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| -rw-r--r-- | sc/inc/kahan.hxx | 240 |
1 files changed, 240 insertions, 0 deletions
diff --git a/sc/inc/kahan.hxx b/sc/inc/kahan.hxx new file mode 100644 index 000000000..6c84f6eee --- /dev/null +++ b/sc/inc/kahan.hxx @@ -0,0 +1,240 @@ +/* -*- 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(double x_0, double err_0) + : m_fSum(x_0) + , m_fError(err_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: */ |