1127 lines
37 KiB
C++
1127 lines
37 KiB
C++
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
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/*
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* This file is part of the LibreOffice project.
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*
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* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/.
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*
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* This file incorporates work covered by the following license notice:
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*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed
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* with this work for additional information regarding copyright
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* ownership. The ASF licenses this file to you under the Apache
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* License, Version 2.0 (the "License"); you may not use this file
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* except in compliance with the License. You may obtain a copy of
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* the License at http://www.apache.org/licenses/LICENSE-2.0 .
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*/
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#include "rtl/math.h"
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#include "osl/diagnose.h"
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#include "rtl/alloc.h"
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#include "rtl/character.hxx"
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#include "rtl/math.hxx"
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#include "rtl/strbuf.h"
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#include "rtl/string.h"
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#include "rtl/ustrbuf.h"
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#include "rtl/ustring.h"
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#include "sal/mathconf.h"
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#include "sal/types.h"
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#include <algorithm>
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#include <cassert>
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#include <float.h>
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#include <limits.h>
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#include <math.h>
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#include <stdlib.h>
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static int const n10Count = 16;
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static double const n10s[2][n10Count] = {
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{ 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8,
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1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16 },
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{ 1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8,
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1e-9, 1e-10, 1e-11, 1e-12, 1e-13, 1e-14, 1e-15, 1e-16 }
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};
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// return pow(10.0,nExp) optimized for exponents in the interval [-16,16]
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static double getN10Exp( int nExp )
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{
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if ( nExp < 0 )
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{
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// && -nExp > 0 necessary for std::numeric_limits<int>::min()
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// because -nExp = nExp
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if ( -nExp <= n10Count && -nExp > 0 )
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return n10s[1][-nExp-1];
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else
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return pow( 10.0, static_cast<double>( nExp ) );
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}
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else if ( nExp > 0 )
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{
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if ( nExp <= n10Count )
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return n10s[0][nExp-1];
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else
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return pow( 10.0, static_cast<double>( nExp ) );
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}
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else // ( nExp == 0 )
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return 1.0;
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}
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namespace {
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double const nKorrVal[] = {
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0, 9e-1, 9e-2, 9e-3, 9e-4, 9e-5, 9e-6, 9e-7, 9e-8,
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9e-9, 9e-10, 9e-11, 9e-12, 9e-13, 9e-14, 9e-15
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};
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struct StringTraits
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{
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typedef sal_Char Char;
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typedef rtl_String String;
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static inline void createString(rtl_String ** pString,
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sal_Char const * pChars, sal_Int32 nLen)
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{
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rtl_string_newFromStr_WithLength(pString, pChars, nLen);
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}
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static inline void createBuffer(rtl_String ** pBuffer,
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sal_Int32 * pCapacity)
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{
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rtl_string_new_WithLength(pBuffer, *pCapacity);
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}
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static inline void appendChars(rtl_String ** pBuffer, sal_Int32 * pCapacity,
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sal_Int32 * pOffset, sal_Char const * pChars,
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sal_Int32 nLen)
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{
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assert(pChars != nullptr);
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rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen);
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*pOffset += nLen;
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}
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static inline void appendAscii(rtl_String ** pBuffer, sal_Int32 * pCapacity,
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sal_Int32 * pOffset, sal_Char const * pStr,
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sal_Int32 nLen)
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{
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assert(pStr != nullptr);
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rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pStr, nLen);
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*pOffset += nLen;
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}
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};
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struct UStringTraits
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{
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typedef sal_Unicode Char;
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typedef rtl_uString String;
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static inline void createString(rtl_uString ** pString,
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sal_Unicode const * pChars, sal_Int32 nLen)
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{
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rtl_uString_newFromStr_WithLength(pString, pChars, nLen);
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}
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static inline void createBuffer(rtl_uString ** pBuffer,
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sal_Int32 * pCapacity)
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{
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rtl_uString_new_WithLength(pBuffer, *pCapacity);
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}
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static inline void appendChars(rtl_uString ** pBuffer,
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sal_Int32 * pCapacity, sal_Int32 * pOffset,
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sal_Unicode const * pChars, sal_Int32 nLen)
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{
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assert(pChars != nullptr);
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rtl_uStringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen);
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*pOffset += nLen;
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}
