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https://gitlab.com/libeigen/eigen.git
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bde6741641
Replaces `std::sqrt` with `complex_sqrt` for all platforms (previously `complex_sqrt` was only used for CUDA and MSVC), and implements custom `complex_rsqrt`. Also introduces `numext::rsqrt` to simplify implementation, and modified `numext::hypot` to adhere to IEEE IEC 6059 for special cases. The `complex_sqrt` and `complex_rsqrt` implementations were found to be significantly faster than `std::sqrt<std::complex<T>>` and `1/numext::sqrt<std::complex<T>>`. Benchmark file attached. ``` GCC 10, Intel Xeon, x86_64: --------------------------------------------------------------------------- Benchmark Time CPU Iterations --------------------------------------------------------------------------- BM_Sqrt<std::complex<float>> 9.21 ns 9.21 ns 73225448 BM_StdSqrt<std::complex<float>> 17.1 ns 17.1 ns 40966545 BM_Sqrt<std::complex<double>> 8.53 ns 8.53 ns 81111062 BM_StdSqrt<std::complex<double>> 21.5 ns 21.5 ns 32757248 BM_Rsqrt<std::complex<float>> 10.3 ns 10.3 ns 68047474 BM_DivSqrt<std::complex<float>> 16.3 ns 16.3 ns 42770127 BM_Rsqrt<std::complex<double>> 11.3 ns 11.3 ns 61322028 BM_DivSqrt<std::complex<double>> 16.5 ns 16.5 ns 42200711 Clang 11, Intel Xeon, x86_64: --------------------------------------------------------------------------- Benchmark Time CPU Iterations --------------------------------------------------------------------------- BM_Sqrt<std::complex<float>> 7.46 ns 7.45 ns 90742042 BM_StdSqrt<std::complex<float>> 16.6 ns 16.6 ns 42369878 BM_Sqrt<std::complex<double>> 8.49 ns 8.49 ns 81629030 BM_StdSqrt<std::complex<double>> 21.8 ns 21.7 ns 31809588 BM_Rsqrt<std::complex<float>> 8.39 ns 8.39 ns 82933666 BM_DivSqrt<std::complex<float>> 14.4 ns 14.4 ns 48638676 BM_Rsqrt<std::complex<double>> 9.83 ns 9.82 ns 70068956 BM_DivSqrt<std::complex<double>> 15.7 ns 15.7 ns 44487798 Clang 9, Pixel 2, aarch64: --------------------------------------------------------------------------- Benchmark Time CPU Iterations --------------------------------------------------------------------------- BM_Sqrt<std::complex<float>> 24.2 ns 24.1 ns 28616031 BM_StdSqrt<std::complex<float>> 104 ns 103 ns 6826926 BM_Sqrt<std::complex<double>> 31.8 ns 31.8 ns 22157591 BM_StdSqrt<std::complex<double>> 128 ns 128 ns 5437375 BM_Rsqrt<std::complex<float>> 31.9 ns 31.8 ns 22384383 BM_DivSqrt<std::complex<float>> 99.2 ns 98.9 ns 7250438 BM_Rsqrt<std::complex<double>> 46.0 ns 45.8 ns 15338689 BM_DivSqrt<std::complex<double>> 119 ns 119 ns 5898944 ```
260 lines
8.4 KiB
C++
260 lines
8.4 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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template<typename T, typename U>
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bool check_if_equal_or_nans(const T& actual, const U& expected) {
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return ((actual == expected) || ((numext::isnan)(actual) && (numext::isnan)(expected)));
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}
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template<typename T, typename U>
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bool check_if_equal_or_nans(const std::complex<T>& actual, const std::complex<U>& expected) {
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return check_if_equal_or_nans(numext::real(actual), numext::real(expected))
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&& check_if_equal_or_nans(numext::imag(actual), numext::imag(expected));
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}
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template<typename T, typename U>
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bool test_is_equal_or_nans(const T& actual, const U& expected)
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{
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if (check_if_equal_or_nans(actual, expected)) {
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return true;
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}
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// false:
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std::cerr
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<< "\n actual = " << actual
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<< "\n expected = " << expected << "\n\n";
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return false;
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}
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#define VERIFY_IS_EQUAL_OR_NANS(a, b) VERIFY(test_is_equal_or_nans(a, b))
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template<typename T>
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void check_abs() {
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typedef typename NumTraits<T>::Real Real;
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Real zero(0);
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if(NumTraits<T>::IsSigned)
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VERIFY_IS_EQUAL(numext::abs(-T(1)), T(1));
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VERIFY_IS_EQUAL(numext::abs(T(0)), T(0));
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VERIFY_IS_EQUAL(numext::abs(T(1)), T(1));
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for(int k=0; k<100; ++k)
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{
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T x = internal::random<T>();
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if(!internal::is_same<T,bool>::value)
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x = x/Real(2);
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if(NumTraits<T>::IsSigned)
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{
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VERIFY_IS_EQUAL(numext::abs(x), numext::abs(-x));
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VERIFY( numext::abs(-x) >= zero );
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}
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VERIFY( numext::abs(x) >= zero );
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VERIFY_IS_APPROX( numext::abs2(x), numext::abs2(numext::abs(x)) );
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}
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}
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template<typename T>
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struct check_sqrt_impl {
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static void run() {
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for (int i=0; i<1000; ++i) {
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const T x = numext::abs(internal::random<T>());
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const T sqrtx = numext::sqrt(x);
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VERIFY_IS_APPROX(sqrtx*sqrtx, x);
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}
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// Corner cases.
