125 lines
6.0 KiB
Plaintext
125 lines
6.0 KiB
Plaintext
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Copyright Matt Borland 2022
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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[section:logaddexp logaddexp and logsumexp]
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[h4 Synopsis]
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#include <boost/math/special_functions/logaddexp.hpp>
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namespace boost { namespace math {
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template <typename Real>
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Real logaddexp (Real x1, Real x2);
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}} // namespaces
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#include <boost/math/special_functions/logsumexp.hpp>
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namespace boost { namespace math {
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template <typename ForwardIterator, typename Real = std::iterator_traits<ForwardIterator>::value_type>
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Real logsumexp (ForwardIterator first, ForwardIterator last);
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template <typename ForwardContainer, typename Real = ForwardContainer::value_type>
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Real logsumexp (const ForwardContainer& c);
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template <typename... Args, typename Real = typename std::common_type<Args...>::type>
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Real logsumexp(Args&& ...args)
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}} // namespace
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The function `logaddexp(x1, x2)` computes log(exp(x1) + exp(x2)).
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The function `logsumexp(x1, x2, ...)` is generalized to compute log(exp(x1) + exp(x2) + ...).
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This function is useful in statistics where the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers.
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In such cases the logarithm of the calculated probability is stored.
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The use is
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using std::log;
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double x1 = log(1e-50);
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double x2 = log(2.5e-50);
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double x3 = log(3e-50);
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std::vector<double> x = {x1, x2, x3};
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double probability1 = boost::math::logaddexp(x1, x2);
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double probability2 = boost::math::logsumexp(x1, x2, x3);
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double probability3 = boost::math::logsumexp(x);
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double probability4 = boost::math::logsumexp(x.begin(), x.end());
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Performance Data:
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```
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Running ./logaddexp_performance
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Run on Apple M1 Pro
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CPU Caches:
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L1 Data 64 KiB (x10)
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L1 Instruction 128 KiB (x10)
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L2 Unified 4096 KiB (x5)
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Load Average: 2.23, 1.89, 1.88
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-----------------------------------------------------------------------------
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Benchmark Time CPU Iterations
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-----------------------------------------------------------------------------
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logaddexp_performance<float> 1.05 ns 1.05 ns 597983940
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logaddexp_performance<double> 1.03 ns 1.03 ns 672682369
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```
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```
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Running ./logsumexp_performance
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Run on Apple M1 Pro
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CPU Caches:
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L1 Data 64 KiB (x10)
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L1 Instruction 128 KiB (x10)
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L2 Unified 4096 KiB (x5)
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Load Average: 1.56, 1.67, 1.81
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-----------------------------------------------------------------------------------------------
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Benchmark Time CPU Iterations
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-----------------------------------------------------------------------------------------------
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logsumexp_performance<float>/64/real_time 388 ns 388 ns 1797191
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logsumexp_performance<float>/128/real_time 761 ns 761 ns 890017
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logsumexp_performance<float>/256/real_time 1513 ns 1513 ns 460217
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logsumexp_performance<float>/512/real_time 3026 ns 3026 ns 231454
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logsumexp_performance<float>/1024/real_time 6043 ns 6043 ns 113901
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logsumexp_performance<float>/2048/real_time 12084 ns 12084 ns 57590
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logsumexp_performance<float>/4096/real_time 24240 ns 24240 ns 28835
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logsumexp_performance<float>/8192/real_time 48326 ns 48323 ns 14478
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logsumexp_performance<float>/16384/real_time 96645 ns 96642 ns 7181
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logsumexp_performance<float>/32768/real_time 193351 ns 193351 ns 3607
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logsumexp_performance<float>/65536/real_time 386537 ns 386538 ns 1810
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logsumexp_performance<float>/131072/real_time 774055 ns 774056 ns 894
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logsumexp_performance<float>/262144/real_time 1548913 ns 1548847 ns 451
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logsumexp_performance<float>/524288/real_time 3092771 ns 3092770 ns 226
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logsumexp_performance<float>/1048576/real_time 6188087 ns 6188089 ns 112
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logsumexp_performance<float>/real_time_BigO 5.90 N 5.90 N
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logsumexp_performance<float>/real_time_RMS 0 % 0 %
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logsumexp_performance<double>/64/real_time 388 ns 388 ns 1806669
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logsumexp_performance<double>/128/real_time 770 ns 770 ns 898340
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logsumexp_performance<double>/256/real_time 1534 ns 1534 ns 454768
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logsumexp_performance<double>/512/real_time 3063 ns 3063 ns 228057
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logsumexp_performance<double>/1024/real_time 6126 ns 6126 ns 112667
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logsumexp_performance<double>/2048/real_time 12243 ns 12243 ns 56963
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logsumexp_performance<double>/4096/real_time 24476 ns 24476 ns 28485
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logsumexp_performance<double>/8192/real_time 48979 ns 48978 ns 14215
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logsumexp_performance<double>/16384/real_time 97929 ns 97929 ns 7070
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logsumexp_performance<double>/32768/real_time 195826 ns 195826 ns 3560
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logsumexp_performance<double>/65536/real_time 391855 ns 391835 ns 1787
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logsumexp_performance<double>/131072/real_time 784119 ns 784110 ns 882
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logsumexp_performance<double>/262144/real_time 1566408 ns 1566386 ns 446
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logsumexp_performance<double>/524288/real_time 3151649 ns 3150955 ns 223
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logsumexp_performance<double>/1048576/real_time 6300578 ns 6299027 ns 110
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logsumexp_performance<double>/real_time_BigO 6.01 N 6.01 N
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```
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[heading References]
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* Higham, Nicholas J. [@https://nhigham.com/2021/01/05/what-is-the-log-sum-exp-function/ What is the Log-Sum-Exp Function?]
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[endsect]
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