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static inline void appendAscii(rtl_uString ** pBuffer,
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sal_Int32 * pCapacity, sal_Int32 * pOffset,
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sal_Char const * pStr, sal_Int32 nLen)
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{
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rtl_uStringbuffer_insert_ascii(pBuffer, pCapacity, *pOffset, pStr,
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nLen);
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*pOffset += nLen;
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}
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};
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// Solaris C++ 5.2 compiler has problems when "StringT ** pResult" is
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// "typename T::String ** pResult" instead:
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template< typename T, typename StringT >
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inline void doubleToString(StringT ** pResult,
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sal_Int32 * pResultCapacity, sal_Int32 nResultOffset,
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double fValue, rtl_math_StringFormat eFormat,
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sal_Int32 nDecPlaces, typename T::Char cDecSeparator,
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sal_Int32 const * pGroups,
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typename T::Char cGroupSeparator,
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bool bEraseTrailingDecZeros)
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{
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static double const nRoundVal[] = {
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5.0e+0, 0.5e+0, 0.5e-1, 0.5e-2, 0.5e-3, 0.5e-4, 0.5e-5, 0.5e-6,
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0.5e-7, 0.5e-8, 0.5e-9, 0.5e-10,0.5e-11,0.5e-12,0.5e-13,0.5e-14
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};
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// sign adjustment, instead of testing for fValue<0.0 this will also fetch
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// -0.0
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bool bSign = rtl::math::isSignBitSet( fValue );
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if( bSign )
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fValue = -fValue;
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if ( rtl::math::isNan( fValue ) )
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{
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// #i112652# XMLSchema-2
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sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("NaN");
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if (pResultCapacity == nullptr)
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{
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pResultCapacity = &nCapacity;
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T::createBuffer(pResult, pResultCapacity);
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nResultOffset = 0;
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}
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T::appendAscii(pResult, pResultCapacity, &nResultOffset,
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RTL_CONSTASCII_STRINGPARAM("NaN"));
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return;
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}
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bool bHuge = fValue == HUGE_VAL; // g++ 3.0.1 requires it this way...
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if ( bHuge || rtl::math::isInf( fValue ) )
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{
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// #i112652# XMLSchema-2
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sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("-INF");
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if (pResultCapacity == nullptr)
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{
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pResultCapacity = &nCapacity;
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T::createBuffer(pResult, pResultCapacity);
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nResultOffset = 0;
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}
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if ( bSign )
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T::appendAscii(pResult, pResultCapacity, &nResultOffset,
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RTL_CONSTASCII_STRINGPARAM("-"));
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T::appendAscii(pResult, pResultCapacity, &nResultOffset,
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RTL_CONSTASCII_STRINGPARAM("INF"));
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return;
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}
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// Use integer representation for integer values that fit into the
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// mantissa (1.((2^53)-1)) with a precision of 1 for highest accuracy.
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const sal_Int64 kMaxInt = (static_cast<sal_Int64>(1) << 53) - 1;
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if ((eFormat == rtl_math_StringFormat_Automatic ||
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eFormat == rtl_math_StringFormat_F) && fValue <= static_cast<double>(kMaxInt))
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{
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sal_Int64 nInt = static_cast<sal_Int64>(fValue);
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// Check the integer range again because double comparison may yield
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// true within the precision range.
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if (nInt <= kMaxInt && static_cast<double>(nInt) == fValue)
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{
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if (nDecPlaces == rtl_math_DecimalPlaces_Max)
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nDecPlaces = 0;
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else
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nDecPlaces = ::std::max<sal_Int32>( ::std::min<sal_Int32>( nDecPlaces, 15), -15);
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if (bEraseTrailingDecZeros && nDecPlaces > 0)
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nDecPlaces = 0;
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// Round before decimal position.
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if (nDecPlaces < 0)
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{
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sal_Int64 nRounding = static_cast<sal_Int64>( getN10Exp( -nDecPlaces - 1));
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sal_Int64 nTemp = nInt / nRounding;
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int nDigit = nTemp % 10;
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nTemp /= 10;
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if (nDigit >= 5)
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++nTemp;
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nTemp *= 10;
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nTemp *= nRounding;
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nInt = nTemp;
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nDecPlaces = 0;
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}
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// Max 1 sign, 16 integer digits, 15 group separators, 1 decimal
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// separator, 15 decimals digits.
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typename T::Char aBuf[64];
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typename T::Char * pBuf = aBuf;
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typename T::Char * p = pBuf;
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// Backward fill.
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size_t nGrouping = 0;
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sal_Int32 nGroupDigits = 0;
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do
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{
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typename T::Char nDigit = nInt % 10;
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nInt /= 10;
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*p++ = nDigit + '0';
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if (pGroups && pGroups[nGrouping] == ++nGroupDigits && nInt > 0 && cGroupSeparator)
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{
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*p++ = cGroupSeparator;
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if (pGroups[nGrouping+1])
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++nGrouping;
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nGroupDigits = 0;
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}
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}
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while (nInt > 0);
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if (bSign)
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*p++ = '-';
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// Reverse buffer content.
