Author: miyuki Date: Mon Feb 19 07:41:36 2018 New Revision: 325510 URL: http://llvm.org/viewvc/llvm-project?rev=325510&view=rev Log: [libcxx] Improve accuracy of complex asinh and acosh
Summary: Currently std::asinh and std::acosh use std::pow to compute x^2. This results in a significant error when computing e.g. asinh(i) or acosh(-1). This patch expresses x^2 directly via x.real() and x.imag(), like it is done in libstdc++/glibc, and adds tests that checks the accuracy. Reviewers: EricWF, mclow.lists Reviewed By: mclow.lists Subscribers: christof, cfe-commits Differential Revision: https://reviews.llvm.org/D41629 Added: libcxx/trunk/test/libcxx/numerics/complex.number/__sqr.pass.cpp Modified: libcxx/trunk/include/complex libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp Modified: libcxx/trunk/include/complex URL: http://llvm.org/viewvc/llvm-project/libcxx/trunk/include/complex?rev=325510&r1=325509&r2=325510&view=diff ============================================================================== --- libcxx/trunk/include/complex (original) +++ libcxx/trunk/include/complex Mon Feb 19 07:41:36 2018 @@ -1125,6 +1125,17 @@ pow(const _Tp& __x, const complex<_Up>& return _VSTD::pow(result_type(__x), result_type(__y)); } +// __sqr, computes pow(x, 2) + +template<class _Tp> +inline _LIBCPP_INLINE_VISIBILITY +complex<_Tp> +__sqr(const complex<_Tp>& __x) +{ + return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()), + _Tp(2) * __x.real() * __x.imag()); +} + // asinh template<class _Tp> @@ -1150,7 +1161,7 @@ asinh(const complex<_Tp>& __x) } if (__libcpp_isinf_or_builtin(__x.imag())) return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag())); - complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1))); + complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _Tp(1))); return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag())); } @@ -1184,7 +1195,7 @@ acosh(const complex<_Tp>& __x) } if (__libcpp_isinf_or_builtin(__x.imag())) return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag())); - complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1))); + complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1))); return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag())); } @@ -1318,7 +1329,7 @@ acos(const complex<_Tp>& __x) return complex<_Tp>(__pi/_Tp(2), -__x.imag()); if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag()))) return complex<_Tp>(__pi/_Tp(2), -__x.imag()); - complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1))); + complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1))); if (signbit(__x.imag())) return complex<_Tp>(abs(__z.imag()), abs(__z.real())); return complex<_Tp>(abs(__z.imag()), -abs(__z.real())); Added: libcxx/trunk/test/libcxx/numerics/complex.number/__sqr.pass.cpp URL: http://llvm.org/viewvc/llvm-project/libcxx/trunk/test/libcxx/numerics/complex.number/__sqr.pass.cpp?rev=325510&view=auto ============================================================================== --- libcxx/trunk/test/libcxx/numerics/complex.number/__sqr.pass.cpp (added) +++ libcxx/trunk/test/libcxx/numerics/complex.number/__sqr.pass.cpp Mon Feb 19 07:41:36 2018 @@ -0,0 +1,81 @@ +//===----------------------------------------------------------------------===// +// +// The LLVM Compiler Infrastructure +// +// This file is dual licensed under the MIT and the University of Illinois Open +// Source Licenses. See LICENSE.TXT for details. +// +//===----------------------------------------------------------------------===// + +// <complex> + +// template<class T> +// complex<T> +// __sqr(const complex<T>& x); + +#include <complex> +#include <cassert> + +template <class T> +void +test() +{ + const T tolerance = std::is_same<T, float>::value ? 1.e-6 : 1.e-14; + + typedef std::complex<T> cplx; + struct test_case + { + cplx value; + cplx expected; + }; + + const test_case cases[] = { + {cplx( 0, 0), cplx( 0, 0)}, + {cplx( 1, 0), cplx( 1, 0)}, + {cplx( 2, 0), cplx( 4, 0)}, + {cplx(-1, 0), cplx( 1, 0)}, + {cplx( 0, 1), cplx(-1, 0)}, + {cplx( 0, 2), cplx(-4, 0)}, + {cplx( 0, -1), cplx(-1, 0)}, + {cplx( 1, 1), cplx( 0, 2)}, + {cplx( 1, -1), cplx( 0, -2)}, + {cplx(-1, -1), cplx( 0, 2)}, + {cplx(0.5, 0), cplx(0.25, 0)}, + }; + + const unsigned num_cases = sizeof(cases) / sizeof(test_case); + for (unsigned i = 0; i < num_cases; ++i) + { + const test_case& test = cases[i]; + const std::complex<T> actual = std::__sqr(test.value); + assert(std::abs(actual.real() - test.expected.real()) < tolerance); + assert(std::abs(actual.imag() - test.expected.imag()) < tolerance); + } + + const cplx nan1 = std::__sqr(cplx(NAN, 0)); + assert(std::isnan(nan1.real())); + assert(std::isnan(nan1.imag())); + + const cplx nan2 = std::__sqr(cplx(0, NAN)); + assert(std::isnan(nan2.real())); + assert(std::isnan(nan2.imag())); + + const cplx nan3 = std::__sqr(cplx(NAN, NAN)); + assert(std::isnan(nan3.real())); + assert(std::isnan(nan3.imag())); + + const cplx inf1 = std::__sqr(cplx(INFINITY, 0)); + assert(std::isinf(inf1.real())); + assert(inf1.real() > 0); + + const cplx inf2 = std::__sqr(cplx(0, INFINITY)); + assert(std::isinf(inf2.real())); + assert(inf2.real() < 0); +} + +int main() +{ + test<float>(); + test<double>(); + test<long double>(); +} Modified: libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp URL: http://llvm.org/viewvc/llvm-project/libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp?rev=325510&r1=325509&r2=325510&view=diff ============================================================================== --- libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp (original) +++ libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/acosh.pass.cpp Mon Feb 19 07:41:36 2018 @@ -54,6 +54,15 @@ void test_edges() assert(r.imag() == 0); assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag())); } + else if (testcases[i].real() == -1 && testcases[i].imag() == 0) + { + assert(r.real() == 0); + assert(!std::signbit(r.real())); + if (std::signbit(testcases[i].imag())) + is_about(r.imag(), -pi); + else + is_about(r.imag(), pi); + } else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag())) { assert(std::isinf(r.real())); Modified: libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp URL: http://llvm.org/viewvc/llvm-project/libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp?rev=325510&r1=325509&r2=325510&view=diff ============================================================================== --- libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp (original) +++ libcxx/trunk/test/std/numerics/complex.number/complex.transcendentals/asinh.pass.cpp Mon Feb 19 07:41:36 2018 @@ -44,6 +44,15 @@ void test_edges() assert(std::signbit(r.real()) == std::signbit(testcases[i].real())); assert(std::signbit(r.imag()) == std::signbit(testcases[i].imag())); } + else if (testcases[i].real() == 0 && std::abs(testcases[i].imag()) == 1) + { + assert(r.real() == 0); + assert(std::signbit(testcases[i].imag()) == std::signbit(r.imag())); + if (std::signbit(testcases[i].imag())) + is_about(r.imag(), -pi/2); + else + is_about(r.imag(), pi/2); + } else if (std::isfinite(testcases[i].real()) && std::isinf(testcases[i].imag())) { assert(std::isinf(r.real())); _______________________________________________ cfe-commits mailing list cfe-commits@lists.llvm.org http://lists.llvm.org/cgi-bin/mailman/listinfo/cfe-commits
