Adding upstream version 1:7.0.4.upstream/1%7.0.4upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1410 insertions, 0 deletions

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 <rtl/math.h>
+
+#include <o3tl/safeint.hxx>
+#include <osl/diagnose.h>
+#include <rtl/alloc.h>
+#include <rtl/character.hxx>
+#include <rtl/math.hxx>
+#include <rtl/strbuf.h>
+#include <rtl/string.h>
+#include <rtl/ustrbuf.h>
+#include <rtl/ustring.h>
+#include <sal/mathconf.h>
+#include <sal/types.h>
+
+#include <algorithm>
+#include <cassert>
+#include <float.h>
+#include <limits>
+#include <limits.h>
+#include <math.h>
+#include <memory>
+#include <stdlib.h>
+
+#include <dtoa.h>
+
+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<int>::min()
+        // because -nExp = nExp
+        if (-nExp <= n10Count && -nExp > 0)
+            return n10s[1][-nExp-1];
+        return pow(10.0, static_cast<double>(nExp));
+    }
+    if (nExp > 0)
+    {
+        if (nExp <= n10Count)
+            return n10s[0][nExp-1];
+
+        return pow(10.0, static_cast<double>(nExp));
+    }
+    return 1.0;
+}
+
+namespace {
+
+double const nCorrVal[] = {
+    0, 9e-1, 9e-2, 9e-3, 9e-4, 9e-5, 9e-6, 9e-7, 9e-8,
+    9e-9, 9e-10, 9e-11, 9e-12, 9e-13, 9e-14, 9e-15
+};
+
+struct StringTraits
+{
+    typedef 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<double>(nInt) == fAbsValue, though we actually want
+        // this here.
+        if (nInt > kMaxInt)
+            return false;
+        double fInt = static_cast< double >(nInt);
+        return !(fInt < fAbsValue) && !(fInt > fAbsValue);
+    }
+    return false;
+}
+
+// Returns 1-based index of least significant bit in a number, or zero if number is zero
+int findFirstSetBit(unsigned n)
+{
+#if defined _WIN32
+    unsigned long pos;
+    unsigned char bNonZero = _BitScanForward(&pos, n);
+    return (bNonZero == 0) ? 0 : pos + 1;
+#else
+    return __builtin_ffs(n);
+#endif
+}
+
+/** Returns number of binary bits for fractional part of the number
+    Expects a proper non-negative double value, not +-INF, not NAN
+ */
+int getBitsInFracPart(double fAbsValue)
+{
+    assert(std::isfinite(fAbsValue) && fAbsValue >= 0.0);
+    if (fAbsValue == 0.0)
+        return 0;
+    auto pValParts = reinterpret_cast< const sal_math_Double * >(&fAbsValue);
+    int nExponent = pValParts->inf_parts.exponent - 1023;
+    if (nExponent >= 52)
+        return 0; // All bits in fraction are in integer part of the number
+    int nLeastSignificant = findFirstSetBit(pValParts->inf_parts.fraction_lo);
+    if (nLeastSignificant == 0)
+    {
+        nLeastSignificant = findFirstSetBit(pValParts->inf_parts.fraction_hi);
+        if (nLeastSignificant == 0)
+            nLeastSignificant = 53; // the implied leading 1 is the least significant
+        else
+            nLeastSignificant += 32;
+    }
+    int nFracSignificant = 53 - nLeastSignificant;
+    int nBitsInFracPart = nFracSignificant - nExponent;
+
+    return std::max(nBitsInFracPart, 0);
+}
+
+template< typename T >
+void doubleToString(typename T::String ** pResult,
+                           sal_Int32 * pResultCapacity, sal_Int32 nResultOffset,
+                           double fValue, rtl_math_StringFormat eFormat,
+                           sal_Int32 nDecPlaces, typename T::Char cDecSeparator,
+                           sal_Int32 const * pGroups,
+                           typename T::Char cGroupSeparator,
+                           bool bEraseTrailingDecZeros)
+{
+    static double const nRoundVal[] = {
+        5.0e+0, 0.5e+0, 0.5e-1, 0.5e-2, 0.5e-3, 0.5e-4, 0.5e-5, 0.5e-6,
+        0.5e-7, 0.5e-8, 0.5e-9, 0.5e-10,0.5e-11,0.5e-12,0.5e-13,0.5e-14
+    };
+
+    // sign adjustment, instead of testing for fValue<0.0 this will also fetch
+    // -0.0
+    bool bSign = std::signbit(fValue);
+
+    if (bSign)
+        fValue = -fValue;
+
+    if (std::isnan(fValue))
+    {
+        // #i112652# XMLSchema-2
+        sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("NaN");
+        if (!pResultCapacity)
+        {
+            pResultCapacity = &nCapacity;
+            T::createBuffer(pResult, pResultCapacity);
+            nResultOffset = 0;
+        }
+
+        T::appendAscii(pResult, pResultCapacity, &nResultOffset,
+                       RTL_CONSTASCII_STRINGPARAM("NaN"));
+
+        return;
+    }
+
+    bool bHuge = fValue == HUGE_VAL; // g++ 3.0.1 requires it this way...
