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office-gobmx/sal/rtl/math.cxx
Mike Kaganski 7e558cd5b9 Optimize the whole range of getN10Exp over IEEE 754 doubles 
Needs 5056 bytes of pre-calculated data.

Change-Id: I138d9dc80c176f675a6854fe906e235c98efcbc0
Reviewed-on: https://gerrit.libreoffice.org/c/core/+/122947
Tested-by: Jenkins
Reviewed-by: Noel Grandin <noel.grandin@collabora.co.uk>
Reviewed-by: Mike Kaganski <mike.kaganski@collabora.com>
2021-10-05 21:19:22 +02:00

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/* -*- 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 <limits.h>
#include <math.h>
#include <memory>
#include <stdlib.h>
#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 {
double const nCorrVal[] = {
0, 9e-1, 9e-2, 9e-3, 9e-4, 9e-5, 9e-6, 9e-7, 9e-8,
9e-9, 9e-10, 9e-11, 9e-12, 9e-13, 9e-14, 9e-15
};
struct StringTraits
{
typedef char Char;
typedef rtl_String String;
static void createString(rtl_String ** pString,
char const * pChars, sal_Int32 nLen)
{
rtl_string_newFromStr_WithLength(pString, pChars, nLen);
}
static void createBuffer(rtl_String ** pBuffer,
const sal_Int32 * pCapacity)
{
rtl_string_new_WithLength(pBuffer, *pCapacity);
}
static void appendChars(rtl_String ** pBuffer, sal_Int32 * pCapacity,
sal_Int32 * pOffset, char const * pChars,
sal_Int32 nLen)
{
assert(pChars);
rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen);
*pOffset += nLen;
}
static void appendAscii(rtl_String ** pBuffer, sal_Int32 * pCapacity,
sal_Int32 * pOffset, char const * pStr,
sal_Int32 nLen)
{
assert(pStr);
rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pStr, nLen);
*pOffset += nLen;
}
};
struct UStringTraits
{
typedef sal_Unicode Char;
typedef rtl_uString String;
static void createString(rtl_uString ** pString,
sal_Unicode const * pChars, sal_Int32 nLen)
{
rtl_uString_newFromStr_WithLength(pString, pChars, nLen);
}
static void createBuffer(rtl_uString ** pBuffer,
const sal_Int32 * pCapacity)
{
rtl_uString_new_WithLength(pBuffer, *pCapacity);
}
static void appendChars(rtl_uString ** pBuffer,
sal_Int32 * pCapacity, sal_Int32 * pOffset,
sal_Unicode const * pChars, sal_Int32 nLen)
{
assert(pChars);
rtl_uStringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen);
*pOffset += nLen;
}
static void appendAscii(rtl_uString ** pBuffer,
sal_Int32 * pCapacity, sal_Int32 * pOffset,
char const * pStr, sal_Int32 nLen)
{
rtl_uStringbuffer_insert_ascii(pBuffer, pCapacity, *pOffset, pStr,
nLen);
*pOffset += nLen;
}
};
/** If value (passed as absolute value) is an integer representable as double,
which we handle explicitly at some places.
*/
bool isRepresentableInteger(double fAbsValue)
{
assert(fAbsValue >= 0.0);
const sal_Int64 kMaxInt = (static_cast< sal_Int64 >(1) << 53) - 1;
if (fAbsValue <= static_cast< double >(kMaxInt))
{
sal_Int64 nInt = static_cast< sal_Int64 >(fAbsValue);
// Check the integer range again because double comparison may yield
// true within the precision range.
// XXX loplugin:fpcomparison complains about floating-point comparison
// for static_cast<double>(nInt) == fAbsValue, though we actually want
// this here.
if (nInt > kMaxInt)
return false;
double fInt = static_cast< double >(nInt);
return !(fInt < fAbsValue) && !(fInt > fAbsValue);
}
return false;
}
// 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);
}
template< typename T >
void doubleToString(typename T::String ** pResult,
sal_Int32 * pResultCapacity, sal_Int32 nResultOffset,
double fValue, rtl_math_StringFormat eFormat,
sal_Int32 nDecPlaces, typename T::Char cDecSeparator,
sal_Int32 const * pGroups,
typename T::Char cGroupSeparator,
bool bEraseTrailingDecZeros)
{
static double const nRoundVal[] = {
5.0e+0, 0.5e+0, 0.5e-1, 0.5e-2, 0.5e-3, 0.5e-4, 0.5e-5, 0.5e-6,
0.5e-7, 0.5e-8, 0.5e-9, 0.5e-10,0.5e-11,0.5e-12,0.5e-13,0.5e-14
};
// sign adjustment, instead of testing for fValue<0.0 this will also fetch
// -0.0
bool bSign = std::signbit(fValue);
if (bSign)
fValue = -fValue;
if (std::isnan(fValue))
{
// #i112652# XMLSchema-2
sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("NaN");
if (!pResultCapacity)
{
pResultCapacity = &nCapacity;
T::createBuffer(pResult, pResultCapacity);
nResultOffset = 0;
}
T::appendAscii(pResult, pResultCapacity, &nResultOffset,
RTL_CONSTASCII_STRINGPARAM("NaN"));
return;
}
bool bHuge = fValue == HUGE_VAL; // g++ 3.0.1 requires it this way...
