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| Original file line number | Diff line number | Diff line change |
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| // This file is part of the Acts project. | ||
| // | ||
| // Copyright (C) 2024 CERN for the benefit of the Acts 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/. | ||
|
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| #pragma once | ||
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| #include <cmath> | ||
| #include <cstdint> | ||
| #include <limits> | ||
| #include <type_traits> | ||
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| namespace Acts { | ||
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| /// @brief Fast inverse square root function | ||
| /// Taken from https://en.wikipedia.org/wiki/Fast_inverse_square_root | ||
| /// @param x the number to calculate the inverse square root of | ||
| /// @param iterations the number of newton iterations to perform | ||
| template <typename T> | ||
| constexpr T fastInverseSqrt(T x, int iterations = 1) noexcept { | ||
| static_assert(std::numeric_limits<T>::is_iec559 && | ||
| "Only IEEE 754 is supported"); | ||
| static_assert(std::is_same_v<T, float> || std::is_same_v<T, double>, | ||
| "Only float and double are supported"); | ||
| using I = std::conditional_t<std::is_same_v<T, float>, std::uint32_t, | ||
| std::uint64_t>; | ||
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| constexpr I magic = | ||
| std::is_same_v<T, float> ? 0x5f3759df : 0x5fe6eb50c7b537a9; | ||
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| union { | ||
| T f; | ||
| I i; | ||
| } u = {x}; | ||
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| u.i = magic - (u.i >> 1); | ||
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| for (int i = 0; i < iterations; ++i) { | ||
| u.f *= 1.5f - 0.5f * x * u.f * u.f; | ||
| } | ||
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| return u.f; | ||
| } | ||
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| /// @brief Fast power function @see `std::pow` | ||
| /// Taken from | ||
| /// https://martin.ankerl.com/2012/01/25/optimized-approximative-pow-in-c-and-cpp | ||
| /// @param a the base | ||
| /// @param b the exponent | ||
| constexpr double fastPow(double a, double b) { | ||
| // enable only on IEEE 754 | ||
| static_assert(std::numeric_limits<double>::is_iec559); | ||
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| constexpr std::int64_t magic = 0x3FEF127F00000000; | ||
|
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| union { | ||
| double f; | ||
| std::int64_t i; | ||
| } u = {a}; | ||
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| u.i = static_cast<std::int64_t>(b * (u.i - magic) + magic); | ||
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| return u.f; | ||
| } | ||
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| /// @brief Fast power function more precise than @see `fastPow` | ||
| /// Taken from | ||
| /// https://martin.ankerl.com/2012/01/25/optimized-approximative-pow-in-c-and-cpp | ||
| /// @param a the base | ||
| /// @param b the exponent | ||
| constexpr double fastPowMorePrecise(double a, double b) { | ||
| // binary exponentiation | ||
| double r = 1.0; | ||
| int exp = std::abs(static_cast<int>(b)); | ||
| double base = b > 0 ? a : 1 / a; | ||
| while (exp != 0) { | ||
| if ((exp & 1) != 0) { | ||
| r *= base; | ||
| } | ||
| base *= base; | ||
| exp >>= 1; | ||
| } | ||
|
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| return r * fastPow(a, b - static_cast<int>(b)); | ||
| } | ||
|
|
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| } // namespace Acts |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,92 @@ | ||
| // This file is part of the Acts project. | ||
| // | ||
| // Copyright (C) 2024 CERN for the benefit of the Acts 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/. | ||
|
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| #include <boost/test/data/test_case.hpp> | ||
| #include <boost/test/unit_test.hpp> | ||
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| #include "Acts/Tests/CommonHelpers/BenchmarkTools.hpp" | ||
| #include "Acts/Utilities/QuickMath.hpp" | ||
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| #include <cmath> | ||
| #include <random> | ||
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| namespace bdata = boost::unit_test::data; | ||
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| namespace Acts::Test { | ||
|
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| /// @brief Another fast power function @see `fastPow` | ||
| // Taken from | ||
| // https://martin.ankerl.com/2007/02/11/optimized-exponential-functions-for-java | ||
| /// @param a the base | ||
| /// @param b the exponent | ||
| constexpr double fastPowAnother(double a, double b) { | ||
| // enable only on IEEE 754 | ||
| static_assert(std::numeric_limits<double>::is_iec559); | ||
|
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| union { | ||
| double f; | ||
| std::int64_t i; | ||
| } u = {}; | ||
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| u.i = static_cast<std::int64_t>( | ||
| 9076650 * (a - 1) / (a + 1 + 4 * std::sqrt(a)) * b + 1072632447); | ||
| u.i <<= 32; | ||
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| // result seems broken? | ||
| return u.f; | ||
| } | ||
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| // Some randomness & number crunching | ||
| const unsigned int nTests = 10; | ||
| const unsigned int nReps = 10000; | ||
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| BOOST_DATA_TEST_CASE( | ||
| benchmark_pow_25, | ||
| bdata::random( | ||
| (bdata::engine = std::mt19937(), bdata::seed = 21, | ||
| bdata::distribution = std::uniform_real_distribution<double>(-4, 4))) ^ | ||
| bdata::xrange(nTests), | ||
| baseExp, index) { | ||
| (void)index; | ||
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| const double base = std::pow(10, baseExp); | ||
| const double exp = 0.25; | ||
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| std::cout << std::endl | ||
| << "Benchmarking base=" << base << ", exp=" << exp << "..." | ||
| << std::endl; | ||
| std::cout << "- void: " | ||
| << Acts::Test::microBenchmark([&] { return 0; }, nReps) | ||
| << std::endl; | ||
| std::cout << "- std::pow: " | ||
| << Acts::Test::microBenchmark([&] { return std::pow(base, exp); }, | ||
| nReps) | ||
| << std::endl; | ||
| std::cout << "- std::exp: " | ||
| << Acts::Test::microBenchmark( | ||
| [&] { return std::exp(std::log(base) * exp); }, nReps) | ||
| << std::endl; | ||
| std::cout << "- std::sqrt: " | ||
| << Acts::Test::microBenchmark( | ||
| [&] { return std::sqrt(std::sqrt(base)); }, nReps) | ||
| << std::endl; | ||
| std::cout << "- fastPow: " | ||
| << Acts::Test::microBenchmark([&] { return fastPow(base, exp); }, | ||
| nReps) | ||
| << std::endl; | ||
| std::cout << "- fastPowMorePrecise: " | ||
| << Acts::Test::microBenchmark( | ||
| [&] { return fastPowMorePrecise(base, exp); }, nReps) | ||
| << std::endl; | ||
| std::cout << "- fastPowAnother: " | ||
| << Acts::Test::microBenchmark( | ||
| [&] { return fastPowAnother(base, exp); }, nReps) | ||
| << std::endl; | ||
| } | ||
|
|
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| } // namespace Acts::Test |
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