+    if (bHuge || std::isinf(fValue))
+    {
+        // #i112652# XMLSchema-2
+        sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("-INF");
+        if (!pResultCapacity)
+        {
+            pResultCapacity = &nCapacity;
+            T::createBuffer(pResult, pResultCapacity);
+            nResultOffset = 0;
+        }
+
+        if ( bSign )
+            T::appendAscii(pResult, pResultCapacity, &nResultOffset,
+                           RTL_CONSTASCII_STRINGPARAM("-"));
+
+        T::appendAscii(pResult, pResultCapacity, &nResultOffset,
+                       RTL_CONSTASCII_STRINGPARAM("INF"));
+
+        return;
+    }
+
+    // Unfortunately the old rounding below writes 1.79769313486232e+308 for
+    // DBL_MAX and 4 subsequent nextafter(...,0).
+    static const double fB1 = std::nextafter( DBL_MAX, 0);
+    static const double fB2 = std::nextafter( fB1, 0);
+    static const double fB3 = std::nextafter( fB2, 0);
+    static const double fB4 = std::nextafter( fB3, 0);
+    if ((fValue >= fB4) && eFormat != rtl_math_StringFormat_F)
+    {
+        // 1.7976931348623157e+308 instead of rounded 1.79769313486232e+308
+        // that can't be converted back as out of range. For rounded values if
+        // they exceed range they should not be written to exchange strings or
+        // file formats.
+
+        // Writing pDig up to decimals(-1,-2) then appending one digit from
+        // pRou xor one or two digits from pSlot[].
+        constexpr char pDig[] = "7976931348623157";
+        constexpr char pRou[] = "8087931359623267";     // the only up-carry is 80
+        static_assert(SAL_N_ELEMENTS(pDig) == SAL_N_ELEMENTS(pRou), "digit count mismatch");
+        constexpr sal_Int32 nDig2 = RTL_CONSTASCII_LENGTH(pRou) - 2;
+        sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH(pRou) + 8;  // + "-1.E+308"
+        const char pSlot[5][2][3] =
+        { // rounded, not
+            "67", "57",     // DBL_MAX
+            "65", "55",
+            "53", "53",
+            "51", "51",
+            "59", "49",
+        };
+
+        if (!pResultCapacity)
+        {
+            pResultCapacity = &nCapacity;
+            T::createBuffer(pResult, pResultCapacity);
+            nResultOffset = 0;
+        }
+
+        if (bSign)
+            T::appendAscii(pResult, pResultCapacity, &nResultOffset,
+                           RTL_CONSTASCII_STRINGPARAM("-"));
+
+        nDecPlaces = std::clamp<sal_Int32>( nDecPlaces, 0, RTL_CONSTASCII_LENGTH(pRou));
+        if (nDecPlaces == 0)
+        {
+            T::appendAscii(pResult, pResultCapacity, &nResultOffset,
+                           RTL_CONSTASCII_STRINGPARAM("2"));
+        }
+        else
+        {
+            T::appendAscii(pResult, pResultCapacity, &nResultOffset,
+                           RTL_CONSTASCII_STRINGPARAM("1"));
+            T::appendChars(pResult, pResultCapacity, &nResultOffset, &cDecSeparator, 1);
+            if (nDecPlaces <= 2)
+            {
+                T::appendAscii(pResult, pResultCapacity, &nResultOffset, pRou, nDecPlaces);
+            }
+            else if (nDecPlaces <= nDig2)
+            {
+                T::appendAscii(pResult, pResultCapacity, &nResultOffset, pDig, nDecPlaces - 1);
+                T::appendAscii(pResult, pResultCapacity, &nResultOffset, pRou + nDecPlaces - 1, 1);
+            }
+            else
+            {
+                const sal_Int32 nDec = nDecPlaces - nDig2;
+                nDecPlaces -= nDec;
+                // nDec-1 is also offset into slot, rounded(1-1=0) or not(2-1=1)
+                const size_t nSlot = ((fValue < fB3) ? 4 : ((fValue < fB2) ? 3
+                            : ((fValue < fB1) ? 2 : ((fValue < DBL_MAX) ? 1 : 0))));
+
+                T::appendAscii(pResult, pResultCapacity, &nResultOffset, pDig, nDecPlaces);
+                T::appendAscii(pResult, pResultCapacity, &nResultOffset, pSlot[nSlot][nDec-1], nDec);
+            }
+        }
+        T::appendAscii(pResult, pResultCapacity, &nResultOffset,
+                       RTL_CONSTASCII_STRINGPARAM("E+308"));
+
+        return;
+    }
+
+    // Use integer representation for integer values that fit into the
+    // mantissa (1.((2^53)-1)) with a precision of 1 for highest accuracy.