if (bHuge || std::isinf(fValue))
{
// #i112652# XMLSchema-2
sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("-INF");
if (!pResultCapacity)
{
pResultCapacity = &nCapacity;
T::createBuffer(pResult, pResultCapacity);
nResultOffset = 0;
}
if ( bSign )
T::appendAscii(pResult, pResultCapacity, &nResultOffset,
RTL_CONSTASCII_STRINGPARAM("-"));
T::appendAscii(pResult, pResultCapacity, &nResultOffset,
RTL_CONSTASCII_STRINGPARAM("INF"));
return;
}
// Unfortunately the old rounding below writes 1.79769313486232e+308 for
// DBL_MAX and 4 subsequent nextafter(...,0).
static const double fB1 = std::nextafter( DBL_MAX, 0);
static const double fB2 = std::nextafter( fB1, 0);
static const double fB3 = std::nextafter( fB2, 0);
static const double fB4 = std::nextafter( fB3, 0);
if ((fValue >= fB4) && eFormat != rtl_math_StringFormat_F)
{
// 1.7976931348623157e+308 instead of rounded 1.79769313486232e+308
// that can't be converted back as out of range. For rounded values if
// they exceed range they should not be written to exchange strings or
// file formats.
// Writing pDig up to decimals(-1,-2) then appending one digit from
// pRou xor one or two digits from pSlot[].
constexpr char pDig[] = "7976931348623157";
constexpr char pRou[] = "8087931359623267"; // the only up-carry is 80
static_assert(SAL_N_ELEMENTS(pDig) == SAL_N_ELEMENTS(pRou), "digit count mismatch");
constexpr sal_Int32 nDig2 = RTL_CONSTASCII_LENGTH(pRou) - 2;
sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH(pRou) + 8; // + "-1.E+308"
const char pSlot[5][2][3] =
{ // rounded, not
"67", "57", // DBL_MAX
"65", "55",
"53", "53",
"51", "51",
"59", "49",
};
if (!pResultCapacity)
{
pResultCapacity = &nCapacity;
T::createBuffer(pResult, pResultCapacity);
nResultOffset = 0;
}
if (bSign)
T::appendAscii(pResult, pResultCapacity, &nResultOffset,
RTL_CONSTASCII_STRINGPARAM("-"));
nDecPlaces = std::clamp<sal_Int32>( nDecPlaces, 0, RTL_CONSTASCII_LENGTH(pRou));
if (nDecPlaces == 0)
{
T::appendAscii(pResult, pResultCapacity, &nResultOffset,
RTL_CONSTASCII_STRINGPARAM("2"));
}
else
{
T::appendAscii(pResult, pResultCapacity, &nResultOffset,
RTL_CONSTASCII_STRINGPARAM("1"));
T::appendChars(pResult, pResultCapacity, &nResultOffset, &cDecSeparator, 1);
if (nDecPlaces <= 2)
{
T::appendAscii(pResult, pResultCapacity, &nResultOffset, pRou, nDecPlaces);
}
else if (nDecPlaces <= nDig2)
{
T::appendAscii(pResult, pResultCapacity, &nResultOffset, pDig, nDecPlaces - 1);
T::appendAscii(pResult, pResultCapacity, &nResultOffset, pRou + nDecPlaces - 1, 1);
}
else
{
const sal_Int32 nDec = nDecPlaces - nDig2;
nDecPlaces -= nDec;
// nDec-1 is also offset into slot, rounded(1-1=0) or not(2-1=1)
const size_t nSlot = ((fValue < fB3) ? 4 : ((fValue < fB2) ? 3
: ((fValue < fB1) ? 2 : ((fValue < DBL_MAX) ? 1 : 0))));
T::appendAscii(pResult, pResultCapacity, &nResultOffset, pDig, nDecPlaces);
T::appendAscii(pResult, pResultCapacity, &nResultOffset, pSlot[nSlot][nDec-1], nDec);
}
}
T::appendAscii(pResult, pResultCapacity, &nResultOffset,
RTL_CONSTASCII_STRINGPARAM("E+308"));
return;
}
// Use integer representation for integer values that fit into the
// mantissa (1.((2^53)-1)) with a precision of 1 for highest accuracy.
