert(std::numeric_limits<double>::is_iec559
|
|
&& std::numeric_limits<double>::digits == 53);
|
|
assert(fAbsValue >= 0.0);
|
|
if (fAbsValue >= 0x1p53)
|
|
return false;
|
|
sal_Int64 nInt = static_cast<sal_Int64>(fAbsValue);
|
|
return nInt == fAbsValue;
|
|
}
|
|
|
|
// Returns 1-based index of least significant bit in a number, or zero if number is zero
|
|
int findFirstSetBit(unsigned n)
|
|
{
|
|
#if defined _WIN32
|
|
unsigned long pos;
|
|
unsigned char bNonZero = _BitScanForward(&pos, n);
|
|
return (bNonZero == 0) ? 0 : pos + 1;
|
|
#else
|
|
return __builtin_ffs(n);
|
|
#endif
|
|
}
|
|
|
|
/** Returns number of binary bits for fractional part of the number
|
|
Expects a proper non-negative double value, not +-INF, not NAN
|
|
*/
|
|
int getBitsInFracPart(double fAbsValue)
|
|
{
|
|
assert(std::isfinite(fAbsValue) && fAbsValue >= 0.0);
|
|
if (fAbsValue == 0.0)
|
|
return 0;
|
|
auto pValParts = reinterpret_cast<const sal_math_Double*>(&fAbsValue);
|
|
int nExponent = pValParts->inf_parts.exponent - 1023;
|
|
if (nExponent >= 52)
|
|
return 0; // All bits in fraction are in integer part of the number
|
|
int nLeastSignificant = findFirstSetBit(pValParts->inf_parts.fraction_lo);
|
|
if (nLeastSignificant == 0)
|
|
{
|
|
nLeastSignificant = findFirstSetBit(pValParts->inf_parts.fraction_hi);
|
|
if (nLeastSignificant == 0)
|
|
nLeastSignificant = 53; // the implied leading 1 is the least significant
|
|
else
|
|
nLeastSignificant += 32;
|
|
}
|
|
int nFracSignificant = 53 - nLeastSignificant;
|
|
int nBitsInFracPart = nFracSignificant - nExponent;
|
|
|
|
return std::max(nBitsInFracPart, 0);
|
|
}
|
|
}
|
|
|
|
void SAL_CALL rtl_math_doubleToString(rtl_String** pResult, sal_Int32* pResultCapacity,
|
|
sal_Int32 nResultOffset, double fValue,
|
|
rtl_math_StringFormat eFormat, sal_Int32 nDecPlaces,
|
|
char cDecSeparator, sal_Int32 const* pGroups,
|
|
char cGroupSeparator, sal_Bool bEraseTrailingDecZeros)
|
|
SAL_THROW_EXTERN_C()
|
|
{
|
|
rtl::str::doubleToString(pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces,
|
|
cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros);
|
|
}
|
|
|
|
void SAL_CALL rtl_math_doubleToUString(rtl_uString** pResult, sal_Int32* pResultCapacity,
|
|
sal_Int32 nResultOffset, double fValue,
|
|
rtl_math_StringFormat eFormat, sal_Int32 nDecPlaces,
|
|
sal_Unicode cDecSeparator, sal_Int32 const* pGroups,
|
|
sal_Unicode cGroupSeparator, sal_Bool bEraseTrailingDecZeros)
|
|
SAL_THROW_EXTERN_C()
|
|
{
|
|
rtl::str::doubleToString(pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces,
|
|
cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros);
|
|
}
|
|
|
|
namespace
|
|
{
|
|
template <typename CharT>
|
|
double stringToDouble(CharT const* pBegin, CharT const* pEnd, CharT cDecSeparator,
|
|