+    const sal_Int64 kMaxInt = (static_cast< sal_Int64 >(1) << 53) - 1;
+    if ((eFormat == rtl_math_StringFormat_Automatic ||
+         eFormat == rtl_math_StringFormat_F) && fValue <= static_cast< double >(kMaxInt))
+    {
+        sal_Int64 nInt = static_cast< sal_Int64 >(fValue);
+        // Check the integer range again because double comparison may yield
+        // true within the precision range.
+        if (nInt <= kMaxInt && static_cast< double >(nInt) == fValue)
+        {
+            if (nDecPlaces == rtl_math_DecimalPlaces_Max)
+                nDecPlaces = 0;
+            else
+                nDecPlaces = ::std::max< sal_Int32 >(::std::min<sal_Int32>(nDecPlaces, 15), -15);
+
+            if (bEraseTrailingDecZeros && nDecPlaces > 0)
+                nDecPlaces = 0;
+
+            // Round before decimal position.
+            if (nDecPlaces < 0)
+            {
+                sal_Int64 nRounding = static_cast< sal_Int64 >(getN10Exp(-nDecPlaces - 1));
+                sal_Int64 nTemp = nInt / nRounding;
+                int nDigit = nTemp % 10;
+                nTemp /= 10;
+
+                if (nDigit >= 5)
+                    ++nTemp;
+
+                nTemp *= 10;
+                nTemp *= nRounding;
+                nInt = nTemp;
+                nDecPlaces = 0;
+            }
+
+            // Max 1 sign, 16 integer digits, 15 group separators, 1 decimal
+            // separator, 15 decimals digits.
+            typename T::Char aBuf[64];
+            typename T::Char * pBuf = aBuf;
+            typename T::Char * p = pBuf;
+
+            // Backward fill.
+            size_t nGrouping = 0;
+            sal_Int32 nGroupDigits = 0;
+            do
+            {
+                typename T::Char nDigit = nInt % 10;
+                nInt /= 10;
+                *p++ = nDigit + '0';
+                if (pGroups && pGroups[nGrouping] == ++nGroupDigits && nInt > 0 && cGroupSeparator)
+                {
+                    *p++ = cGroupSeparator;
+                    if (pGroups[nGrouping+1])
+                        ++nGrouping;
+                    nGroupDigits = 0;
+                }
+            }
+            while (nInt > 0);
+            if (bSign)
+                *p++ = '-';
+
+            // Reverse buffer content.
+            sal_Int32 n = (p - pBuf) / 2;
+            for (sal_Int32 i=0; i < n; ++i)
+            {
+                ::std::swap( pBuf[i], p[-i-1]);
+            }
+
+            // Append decimals.
