| /************************************************************** |
| * |
| * 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 |
| * |
| * Unless required by applicable law or agreed to in writing, |
| * software distributed under the License is distributed on an |
| * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY |
| * KIND, either express or implied. See the License for the |
| * specific language governing permissions and limitations |
| * under the License. |
| * |
| *************************************************************/ |
| |
| |
| |
| // MARKER(update_precomp.py): autogen include statement, do not remove |
| #include "precompiled_sal.hxx" |
| |
| #include "rtl/math.h" |
| |
| #include "osl/diagnose.h" |
| #include "rtl/alloc.h" |
| #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 <float.h> |
| #include <limits.h> |
| #include <math.h> |
| #include <stdlib.h> |
| |
| |
| 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 ) |
| { |
| if ( -nExp <= n10Count ) |
| return n10s[1][-nExp-1]; |
| else |
| return pow( 10.0, static_cast<double>( nExp ) ); |
| } |
| else if ( nExp > 0 ) |
| { |
| if ( nExp <= n10Count ) |
| return n10s[0][nExp-1]; |
| else |
| return pow( 10.0, static_cast<double>( nExp ) ); |
| } |
| else // ( nExp == 0 ) |
| return 1.0; |
| } |
| |
| /** Approximation algorithm for erf for 0 < x < 0.65. */ |
| void lcl_Erf0065( double x, double& fVal ) |
| { |
| static const double pn[] = { |
| 1.12837916709551256, |
| 1.35894887627277916E-1, |
| 4.03259488531795274E-2, |
| 1.20339380863079457E-3, |
| 6.49254556481904354E-5 |
| }; |
| static const double qn[] = { |
| 1.00000000000000000, |
| 4.53767041780002545E-1, |
| 8.69936222615385890E-2, |
| 8.49717371168693357E-3, |
| 3.64915280629351082E-4 |
| }; |
| double fPSum = 0.0; |
| double fQSum = 0.0; |
| double fXPow = 1.0; |
| for ( unsigned int i = 0; i <= 4; ++i ) |
| { |
| fPSum += pn[i]*fXPow; |
| fQSum += qn[i]*fXPow; |
| fXPow *= x*x; |
| } |
| fVal = x * fPSum / fQSum; |
| } |
| |
| /** Approximation algorithm for erfc for 0.65 < x < 6.0. */ |
| void lcl_Erfc0600( double x, double& fVal ) |
| { |
| double fPSum = 0.0; |
| double fQSum = 0.0; |
| double fXPow = 1.0; |
| const double *pn; |
| const double *qn; |
| |
| if ( x < 2.2 ) |
| { |
| static const double pn22[] = { |
| 9.99999992049799098E-1, |
| 1.33154163936765307, |
| 8.78115804155881782E-1, |
| 3.31899559578213215E-1, |
| 7.14193832506776067E-2, |
| 7.06940843763253131E-3 |
| }; |
| static const double qn22[] = { |
| 1.00000000000000000, |
| 2.45992070144245533, |
| 2.65383972869775752, |
| 1.61876655543871376, |
| 5.94651311286481502E-1, |
| 1.26579413030177940E-1, |
| 1.25304936549413393E-2 |
| }; |
| pn = pn22; |
| qn = qn22; |
| } |
| else /* if ( x < 6.0 ) this is true, but the compiler does not know */ |
| { |
| static const double pn60[] = { |
| 9.99921140009714409E-1, |
| 1.62356584489366647, |
| 1.26739901455873222, |
| 5.81528574177741135E-1, |
| 1.57289620742838702E-1, |
| 2.25716982919217555E-2 |
| }; |
| static const double qn60[] = { |
| 1.00000000000000000, |
| 2.75143870676376208, |
| 3.37367334657284535, |
| 2.38574194785344389, |