CharT cGroupSeparator, rtl_math_ConversionStatus* pStatus,
|
|
CharT const** pParsedEnd)
|
|
{
|
|
double fVal = 0.0;
|
|
rtl_math_ConversionStatus eStatus = rtl_math_ConversionStatus_Ok;
|
|
|
|
CharT const* p0 = pBegin;
|
|
while (p0 != pEnd && (*p0 == ' ' || *p0 == '\t'))
|
|
{
|
|
++p0;
|
|
}
|
|
|
|
bool bSign;
|
|
bool explicitSign = false;
|
|
if (p0 != pEnd && *p0 == '-')
|
|
{
|
|
bSign = true;
|
|
explicitSign = true;
|
|
++p0;
|
|
}
|
|
else
|
|
{
|
|
bSign = false;
|
|
if (p0 != pEnd && *p0 == '+')
|
|
{
|
|
explicitSign = true;
|
|
++p0;
|
|
}
|
|
}
|
|
|
|
CharT const* p = p0;
|
|
bool bDone = false;
|
|
|
|
// #i112652# XMLSchema-2
|
|
if ((pEnd - p) >= 3)
|
|
{
|
|
if (!explicitSign && ('N' == p[0]) && ('a' == p[1]) && ('N' == p[2]))
|
|
{
|
|
p += 3;
|
|
fVal = std::numeric_limits<double>::quiet_NaN();
|
|
bDone = true;
|
|
}
|
|
else if (('I' == p[0]) && ('N' == p[1]) && ('F' == p[2]))
|
|
{
|
|
p += 3;
|
|
fVal = HUGE_VAL;
|
|
eStatus = rtl_math_ConversionStatus_OutOfRange;
|
|
bDone = true;
|
|
}
|
|
}
|
|
|
|
if (!bDone) // do not recognize e.g. NaN1.23
|
|
{
|
|
std::unique_ptr<char[]> bufInHeap;
|
|
std::unique_ptr<const CharT* []> bufInHeapMap;
|
|
constexpr int bufOnStackSize = 256;
|
|
char bufOnStack[bufOnStackSize];
|
|
const CharT* bufOnStackMap[bufOnStackSize];
|
|
char* buf = bufOnStack;
|
|
const CharT** bufmap = bufOnStackMap;
|
|
int bufpos = 0;
|
|
const size_t bufsize = pEnd - p + (bSign ? 2 : 1);
|
|
if (bufsize > bufOnStackSize)
|
|
{
|
|
bufInHeap = std::make_unique<char[]>(bufsize);
|
|
bufInHeapMap = std::make_unique<const CharT* []>(bufsize);
|
|
buf = bufInHeap.get();
|
|
bufmap = bufInHeapMap.get();
|
|
}
|
|
|
|
if (bSign)
|
|
{
|
|
buf[0] = '-';
|
|
bufmap[0] = p; // yes, this may be the same pointer as for the next mapping
|
|
bufpos = 1;
|
|
}
|
|
// Put first zero to buffer for strings like "-0"
|
|
if (p != pEnd && *p == '0')
|
|
{
|
|
buf[bufpos] = '0';
|
|
bufmap[bufpos] = p;
|
|
++bufpos;
|
|
++p;
|
|
}
|
|
// Leading zeros and group separators between digits may be safely
|
|
// ignored. p0 < p implies that there was a leading 0 already,
|
|
// consecutive group separators may not happen as *(p+1) is checked for
|
|
// digit.
|
|
while (p != pEnd
|
|
&& (*p == '0'
|
|
|| (*p == cGroupSeparator && p0 < p && p + 1 < pEnd
|
|
&& rtl::isAsciiDigit(*(p + 1)))))
|
|
{
|
|
++p;
|
|
}
|
|
|
|
// integer part of mantissa
|
|
for (; p != pEnd; ++p)
|
|
{
|
|
CharT c = *p;
|
|
if (rtl::isAsciiDigit(c))
|
|
{
|
|
buf[bufpos] = static_cast<char>(c);
|
|
bufmap[bufpos] = p;
|
|
++bufpos;
|
|
}
|
|
else if (c != cGroupSeparator)
|
|
{
|
|
break;
|
|
}
|
|
else if (p == p0 || (p + 1 == pEnd) || !rtl::isAsciiDigit(*(p + 1)))
|
|
{
|
|
// A leading or trailing (not followed by a digit) group
|
|
// separator character is not a group separator.