+            if (nDecPlaces > 0)
+            {
+                *p++ = cDecSeparator;
+                while (nDecPlaces--)
+                    *p++ = '0';
+            }
+
+            if (!pResultCapacity)
+                T::createString(pResult, pBuf, p - pBuf);
+            else
+                T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf, p - pBuf);
+
+            return;
+        }
+    }
+
+    // find the exponent
+    int nExp = 0;
+    if ( fValue > 0.0 )
+    {
+        // Cap nExp at a small value beyond which "fValue /= N10Exp" would lose precision (or N10Exp
+        // might even be zero); that will produce output with the decimal point in a non-normalized
+        // position, but the current quality of output for such small values is probably abysmal,
+        // anyway:
+        nExp = std::max(
+            static_cast< int >(floor(log10(fValue))), std::numeric_limits<double>::min_exponent10);
+        double const N10Exp = getN10Exp(nExp);
+        assert(N10Exp != 0);
+        fValue /= N10Exp;
+    }
+
+    switch (eFormat)
+    {
+        case rtl_math_StringFormat_Automatic:
+        {   // E or F depending on exponent magnitude
+            int nPrec;
+            if (nExp <= -15 || nExp >= 15)  // was <-16, >16 in ancient versions, which leads to inaccuracies
+            {
+                nPrec = 14;
+                eFormat = rtl_math_StringFormat_E;
+            }
+            else
+            {
+                if (nExp < 14)
+                {
+                    nPrec = 15 - nExp - 1;
+                    eFormat = rtl_math_StringFormat_F;
+                }
+                else
+                {
+                    nPrec = 15;
+                    eFormat = rtl_math_StringFormat_F;
+                }
+            }
+
+            if (nDecPlaces == rtl_math_DecimalPlaces_Max)
+                nDecPlaces = nPrec;
+        }
+        break;
+
+        case rtl_math_StringFormat_G :
+        case rtl_math_StringFormat_G1 :
+        case rtl_math_StringFormat_G2 :
+        {   // G-Point, similar to sprintf %G
+            if (nDecPlaces == rtl_math_DecimalPlaces_DefaultSignificance)
+                nDecPlaces = 6;
+
+            if (nExp < -4 || nExp >= nDecPlaces)
+            {
+                nDecPlaces = std::max< sal_Int32 >(1, nDecPlaces - 1);
+
+                if (eFormat == rtl_math_StringFormat_G)
+                    eFormat = rtl_math_StringFormat_E;
+                else if (eFormat == rtl_math_StringFormat_G2)
+                    eFormat = rtl_math_StringFormat_E2;
+                else if (eFormat == rtl_math_StringFormat_G1)
+                    eFormat = rtl_math_StringFormat_E1;
+            }
+            else
+            {
+                nDecPlaces = std::max< sal_Int32 >(0, nDecPlaces - nExp - 1);
+                eFormat = rtl_math_StringFormat_F;
+            }
+        }
+        break;
+        default:
+        break;
+    }
+
+    // Too large values for nDecPlaces make no sense; it might also be
+    // rtl_math_DecimalPlaces_Max was passed with rtl_math_StringFormat_F or
+    // others, but we don't want to allocate/deallocate 2GB just to fill it
+    // with trailing '0' characters..
+    nDecPlaces = std::max<sal_Int32>(std::min<sal_Int32>(nDecPlaces, 20), -20);
+
+    sal_Int32 nDigits = nDecPlaces + 1;
+
+    if (eFormat == rtl_math_StringFormat_F)
+        nDigits += nExp;
+
+    // Round the number
+    if(nDigits >= 0)
+    {
+        fValue += nRoundVal[std::min<sal_Int32>(nDigits, 15)];
+        if (fValue >= 10)
+        {
+            fValue = 1.0;
+            nExp++;
+
+            if (eFormat == rtl_math_StringFormat_F)
+                nDigits++;
+        }
+    }
+
+    static sal_Int32 const nBufMax = 256;
+    typename T::Char aBuf[nBufMax];
+    typename T::Char * pBuf;
+    sal_Int32 nBuf = static_cast< sal_Int32 >
+        (nDigits <= 0 ? std::max< sal_Int32 >(nDecPlaces, abs(nExp))
+          : nDigits + nDecPlaces ) + 10 + (pGroups ? abs(nDigits) * 2 : 0);
+
+    if (nBuf > nBufMax)
+    {
+        pBuf = static_cast< typename T::Char * >(
+            malloc(nBuf * sizeof (typename T::Char)));
+        OSL_ENSURE(pBuf, "Out of memory");
+    }
+    else
+    {
+        pBuf = aBuf;
+    }
+
+    typename T::Char * p = pBuf;
+    if ( bSign )
+        *p++ = static_cast< typename T::Char >('-');
+
+    bool bHasDec = false;
+
+    int nDecPos;
+    // Check for F format and number < 1
+    if(eFormat == rtl_math_StringFormat_F)
+    {
+        if(nExp < 0)
+        {
+            *p++ = static_cast< typename T::Char >('0');
+            if (nDecPlaces > 0)
+            {
+                *p++ = cDecSeparator;
+                bHasDec = true;
+            }
+
+            sal_Int32 i = (nDigits <= 0 ? nDecPlaces : -nExp - 1);
+
+            while((i--) > 0)
+            {
+                *p++ = static_cast< typename T::Char >('0');
+            }
+
+            nDecPos = 0;
+        }
+        else
+        {
+            nDecPos = nExp + 1;
+        }
+    }
+    else
+    {
+        nDecPos = 1;
+    }
+
+    int nGrouping = 0, nGroupSelector = 0, nGroupExceed = 0;
+    if (nDecPos > 1 && pGroups && pGroups[0] && cGroupSeparator)
+    {
+        while (nGrouping + pGroups[nGroupSelector] < nDecPos)
+        {
+            nGrouping += pGroups[nGroupSelector];
+            if (pGroups[nGroupSelector+1])
+            {
+                if (nGrouping + pGroups[nGroupSelector+1] >= nDecPos)
+                    break;  // while
+
+                ++nGroupSelector;
+            }
+            else if (!nGroupExceed)
+            {
+                nGroupExceed = nGrouping;
+            }
+        }
+    }
+
+    // print the number
+    if (nDigits > 0)
+    {
+        for (int i = 0; ; i++)
+        {
+            if (i < 15)     // was 16 in ancient versions, which leads to inaccuracies
+            {
+                int nDigit;
+                if (nDigits-1 == 0 && i > 0 && i < 14)
+                    nDigit = static_cast< int >(floor( fValue + nCorrVal[15-i]));
+                else
+                    nDigit = static_cast< int >(fValue + 1E-15);
+
+                if (nDigit >= 10)
+                {   // after-treatment of up-rounding to the next decade
+                    sal_Int32 sLen = static_cast< long >(p-pBuf)-1;
+                    if (sLen == -1 || (sLen == 0 && bSign))
+                    {
+                        // Assert that no one changed the logic we rely on.
