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76 lines
3.0 KiB
76 lines
3.0 KiB
#ifndef Magnum_Math_Algorithms_KahanSum_h |
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#define Magnum_Math_Algorithms_KahanSum_h |
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/* |
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This file is part of Magnum. |
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Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019 |
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Vladimír Vondruš <mosra@centrum.cz> |
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Permission is hereby granted, free of charge, to any person obtaining a |
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copy of this software and associated documentation files (the "Software"), |
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to deal in the Software without restriction, including without limitation |
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the rights to use, copy, modify, merge, publish, distribute, sublicense, |
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and/or sell copies of the Software, and to permit persons to whom the |
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Software is furnished to do so, subject to the following conditions: |
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The above copyright notice and this permission notice shall be included |
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in all copies or substantial portions of the Software. |
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
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THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING |
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER |
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DEALINGS IN THE SOFTWARE. |
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*/ |
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/** @file |
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* @brief Function @ref Magnum::Math::Algorithms::kahanSum() |
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*/ |
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#include <utility> |
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namespace Magnum { namespace Math { namespace Algorithms { |
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/** |
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@brief Kahan summation algorithm |
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@param[in] begin Range begin |
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@param[in] end Range end |
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@param[in] sum Initial value for the sum |
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@param[in,out] compensation Floating-point roundoff error compensation value. |
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If non-@cpp nullptr @ce, value behind the pointer is used as initial |
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compensation value and the resulting value is |
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Calculates a sum of a large range of floating-point numbers with roundoff error |
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compensation. Compared to for example @ref std::accumulate() the algorithm |
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significantly reduces numerical error in the total. See the |
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[Kahan summation algorithm](https://en.wikipedia.org/wiki/Kahan_summation_algorithm) |
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article on Wikipedia for an in-depth explanation. Example with summation of a |
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hundred million ones: |
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@snippet MagnumMathAlgorithms.cpp kahanSum |
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If required, it is also possible to use this algorithm on non-contiguous ranges |
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or single values (for example when calculating sum of pixel values in an image |
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with some row padding or when the inputs are generated / converted from other |
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values): |
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@snippet MagnumMathAlgorithms.cpp kahanSum-iterative |
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*/ |
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template<class Iterator, class T = typename std::decay<decltype(*std::declval<Iterator>())>::type> T kahanSum(Iterator begin, Iterator end, T sum = T(0), T* compensation = nullptr) { |
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T c = compensation ? *compensation : T(0); |
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for(Iterator it = begin; it != end; ++it) { |
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const T y = *it - c; |
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const T t = sum + y; |
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c = (t - sum) - y; |
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sum = t; |
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} |
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if(compensation) *compensation = c; |
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return sum; |
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} |
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}}} |
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#endif
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