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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4; fill-column: 100 -*- */
/*
* 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/.
*/
#pragma once
#include <rtl/math.hxx>
#include <cmath>
/**
* This class provides LO with Kahan summation algorithm
* About this algorithm: https://en.wikipedia.org/wiki/Kahan_summation_algorithm
* For general purpose software we assume first order error is enough.
*
* Additionally queue and remember the last recent non-zero value and add it
* similar to approxAdd() when obtaining the final result to further eliminate
* accuracy errors. (e.g. for the dreaded 0.1 + 0.2 - 0.3 != 0.0)
*/
class KahanSum
{
public:
constexpr KahanSum() = default;
constexpr KahanSum(double x_0)
: m_fSum(x_0)
{
}
constexpr KahanSum(const KahanSum& fSum) = default;
public:
/**
* Adds a value to the sum using Kahan summation.
* @param x_i
*/
void add(double x_i)
{
if (x_i == 0.0)
return;
if (!m_fMem)
{
m_fMem = x_i;
return;
}
double t = m_fSum + m_fMem;
if (std::abs(m_fSum) >= std::abs(m_fMem))
m_fError += (m_fSum - t) + m_fMem;
else
m_fError += (m_fMem - t) + m_fSum;
m_fSum = t;
m_fMem = x_i;
}
/**
* Adds a value to the sum using Kahan summation.
* @param fSum
*/
inline void add(const KahanSum& fSum)
{
add(fSum.m_fSum);
add(fSum.m_fError);
add(fSum.m_fMem);
}
/**
* Substracts a value to the sum using Kahan summation.
* @param fSum
*/
inline void subtract(const KahanSum& fSum)
{
add(-fSum.m_fSum);
add(-fSum.m_fError);
add(-fSum.m_fMem);
}
public:
constexpr KahanSum operator-() const
{
KahanSum fKahanSum;
fKahanSum.m_fSum = -m_fSum;
fKahanSum.m_fError = -m_fError;
fKahanSum.m_fMem = -m_fMem;
return fKahanSum;
}
constexpr KahanSum& operator=(double fSum)
{
m_fSum = fSum;
m_fError = 0;
m_fMem = 0;
return *this;
}
constexpr KahanSum& operator=(const KahanSum& fSum) = default;
inline void operator+=(const KahanSum& fSum) { add(fSum); }
inline void operator+=(double fSum) { add(fSum); }
inline void operator-=(const KahanSum& fSum) { subtract(fSum); }
inline void operator-=(double fSum) { add(-fSum); }
inline KahanSum operator+(double fSum) const
{
KahanSum fNSum(*this);
fNSum.add(fSum);
return fNSum;
}
inline KahanSum operator+(const KahanSum& fSum) const
{
KahanSum fNSum(*this);
fNSum += fSum;
return fNSum;
}
inline KahanSum operator-(double fSum) const
{
KahanSum fNSum(*this);
fNSum.add(-fSum);
return fNSum;
}
inline KahanSum operator-(const KahanSum& fSum) const
{
KahanSum fNSum(*this);
fNSum -= fSum;
return fNSum;
}
/**
* In some parts of the code of interpr_.cxx this may be used for
* product instead of sum. This operator shall be used for that task.
*/
constexpr void operator*=(double fTimes)
{
if (m_fMem)
{
m_fSum = get() * fTimes;
m_fMem = 0.0;
}
else
{
m_fSum = (m_fSum + m_fError) * fTimes;
}
m_fError = 0.0;
}
constexpr void operator/=(double fDivides)
{
if (m_fMem)
{
m_fSum = get() / fDivides;
m_fMem = 0.0;
}
else
{
m_fSum = (m_fSum + m_fError) / fDivides;
}
m_fError = 0.0;
}
inline KahanSum operator*(const KahanSum& fTimes) const { return get() * fTimes.get(); }
inline KahanSum operator*(double fTimes) const { return get() * fTimes; }
inline KahanSum operator/(const KahanSum& fDivides) const { return get() / fDivides.get(); }
inline KahanSum operator/(double fDivides) const { return get() / fDivides; }
inline bool operator<(const KahanSum& fSum) const { return get() < fSum.get(); }
inline bool operator<(double fSum) const { return get() < fSum; }
inline bool operator>(const KahanSum& fSum) const { return get() > fSum.get(); }
inline bool operator>(double fSum) const { return get() > fSum; }
inline bool operator<=(const KahanSum& fSum) const { return get() <= fSum.get(); }
inline bool operator<=(double fSum) const { return get() <= fSum; }
inline bool operator>=(const KahanSum& fSum) const { return get() >= fSum.get(); }
inline bool operator>=(double fSum) const { return get() >= fSum; }
inline bool operator==(const KahanSum& fSum) const { return get() == fSum.get(); }
inline bool operator!=(const KahanSum& fSum) const { return get() != fSum.get(); }
public:
/**
* Returns the final sum.
* @return final sum
*/
double get() const
{
const double fTotal = m_fSum + m_fError;
if (!m_fMem)
return fTotal;
// Check the same condition as rtl::math::approxAdd() and if true
// return 0.0, if false use another Kahan summation adding m_fMem.
if (((m_fMem < 0.0 && fTotal > 0.0) || (fTotal < 0.0 && m_fMem > 0.0))
&& rtl::math::approxEqual(m_fMem, -fTotal))
{
/* TODO: should we reset all values to zero here for further
* summation, or is it better to keep them as they are? */
return 0.0;
}
// The actual argument passed to add() here does not matter as long as
// it is not 0, m_fMem is not 0 and will be added anyway, see add().
const_cast<KahanSum*>(this)->add(m_fMem);
const_cast<KahanSum*>(this)->m_fMem = 0.0;
return m_fSum + m_fError;
}
private:
double m_fSum = 0;
double m_fError = 0;
double m_fMem = 0;
};
/* vim:set shiftwidth=4 softtabstop=4 expandtab cinoptions=b1,g0,N-s cinkeys+=0=break: */
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