+                        assert(!bSign || *pBuf == static_cast< typename T::Char >('-'));
+                        p = pBuf;
+                        if (bSign)
+                            ++p;
+                        if (eFormat == rtl_math_StringFormat_F)
+                        {
+                            *p++ = static_cast< typename T::Char >('1');
+                            *p++ = static_cast< typename T::Char >('0');
+                        }
+                        else
+                        {
+                            *p++ = static_cast< typename T::Char >('1');
+                            *p++ = cDecSeparator;
+                            *p++ = static_cast< typename T::Char >('0');
+                            nExp++;
+                            bHasDec = true;
+                        }
+                    }
+                    else
+                    {
+                        for (sal_Int32 j = sLen; j >= 0; j--)
+                        {
+                            typename T::Char cS = pBuf[j];
+                            if (j == 0 && bSign)
+                            {
+                                // Do not touch leading minus sign put earlier.
+                                assert(cS == static_cast< typename T::Char >('-'));
+                                break;  // for, this is the last character backwards.
+                            }
+                            if (cS != cDecSeparator)
+                            {
+                                if (cS != static_cast< typename T::Char >('9'))
+                                {
+                                    pBuf[j] = ++cS;
+                                    j = -1;                 // break loop
+                                }
+                                else
+                                {
+                                    pBuf[j] = static_cast< typename T::Char >('0');
+                                    if (j == 0 || (j == 1 && bSign))
+                                    {
+                                        if (eFormat == rtl_math_StringFormat_F)
+                                        {   // insert '1'
+                                            typename T::Char * px = p++;
+                                            while (pBuf < px)
+                                            {
+                                                *px = *(px-1);
+                                                px--;
+                                            }
+
+                                            pBuf[0] = static_cast< typename T::Char >('1');
+                                        }
+                                        else
+                                        {
+                                            pBuf[j] = static_cast< typename T::Char >('1');
+                                            nExp++;
+                                        }
+                                    }
+                                }
+                            }
+                        }
+
+                        *p++ = static_cast< typename T::Char >('0');
+                    }
+                    fValue = 0.0;
+                }
+                else
+                {
+                    *p++ = static_cast< typename T::Char >(
+                        nDigit + static_cast< typename T::Char >('0') );
+                    fValue = (fValue - nDigit) * 10.0;
+                }
+            }
+            else
+            {
+                *p++ = static_cast< typename T::Char >('0');
+            }
+
+            if (!--nDigits)
+                break;  // for
+
+            if (nDecPos)
+            {
+                if(!--nDecPos)
+                {
+                    *p++ = cDecSeparator;
+                    bHasDec = true;
+                }
+                else if (nDecPos == nGrouping)
+                {
+                    *p++ = cGroupSeparator;
+                    nGrouping -= pGroups[nGroupSelector];
+
+                    if (nGroupSelector && nGrouping < nGroupExceed)
+                        --nGroupSelector;
+                }
+            }
+        }
+    }
+
+    if (!bHasDec && eFormat == rtl_math_StringFormat_F)
+    {   // nDecPlaces < 0 did round the value
+        while (--nDecPos > 0)
+        {   // fill before decimal point
+            if (nDecPos == nGrouping)
+            {
+                *p++ = cGroupSeparator;
+                nGrouping -= pGroups[nGroupSelector];
+
+                if (nGroupSelector && nGrouping < nGroupExceed)
+                    --nGroupSelector;
+            }
+
+            *p++ = static_cast< typename T::Char >('0');
+        }
+    }
+
+    if (bEraseTrailingDecZeros && bHasDec && p > pBuf)
+    {
+        while (*(p-1) == static_cast< typename T::Char >('0'))
+        {
+            p--;
+        }
+
+        if (*(p-1) == cDecSeparator)
+            p--;
+    }
+
+    // Print the exponent ('E', followed by '+' or '-', followed by exactly
+    // three digits for rtl_math_StringFormat_E).  The code in
+    // rtl_[u]str_valueOf{Float|Double} relies on this format.
