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+/*************************************************************************
+ *
+ * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
+ *
+ * Copyright 2000, 2010 Oracle and/or its affiliates.
+ *
+ * OpenOffice.org - a multi-platform office productivity suite
+ *
+ * This file is part of OpenOffice.org.
+ *
+ * OpenOffice.org is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser General Public License version 3
+ * only, as published by the Free Software Foundation.
+ *
+ * OpenOffice.org is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Lesser General Public License version 3 for more details
+ * (a copy is included in the LICENSE file that accompanied this code).
+ *
+ * You should have received a copy of the GNU Lesser General Public License
+ * version 3 along with OpenOffice.org. If not, see
+ * <http://www.openoffice.org/license.html>
+ * for a copy of the LGPLv3 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 ) )
+ {
+ sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("-1.#NAN");
+ 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("1"));
+ T::appendChar(pResult, pResultCapacity, &nResultOffset, cDecSeparator);
+ 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 ) )
+ {
+ sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("-1.#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("1"));
+ T::appendChar(pResult, pResultCapacity, &nResultOffset, cDecSeparator);
+ 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;
+
+ // 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;
+
+ 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);
+}
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