| 1.05074004614827206, |
| 2.78788439273628983E-1, |
| 4.00072964526861362E-2 |
| }; |
| pn = pn60; |
| qn = qn60; |
| } |
| |
| for ( unsigned int i = 0; i < 6; ++i ) |
| { |
| fPSum += pn[i]*fXPow; |
| fQSum += qn[i]*fXPow; |
| fXPow *= x; |
| } |
| fQSum += qn[6]*fXPow; |
| fVal = exp( -1.0*x*x )* fPSum / fQSum; |
| } |
| |
| /** Approximation algorithm for erfc for 6.0 < x < 26.54 (but used for all |
| x > 6.0). */ |
| void lcl_Erfc2654( double x, double& fVal ) |
| { |
| static const double pn[] = { |
| 5.64189583547756078E-1, |
| 8.80253746105525775, |
| 3.84683103716117320E1, |
| 4.77209965874436377E1, |
| 8.08040729052301677 |
| }; |
| static const double qn[] = { |
| 1.00000000000000000, |
| 1.61020914205869003E1, |
| 7.54843505665954743E1, |
| 1.12123870801026015E2, |
| 3.73997570145040850E1 |
| }; |
| |
| double fPSum = 0.0; |
| double fQSum = 0.0; |
| double fXPow = 1.0; |
| |
| for ( unsigned int i = 0; i <= 4; ++i ) |
| { |
| fPSum += pn[i]*fXPow; |
| fQSum += qn[i]*fXPow; |
| fXPow /= x*x; |
| } |
| fVal = exp(-1.0*x*x)*fPSum / (x*fQSum); |
| } |
| |
| namespace { |
| |
| double const nKorrVal[] = { |
| 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 inline void createString(rtl_String ** pString, |
| sal_Char const * pChars, sal_Int32 nLen) |
| { |
| rtl_string_newFromStr_WithLength(pString, pChars, nLen); |
| } |
| |
| static inline void createBuffer(rtl_String ** pBuffer, |
| sal_Int32 * pCapacity) |
| { |
| rtl_string_new_WithLength(pBuffer, *pCapacity); |
| } |
| |
| static inline void appendChar(rtl_String ** pBuffer, sal_Int32 * pCapacity, |
| sal_Int32 * pOffset, sal_Char cChar) |
| { |
| rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, &cChar, 1); |
| ++*pOffset; |
| } |
| |
| static inline void appendChars(rtl_String ** pBuffer, sal_Int32 * pCapacity, |
| sal_Int32 * pOffset, sal_Char const * pChars, |
| sal_Int32 nLen) |
| { |
| rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen); |
| *pOffset += nLen; |
| } |
| |
| static inline void appendAscii(rtl_String ** pBuffer, sal_Int32 * pCapacity, |
| sal_Int32 * pOffset, sal_Char const * pStr, |
| sal_Int32 nLen) |
| { |
| rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pStr, nLen); |
| *pOffset += nLen; |
| } |
| }; |
| |
| struct UStringTraits |
| { |
| typedef sal_Unicode Char; |
| |
| typedef rtl_uString String; |
| |
| static inline void createString(rtl_uString ** pString, |
| sal_Unicode const * pChars, sal_Int32 nLen) |
| { |
| rtl_uString_newFromStr_WithLength(pString, pChars, nLen); |
| } |
| |
| static inline void createBuffer(rtl_uString ** pBuffer, |
| sal_Int32 * pCapacity) |
| { |
| rtl_uString_new_WithLength(pBuffer, *pCapacity); |
| } |
| |
| static inline void appendChar(rtl_uString ** pBuffer, sal_Int32 * pCapacity, |
| sal_Int32 * pOffset, sal_Unicode cChar) |
| { |
| rtl_uStringbuffer_insert(pBuffer, pCapacity, *pOffset, &cChar, 1); |
| ++*pOffset; |
| } |
| |
| static inline void appendChars(rtl_uString ** pBuffer, |
| sal_Int32 * pCapacity, sal_Int32 * pOffset, |
| sal_Unicode const * pChars, sal_Int32 nLen) |
| { |
| rtl_uStringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen); |
