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office-gobmx/sal/rtl/math.cxx
Eike Rathke ecfcd99abd Check intermediate for not to be rounded value, tdf#138360 follow-up 
Change-Id: I98cc25267e7a10c34179bab50d19f49436e1c48c
Reviewed-on: https://gerrit.libreoffice.org/c/core/+/107929
Tested-by: Jenkins
Reviewed-by: Eike Rathke <erack@redhat.com>
2020-12-18 03:17:21 +01:00

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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 <o3tl/safeint.hxx>
#include <osl/diagnose.h>
#include <rtl/alloc.h>
#include <rtl/character.hxx>
#include <rtl/math.hxx>
#include <rtl/strbuf.h>
#include <rtl/string.h>
#include <rtl/ustrbuf.h>
#include <rtl/ustring.h>
#include <sal/mathconf.h>
#include <sal/types.h>
#include <algorithm>
#include <cassert>
#include <float.h>
#include <limits>
#include <limits.h>
#include <math.h>
#include <memory>
#include <stdlib.h>
#include <dtoa.h>
int const n10Count = 16;
double const n10s[2][n10Count] = {
{ 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8,
1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16 },
{ 1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8,
1e-9, 1e-10, 1e-11, 1e-12, 1e-13, 1e-14, 1e-15, 1e-16 }
};
// return pow(10.0,nExp) optimized for exponents in the interval [-16,16]
static double getN10Exp(int nExp)
{
if (nExp < 0)
{
// && -nExp > 0 necessary for std::numeric_limits<int>::min()
// because -nExp = nExp
if (-nExp <= n10Count && -nExp > 0)
return n10s[1][-nExp-1];
return pow(10.0, static_cast<double>(nExp));
}
if (nExp > 0)
{
if (nExp <= n10Count)
return n10s[0][nExp-1];
return pow(10.0, static_cast<double>(nExp));
}
return 1.0;
}
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.
const sal_Int64 kMaxInt = (static_cast< sal_Int64 >(1) << 53) - 1;
if ((eFormat == rtl_math_StringFormat_Automatic ||
eFormat == rtl_math_StringFormat_F) && fValue <= static_cast< double >(kMaxInt))
{
sal_Int64 nInt = static_cast< sal_Int64 >(fValue);
// Check the integer range again because double comparison may yield
// true within the precision range.
if (nInt <= kMaxInt && static_cast< double >(nInt) == 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));
sal_Int64 nTemp = nInt / nRounding;
int nDigit = nTemp % 10;
nTemp /= 10;
if (nDigit >= 5)
++nTemp;
nTemp *= 10;
nTemp *= nRounding;
nInt = nTemp;
nDecPlaces = 0;
}
// Max 1 sign, 16 integer digits, 15 group separators, 1 decimal
// separator, 15 decimals digits.
typename T::Char aBuf[64];
typename T::Char * pBuf = aBuf;
typename T::Char * p = pBuf;
// Backward fill.
size_t nGrouping = 0;
sal_Int32 nGroupDigits = 0;
do
{
typename T::Char nDigit = nInt % 10;
nInt /= 10;
*p++ = nDigit + '0';
if (pGroups && pGroups[nGrouping] == ++nGroupDigits && nInt > 0 && cGroupSeparator)
{
*p++ = cGroupSeparator;
if (pGroups[nGrouping+1])
++nGrouping;
nGroupDigits = 0;
}
}
while (nInt > 0);
if (bSign)
*p++ = '-';
// Reverse buffer content.
sal_Int32 n = (p - pBuf) / 2;
for (sal_Int32 i=0; i < n; ++i)
{
::std::swap( pBuf[i], p[-i-1]);
}
// Append decimals.
if (nDecPlaces > 0)
{
*p++ = cDecSeparator;
while (nDecPlaces--)
*p++ = '0';
}
if (!pResultCapacity)
T::createString(pResult, pBuf, p - pBuf);
else
T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf, p - pBuf);
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++;
}
}
static sal_Int32 const nBufMax = 256;
typename T::Char aBuf[nBufMax];
typename T::Char * pBuf;
sal_Int32 nBuf = static_cast< sal_Int32 >
(nDigits <= 0 ? std::max< sal_Int32 >(nDecPlaces, abs(nExp))
: nDigits + nDecPlaces ) + 10 + (pGroups ? abs(nDigits) * 2 : 0);
if (nBuf > nBufMax)
{
pBuf = static_cast< typename T::Char * >(
malloc(nBuf * sizeof (typename T::Char)));
OSL_ENSURE(pBuf, "Out of memory");
}
else
{
pBuf = aBuf;
}
typename T::Char * p = pBuf;
if ( bSign )
*p++ = static_cast< typename T::Char >('-');
bool bHasDec = false;
int nDecPos;
// Check for F format and number < 1
if(eFormat == rtl_math_StringFormat_F)
{
if(nExp < 0)
{
*p++ = static_cast< typename T::Char >('0');
if (nDecPlaces > 0)
{
*p++ = cDecSeparator;
bHasDec = true;
}
sal_Int32 i = (nDigits <= 0 ? nDecPlaces : -nExp - 1);
while((i--) > 0)
{
*p++ = static_cast< typename T::Char >('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 = static_cast< int >(floor( fValue + nCorrVal[15-i]));
else
nDigit = static_cast< int >(fValue + 1E-15);
if (nDigit >= 10)
{ // after-treatment of up-rounding to the next decade
sal_Int32 sLen = static_cast< long >(p-pBuf)-1;
if (sLen == -1 || (sLen == 0 && bSign))
{
// Assert that no one changed the logic we rely on.
