From 940b4d1848e8c70ab7642901a68594e8016caffc Mon Sep 17 00:00:00 2001 From: Daniel Baumann Date: Sat, 27 Apr 2024 18:51:28 +0200 Subject: Adding upstream version 1:7.0.4. Signed-off-by: Daniel Baumann --- sal/rtl/math.cxx | 1410 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1410 insertions(+) create mode 100644 sal/rtl/math.cxx (limited to 'sal/rtl/math.cxx') diff --git a/sal/rtl/math.cxx b/sal/rtl/math.cxx new file mode 100644 index 000000000..bd9d2c8a6 --- /dev/null +++ b/sal/rtl/math.cxx @@ -0,0 +1,1410 @@ +/* -*- 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 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include +#include +#include + +#include + +static int const n10Count = 16; +static 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::min() + // because -nExp = nExp + if (-nExp <= n10Count && -nExp > 0) + return n10s[1][-nExp-1]; + return pow(10.0, static_cast(nExp)); + } + if (nExp > 0) + { + if (nExp <= n10Count) + return n10s[0][nExp-1]; + + return pow(10.0, static_cast(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 sal_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(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( 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::max< sal_Int32 >(::std::min(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::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::max(std::min(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(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 bufInHeap; + std::unique_ptr 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(bufsize); + bufInHeapMap = std::make_unique(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(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(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(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(pBegin), + reinterpret_cast(pEnd), + static_cast(cDecSeparator), + static_cast(cGroupSeparator), pStatus, + reinterpret_cast(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 (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; + + double fFac = 0; + if (nDecPlaces != 0) + { + // 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; + + fFac = getN10Exp(nDecPlaces); + fValue *= fFac; + } + + switch ( eMode ) + { + case rtl_math_RoundingMode_Corrected : + { + int nExp; // exponent for correction + if ( fValue > 0.0 ) + nExp = static_cast( floor( log10( fValue ) ) ); + else + nExp = 0; + + int nIndex; + + if (nExp < 0) + nIndex = 15; + else if (nExp >= 14) + nIndex = 0; + else + nIndex = 15 - nExp; + + fValue = floor(fValue + 0.5 + nCorrVal[nIndex]); + } + 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) + 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(nExp); + + 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 = rtl_math_round(fValue, 0, rtl_math_RoundingMode_Corrected); + 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: */ -- cgit v1.2.3