|
|
break;
|
|
}
|
|
}
|
|
|
|
// fraction part of mantissa
|
|
if (p != pEnd && *p == cDecSeparator)
|
|
{
|
|
buf[bufpos] = '.';
|
|
bufmap[bufpos] = p;
|
|
++bufpos;
|
|
++p;
|
|
|
|
for (; p != pEnd; ++p)
|
|
{
|
|
CharT c = *p;
|
|
if (!rtl::isAsciiDigit(c))
|
|
{
|
|
break;
|
|
}
|
|
buf[bufpos] = static_cast<char>(c);
|
|
bufmap[bufpos] = p;
|
|
++bufpos;
|
|
}
|
|
}
|
|
|
|
// Exponent
|
|
if (p != p0 && p != pEnd && (*p == 'E' || *p == 'e'))
|
|
{
|
|
buf[bufpos] = 'E';
|
|
bufmap[bufpos] = p;
|
|
++bufpos;
|
|
++p;
|
|
if (p != pEnd && *p == '-')
|
|
{
|
|
buf[bufpos] = '-';
|
|
bufmap[bufpos] = p;
|
|
++bufpos;
|
|
++p;
|
|
}
|
|
else if (p != pEnd && *p == '+')
|
|
++p;
|
|
|
|
for (; p != pEnd; ++p)
|
|
{
|
|
CharT c = *p;
|
|
if (!rtl::isAsciiDigit(c))
|
|
break;
|
|
|
|
buf[bufpos] = static_cast<char>(c);
|
|
bufmap[bufpos] = p;
|
|
++bufpos;
|
|
}
|
|
}
|
|
else if (p - p0 == 2 && p != pEnd && p[0] == '#' && p[-1] == cDecSeparator && p[-2] == '1')
|
|
{
|
|
if (pEnd - p >= 4 && p[1] == 'I' && p[2] == 'N' && p[3] == 'F')
|
|
{
|
|
// "1.#INF", "+1.#INF", "-1.#INF"
|
|
p += 4;
|
|
fVal = HUGE_VAL;
|
|
eStatus = rtl_math_ConversionStatus_OutOfRange;
|
|
// Eat any further digits:
|
|
while (p != pEnd && rtl::isAsciiDigit(*p))
|
|
++p;
|
|
bDone = true;
|
|
}
|
|
else if (pEnd - p >= 4 && p[1] == 'N' && p[2] == 'A' && p[3] == 'N')
|
|
{
|
|
// "1.#NAN", "+1.#NAN", "-1.#NAN"
|
|
p += 4;
|
|
fVal = std::copysign(std::numeric_limits<double>::quiet_NaN(), bSign ? -1.0 : 1.0);
|
|
bSign = false; // don't negate again
|
|
|
|
// Eat any further digits:
|
|
while (p != pEnd && rtl::isAsciiDigit(*p))
|
|
{
|
|
++p;
|
|
}
|
|
bDone = true;
|
|
}
|
|
}
|
|
|
|
if (!bDone)
|
|
{
|
|
buf[bufpos] = '\0';
|
|
bufmap[bufpos] = p;
|
|
char* pCharParseEnd;
|
|
errno = 0;
|
|
fVal = strtod_nolocale(buf, &pCharParseEnd);
|
|
if (errno == ERANGE)
|
|
{
|
|
// Check for the dreaded rounded to 15 digits max value
|
|
// 1.79769313486232e+308 for 1.7976931348623157e+308 we wrote
|
|
// everywhere, accept with or without plus sign in exponent.
|
|
const char* b = buf;
|
|
if (b[0] == '-')
|
|
++b;
|
|
if (((pCharParseEnd - b == 21) || (pCharParseEnd - b == 20))
|
|
&& !strncmp(b, "1.79769313486232", 16) && (b[16] == 'e' || b[16] == 'E')
|
|
&& (((pCharParseEnd - b == 21) && !strncmp(b + 17, "+308", 4))
|
|
|| ((pCharParseEnd - b == 20) && !strncmp(b + 17, "308", 3))))
|
|
{
|
|
fVal = (buf < b) ? -DBL_MAX : DBL_MAX;
|
|
}
|
|
else
|
|
{
|
|
eStatus = rtl_math_ConversionStatus_OutOfRange;
|
|
}
|
|
}
|
|
p = bufmap[pCharParseEnd - buf];
|
|
bSign = false;
|
|
}
|
|
}
|
|
|
|
// overflow also if more than DBL_MAX_10_EXP digits without decimal
|
|
// separator, or 0. and more than DBL_MIN_10_EXP digits, ...
|
|
bool bHuge = fVal == HUGE_VAL; // g++ 3.0.1 requires it this way...