assert(!bSign || *pBuf == static_cast< typename T::Char >('-'));
p = pBuf;
if (bSign)
++p;
if (eFormat == rtl_math_StringFormat_F)
{
*p++ = static_cast< typename T::Char >('1');
*p++ = static_cast< typename T::Char >('0');
}
else
{
*p++ = static_cast< typename T::Char >('1');
*p++ = cDecSeparator;
*p++ = static_cast< typename T::Char >('0');
nExp++;
bHasDec = true;
}
}
else
{
for (sal_Int32 j = sLen; j >= 0; j--)
{
typename T::Char cS = pBuf[j];
if (j == 0 && bSign)
{
// Do not touch leading minus sign put earlier.
assert(cS == static_cast< typename T::Char >('-'));
break; // for, this is the last character backwards.
}
if (cS != cDecSeparator)
{
if (cS != static_cast< typename T::Char >('9'))
{
pBuf[j] = ++cS;
j = -1; // break loop
}
else
{
pBuf[j] = static_cast< typename T::Char >('0');
if (j == 0 || (j == 1 && bSign))
{
if (eFormat == rtl_math_StringFormat_F)
{ // insert '1'
typename T::Char * px = p++;
while (pBuf < px)
{
*px = *(px-1);
px--;
}
pBuf[0] = static_cast< typename T::Char >('1');
}
else
{
pBuf[j] = static_cast< typename T::Char >('1');
nExp++;
}
}
}
}
}
*p++ = static_cast< typename T::Char >('0');
}
fValue = 0.0;
}
else
{
*p++ = static_cast< typename T::Char >(
nDigit + static_cast< typename T::Char >('0') );
fValue = (fValue - nDigit) * 10.0;
}
}
else
{
*p++ = static_cast< typename T::Char >('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++ = static_cast< typename T::Char >('0');
}
}
if (bEraseTrailingDecZeros && bHasDec && p > pBuf)
{
while (*(p-1) == static_cast< typename T::Char >('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++ = static_cast< typename T::Char >('1');
// maybe no nDigits if nDecPlaces < 0
*p++ = static_cast< typename T::Char >('E');
if(nExp < 0)
{
nExp = -nExp;
*p++ = static_cast< typename T::Char >('-');
}
else
{
*p++ = static_cast< typename T::Char >('+');
}
if (eFormat == rtl_math_StringFormat_E || nExp >= 100)
*p++ = static_cast< typename T::Char >(
nExp / 100 + static_cast< typename T::Char >('0') );
nExp %= 100;
if (eFormat == rtl_math_StringFormat_E || eFormat == rtl_math_StringFormat_E2 || nExp >= 10)
*p++ = static_cast< typename T::Char >(
nExp / 10 + static_cast< typename T::Char >('0') );
*p++ = static_cast< typename T::Char >(
nExp % 10 + static_cast< typename T::Char >('0') );
}
if (!pResultCapacity)
T::createString(pResult, pBuf, p - pBuf);
else
T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf, p - pBuf);
if (pBuf != &aBuf[0])
free(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;
if (p0 != pEnd && *p0 == CharT('-'))
{
bSign = true;
++p0;
}
else
{
bSign = false;
if (p0 != pEnd && *p0 == CharT('+'))
++p0;
}
CharT const * p = p0;
bool bDone = false;
// #i112652# XMLSchema-2
if ((pEnd - p) >= 3)
{
if ((CharT('N') == p[0]) && (CharT('a') == p[1])
&& (CharT('N') == p[2]))
{
p += 3;
rtl::math::setNan( &fVal );
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;
rtl::math::setNan( &fVal );
if (bSign)
{
union {
double sd;
sal_math_Double md;
} m;
m.sd = fVal;
m.md.w32_parts.msw |= 0x80000000; // create negative NaN
fVal = m.sd;
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()
{
OSL_ASSERT(nDecPlaces >= -20 && nDecPlaces <= 20);
if (!std::isfinite(fValue))
return fValue;
if (fValue == 0.0)
return fValue;
if ( nDecPlaces == 0 && eMode == rtl_math_RoundingMode_Corrected )
return std::round( 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 bSign ? -fValue : fValue;
double fFac = 0;
if (nDecPlaces != 0)
{
if (nDecPlaces > 1 && fValue > 4294967296.0)
{
// 4294967296 is 2^32 with room for at least 20 decimals, checking
// smaller values is not necessary. Lower the limit if more than 20
// decimals were to be allowed.
// 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 < nDecPlaces)
nDecPlaces = nDec;
}
/* TODO: this was without the inverse factor and determining max
* possible decimals, it could now be adjusted to be more lenient. */
// max 20 decimals, we don't have unlimited precision
// #38810# and no overflow on fValue*=fFac
if (nDecPlaces < -20 || 20 < nDecPlaces || fValue > (DBL_MAX / 1e20))
return bSign ? -fValue : fValue;
// 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 (nDecPlaces < 0)
fValue /= fFac;
else
fValue *= fFac;
}
// 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;
}
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)
{
double fResult;
::rtl::math::setNan( &fResult );
return fResult;
}
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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