| *pOffset += nLen; |
| } |
| |
| static inline void appendAscii(rtl_uString ** pBuffer, |
| sal_Int32 * pCapacity, sal_Int32 * pOffset, |
| sal_Char const * pStr, sal_Int32 nLen) |
| { |
| rtl_uStringbuffer_insert_ascii(pBuffer, pCapacity, *pOffset, pStr, |
| nLen); |
| *pOffset += nLen; |
| } |
| }; |
| |
| |
| // Solaris C++ 5.2 compiler has problems when "StringT ** pResult" is |
| // "typename T::String ** pResult" instead: |
| template< typename T, typename StringT > |
| inline void doubleToString(StringT ** 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 = rtl::math::isSignBitSet( fValue ); |
| if( bSign ) |
| fValue = -fValue; |
| |
| if ( rtl::math::isNan( fValue ) ) |
| { |
| // #i112652# XMLSchema-2 |
| sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("NaN"); |
| if (pResultCapacity == 0) |
| { |
| 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 || rtl::math::isInf( fValue ) ) |
| { |
| // #i112652# XMLSchema-2 |
| sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("-INF"); |
| if (pResultCapacity == 0) |
| { |
| 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; |
| } |
| |
| // find the exponent |
| int nExp = 0; |
| if ( fValue > 0.0 ) |
| { |
| nExp = static_cast< int >( floor( log10( fValue ) ) ); |
| fValue /= getN10Exp( nExp ); |
| } |
| |
| switch ( eFormat ) |
| { |
| case rtl_math_StringFormat_Automatic : |
| { // E or F depending on exponent magnitude |
| int nPrec; |
| if ( nExp <= -15 || nExp >= 15 ) // #58531# was <-16, >16 |
| { |
| 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 : |
| { // 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 ); |
| eFormat = rtl_math_StringFormat_E; |
| } |
| else |
| { |
| nDecPlaces = std::max< sal_Int32 >( 0, nDecPlaces - nExp - 1 ); |
| eFormat = rtl_math_StringFormat_F; |
| } |
| } |
| break; |
| default: |
| break; |
| } |
| |
| sal_Int32 nDigits = nDecPlaces + 1; |
| |
| if( eFormat == rtl_math_StringFormat_F ) |
| nDigits += nExp; |
| |
| // Round the number |
| if( nDigits >= 0 ) |
| { |
| if( ( fValue += nRoundVal[ nDigits > 15 ? 15 : nDigits ] ) >= 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 = reinterpret_cast< typename T::Char * >( |
| rtl_allocateMemory(nBuf * sizeof (typename T::Char))); |
| OSL_ENSURE(pBuf != 0, "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 ) |
| { |
| int nDigit; |
| if (nDigits-1 == 0 && i > 0 && i < 14) |
| nDigit = static_cast< int >( floor( fValue |
| + nKorrVal[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) |
| { |
| p = pBuf; |
| 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 (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) |
| { |
| 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). The code in rtl_[u]str_valueOf{Float|Double} relies on |
| // this format. |
| if( eFormat == rtl_math_StringFormat_E ) |
| { |
| 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 (nExp >= 100 ) |
| *p++ = static_cast< typename T::Char >( |
| nExp / 100 + static_cast< typename T::Char >('0') ); |
| nExp %= 100; |
| *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 == 0) |
| T::createString(pResult, pBuf, p - pBuf); |
| else |