if ((eFormat == rtl_math_StringFormat_Automatic ||
eFormat == rtl_math_StringFormat_F) && isRepresentableInteger(fValue))
{
sal_Int64 nInt = static_cast< sal_Int64 >(fValue);
if (nDecPlaces == rtl_math_DecimalPlaces_Max)
nDecPlaces = 0;
else
nDecPlaces = ::std::clamp< sal_Int32 >(nDecPlaces, -15, 15);
if (bEraseTrailingDecZeros && nDecPlaces > 0)
nDecPlaces = 0;
// Round before decimal position.
if (nDecPlaces < 0)
{
sal_Int64 nRounding = static_cast< sal_Int64 >(getN10Exp(-nDecPlaces - 1));
const sal_Int64 nTemp = (nInt / nRounding + 5) / 10;
nInt = nTemp * 10 * nRounding;
}
// Max 1 sign, 16 integer digits, 15 group separators, 1 decimal
// separator, 15 decimals digits.
typename T::Char aBuf[64];
typename T::Char* pEnd = aBuf + 40;
typename T::Char* pStart = pEnd;
// Backward fill.
sal_Int32 nGrouping = cGroupSeparator && pGroups ? *pGroups : 0;
sal_Int32 nGroupDigits = 0;
do
{
typename T::Char nDigit = nInt % 10;
nInt /= 10;
*--pStart = nDigit + '0';
if (nGrouping && nGrouping == ++nGroupDigits && nInt)
{
*--pStart = cGroupSeparator;
if (*(pGroups + 1))
nGrouping = *++pGroups;
nGroupDigits = 0;
}
}
while (nInt);
if (bSign)
*--pStart = '-';
// Append decimals.
if (nDecPlaces > 0)
{
*pEnd++ = cDecSeparator;
pEnd = std::fill_n(pEnd, nDecPlaces, '0');
}
if (!pResultCapacity)
T::createString(pResult, pStart, pEnd - pStart);
else
T::appendChars(pResult, pResultCapacity, &nResultOffset, pStart, pEnd - pStart);
return;
}
// find the exponent
int nExp = 0;
if ( fValue > 0.0 )
{
// Cap nExp at a small value beyond which "fValue /= N10Exp" would lose precision (or N10Exp
// might even be zero); that will produce output with the decimal point in a non-normalized
// position, but the current quality of output for such small values is probably abysmal,
// anyway:
nExp = std::max(
static_cast< int >(floor(log10(fValue))), std::numeric_limits<double>::min_exponent10);
double const N10Exp = getN10Exp(nExp);
assert(N10Exp != 0);
fValue /= N10Exp;
}
switch (eFormat)
{
case rtl_math_StringFormat_Automatic:
{ // E or F depending on exponent magnitude
int nPrec;
if (nExp <= -15 || nExp >= 15) // was <-16, >16 in ancient versions, which leads to inaccuracies
{
nPrec = 14;
eFormat = rtl_math_StringFormat_E;
}
else
{
if (nExp < 14)
{
nPrec = 15 - nExp - 1;
eFormat = rtl_math_StringFormat_F;
}
else
{
nPrec = 15;
eFormat = rtl_math_StringFormat_F;
}
}
if (nDecPlaces == rtl_math_DecimalPlaces_Max)
nDecPlaces = nPrec;
}
break;
case rtl_math_StringFormat_G :
case rtl_math_StringFormat_G1 :
case rtl_math_StringFormat_G2 :
{ // G-Point, similar to sprintf %G
if (nDecPlaces == rtl_math_DecimalPlaces_DefaultSignificance)
nDecPlaces = 6;
if (nExp < -4 || nExp >= nDecPlaces)
{
nDecPlaces = std::max< sal_Int32 >(1, nDecPlaces - 1);
if (eFormat == rtl_math_StringFormat_G)
eFormat = rtl_math_StringFormat_E;
else if (eFormat == rtl_math_StringFormat_G2)
eFormat = rtl_math_StringFormat_E2;
else if (eFormat == rtl_math_StringFormat_G1)
eFormat = rtl_math_StringFormat_E1;
}
else
{
nDecPlaces = std::max< sal_Int32 >(0, nDecPlaces - nExp - 1);
eFormat = rtl_math_StringFormat_F;
}
}
break;
default:
break;
}
// Too large values for nDecPlaces make no sense; it might also be
// rtl_math_DecimalPlaces_Max was passed with rtl_math_StringFormat_F or
// others, but we don't want to allocate/deallocate 2GB just to fill it
// with trailing '0' characters..