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const T zero = T(0);
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const T one = T(1);
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const T inf = std::numeric_limits<T>::infinity();
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const T nan = std::numeric_limits<T>::quiet_NaN();
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VERIFY_IS_EQUAL(numext::sqrt(zero), zero);
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VERIFY_IS_EQUAL(numext::sqrt(inf), inf);
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VERIFY((numext::isnan)(numext::sqrt(nan)));
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VERIFY((numext::isnan)(numext::sqrt(-one)));
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}
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};
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template<typename T>
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struct check_sqrt_impl<std::complex<T> > {
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static void run() {
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typedef typename std::complex<T> ComplexT;
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for (int i=0; i<1000; ++i) {
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const ComplexT x = internal::random<ComplexT>();
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const ComplexT sqrtx = numext::sqrt(x);
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VERIFY_IS_APPROX(sqrtx*sqrtx, x);
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}
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// Corner cases.
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const T zero = T(0);
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const T one = T(1);
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const T inf = std::numeric_limits<T>::infinity();
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const T nan = std::numeric_limits<T>::quiet_NaN();
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// Set of corner cases from https://en.cppreference.com/w/cpp/numeric/complex/sqrt
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const int kNumCorners = 20;
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const ComplexT corners[kNumCorners][2] = {
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{ComplexT(zero, zero), ComplexT(zero, zero)},
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{ComplexT(-zero, zero), ComplexT(zero, zero)},
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{ComplexT(zero, -zero), ComplexT(zero, zero)},
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{ComplexT(-zero, -zero), ComplexT(zero, zero)},
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{ComplexT(one, inf), ComplexT(inf, inf)},
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{ComplexT(nan, inf), ComplexT(inf, inf)},
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{ComplexT(one, -inf), ComplexT(inf, -inf)},
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{ComplexT(nan, -inf), ComplexT(inf, -inf)},
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{ComplexT(-inf, one), ComplexT(zero, inf)},
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{ComplexT(inf, one), ComplexT(inf, zero)},
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{ComplexT(-inf, -one), ComplexT(zero, -inf)},
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{ComplexT(inf, -one), ComplexT(inf, -zero)},
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{ComplexT(-inf, nan), ComplexT(nan, inf)},
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{ComplexT(inf, nan), ComplexT(inf, nan)},
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{ComplexT(zero, nan), ComplexT(nan, nan)},
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{ComplexT(one, nan), ComplexT(nan, nan)},
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{ComplexT(nan, zero), ComplexT(nan, nan)},
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{ComplexT(nan, one), ComplexT(nan, nan)},
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{ComplexT(nan, -one), ComplexT(nan, nan)},
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{ComplexT(nan, nan), ComplexT(nan, nan)},
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};
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for (int i=0; i<kNumCorners; ++i) {
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const ComplexT& x = corners[i][0];
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const ComplexT sqrtx = corners[i][1];
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VERIFY_IS_EQUAL_OR_NANS(numext::sqrt(x), sqrtx);
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}
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}
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};
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template<typename T>
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void check_sqrt() {
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check_sqrt_impl<T>::run();
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}
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template<typename T>
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struct check_rsqrt_impl {
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static void run() {
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const T zero = T(0);
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const T one = T(1);
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const T inf = std::numeric_limits<T>::infinity();
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const T nan = std::numeric_limits<T>::quiet_NaN();
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for (int i=0; i<1000; ++i) {
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const T x = numext::abs(internal::random<T>());
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const T rsqrtx = numext::rsqrt(x);
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const T invx = one / x;
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VERIFY_IS_APPROX(rsqrtx*rsqrtx, invx);
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}
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// Corner cases.