| T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf, |
| p - pBuf); |
| |
| if ( pBuf != &aBuf[0] ) |
| rtl_freeMemory(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, |
| sal_Char cDecSeparator, |
| sal_Int32 const * pGroups, |
| sal_Char cGroupSeparator, |
| sal_Bool bEraseTrailingDecZeros) |
| SAL_THROW_EXTERN_C() |
| { |
| doubleToString< StringTraits, StringTraits::String >( |
| 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, UStringTraits::String >( |
| pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces, |
| cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros); |
| } |
| |
| |
| namespace { |
| |
| // if nExp * 10 + nAdd would result in overflow |
| inline bool long10Overflow( long& nExp, int nAdd ) |
| { |
| if ( nExp > (LONG_MAX/10) |
| || (nExp == (LONG_MAX/10) && nAdd > (LONG_MAX%10)) ) |
| { |
| nExp = LONG_MAX; |
| return true; |
| } |
| return false; |
| } |
| |
| // We are only concerned about ASCII arabic numerical digits here |
| template< typename CharT > |
| inline bool isDigit( CharT c ) |
| { |
| return 0x30 <= c && c <= 0x39; |
| } |
| |
| template< typename CharT > |
| inline 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 (3 >= (pEnd - p)) |
| { |
| 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 |
| { |
| // leading zeros and group separators may be safely ignored |
| while (p != pEnd && (*p == CharT('0') || *p == cGroupSeparator)) |
| ++p; |
| |
| long nValExp = 0; // carry along exponent of mantissa |
| |
| // integer part of mantissa |
| for (; p != pEnd; ++p) |
| { |
| CharT c = *p; |
| if (isDigit(c)) |
| { |
| fVal = fVal * 10.0 + static_cast< double >( c - CharT('0') ); |
| ++nValExp; |
| } |
| else if (c != cGroupSeparator) |
| break; |
| } |
| |
| // fraction part of mantissa |
| if (p != pEnd && *p == cDecSeparator) |
| { |
| ++p; |
| double fFrac = 0.0; |
| long nFracExp = 0; |
| while (p != pEnd && *p == CharT('0')) |
| { |
| --nFracExp; |
| ++p; |
| } |
| if ( nValExp == 0 ) |
| nValExp = nFracExp - 1; // no integer part => fraction exponent |
| // one decimal digit needs ld(10) ~= 3.32 bits |
| static const int nSigs = (DBL_MANT_DIG / 3) + 1; |
| int nDigs = 0; |
| for (; p != pEnd; ++p) |
| { |
| CharT c = *p; |
| if (!isDigit(c)) |
| break; |
| if ( nDigs < nSigs ) |
| { // further digits (more than nSigs) don't have any |
| // significance |
| fFrac = fFrac * 10.0 + static_cast<double>(c - CharT('0')); |
| --nFracExp; |
| ++nDigs; |
| } |
| } |
| if ( fFrac != 0.0 ) |
| fVal += rtl::math::pow10Exp( fFrac, nFracExp ); |
| else if ( nValExp < 0 ) |
| nValExp = 0; // no digit other than 0 after decimal point |
| } |
| |
| if ( nValExp > 0 ) |
| --nValExp; // started with offset +1 at the first mantissa digit |
| |
| // Exponent |
| if (p != p0 && p != pEnd && (*p == CharT('E') || *p == CharT('e'))) |
| { |
| ++p; |
| bool bExpSign; |
| if (p != pEnd && *p == CharT('-')) |
| { |
| bExpSign = true; |
| ++p; |
| } |
| else |
| { |
| bExpSign = false; |
| if (p != pEnd && *p == CharT('+')) |
| ++p; |
| } |
| if ( fVal == 0.0 ) |
| { // no matter what follows, zero stays zero, but carry on the |
| // offset |
| while (p != pEnd && isDigit(*p)) |
| ++p; |
| } |
| else |