|
|
if (bHuge)
|
|
eStatus = rtl_math_ConversionStatus_OutOfRange;
|
|
|
|
if (bSign)
|
|
fVal = -fVal;
|
|
|
|
if (pStatus)
|
|
*pStatus = eStatus;
|
|
|
|
if (pParsedEnd)
|
|
*pParsedEnd = p == p0 ? pBegin : p;
|
|
|
|
return fVal;
|
|
}
|
|
}
|
|
|
|
double SAL_CALL rtl_math_stringToDouble(char const* pBegin, char const* pEnd, char cDecSeparator,
|
|
char cGroupSeparator, rtl_math_ConversionStatus* pStatus,
|
|
char const** pParsedEnd) SAL_THROW_EXTERN_C()
|
|
{
|
|
return stringToDouble(reinterpret_cast<unsigned char const*>(pBegin),
|
|
reinterpret_cast<unsigned char const*>(pEnd),
|
|
static_cast<unsigned char>(cDecSeparator),
|
|
static_cast<unsigned char>(cGroupSeparator), pStatus,
|
|
reinterpret_cast<unsigned char const**>(pParsedEnd));
|
|
}
|
|
|
|
double SAL_CALL rtl_math_uStringToDouble(sal_Unicode const* pBegin, sal_Unicode const* pEnd,
|
|
sal_Unicode cDecSeparator, sal_Unicode cGroupSeparator,
|
|
rtl_math_ConversionStatus* pStatus,
|
|
sal_Unicode const** pParsedEnd) SAL_THROW_EXTERN_C()
|
|
{
|
|
return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus, pParsedEnd);
|
|
}
|
|
|
|
double SAL_CALL rtl_math_round(double fValue, int nDecPlaces, enum rtl_math_RoundingMode eMode)
|
|
SAL_THROW_EXTERN_C()
|
|
{
|
|
if (!std::isfinite(fValue))
|
|
return fValue;
|
|
|
|
if (fValue == 0.0)
|
|
return fValue;
|
|
|
|
if (nDecPlaces == 0)
|
|
{
|
|
switch (eMode)
|
|
{
|
|
case rtl_math_RoundingMode_Corrected:
|
|
return std::round(fValue);
|
|
case rtl_math_RoundingMode_HalfEven:
|
|
if (const int oldMode = std::fegetround(); std::fesetround(FE_TONEAREST) == 0)
|
|
{
|
|
fValue = std::nearbyint(fValue);
|
|
std::fesetround(oldMode);
|
|
return fValue;
|
|
}
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
}
|
|
|
|
const double fOrigValue = fValue;
|
|
|
|
// sign adjustment
|
|
bool bSign = std::signbit(fValue);
|
|
if (bSign)
|
|
fValue = -fValue;
|
|
|
|
// Rounding to decimals between integer distance precision (gaps) does not
|
|
// make sense, do not even try to multiply/divide and introduce inaccuracy.
|
|
// For same reasons, do not attempt to round integers to decimals.
|
|
if (nDecPlaces >= 0 && (fValue >= 0x1p52 || isRepresentableInteger(fValue)))
|
|
return fOrigValue;
|
|
|
|
double fFac = 0;
|
|
if (nDecPlaces != 0)
|
|
{
|
|
if (nDecPlaces > 0)
|
|
{
|
|
// Determine how many decimals are representable in the precision.
|
|
// Anything greater 2^52 and 0.0 was already ruled out above.
|
|
// Theoretically 0.5, 0.25, 0.125, 0.0625, 0.03125, ...
|
|
const sal_math_Double* pd = reinterpret_cast<const sal_math_Double*>(&fValue);
|
|
const sal_Int32 nDec = 52 - (pd->parts.exponent - 1023);
|
|
|
|
if (nDec <= 0)
|
|
{
|
|
assert(!"Shouldn't this had been caught already as large number?");
|
|
return fOrigValue;
|
|
}
|
|
|
|
if (nDec < nDecPlaces)
|
|
nDecPlaces = nDec;
|
|
}
|
|
|
|
// Avoid 1e-5 (1.0000000000000001e-05) and such inaccurate fractional
|
|
// factors that later when dividing back spoil things. For negative
|
|
// decimals divide first with the inverse, then multiply the rounded
|
|
// value back.
|
|
fFac = getN10Exp(abs(nDecPlaces));
|
|
|
|
if (fFac == 0.0 || (nDecPlaces < 0 && !std::isfinite(fFac)))
|
|
// Underflow, rounding to that many integer positions would be 0.
|
|
return 0.0;
|
|
|
|
if (!std::isfinite(fFac))
|
|
// Overflow with very small values and high number of decimals.
|
|
return fOrigValue;
|
|
|
|
if (nDecPlaces < 0)
|
|
fValue /= fFac;
|
|
else
|
|
fValue *= fFac;
|
|
|
|
if (!std::isfinite(fValue))
|
|
return fOrigValue;
|
|
}
|
|
|
|
// Round only if not already in distance precision gaps of integers, where
|
|
// for [2^52,2^53) adding 0.5 would even yield the next representable
|
|
// integer.