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sal_Int32 n = (p - pBuf) / 2;
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for (sal_Int32 i=0; i < n; ++i)
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{
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::std::swap( pBuf[i], p[-i-1]);
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}
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// Append decimals.
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if (nDecPlaces > 0)
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{
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*p++ = cDecSeparator;
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while (nDecPlaces--)
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*p++ = '0';
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}
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if (pResultCapacity == nullptr)
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T::createString(pResult, pBuf, p - pBuf);
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else
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T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf, p - pBuf);
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return;
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}
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}
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// find the exponent
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int nExp = 0;
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if ( fValue > 0.0 )
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{
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nExp = static_cast< int >( floor( log10( fValue ) ) );
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fValue /= getN10Exp( nExp );
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}
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switch ( eFormat )
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{
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case rtl_math_StringFormat_Automatic :
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{ // E or F depending on exponent magnitude
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int nPrec;
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if ( nExp <= -15 || nExp >= 15 ) // #58531# was <-16, >16
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{
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nPrec = 14;
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eFormat = rtl_math_StringFormat_E;
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}
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else
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{
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if ( nExp < 14 )
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{
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nPrec = 15 - nExp - 1;
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eFormat = rtl_math_StringFormat_F;
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}
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else
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{
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nPrec = 15;
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eFormat = rtl_math_StringFormat_F;
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}
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}
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if ( nDecPlaces == rtl_math_DecimalPlaces_Max )
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nDecPlaces = nPrec;
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}
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break;
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case rtl_math_StringFormat_G :
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case rtl_math_StringFormat_G1 :
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case rtl_math_StringFormat_G2 :
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{ // G-Point, similar to sprintf %G
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if ( nDecPlaces == rtl_math_DecimalPlaces_DefaultSignificance )
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nDecPlaces = 6;
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if ( nExp < -4 || nExp >= nDecPlaces )
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{
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nDecPlaces = std::max< sal_Int32 >( 1, nDecPlaces - 1 );
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if( eFormat == rtl_math_StringFormat_G )
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eFormat = rtl_math_StringFormat_E;
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else if( eFormat == rtl_math_StringFormat_G2 )
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eFormat = rtl_math_StringFormat_E2;
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else if( eFormat == rtl_math_StringFormat_G1 )
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eFormat = rtl_math_StringFormat_E1;
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}
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else
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{
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nDecPlaces = std::max< sal_Int32 >( 0, nDecPlaces - nExp - 1 );
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eFormat = rtl_math_StringFormat_F;
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}
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}
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break;
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default:
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break;
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}
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sal_Int32 nDigits = nDecPlaces + 1;
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if( eFormat == rtl_math_StringFormat_F )
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nDigits += nExp;
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// Round the number
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if( nDigits >= 0 )
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{
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if( ( fValue += nRoundVal[ nDigits > 15 ? 15 : nDigits ] ) >= 10 )
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{
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fValue = 1.0;
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nExp++;
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if( eFormat == rtl_math_StringFormat_F )
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nDigits++;
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}
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}
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static sal_Int32 const nBufMax = 256;
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typename T::Char aBuf[nBufMax];
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typename T::Char * pBuf;
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sal_Int32 nBuf = static_cast< sal_Int32 >
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( nDigits <= 0 ? std::max< sal_Int32 >( nDecPlaces, abs(nExp) )
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: nDigits + nDecPlaces ) + 10 + (pGroups ? abs(nDigits) * 2 : 0);
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if ( nBuf > nBufMax )
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{
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pBuf = static_cast< typename T::Char * >(
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rtl_allocateMemory(nBuf * sizeof (typename T::Char)));
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OSL_ENSURE(pBuf != nullptr, "Out of memory");
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}
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else
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pBuf = aBuf;
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typename T::Char * p = pBuf;
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if ( bSign )
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*p++ = static_cast< typename T::Char >('-');
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bool bHasDec = false;
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int nDecPos;
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// Check for F format and number < 1
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if( eFormat == rtl_math_StringFormat_F )
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{
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if( nExp < 0 )
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{
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*p++ = static_cast< typename T::Char >('0');
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if ( nDecPlaces > 0 )
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{
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*p++ = cDecSeparator;
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bHasDec = true;
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}