+    if (eFormat == rtl_math_StringFormat_E || eFormat == rtl_math_StringFormat_E2 || eFormat == rtl_math_StringFormat_E1)
+    {
+        if (p == pBuf)
+            *p++ = static_cast< typename T::Char >('1');
+                // maybe no nDigits if nDecPlaces < 0
+
+        *p++ = static_cast< typename T::Char >('E');
+        if(nExp < 0)
+        {
+            nExp = -nExp;
+            *p++ = static_cast< typename T::Char >('-');
+        }
+        else
+        {
+            *p++ = static_cast< typename T::Char >('+');
+        }
+
+        if (eFormat == rtl_math_StringFormat_E || nExp >= 100)
+            *p++ = static_cast< typename T::Char >(
+                nExp / 100 + static_cast< typename T::Char >('0') );
+
+        nExp %= 100;
+
+        if (eFormat == rtl_math_StringFormat_E || eFormat == rtl_math_StringFormat_E2 || nExp >= 10)
+            *p++ = static_cast< typename T::Char >(
+                nExp / 10 + static_cast< typename T::Char >('0') );
+
+        *p++ = static_cast< typename T::Char >(
+            nExp % 10 + static_cast< typename T::Char >('0') );
+    }
+
+    if (!pResultCapacity)
+        T::createString(pResult, pBuf, p - pBuf);
+    else
+        T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf, p - pBuf);
+
+    if (pBuf != &aBuf[0])
+        free(pBuf);
+}
+
+}
+
+void SAL_CALL rtl_math_doubleToString(rtl_String ** pResult,
+                                      sal_Int32 * pResultCapacity,
+                                      sal_Int32 nResultOffset, double fValue,
+                                      rtl_math_StringFormat eFormat,
+                                      sal_Int32 nDecPlaces,
+                                      char cDecSeparator,
+                                      sal_Int32 const * pGroups,
+                                      char cGroupSeparator,
+                                      sal_Bool bEraseTrailingDecZeros)
+    SAL_THROW_EXTERN_C()
+{
+    doubleToString< StringTraits >(
+        pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces,
+        cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros);
+}
+
+void SAL_CALL rtl_math_doubleToUString(rtl_uString ** pResult,
+                                       sal_Int32 * pResultCapacity,
+                                       sal_Int32 nResultOffset, double fValue,
+                                       rtl_math_StringFormat eFormat,
+                                       sal_Int32 nDecPlaces,
+                                       sal_Unicode cDecSeparator,
+                                       sal_Int32 const * pGroups,
+                                       sal_Unicode cGroupSeparator,
+                                       sal_Bool bEraseTrailingDecZeros)
+    SAL_THROW_EXTERN_C()
+{
+    doubleToString< UStringTraits >(
+        pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces,
+        cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros);
+}
+
+namespace {
+
+template< typename CharT >
+double stringToDouble(CharT const * pBegin, CharT const * pEnd,
+                             CharT cDecSeparator, CharT cGroupSeparator,
+                             rtl_math_ConversionStatus * pStatus,
+                             CharT const ** pParsedEnd)
+{
+    double fVal = 0.0;
+    rtl_math_ConversionStatus eStatus = rtl_math_ConversionStatus_Ok;
+
+    CharT const * p0 = pBegin;
+    while (p0 != pEnd && (*p0 == CharT(' ') || *p0 == CharT('\t')))
+    {
+        ++p0;
+    }
+
+    bool bSign;
+    if (p0 != pEnd && *p0 == CharT('-'))
+    {
+        bSign = true;
+        ++p0;
+    }
+    else
+    {
+        bSign = false;
+        if (p0 != pEnd && *p0 == CharT('+'))
+            ++p0;
+    }
+
+    CharT const * p = p0;
+    bool bDone = false;
+
+    // #i112652# XMLSchema-2
+    if ((pEnd - p) >= 3)
+    {
+        if ((CharT('N') == p[0]) && (CharT('a') == p[1])
+            && (CharT('N') == p[2]))
+        {
+            p += 3;
+            rtl::math::setNan( &fVal );
+            bDone = true;
+        }
+        else if ((CharT('I') == p[0]) && (CharT('N') == p[1])
+                 && (CharT('F') == p[2]))
+        {
+            p += 3;
+            fVal = HUGE_VAL;
+            eStatus = rtl_math_ConversionStatus_OutOfRange;
