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Diffstat (limited to 'tools/source/generic/fract.cxx')
| -rw-r--r-- | tools/source/generic/fract.cxx | 519 |
1 files changed, 519 insertions, 0 deletions
diff --git a/tools/source/generic/fract.cxx b/tools/source/generic/fract.cxx new file mode 100644 index 000000000..8ec17b94a --- /dev/null +++ b/tools/source/generic/fract.cxx @@ -0,0 +1,519 @@ +/* -*- 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 <tools/fract.hxx> +#include <tools/debug.hxx> +#include <tools/stream.hxx> +#include <o3tl/safeint.hxx> +#include <sal/log.hxx> +#include <osl/diagnose.h> + +#include <algorithm> +#include <cmath> + +#include <boost/version.hpp> +#if BOOST_VERSION >= 106700 +#include <boost/integer/common_factor_rt.hpp> +#else +#include <boost/math/common_factor_rt.hpp> +#endif +#include <boost/rational.hpp> + +static boost::rational<sal_Int32> rational_FromDouble(double dVal); + +static void rational_ReduceInaccurate(boost::rational<sal_Int32>& rRational, unsigned nSignificantBits); + +static boost::rational<sal_Int32> toRational(sal_Int32 n, sal_Int32 d) +{ + return boost::rational<sal_Int32>(n, d); +} + +// Initialized by setting nNum as nominator and nDen as denominator +// Negative values in the denominator are invalid and cause the +// inversion of both nominator and denominator signs +// in order to return the correct value. +Fraction::Fraction( sal_Int64 nNum, sal_Int64 nDen ) : mnNumerator(nNum), mnDenominator(nDen) +{ + assert( nNum >= std::numeric_limits<sal_Int32>::min() ); + assert( nNum <= std::numeric_limits<sal_Int32>::max( )); + assert( nDen >= std::numeric_limits<sal_Int32>::min() ); + assert( nDen <= std::numeric_limits<sal_Int32>::max( )); + if ( nDen == 0 ) + { + mbValid = false; + SAL_WARN( "tools.fraction", "'Fraction(" << nNum << ",0)' invalid fraction created" ); + return; + } +} + +/** + * only here to prevent passing of NaN + */ +Fraction::Fraction( double nNum, double nDen ) : mnNumerator(sal_Int64(nNum)), mnDenominator(sal_Int64(nDen)) +{ + assert( !std::isnan(nNum) ); + assert( !std::isnan(nDen) ); + assert( nNum >= std::numeric_limits<sal_Int32>::min() ); + assert( nNum <= std::numeric_limits<sal_Int32>::max( )); + assert( nDen >= std::numeric_limits<sal_Int32>::min() ); + assert( nDen <= std::numeric_limits<sal_Int32>::max( )); + if ( nDen == 0 ) + { + mbValid = false; + SAL_WARN( "tools.fraction", "'Fraction(" << nNum << ",0)' invalid fraction created" ); + return; + } +} + +Fraction::Fraction( double dVal ) +{ + try + { + boost::rational<sal_Int32> v = rational_FromDouble( dVal ); + mnNumerator = v.numerator(); + mnDenominator = v.denominator(); + } + catch (const boost::bad_rational&) + { + mbValid = false; + SAL_WARN( "tools.fraction", "'Fraction(" << dVal << ")' invalid fraction created" ); + } +} + +Fraction::operator double() const +{ + if (!mbValid) + { + SAL_WARN( "tools.fraction", "'double()' on invalid fraction" ); + return 0.0; + } + + // https://github.com/boostorg/boost/issues/335 when these are std::numeric_limits<sal_Int32>::min + if (mnNumerator == mnDenominator) + return 1.0; + + return boost::rational_cast<double>(toRational(mnNumerator, mnDenominator)); +} + +// This methods first validates both values. +// If one of the arguments is invalid, the whole operation is invalid. +// After computation detect if result overflows a sal_Int32 value +// which cause the operation to be marked as invalid +Fraction& Fraction::operator += ( const Fraction& rVal ) +{ + if ( !rVal.mbValid ) + mbValid = false; + + if ( !mbValid ) + { + SAL_WARN( "tools.fraction", "'operator +=' with invalid fraction" ); + return *this; + } + + boost::rational<sal_Int32> a = toRational(mnNumerator, mnDenominator); + a += toRational(rVal.mnNumerator, rVal.mnDenominator); + mnNumerator = a.numerator(); + mnDenominator = a.denominator(); + + return *this; +} + +Fraction& Fraction::operator -= ( const Fraction& rVal ) +{ + if ( !rVal.mbValid ) + mbValid = false; + + if ( !mbValid ) + { + SAL_WARN( "tools.fraction", "'operator -=' with invalid fraction" ); + return *this; + } + + boost::rational<sal_Int32> a = toRational(mnNumerator, mnDenominator); + a -= toRational(rVal.mnNumerator, rVal.mnDenominator); + mnNumerator = a.numerator(); + mnDenominator = a.denominator(); + + return *this; +} + +namespace +{ + template<typename T> bool checked_multiply_by(boost::rational<T>& i, const boost::rational<T>& r) + { + // Protect against self-modification + T num = r.numerator(); + T den = r.denominator(); + + // Avoid overflow and preserve normalization +#if BOOST_VERSION >= 106700 + T gcd1 = boost::integer::gcd(i.numerator(), den); + T gcd2 = boost::integer::gcd(num, i.denominator()); +#else + T gcd1 = boost::math::gcd(i.numerator(), den); + T gcd2 = boost::math::gcd(num, i.denominator()); +#endif + + bool fail = false; + fail |= o3tl::checked_multiply(i.numerator() / gcd1, num / gcd2, num); + fail |= o3tl::checked_multiply(i.denominator() / gcd2, den / gcd1, den); + + if (!fail) + i.assign(num, den); + + return fail; + } +} + +Fraction& Fraction::operator *= ( const Fraction& rVal ) +{ + if ( !rVal.mbValid ) + mbValid = false; + + if ( !mbValid ) + { + SAL_WARN( "tools.fraction", "'operator *=' with invalid fraction" ); + return *this; + } + + boost::rational<sal_Int32> a = toRational(mnNumerator, mnDenominator); + boost::rational<sal_Int32> b = toRational(rVal.mnNumerator, rVal.mnDenominator); + bool bFail = checked_multiply_by(a, b); + mnNumerator = a.numerator(); + mnDenominator = a.denominator(); + + if (bFail) + { + mbValid = false; + } + + return *this; +} + +Fraction& Fraction::operator /= ( const Fraction& rVal ) +{ + if ( !rVal.mbValid ) + mbValid = false; + + if ( !mbValid ) + { + SAL_WARN( "tools.fraction", "'operator /=' with invalid fraction" ); + return *this; + } + + boost::rational<sal_Int32> a = toRational(mnNumerator, mnDenominator); + a /= toRational(rVal.mnNumerator, rVal.mnDenominator); + mnNumerator = a.numerator(); + mnDenominator = a.denominator(); + + return *this; +} + +/** Inaccurate cancellation for a fraction. + + Clip both nominator and denominator to said number of bits. If + either of those already have equal or less number of bits used, + this method does nothing. + + @param nSignificantBits denotes, how many significant binary + digits to maintain, in both nominator and denominator. + + @example ReduceInaccurate(8) has an error <1% [1/2^(8-1)] - the + largest error occurs with the following pair of values: + + binary 1000000011111111111111111111111b/1000000000000000000000000000000b + = 1082130431/1073741824 + = approx. 