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VERIFY_IS_EQUAL(numext::rsqrt(zero), inf);
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VERIFY_IS_EQUAL(numext::rsqrt(inf), zero);
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VERIFY((numext::isnan)(numext::rsqrt(nan)));
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VERIFY((numext::isnan)(numext::rsqrt(-one)));
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}
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};
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template<typename T>
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struct check_rsqrt_impl<std::complex<T> > {
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static void run() {
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typedef typename std::complex<T> ComplexT;
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const T zero = T(0);
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const T one = T(1);
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const T inf = std::numeric_limits<T>::infinity();
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const T nan = std::numeric_limits<T>::quiet_NaN();
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for (int i=0; i<1000; ++i) {
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const ComplexT x = internal::random<ComplexT>();
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const ComplexT invx = ComplexT(one, zero) / x;
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const ComplexT rsqrtx = numext::rsqrt(x);
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VERIFY_IS_APPROX(rsqrtx*rsqrtx, invx);
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}
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// GCC and MSVC differ in their treatment of 1/(0 + 0i)
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// GCC/clang = (inf, nan)
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// MSVC = (nan, nan)
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// and 1 / (x + inf i)
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// GCC/clang = (0, 0)
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// MSVC = (nan, nan)
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#if (EIGEN_COMP_GNUC)
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{
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const int kNumCorners = 20;
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const ComplexT corners[kNumCorners][2] = {
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// Only consistent across GCC, clang
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{ComplexT(zero, zero), ComplexT(zero, zero)},
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{ComplexT(-zero, zero), ComplexT(zero, zero)},
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{ComplexT(zero, -zero), ComplexT(zero, zero)},
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{ComplexT(-zero, -zero), ComplexT(zero, zero)},
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{ComplexT(one, inf), ComplexT(inf, inf)},
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{ComplexT(nan, inf), ComplexT(inf, inf)},
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{ComplexT(one, -inf), ComplexT(inf, -inf)},
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{ComplexT(nan, -inf), ComplexT(inf, -inf)},
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// Consistent across GCC, clang, MSVC
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{ComplexT(-inf, one), ComplexT(zero, inf)},
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{ComplexT(inf, one), ComplexT(inf, zero)},
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{ComplexT(-inf, -one), ComplexT(zero, -inf)},
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{ComplexT(inf, -one), ComplexT(inf, -zero)},
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{ComplexT(-inf, nan), ComplexT(nan, inf)},
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{ComplexT(inf, nan), ComplexT(inf, nan)},
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{ComplexT(zero, nan), ComplexT(nan, nan)},
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{ComplexT(one, nan), ComplexT(nan, nan)},
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{ComplexT(nan, zero), ComplexT(nan, nan)},
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{ComplexT(nan, one), ComplexT(nan, nan)},
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{ComplexT(nan, -one), ComplexT(nan, nan)},
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{ComplexT(nan, nan), ComplexT(nan, nan)},
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};
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for (int i=0; i<kNumCorners; ++i) {
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const ComplexT& x = corners[i][0];
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const ComplexT rsqrtx = ComplexT(one, zero) / corners[i][1];
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VERIFY_IS_EQUAL_OR_NANS(numext::rsqrt(x), rsqrtx);
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}
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}
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#endif
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}
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};
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template<typename T>
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void check_rsqrt() {
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check_rsqrt_impl<T>::run();
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}
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EIGEN_DECLARE_TEST(numext) {
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for(int k=0; k<g_repeat; ++k)
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{
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CALL_SUBTEST( check_abs<bool>() );
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CALL_SUBTEST( check_abs<signed char>() );
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CALL_SUBTEST( check_abs<unsigned char>() );
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CALL_SUBTEST( check_abs<short>() );
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CALL_SUBTEST( check_abs<unsigned short>() );
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CALL_SUBTEST( check_abs<int>() );
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CALL_SUBTEST( check_abs<unsigned int>() );
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CALL_SUBTEST( check_abs<long>() );
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CALL_SUBTEST( check_abs<unsigned long>() );
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CALL_SUBTEST( check_abs<half>() );
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CALL_SUBTEST( check_abs<bfloat16>() );
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CALL_SUBTEST( check_abs<float>() );
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CALL_SUBTEST( check_abs<double>() );
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CALL_SUBTEST( check_abs<long double>() );
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CALL_SUBTEST( check_abs<std::complex<float> >() );
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CALL_SUBTEST( check_abs<std::complex<double> >() );
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CALL_SUBTEST( check_sqrt<float>() );
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CALL_SUBTEST( check_sqrt<double>() );
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CALL_SUBTEST( check_sqrt<std::complex<float> >() );
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CALL_SUBTEST( check_sqrt<std::complex<double> >() );
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CALL_SUBTEST( check_rsqrt<float>() );
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CALL_SUBTEST( check_rsqrt<double>() );
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CALL_SUBTEST( check_rsqrt<std::complex<float> >() );
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CALL_SUBTEST( check_rsqrt<std::complex<double> >() );
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}
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}
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