+            bDone = true;
+        }
+    }
+
+    if (!bDone) // do not recognize e.g. NaN1.23
+    {
+        std::unique_ptr<char[]> bufInHeap;
+        std::unique_ptr<const CharT * []> bufInHeapMap;
+        constexpr int bufOnStackSize = 256;
+        char bufOnStack[bufOnStackSize];
+        const CharT* bufOnStackMap[bufOnStackSize];
+        char* buf = bufOnStack;
+        const CharT** bufmap = bufOnStackMap;
+        int bufpos = 0;
+        const size_t bufsize = pEnd - p + (bSign ? 2 : 1);
+        if (bufsize > bufOnStackSize)
+        {
+            bufInHeap = std::make_unique<char[]>(bufsize);
+            bufInHeapMap = std::make_unique<const CharT*[]>(bufsize);
+            buf = bufInHeap.get();
+            bufmap = bufInHeapMap.get();
+        }
+
+        if (bSign)
+        {
+            buf[0] = '-';
+            bufmap[0] = p; // yes, this may be the same pointer as for the next mapping
+            bufpos = 1;
+        }
+        // Put first zero to buffer for strings like "-0"
+        if (p != pEnd && *p == CharT('0'))
+        {
+            buf[bufpos] = '0';
+            bufmap[bufpos] = p;
+            ++bufpos;
+            ++p;
+        }
+        // Leading zeros and group separators between digits may be safely
+        // ignored. p0 < p implies that there was a leading 0 already,
+        // consecutive group separators may not happen as *(p+1) is checked for
+        // digit.
+        while (p != pEnd && (*p == CharT('0') || (*p == cGroupSeparator
+                        && p0 < p && p+1 < pEnd && rtl::isAsciiDigit(*(p+1)))))
+        {
+            ++p;
+        }
+
+        // integer part of mantissa
+        for (; p != pEnd; ++p)
+        {
+            CharT c = *p;
+            if (rtl::isAsciiDigit(c))
+            {
+                buf[bufpos] = static_cast<char>(c);
+                bufmap[bufpos] = p;
+                ++bufpos;
+            }
+            else if (c != cGroupSeparator)
+            {
+                break;
+            }
+            else if (p == p0 || (p+1 == pEnd) || !rtl::isAsciiDigit(*(p+1)))
+            {
+                // A leading or trailing (not followed by a digit) group
+                // separator character is not a group separator.
+                break;
+            }
+        }
+
+        // fraction part of mantissa
+        if (p != pEnd && *p == cDecSeparator)
+        {
+            buf[bufpos] = '.';
+            bufmap[bufpos] = p;
+            ++bufpos;
+            ++p;
+
+            for (; p != pEnd; ++p)
+            {
+                CharT c = *p;
+                if (!rtl::isAsciiDigit(c))
+                {
+                    break;
+                }
+                buf[bufpos] = static_cast<char>(c);
+                bufmap[bufpos] = p;
+                ++bufpos;
+            }
+        }
+
+        // Exponent
+        if (p != p0 && p != pEnd && (*p == CharT('E') || *p == CharT('e')))
+        {
+            buf[bufpos] = 'E';
+            bufmap[bufpos] = p;
+            ++bufpos;
+            ++p;
+            if (p != pEnd && *p == CharT('-'))
+            {
+                buf[bufpos] = '-';
+                bufmap[bufpos] = p;
+                ++bufpos;
+                ++p;
+            }
+            else if (p != pEnd && *p == CharT('+'))
+                ++p;
+
+            for (; p != pEnd; ++p)
+            {
+                CharT c = *p;
+                if (!rtl::isAsciiDigit(c))
+                    break;
+
+                buf[bufpos] = static_cast<char>(c);
+                bufmap[bufpos] = p;
+                ++bufpos;
+            }
+        }
+        else if (p - p0 == 2 && p != pEnd && p[0] == CharT('#')
+                 && p[-1] == cDecSeparator && p[-2] == CharT('1'))
+        {
+            if (pEnd - p >= 4 && p[1] == CharT('I') && p[2] == CharT('N')
+                && p[3] == CharT('F'))
+            {
+                // "1.#INF", "+1.#INF", "-1.#INF"
+                p += 4;
+                fVal = HUGE_VAL;
+                eStatus = rtl_math_ConversionStatus_OutOfRange;
+                // Eat any further digits:
+                while (p != pEnd && rtl::isAsciiDigit(*p))
+                    ++p;
+                bDone = true;
+            }