nDecPlaces = std::clamp<sal_Int32>(nDecPlaces, -20, 20);
sal_Int32 nDigits = nDecPlaces + 1;
if (eFormat == rtl_math_StringFormat_F)
nDigits += nExp;
// Round the number
if(nDigits >= 0)
{
fValue += nRoundVal[std::min<sal_Int32>(nDigits, 15)];
if (fValue >= 10)
{
fValue = 1.0;
nExp++;
if (eFormat == rtl_math_StringFormat_F)
nDigits++;
}
}
sal_Int32 nBuf =
(nDigits <= 0 ? std::max< sal_Int32 >(nDecPlaces, abs(nExp))
: nDigits + nDecPlaces ) + 10 + (pGroups ? abs(nDigits) * 2 : 0);
// max(nDigits) = max(nDecPlaces) + 1 + max(nExp) + 1 = 20 + 1 + 308 + 1 = 330
// max(nBuf) = max(nDigits) + max(nDecPlaces) + 10 + max(nDigits) * 2 = 330 * 3 + 20 + 10 = 1020
assert(nBuf <= 1024);
typename T::Char* pBuf = static_cast<typename T::Char*>(alloca(nBuf * sizeof(typename T::Char)));
typename T::Char * p = pBuf;
if ( bSign )
*p++ = '-';
bool bHasDec = false;
int nDecPos;
// Check for F format and number < 1
if(eFormat == rtl_math_StringFormat_F)
{
if(nExp < 0)
{
*p++ = '0';
if (nDecPlaces > 0)
{
*p++ = cDecSeparator;
bHasDec = true;
}
sal_Int32 i = (nDigits <= 0 ? nDecPlaces : -nExp - 1);
while((i--) > 0)
{
*p++ = '0';
}
nDecPos = 0;
}
else
{
nDecPos = nExp + 1;
}
}
else
{
nDecPos = 1;
}
int nGrouping = 0, nGroupSelector = 0, nGroupExceed = 0;
if (nDecPos > 1 && pGroups && pGroups[0] && cGroupSeparator)
{
while (nGrouping + pGroups[nGroupSelector] < nDecPos)
{
nGrouping += pGroups[nGroupSelector];
if (pGroups[nGroupSelector+1])
{
if (nGrouping + pGroups[nGroupSelector+1] >= nDecPos)
break; // while
++nGroupSelector;
}
else if (!nGroupExceed)
{
nGroupExceed = nGrouping;
}
}
}
// print the number
if (nDigits > 0)
{
for (int i = 0; ; i++)
{
if (i < 15) // was 16 in ancient versions, which leads to inaccuracies
{
int nDigit;
if (nDigits-1 == 0 && i > 0 && i < 14)
nDigit = floor( fValue + nCorrVal[15-i]);
else
nDigit = fValue + 1E-15;
if (nDigit >= 10)
{ // after-treatment of up-rounding to the next decade
typename T::Char* p1 = pBuf;
// Assert that no one changed the logic we rely on.
assert(!bSign || *p1 == '-');
// Do not touch leading minus sign put earlier.
if (bSign)
++p1;
assert(p1 <= p);
if (p1 == p)
{
*p++ = '1';
if (eFormat != rtl_math_StringFormat_F)
{
*p++ = cDecSeparator;
nExp++;
bHasDec = true;
}
*p++ = '0';
}
else
{
for (typename T::Char* p2 = p - 1; p2 >= p1; --p2)
{
typename T::Char cS = *p2;
if (cS == cDecSeparator)
continue;
if (cS != '9')
{
++*p2;
break;
}
*p2 = '0';
if (p2 == p1) // The number consisted of all 9s replaced to all 0s
{
if (eFormat == rtl_math_StringFormat_F)
{ // move everything to the right before inserting '1'
std::memmove(p2 + 1, p2, (p++ - p2) * sizeof(*p));
}
else
{
nExp++;
}
*p2 = '1';
}
}
*p++ = '0';
}
fValue = 0.0;
}
else
{
*p++ = nDigit + '0';
fValue = (fValue - nDigit) * 10.0;
}
}
else
{
*p++ = '0';
}
if (!--nDigits)
break; // for
if (nDecPos)
{
if(!--nDecPos)
{
*p++ = cDecSeparator;
bHasDec = true;
}
else if (nDecPos == nGrouping)
{
*p++ = cGroupSeparator;
nGrouping -= pGroups[nGroupSelector];
if (nGroupSelector && nGrouping < nGroupExceed)
--nGroupSelector;
}
}
}
}
if (!bHasDec && eFormat == rtl_math_StringFormat_F)
{ // nDecPlaces < 0 did round the value
while (--nDecPos > 0)
{ // fill before decimal point
if (nDecPos == nGrouping)
{
*p++ = cGroupSeparator;
nGrouping -= pGroups[nGroupSelector];
if (nGroupSelector && nGrouping < nGroupExceed)
--nGroupSelector;
}
*p++ = '0';
}
}
if (bEraseTrailingDecZeros && bHasDec && p > pBuf)
{
while (*(p-1) == '0')
{
p--;
}
if (*(p-1) == cDecSeparator)
p--;
}
// Print the exponent ('E', followed by '+' or '-', followed by exactly
// three digits for rtl_math_StringFormat_E). The code in
// rtl_[u]str_valueOf{Float|Double} relies on this format.