| { |
| bool bOverFlow = false; |
| long nExp = 0; |
| for (; p != pEnd; ++p) |
| { |
| CharT c = *p; |
| if (!isDigit(c)) |
| break; |
| int i = c - CharT('0'); |
| if ( long10Overflow( nExp, i ) ) |
| bOverFlow = true; |
| else |
| nExp = nExp * 10 + i; |
| } |
| if ( nExp ) |
| { |
| if ( bExpSign ) |
| nExp = -nExp; |
| long nAllExp = ( bOverFlow ? 0 : nExp + nValExp ); |
| if ( nAllExp > DBL_MAX_10_EXP || (bOverFlow && !bExpSign) ) |
| { // overflow |
| fVal = HUGE_VAL; |
| eStatus = rtl_math_ConversionStatus_OutOfRange; |
| } |
| else if ((nAllExp < DBL_MIN_10_EXP) || |
| (bOverFlow && bExpSign) ) |
| { // underflow |
| fVal = 0.0; |
| eStatus = rtl_math_ConversionStatus_OutOfRange; |
| } |
| else if ( nExp > DBL_MAX_10_EXP || nExp < DBL_MIN_10_EXP ) |
| { // compensate exponents |
| fVal = rtl::math::pow10Exp( fVal, -nValExp ); |
| fVal = rtl::math::pow10Exp( fVal, nAllExp ); |
| } |
| else |
| fVal = rtl::math::pow10Exp( fVal, nExp ); // normal |
| } |
| } |
| } |
| 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 && isDigit(*p)) |
| ++p; |
| } |
| 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 && isDigit(*p)) |
| ++p; |
| } |
| } |
| } |
| |
| // 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 != 0) |
| *pStatus = eStatus; |
| if (pParsedEnd != 0) |
| *pParsedEnd = p == p0 ? pBegin : p; |
| |
| return fVal; |
| } |
| |
| } |
| |
| double SAL_CALL rtl_math_stringToDouble(sal_Char const * pBegin, |
| sal_Char const * pEnd, |
| sal_Char cDecSeparator, |
| sal_Char cGroupSeparator, |
| rtl_math_ConversionStatus * pStatus, |
| sal_Char const ** pParsedEnd) |
| SAL_THROW_EXTERN_C() |
| { |
| return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus, |
| 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; |
| |
| // sign adjustment |
| bool bSign = rtl::math::isSignBitSet( 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; |
| } |
| //else //! uninitialized fFac, not needed |
| |
| switch ( eMode ) |
| { |
| case rtl_math_RoundingMode_Corrected : |
| { |
| int nExp; // exponent for correction |
| if ( fValue > 0.0 ) |
| nExp = static_cast<int>( floor( log10( fValue ) ) ); |
| else |
| nExp = 0; |
| int nIndex = 15 - nExp; |
| if ( nIndex > 15 ) |
| nIndex = 15; |
| else if ( nIndex <= 1 ) |
| nIndex = 0; |
| fValue = floor( fValue + 0.5 + nKorrVal[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() |
| { |
| if (fValue == 0.0 || fValue == HUGE_VAL || !::rtl::math::isFinite( fValue)) |
| // We don't handle these conditions. Bail out. |
| return fValue; |
| |
| double fOrigValue = fValue; |
| |
| bool bSign = ::rtl::math::isSignBitSet( fValue); |
| if (bSign) |
| fValue = -fValue; |
| |
| 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 (!rtl::math::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 (!rtl::math::isFinite( fValue)) |
| return fOrigValue; |
| |
| return bSign ? -fValue : fValue; |
| } |
| |
| |
| double SAL_CALL rtl_math_expm1( double fValue ) SAL_THROW_EXTERN_C() |
| { |
| double fe = exp( fValue ); |
| if (fe == 1.0) |
| return fValue; |
| if (fe-1.0 == -1.0) |
| return -1.0; |
| return (fe-1.0) * fValue / log(fe); |
| } |
| |
| |