+            else if (pEnd - p >= 4 && p[1] == CharT('N') && p[2] == CharT('A')
+                && p[3] == CharT('N'))
+            {
+                // "1.#NAN", "+1.#NAN", "-1.#NAN"
+                p += 4;
+                rtl::math::setNan( &fVal );
+                if (bSign)
+                {
+                    union {
+                        double sd;
+                        sal_math_Double md;
+                    } m;
+
+                    m.sd = fVal;
+                    m.md.w32_parts.msw |= 0x80000000; // create negative NaN
+                    fVal = m.sd;
+                    bSign = false; // don't negate again
+                }
+
+                // Eat any further digits:
+                while (p != pEnd && rtl::isAsciiDigit(*p))
+                {
+                    ++p;
+                }
+                bDone = true;
+            }
+        }
+
+        if (!bDone)
+        {
+            buf[bufpos] = '\0';
+            bufmap[bufpos] = p;
+            char* pCharParseEnd;
+            errno = 0;
+            fVal = strtod_nolocale(buf, &pCharParseEnd);
+            if (errno == ERANGE)
+            {
+                // Check for the dreaded rounded to 15 digits max value
+                // 1.79769313486232e+308 for 1.7976931348623157e+308 we wrote
+                // everywhere, accept with or without plus sign in exponent.
+                const char* b = buf;
+                if (b[0] == '-')
+                    ++b;
+                if (((pCharParseEnd - b == 21) || (pCharParseEnd - b == 20))
+                        && !strncmp( b, "1.79769313486232", 16)
+                        && (b[16] == 'e' || b[16] == 'E')
+                        && (((pCharParseEnd - b == 21) && !strncmp( b+17, "+308", 4))
+                         || ((pCharParseEnd - b == 20) && !strncmp( b+17, "308", 3))))
+                {
+                    fVal = (buf < b) ? -DBL_MAX : DBL_MAX;
+                }
+                else
+                {
+                    eStatus = rtl_math_ConversionStatus_OutOfRange;
+                }
+            }
+            p = bufmap[pCharParseEnd - buf];
+            bSign = false;
+        }
+    }
+
+    // overflow also if more than DBL_MAX_10_EXP digits without decimal
+    // separator, or 0. and more than DBL_MIN_10_EXP digits, ...
+    bool bHuge = fVal == HUGE_VAL; // g++ 3.0.1 requires it this way...
+    if (bHuge)
+        eStatus = rtl_math_ConversionStatus_OutOfRange;
+
+    if (bSign)
+        fVal = -fVal;
+
+    if (pStatus)
+        *pStatus = eStatus;
+
+    if (pParsedEnd)
+        *pParsedEnd = p == p0 ? pBegin : p;
+
+    return fVal;
+}
+
+}
+
+double SAL_CALL rtl_math_stringToDouble(char const * pBegin,
+                                        char const * pEnd,
+                                        char cDecSeparator,
+                                        char cGroupSeparator,
+                                        rtl_math_ConversionStatus * pStatus,
+                                        char const ** pParsedEnd)
+    SAL_THROW_EXTERN_C()
+{
+    return stringToDouble(
+        reinterpret_cast<unsigned char const *>(pBegin),
+        reinterpret_cast<unsigned char const *>(pEnd),
+        static_cast<unsigned char>(cDecSeparator),
+        static_cast<unsigned char>(cGroupSeparator), pStatus,
+        reinterpret_cast<unsigned char const **>(pParsedEnd));
+}
+
+double SAL_CALL rtl_math_uStringToDouble(sal_Unicode const * pBegin,
+                                         sal_Unicode const * pEnd,
+                                         sal_Unicode cDecSeparator,
+                                         sal_Unicode cGroupSeparator,
+                                         rtl_math_ConversionStatus * pStatus,
+                                         sal_Unicode const ** pParsedEnd)
+    SAL_THROW_EXTERN_C()
+{
+    return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus,
+                          pParsedEnd);
+}
+
+double SAL_CALL rtl_math_round(double fValue, int nDecPlaces,
+                               enum rtl_math_RoundingMode eMode)
+    SAL_THROW_EXTERN_C()
+{
+    OSL_ASSERT(nDecPlaces >= -20 && nDecPlaces <= 20);
+
+    if (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<int>( 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: */