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sal_Int32 i = ( nDigits <= 0 ? nDecPlaces : -nExp - 1 );
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while( (i--) > 0 )
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*p++ = static_cast< typename T::Char >('0');
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nDecPos = 0;
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}
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else
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nDecPos = nExp + 1;
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}
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else
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nDecPos = 1;
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int nGrouping = 0, nGroupSelector = 0, nGroupExceed = 0;
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if ( nDecPos > 1 && pGroups && pGroups[0] && cGroupSeparator )
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{
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while ( nGrouping + pGroups[nGroupSelector] < nDecPos )
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{
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nGrouping += pGroups[ nGroupSelector ];
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if ( pGroups[nGroupSelector+1] )
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{
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if ( nGrouping + pGroups[nGroupSelector+1] >= nDecPos )
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break; // while
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++nGroupSelector;
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}
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else if ( !nGroupExceed )
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nGroupExceed = nGrouping;
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}
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}
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// print the number
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if( nDigits > 0 )
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{
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for ( int i = 0; ; i++ )
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{
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if( i < 15 )
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{
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int nDigit;
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if (nDigits-1 == 0 && i > 0 && i < 14)
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nDigit = static_cast< int >( floor( fValue
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+ nKorrVal[15-i] ) );
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else
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nDigit = static_cast< int >( fValue + 1E-15 );
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if (nDigit >= 10)
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{ // after-treatment of up-rounding to the next decade
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sal_Int32 sLen = static_cast< long >(p-pBuf)-1;
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if (sLen == -1)
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{
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p = pBuf;
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if ( eFormat == rtl_math_StringFormat_F )
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{
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*p++ = static_cast< typename T::Char >('1');
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*p++ = static_cast< typename T::Char >('0');
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}
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else
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{
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*p++ = static_cast< typename T::Char >('1');
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*p++ = cDecSeparator;
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*p++ = static_cast< typename T::Char >('0');
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nExp++;
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bHasDec = true;
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}
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}
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else
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{
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for (sal_Int32 j = sLen; j >= 0; j--)
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{
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typename T::Char cS = pBuf[j];
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if (cS != cDecSeparator)
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{
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if ( cS != static_cast< typename T::Char >('9'))
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{
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pBuf[j] = ++cS;
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j = -1; // break loop
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}
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else
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{
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pBuf[j]
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= static_cast< typename T::Char >('0');
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if (j == 0)
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{
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if ( eFormat == rtl_math_StringFormat_F)
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{ // insert '1'
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typename T::Char * px = p++;
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while ( pBuf < px )
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{
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*px = *(px-1);
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px--;
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}
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pBuf[0] = static_cast<
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typename T::Char >('1');
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}
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else
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{
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pBuf[j] = static_cast<
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typename T::Char >('1');
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nExp++;
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}
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}
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}
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}
|
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}
|
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*p++ = static_cast< typename T::Char >('0');
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}
|
|
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 == nullptr)
|
|
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;
|
|
}
|
|
|
|
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 (rtl::isAsciiDigit(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 (!rtl::isAsciiDigit(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')))
|
|
{
|
|
CharT const * const pExponent = p;
|
|
++p;
|
|
bool bExpSign;
|
|
if (p != pEnd && *p == CharT('-'))
|
|
{
|
|
bExpSign = true;
|
|
++p;
|
|
}
|
|
else
|
|
{
|
|
bExpSign = false;
|
|
if (p != pEnd && *p == CharT('+'))
|
|
++p;
|
|
}
|
|
CharT const * const pFirstExpDigit = p;
|
|
if ( fVal == 0.0 )
|
|
{ // no matter what follows, zero stays zero, but carry on the
|
|
// offset
|
|
while (p != pEnd && rtl::isAsciiDigit(*p))
|
|
++p;
|
|
if (p == pFirstExpDigit)
|
|
{ // no digits in exponent, reset end of scan
|
|
p = pExponent;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
bool bOverflow = false;
|
|
long nExp = 0;
|
|
for (; p != pEnd; ++p)
|
|
{
|
|
CharT c = *p;
|
|
if (!rtl::isAsciiDigit(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 == pFirstExpDigit)
|
|
{ // no digits in exponent, reset end of scan
|
|
p = pExponent;
|
|
}
|
|
}
|
|
}
|
|
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;
|
|
}
|
|
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;
|
|
}
|
|
}
|
|
}
|
|
|
|
// 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 != nullptr)
|
|
*pStatus = eStatus;
|
|
if (pParsedEnd != nullptr)
|
|
*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()
|
|
{
|
|
return expm1(fValue);
|
|
}
|
|
|
|
double SAL_CALL rtl_math_log1p( double fValue ) SAL_THROW_EXTERN_C()
|
|
{
|
|
return log1p(fValue);
|
|
}
|
|
|
|
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) */
|
|
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;
|
|
else
|
|
{
|
|
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)));
|
|
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);
|
|
}
|
|
|
|
/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
|