| double SAL_CALL rtl_math_log1p( double fValue ) SAL_THROW_EXTERN_C() |
| { |
| // Use volatile because a compiler may be too smart "optimizing" the |
| // condition such that in certain cases the else path was called even if |
| // (fp==1.0) was true, where the term (fp-1.0) then resulted in 0.0 and |
| // hence the entire expression resulted in NaN. |
| // Happened with g++ 3.4.1 and an input value of 9.87E-18 |
| volatile double fp = 1.0 + fValue; |
| if (fp == 1.0) |
| return fValue; |
| else |
| return log(fp) * fValue / (fp-1.0); |
| } |
| |
| |
| double SAL_CALL rtl_math_atanh( double fValue ) SAL_THROW_EXTERN_C() |
| { |
| return 0.5 * rtl_math_log1p( 2.0 * fValue / (1.0-fValue) ); |
| } |
| |
| |
| /** Parent error function (erf) that calls different algorithms based on the |
| value of x. It takes care of cases where x is negative as erf is an odd |
| function i.e. erf(-x) = -erf(x). |
| |
| Kramer, W., and Blomquist, F., 2000, Algorithms with Guaranteed Error Bounds |
| for the Error Function and the Complementary Error Function |
| |
| http://www.math.uni-wuppertal.de/wrswt/literatur_en.html |
| |
| @author Kohei Yoshida <kohei@openoffice.org> |
| |
| @see #i55735# |
| */ |
| double SAL_CALL rtl_math_erf( double x ) SAL_THROW_EXTERN_C() |
| { |
| if( x == 0.0 ) |
| return 0.0; |
| |
| bool bNegative = false; |
| if ( x < 0.0 ) |
| { |
| x = fabs( x ); |
| bNegative = true; |
| } |
| |
| double fErf = 1.0; |
| if ( x < 1.0e-10 ) |
| fErf = (double) (x*1.1283791670955125738961589031215452L); |
| else if ( x < 0.65 ) |
| lcl_Erf0065( x, fErf ); |
| else |
| fErf = 1.0 - rtl_math_erfc( x ); |
| |
| if ( bNegative ) |
| fErf *= -1.0; |
| |
| return fErf; |
| } |
| |
| |
| /** Parent complementary error function (erfc) that calls different algorithms |
| based on the value of x. It takes care of cases where x is negative as erfc |
| satisfies relationship erfc(-x) = 2 - erfc(x). See the comment for Erf(x) |
| for the source publication. |
| |
| @author Kohei Yoshida <kohei@openoffice.org> |
| |
| @see #i55735#, moved from module scaddins (#i97091#) |
| |
| */ |
| double SAL_CALL rtl_math_erfc( double x ) SAL_THROW_EXTERN_C() |
| { |
| if ( x == 0.0 ) |
| return 1.0; |
| |
| bool bNegative = false; |
| if ( x < 0.0 ) |
| { |
| x = fabs( x ); |
| bNegative = true; |
| } |
| |
| double fErfc = 0.0; |
| if ( x >= 0.65 ) |
| { |
| if ( x < 6.0 ) |
| lcl_Erfc0600( x, fErfc ); |
| else |
| lcl_Erfc2654( x, fErfc ); |
| } |
| else |
| fErfc = 1.0 - rtl_math_erf( x ); |
| |
| if ( bNegative ) |
| fErfc = 2.0 - fErfc; |
| |
| return fErfc; |
| } |
| |
| /** 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() |
| { |
| double fSign = 1.0; |
| if ( fX == 0.0 ) |
| return 0.0; |
| else |
| { |
| 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))); |
| else if ( fX < 1.25e7 ) |
| return fSign * log( fX + sqrt( 1.0 + fX*fX)); |
| else |
| 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; |
| } |
| else if ( fX == 1.0 ) |
| return 0.0; |
| else if ( fX < 1.1 ) |
| return rtl_math_log1p( fZ + sqrt( fZ*fZ + 2.0*fZ)); |
| else if ( fX < 1.25e7 ) |
| return log( fX + sqrt( fX*fX - 1.0)); |
| else |
| return log( 2.0*fX); |
| } |