|
|
if (fValue < 0x1p52)
|
|
{
|
|
switch (eMode)
|
|
{
|
|
case rtl_math_RoundingMode_Corrected:
|
|
fValue = rtl::math::approxFloor(fValue + 0.5);
|
|
break;
|
|
case rtl_math_RoundingMode_Down:
|
|
fValue = rtl::math::approxFloor(fValue);
|
|
break;
|
|
case rtl_math_RoundingMode_Up:
|
|
fValue = rtl::math::approxCeil(fValue);
|
|
break;
|
|
case rtl_math_RoundingMode_Floor:
|
|
fValue = bSign ? rtl::math::approxCeil(fValue) : rtl::math::approxFloor(fValue);
|
|
break;
|
|
case rtl_math_RoundingMode_Ceiling:
|
|
fValue = bSign ? rtl::math::approxFloor(fValue) : rtl::math::approxCeil(fValue);
|
|
break;
|
|
case rtl_math_RoundingMode_HalfDown:
|
|
{
|
|
double f = floor(fValue);
|
|
fValue = ((fValue - f) <= 0.5) ? f : ceil(fValue);
|
|
}
|
|
break;
|
|
case rtl_math_RoundingMode_HalfUp:
|
|
{
|
|
double f = floor(fValue);
|
|
fValue = ((fValue - f) < 0.5) ? f : ceil(fValue);
|
|
}
|
|
break;
|
|
case rtl_math_RoundingMode_HalfEven:
|
|
#if defined FLT_ROUNDS
|
|
/*
|
|
Use fast version. FLT_ROUNDS may be defined to a function by some compilers!
|
|
|
|
DBL_EPSILON is the smallest fractional number which can be represented,
|
|
its reciprocal is therefore the smallest number that cannot have a
|
|
fractional part. Once you add this reciprocal to `x', its fractional part
|
|
is stripped off. Simply subtracting the reciprocal back out returns `x'
|
|
without its fractional component.
|
|
Simple, clever, and elegant - thanks to Ross Cottrell, the original author,
|
|
who placed it into public domain.
|
|
|
|
volatile: prevent compiler from being too smart
|
|
*/
|
|
if (FLT_ROUNDS == 1)
|
|
{
|
|
volatile double x = fValue + 1.0 / DBL_EPSILON;
|
|
fValue = x - 1.0 / DBL_EPSILON;
|
|
}
|
|
else
|
|
#endif // FLT_ROUNDS
|
|
{
|
|
double f = floor(fValue);
|
|
if ((fValue - f) != 0.5)
|
|
{
|
|
fValue = floor(fValue + 0.5);
|
|
}
|
|
else
|
|
{
|
|
double g = f / 2.0;
|
|
fValue = (g == floor(g)) ? f : (f + 1.0);
|
|
}
|
|
}
|
|
break;
|
|
default:
|
|
OSL_ASSERT(false);
|
|
break;
|
|
}
|
|
}
|
|
|
|
if (nDecPlaces != 0)
|
|
{
|
|
if (nDecPlaces < 0)
|
|
fValue *= fFac;
|
|
else
|
|
fValue /= fFac;
|
|
}
|
|
|
|
if (!std::isfinite(fValue))
|
|
return fOrigValue;
|
|
|
|
return bSign ? -fValue : fValue;
|
|
}
|
|
|
|
double SAL_CALL rtl_math_pow10Exp(double fValue, int nExp) SAL_THROW_EXTERN_C()
|
|
{
|
|
return fValue * getN10Exp(nExp);
|
|
}
|
|
|
|
double SAL_CALL rtl_math_approxValue(double fValue) SAL_THROW_EXTERN_C()
|
|
{
|
|
const double fBigInt = 0x1p41; // 2^41 -> only 11 bits left for fractional part, fine as decimal
|
|
if (fValue == 0.0 || fValue == HUGE_VAL || !std::isfinite(fValue) || fValue > fBigInt)
|
|
{
|
|
// We don't handle these conditions. Bail out.
|
|
return fValue;
|
|
}
|
|
|
|
double fOrigValue = fValue;
|
|
|
|
bool bSign = std::signbit(fValue);
|
|
if (bSign)
|
|
fValue = -fValue;
|
|
|
|
// If the value is either integer representable as double,
|
|
// or only has small number of bits in fraction part, then we need not do any approximation
|
|
if (isRepresentableInteger(fValue) || getBitsInFracPart(fValue) <= 11)
|
|
return fOrigValue;
|
|
|
|
int nExp = static_cast<int>(floor(log10(fValue)));
|
|
nExp = 14 - nExp;
|
|
double fExpValue = getN10Exp(abs(nExp));
|
|
|
|
if (nExp < 0)
|
|
fValue /= fExpValue;
|
|
else
|
|
fValue *= fExpValue;
|
|
|
|
// If the original value was near DBL_MIN we got an overflow. Restore and
|
|
// bail out.