if (eFormat == rtl_math_StringFormat_E || eFormat == rtl_math_StringFormat_E2 || eFormat == rtl_math_StringFormat_E1)
{
if (p == pBuf)
*p++ = '1';
// maybe no nDigits if nDecPlaces < 0
*p++ = 'E';
if(nExp < 0)
{
nExp = -nExp;
*p++ = '-';
}
else
{
*p++ = '+';
}
if (eFormat == rtl_math_StringFormat_E || nExp >= 100)
*p++ = nExp / 100 + '0';
nExp %= 100;
if (eFormat == rtl_math_StringFormat_E || eFormat == rtl_math_StringFormat_E2 || nExp >= 10)
*p++ = nExp / 10 + '0';
*p++ = nExp % 10 + '0';
}
if (!pResultCapacity)
T::createString(pResult, pBuf, p - pBuf);
else
T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf, p - pBuf);
}
}
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()
{
doubleToString< StringTraits >(
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()
{
doubleToString< UStringTraits >(
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 == CharT(' ') || *p0 == CharT('\t')))
{
++p0;
}
bool bSign;
bool explicitSign = false;
if (p0 != pEnd && *p0 == CharT('-'))
{
bSign = true;
explicitSign = true;
++p0;
}
else
{
bSign = false;
if (p0 != pEnd && *p0 == CharT('+'))
{
explicitSign = true;
++p0;
}
}
CharT const * p = p0;
bool bDone = false;
// #i112652# XMLSchema-2
if ((pEnd - p) >= 3)
{
if (!explicitSign && (CharT('N') == p[0]) && (CharT('a') == p[1])
&& (CharT('N') == p[2]))
{
p += 3;
fVal = std::numeric_limits<double>::quiet_NaN();
bDone = true;
}
else if ((CharT('I') == p[0]) && (CharT('N') == p[1])
&& (CharT('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 == CharT('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 == CharT('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 == CharT('E') || *p == CharT('e')))
{
buf[bufpos] = 'E';
bufmap[bufpos] = p;
++bufpos;
++p;
if (p != pEnd && *p == CharT('-'))
{
buf[bufpos] = '-';
bufmap[bufpos] = p;
++bufpos;
++p;
}
else if (p != pEnd && *p == CharT('+'))
++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] == CharT('#')
&& p[-1] == cDecSeparator && p[-2] == CharT('1'))
{
if (pEnd - p >= 4 && p[1] == CharT('I') && p[2] == CharT('N')
&& p[3] == CharT('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] == CharT('N') && p[2] == CharT('A')
&& p[3] == CharT('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 >= (static_cast<sal_Int64>(1) << 52)
|| 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 < (static_cast<sal_Int64>(1) << 52))
{
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 = 2199023255552.0; // 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 = 1.0 / (16777216.0 * 16777216.0);
static const double e44 = e48 * 16.0;
if (a == b)
return true;
if (a == 0.0 || b == 0.0)
return false;
const double d = fabs(a - b);
if (!std::isfinite(d))
return false; // Nan or Inf involved
a = fabs(a);
if (d > (a * e44))
return false;
b = fabs(b);
if (d > (b * e44))
return false;
if (isRepresentableInteger(d) && isRepresentableInteger(a) && isRepresentableInteger(b))
return false; // special case for representable integers.
return (d < a * e48 && d < b * e48);
}
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()
#if defined __clang__
__attribute__((no_sanitize("float-divide-by-zero"))) // atahn(1) -> inf
#endif
{
return 0.5 * rtl_math_log1p(2.0 * fValue / (1.0-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: */
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