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0f0b4bf029
This PR removes unused header inclusion in C++ files. Pull Request resolved: https://github.com/pytorch/pytorch/pull/165763 Approved by: https://github.com/Skylion007
92 lines
3.1 KiB
C++
92 lines
3.1 KiB
C++
#include <c10/util/complex.h>
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// Note [ Complex Square root in libc++]
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// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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// In libc++ complex square root is computed using polar form
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// This is a reasonably fast algorithm, but can result in significant
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// numerical errors when arg is close to 0, pi/2, pi, or 3pi/4
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// In that case provide a more conservative implementation which is
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// slower but less prone to those kinds of errors
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// In libstdc++ complex square root yield invalid results
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// for -x-0.0j unless C99 csqrt/csqrtf fallbacks are used
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#if defined(_LIBCPP_VERSION) || \
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(defined(__GLIBCXX__) && !defined(_GLIBCXX11_USE_C99_COMPLEX))
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namespace {
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template <typename T>
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c10::complex<T> compute_csqrt(const c10::complex<T>& z) {
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constexpr auto half = T(.5);
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// Trust standard library to correctly handle infs and NaNs
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if (std::isinf(z.real()) || std::isinf(z.imag()) || std::isnan(z.real()) ||
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std::isnan(z.imag())) {
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return static_cast<c10::complex<T>>(
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std::sqrt(static_cast<std::complex<T>>(z)));
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}
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// Special case for square root of pure imaginary values
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if (z.real() == T(0)) {
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if (z.imag() == T(0)) {
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return c10::complex<T>(T(0), z.imag());
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}
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auto v = std::sqrt(half * std::abs(z.imag()));
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return c10::complex<T>(v, std::copysign(v, z.imag()));
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}
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// At this point, z is non-zero and finite
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if (z.real() >= 0.0) {
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auto t = std::sqrt((z.real() + std::abs(z)) * half);
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return c10::complex<T>(t, half * (z.imag() / t));
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}
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auto t = std::sqrt((-z.real() + std::abs(z)) * half);
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return c10::complex<T>(
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half * std::abs(z.imag() / t), std::copysign(t, z.imag()));
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}
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// Compute complex arccosine using formula from W. Kahan
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// "Branch Cuts for Complex Elementary Functions" 1986 paper:
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// cacos(z).re = 2*atan2(sqrt(1-z).re(), sqrt(1+z).re())
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// cacos(z).im = asinh((sqrt(conj(1+z))*sqrt(1-z)).im())
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template <typename T>
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c10::complex<T> compute_cacos(const c10::complex<T>& z) {
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auto constexpr one = T(1);
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// Trust standard library to correctly handle infs and NaNs
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if (std::isinf(z.real()) || std::isinf(z.imag()) || std::isnan(z.real()) ||
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std::isnan(z.imag())) {
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return static_cast<c10::complex<T>>(
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std::acos(static_cast<std::complex<T>>(z)));
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}
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auto a = compute_csqrt(c10::complex<T>(one - z.real(), -z.imag()));
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auto b = compute_csqrt(c10::complex<T>(one + z.real(), z.imag()));
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auto c = compute_csqrt(c10::complex<T>(one + z.real(), -z.imag()));
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auto r = T(2) * std::atan2(a.real(), b.real());
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// Explicitly unroll (a*c).imag()
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auto i = std::asinh(a.real() * c.imag() + a.imag() * c.real());
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return c10::complex<T>(r, i);
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}
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} // anonymous namespace
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namespace c10_complex_math {
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namespace _detail {
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c10::complex<float> sqrt(const c10::complex<float>& in) {
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return compute_csqrt(in);
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}
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c10::complex<double> sqrt(const c10::complex<double>& in) {
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return compute_csqrt(in);
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}
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c10::complex<float> acos(const c10::complex<float>& in) {
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return compute_cacos(in);
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}
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c10::complex<double> acos(const c10::complex<double>& in) {
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return compute_cacos(in);
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}
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} // namespace _detail
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} // namespace c10_complex_math
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#endif
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