|
|
if (!std::isfinite(fValue))
|
|
return fOrigValue;
|
|
|
|
fValue = std::round(fValue);
|
|
|
|
if (nExp < 0)
|
|
fValue *= fExpValue;
|
|
else
|
|
fValue /= fExpValue;
|
|
|
|
// If the original value was near DBL_MAX we got an overflow. Restore and
|
|
// bail out.
|
|
if (!std::isfinite(fValue))
|
|
return fOrigValue;
|
|
|
|
return bSign ? -fValue : fValue;
|
|
}
|
|
|
|
bool SAL_CALL rtl_math_approxEqual(double a, double b) SAL_THROW_EXTERN_C()
|
|
{
|
|
static const double e48 = 0x1p-48;
|
|
|
|
if (a == b)
|
|
return true;
|
|
|
|
if (a == 0.0 || b == 0.0 || std::signbit(a) != std::signbit(b))
|
|
return false;
|
|
|
|
const double d = fabs(a - b);
|
|
if (!std::isfinite(d))
|
|
return false; // Nan or Inf involved
|
|
|
|
a = fabs(a);
|
|
if (d >= (a * e48))
|
|
return false;
|
|
b = fabs(b);
|
|
if (d >= (b * e48))
|
|
return false;
|
|
|
|
if (isRepresentableInteger(a) && isRepresentableInteger(b))
|
|
return false; // special case for representable integers.
|
|
|
|
return true;
|
|
}
|
|
|
|
double SAL_CALL rtl_math_expm1(double fValue) SAL_THROW_EXTERN_C() { return expm1(fValue); }
|
|
|
|
double SAL_CALL rtl_math_log1p(double fValue) SAL_THROW_EXTERN_C()
|
|
{
|
|
#ifdef __APPLE__
|
|
if (fValue == -0.0)
|
|
return fValue; // macOS 10.8 libc returns 0.0 for -0.0
|
|
#endif
|
|
|
|
return log1p(fValue);
|
|
}
|
|
|
|
double SAL_CALL rtl_math_atanh(double fValue) SAL_THROW_EXTERN_C() { return ::atanh(fValue); }
|
|
|
|
/** Parent error function (erf) */
|
|
double SAL_CALL rtl_math_erf(double x) SAL_THROW_EXTERN_C() { return erf(x); }
|
|
|
|
/** Parent complementary error function (erfc) */
|
|
double SAL_CALL rtl_math_erfc(double x) SAL_THROW_EXTERN_C() { return erfc(x); }
|
|
|
|
/** improved accuracy of asinh for |x| large and for x near zero
|
|
@see #i97605#
|
|
*/
|
|
double SAL_CALL rtl_math_asinh(double fX) SAL_THROW_EXTERN_C()
|
|
{
|
|
if (fX == 0.0)
|
|
return 0.0;
|
|
|
|
double fSign = 1.0;
|
|
if (fX < 0.0)
|
|
{
|
|
fX = -fX;
|
|
fSign = -1.0;
|
|
}
|
|
|
|
if (fX < 0.125)
|
|
return fSign * rtl_math_log1p(fX + fX * fX / (1.0 + sqrt(1.0 + fX * fX)));
|
|
|
|
if (fX < 1.25e7)
|
|
return fSign * log(fX + sqrt(1.0 + fX * fX));
|
|
|
|
return fSign * log(2.0 * fX);
|
|
}
|
|
|
|
/** improved accuracy of acosh for x large and for x near 1
|
|
@see #i97605#
|
|
*/
|
|
double SAL_CALL rtl_math_acosh(double fX) SAL_THROW_EXTERN_C()
|
|
{
|
|
volatile double fZ = fX - 1.0;
|
|
if (fX < 1.0)
|
|
return std::numeric_limits<double>::quiet_NaN();
|
|
if (fX == 1.0)
|
|
return 0.0;
|
|
|
|
if (fX < 1.1)
|
|
return rtl_math_log1p(fZ + sqrt(fZ * fZ + 2.0 * fZ));
|
|
|
|
if (fX < 1.25e7)
|
|
return log(fX + sqrt(fX * fX - 1.0));
|
|
|
|
return log(2.0 * fX);
|
|
}
|
|
|
|
/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
|