1.007812499 + + A ReduceInaccurate(8) yields 1/1. +*/ +void Fraction::ReduceInaccurate( unsigned nSignificantBits ) +{ + if ( !mbValid ) + { + SAL_WARN( "tools.fraction", "'ReduceInaccurate' on invalid fraction" ); + return; + } + + if ( !mnNumerator ) + return; + + auto a = toRational(mnNumerator, mnDenominator); + rational_ReduceInaccurate(a, nSignificantBits); + mnNumerator = a.numerator(); + mnDenominator = a.denominator(); +} + +sal_Int32 Fraction::GetNumerator() const +{ + if ( !mbValid ) + { + SAL_WARN( "tools.fraction", "'GetNumerator()' on invalid fraction" ); + return 0; + } + return mnNumerator; +} + +sal_Int32 Fraction::GetDenominator() const +{ + if ( !mbValid ) + { + SAL_WARN( "tools.fraction", "'GetDenominator()' on invalid fraction" ); + return -1; + } + return mnDenominator; +} + +Fraction::operator sal_Int32() const +{ + if ( !mbValid ) + { + SAL_WARN( "tools.fraction", "'operator sal_Int32()' on invalid fraction" ); + return 0; + } + return boost::rational_cast<sal_Int32>(toRational(mnNumerator, mnDenominator)); +} + +Fraction operator+( const Fraction& rVal1, const Fraction& rVal2 ) +{ + Fraction aErg( rVal1 ); + aErg += rVal2; + return aErg; +} + +Fraction operator-( const Fraction& rVal1, const Fraction& rVal2 ) +{ + Fraction aErg( rVal1 ); + aErg -= rVal2; + return aErg; +} + +Fraction operator*( const Fraction& rVal1, const Fraction& rVal2 ) +{ + Fraction aErg( rVal1 ); + aErg *= rVal2; + return aErg; +} + +Fraction operator/( const Fraction& rVal1, const Fraction& rVal2 ) +{ + Fraction aErg( rVal1 ); + aErg /= rVal2; + return aErg; +} + +bool operator !=( const Fraction& rVal1, const Fraction& rVal2 ) +{ + return !(rVal1 == rVal2); +} + +bool operator <=( const Fraction& rVal1, const Fraction& rVal2 ) +{ + return !(rVal1 > rVal2); +} + +bool operator >=( const Fraction& rVal1, const Fraction& rVal2 ) +{ + return !(rVal1 < rVal2); +} + +bool operator == ( const Fraction& rVal1, const Fraction& rVal2 ) +{ + if ( !rVal1.mbValid || !rVal2.mbValid ) + { + SAL_WARN( "tools.fraction", "'operator ==' with an invalid fraction" ); + return false; + } + + return toRational(rVal1.mnNumerator, rVal1.mnDenominator) == toRational(rVal2.mnNumerator, rVal2.mnDenominator); +} + +bool operator < ( const Fraction& rVal1, const Fraction& rVal2 ) +{ + if ( !rVal1.mbValid || !rVal2.mbValid ) + { + SAL_WARN( "tools.fraction", "'operator <' with an invalid fraction" ); + return false; + } + + return toRational(rVal1.mnNumerator, rVal1.mnDenominator) < toRational(rVal2.mnNumerator, rVal2.mnDenominator); +} + +bool operator > ( const Fraction& rVal1, const Fraction& rVal2 ) +{ + if ( !rVal1.mbValid || !rVal2.mbValid ) + { + SAL_WARN( "tools.fraction", "'operator >' with an invalid fraction" ); + return false; + } + + return toRational(rVal1.mnNumerator, rVal1.mnDenominator) > toRational(rVal2.mnNumerator, rVal2.mnDenominator); +} + +SvStream& ReadFraction( SvStream& rIStream, Fraction & rFract ) +{ + sal_Int32 num(0), den(0); + rIStream.ReadInt32( num ); + rIStream.ReadInt32( den ); + if ( den <= 0 ) + { + SAL_WARN( "tools.fraction", "'ReadFraction()' read an invalid fraction" ); + rFract.mbValid = false; + } + else + { + rFract.mnNumerator = num; + rFract.mnDenominator = den; + rFract.mbValid = true; + } + return rIStream; +} + +SvStream& WriteFraction( SvStream& rOStream, const Fraction& rFract ) +{ + if ( !rFract.mbValid ) + { + SAL_WARN( "tools.fraction", "'WriteFraction()' write an invalid fraction" ); + rOStream.WriteInt32( 0 ); + rOStream.WriteInt32( -1 ); + } else { + rOStream.WriteInt32( rFract.mnNumerator ); + rOStream.WriteInt32( rFract.mnDenominator ); + } + return rOStream; +} + +// If dVal > LONG_MAX or dVal < LONG_MIN, the rational throws a boost::bad_rational. +// Otherwise, dVal and denominator are multiplied by 10, until one of them +// is larger than (LONG_MAX / 10). +// +// NOTE: here we use 'sal_Int32' due that only values in sal_Int32 range are valid. +static boost::rational<sal_Int32> rational_FromDouble(double dVal) +{ + if ( dVal > std::numeric_limits<sal_Int32>::max() || + dVal < std::numeric_limits<sal_Int32>::min() || + std::isnan(dVal) ) + throw boost::bad_rational(); + + const sal_Int32 nMAX = std::numeric_limits<sal_Int32>::max() / 10; + sal_Int32 nDen = 1; + while ( std::abs( dVal ) < nMAX && nDen < nMAX ) { + dVal *= 10; + nDen *= 10; + } + return boost::rational<sal_Int32>( sal_Int32(dVal), nDen ); +} + +// Similar to clz_table that can be googled +const char nbits_table[32] = +{ + 32, 1, 23, 2, 29, 24, 14, 3, + 30, 27, 25, 18, 20, 15, 10, 4, + 31, 22, 28, 13, 26, 17, 19, 9, + 21, 12, 16, 8, 11, 7, 6, 5 +}; + +static int impl_NumberOfBits( sal_uInt32 nNum ) +{ + // http://en.wikipedia.org/wiki/De_Bruijn_sequence + // background paper: Using de Bruijn Sequences to Index a 1 in a + // Computer Word (1998) Charles E. Leiserson, + // Harald Prokop, Keith H. Randall + // (e.g. http://citeseer.ist.psu.edu/leiserson98using.html) + const sal_uInt32 nDeBruijn = 0x7DCD629; + + if ( nNum == 0 ) + return 0; + + // Get it to form like 0000001111111111b + nNum |= ( nNum >> 1 ); + nNum |= ( nNum >> 2 ); + nNum |= ( nNum >> 4 ); + nNum |= ( nNum >> 8 ); + nNum |= ( nNum >> 16 ); + + sal_uInt32 nNumber; + int nBonus; + + nNumber = nNum; + nBonus = 0; + + // De facto shift left of nDeBruijn using multiplication (nNumber + // is all ones from topmost bit, thus nDeBruijn + (nDeBruijn * + // nNumber) => nDeBruijn * (nNumber+1) clears all those bits to + // zero, sets the next bit to one, and thus effectively shift-left + // nDeBruijn by lg2(nNumber+1). This generates a distinct 5bit + // sequence in the msb for each distinct position of the last + // leading 0 bit - that's the property of a de Bruijn number. + nNumber = nDeBruijn + ( nDeBruijn * nNumber ); + + // 5-bit window indexes the result + return ( nbits_table[nNumber >> 27] ) + nBonus; +} + +/** Inaccurate cancellation for a fraction. + + Clip both nominator and denominator to said number of bits. If + either of those already have equal or less number of bits used, + this method does nothing. + + @param nSignificantBits denotes, how many significant binary + digits to maintain, in both nominator and denominator. + + @example ReduceInaccurate(8) has an error <1% [1/2^(8-1)] - the + largest error occurs with the following pair of values: + + binary 1000000011111111111111111111111b/1000000000000000000000000000000b + = 1082130431/1073741824 + = approx. 1.007812499 + + A ReduceInaccurate(8) yields 1/1. +*/ +static void rational_ReduceInaccurate(boost::rational<sal_Int32>& rRational, unsigned nSignificantBits) +{ + if ( !rRational ) + return; + + // http://www.boost.org/doc/libs/release/libs/rational/rational.html#Internal%20representation + const bool bNeg = ( rRational.numerator() < 0 ); + sal_Int32 nMul = bNeg? -rRational.numerator(): rRational.numerator(); + sal_Int32 nDiv = rRational.denominator(); + + DBG_ASSERT(nSignificantBits<65, "More than 64 bit of significance is overkill!"); + + // How much bits can we lose? + const int nMulBitsToLose = std::max( ( impl_NumberOfBits( nMul ) - int( nSignificantBits ) ), 0 ); + const int nDivBitsToLose = std::max( ( impl_NumberOfBits( nDiv ) - int( nSignificantBits ) ), 0 ); + + const int nToLose = std::min( nMulBitsToLose, nDivBitsToLose ); + + // Remove the bits + nMul >>= nToLose; + nDiv >>= nToLose; + + if ( !nMul || !nDiv ) { + // Return without reduction + OSL_FAIL( "Oops, we reduced too much..." ); + return; + } + + rRational.assign( bNeg ? -nMul : nMul, nDiv ); +} + +/* vim:set shiftwidth=4 softtabstop=4 expandtab: */ |