mirror of
https://github.com/bolero-MURAKAMI/Sprout
synced 2024-11-12 21:09:01 +00:00
86 lines
4 KiB
C++
86 lines
4 KiB
C++
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/*=============================================================================
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Copyright (c) 2011-2014 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_COMPLEX_SQRT_HPP
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#define SPROUT_COMPLEX_SQRT_HPP
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#include <sprout/config.hpp>
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#include <sprout/limits.hpp>
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#include <sprout/math/isnan.hpp>
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#include <sprout/math/isinf.hpp>
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#include <sprout/math/copysign.hpp>
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#include <sprout/math/signbit.hpp>
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#include <sprout/math/abs.hpp>
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#include <sprout/math/sqrt.hpp>
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#include <sprout/complex/complex.hpp>
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#include <sprout/complex/abs.hpp>
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namespace sprout {
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//
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// sqrt
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//
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// G.6.4.2 The csqrt functions
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// csqrt(conj(z)) = conj(csqrt(z)).
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// csqrt(<28>}0 + i0) returns +0 + i0.
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// csqrt(x + i<><69>) returns +<2B><>+ i<><69>, for all x (including NaN).
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// csqrt(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
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// csqrt(-<2D><>+ iy) returns +0 + i<><69>, for finite positive-signed y.
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// csqrt(+<2B><>+ iy) returns +<2B><>+ i0, for finite positive-signed y.
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// csqrt(-<2D><>+ iNaN) returns NaN <20>} i<><69> (where the sign of the imaginary part of the result is unspecified).
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// csqrt(+<2B><>+ iNaN) returns +<2B><>+ iNaN.
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// csqrt(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite y.
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// csqrt(NaN + iNaN) returns NaN + iNaN.
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//
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::complex<T>
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sqrt_impl_1(sprout::complex<T> const& x, T const& t) {
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return sprout::complex<T>(t, sprout::math::signbit(x.imag()) ? -t : t);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::complex<T>
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sqrt_impl_2_1(sprout::complex<T> const& x, T const& t, T const& u) {
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return x.real() > T(0) ? sprout::complex<T>(u, x.imag() / t)
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: sprout::complex<T>(sprout::math::abs(x.imag()) / t, sprout::math::signbit(x.imag()) ? -u : u)
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;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::complex<T>
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sqrt_impl_2(sprout::complex<T> const& x, T const& t) {
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return sprout::detail::sqrt_impl_2_1(x, t, t / T(2));
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}
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} // namespace detail
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::complex<T>
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sqrt(sprout::complex<T> const& x) {
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typedef sprout::complex<T> type;
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return sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), x.imag())
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: sprout::math::isnan(x.real())
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? sprout::math::isnan(x.imag()) ? type(sprout::numeric_limits<T>::quiet_NaN(), sprout::numeric_limits<T>::quiet_NaN())
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: type(sprout::numeric_limits<T>::quiet_NaN(), sprout::numeric_limits<T>::quiet_NaN())
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: sprout::math::isnan(x.imag())
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? x.real() == sprout::numeric_limits<T>::infinity()
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? type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::numeric_limits<T>::quiet_NaN(), x.imag()))
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: x.real() == -sprout::numeric_limits<T>::infinity()
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? type(
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sprout::math::copysign(sprout::numeric_limits<T>::quiet_NaN(), x.imag()),
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sprout::math::copysign(sprout::numeric_limits<T>::infinity(), x.imag())
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)
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: type(sprout::numeric_limits<T>::quiet_NaN(), sprout::numeric_limits<T>::quiet_NaN())
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: x.real() == sprout::numeric_limits<T>::infinity()
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? type(sprout::numeric_limits<T>::infinity(), (x.imag() == 0 ? x.imag() : sprout::math::copysign(T(0), x.imag())))
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: x.real() == -sprout::numeric_limits<T>::infinity()
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? type(T(0), sprout::math::copysign(T(0), x.imag()))
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: x.real() == 0 && x.imag() == 0 ? type(T(0), x.imag())
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: x.real() == 0 ? sprout::detail::sqrt_impl_1(x, sprout::math::sqrt(sprout::math::abs(x.imag()) / T(2)))
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: sprout::detail::sqrt_impl_2(x, sprout::math::sqrt(T(2) * (sprout::abs(x) + sprout::math::abs(x.real()))))
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;
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}
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} // namespace sprout
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#endif // #ifndef SPROUT_COMPLEX_SQRT_HPP
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