mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-12-25 21:35:41 +00:00
86 lines
4 KiB
C++
86 lines
4 KiB
C++
|
/*=============================================================================
|
|||
|
|
Copyright (c) 2011-2014 Bolero MURAKAMI
|
|||
|
|
https://github.com/bolero-MURAKAMI/Sprout
|
|||
|
|
|
|||
|
|
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
|||
|
|
file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
|
|||
|
|
=============================================================================*/
|
|||
|
|
#ifndef SPROUT_COMPLEX_SQRT_HPP
|
|||
|
|
#define SPROUT_COMPLEX_SQRT_HPP
|
|||
|
|
|
|||
|
|
#include <sprout/config.hpp>
|
|||
|
|
#include <sprout/limits.hpp>
|
|||
|
|
#include <sprout/math/isnan.hpp>
|
|||
|
|
#include <sprout/math/isinf.hpp>
|
|||
|
|
#include <sprout/math/copysign.hpp>
|
|||
|
|
#include <sprout/math/signbit.hpp>
|
|||
|
|
#include <sprout/math/abs.hpp>
|
|||
|
|
#include <sprout/math/sqrt.hpp>
|
|||
|
|
#include <sprout/complex/complex.hpp>
|
|||
|
|
#include <sprout/complex/abs.hpp>
|
|||
|
|
|
|||
|
|
namespace sprout {
|
|||
|
|
//
|
|||
|
|
// sqrt
|
|||
|
|
//
|
|||
|
|
// G.6.4.2 The csqrt functions
|
|||
|
|
// csqrt(conj(z)) = conj(csqrt(z)).
|
|||
|
|
// csqrt(<28>}0 + i0) returns +0 + i0.
|
|||
|
|
// csqrt(x + i<><69>) returns +<2B><>+ i<><69>, for all x (including NaN).
|
|||
|
|
// csqrt(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
|
|||
|
|
// csqrt(-<2D><>+ iy) returns +0 + i<><69>, for finite positive-signed y.
|
|||
|
|
// csqrt(+<2B><>+ iy) returns +<2B><>+ i0, for finite positive-signed y.
|
|||
|
|
// csqrt(-<2D><>+ iNaN) returns NaN <20>} i<><69> (where the sign of the imaginary part of the result is unspecified).
|
|||
|
|
// csqrt(+<2B><>+ iNaN) returns +<2B><>+ iNaN.
|
|||
|
|
// csqrt(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite y.
|
|||
|
|
// csqrt(NaN + iNaN) returns NaN + iNaN.
|
|||
|
|
//
|
|||
|
|
namespace detail {
|
|||
|
|
template<typename T>
|
|||
|
|
inline SPROUT_CONSTEXPR sprout::complex<T>
|
|||
|
|
sqrt_impl_1(sprout::complex<T> const& x, T const& t) {
|
|||
|
|
return sprout::complex<T>(t, sprout::math::signbit(x.imag()) ? -t : t);
|
|||
|
|
}
|
|||
|
|
template<typename T>
|
|||
|
|
inline SPROUT_CONSTEXPR sprout::complex<T>
|
|||
|
|
sqrt_impl_2_1(sprout::complex<T> const& x, T const& t, T const& u) {
|
|||
|
|
return x.real() > T(0) ? sprout::complex<T>(u, x.imag() / t)
|
|||
|
|
: sprout::complex<T>(sprout::math::abs(x.imag()) / t, sprout::math::signbit(x.imag()) ? -u : u)
|
|||
|
|
;
|
|||
|
|
}
|
|||
|
|
template<typename T>
|
|||
|
|
inline SPROUT_CONSTEXPR sprout::complex<T>
|
|||
|
|
sqrt_impl_2(sprout::complex<T> const& x, T const& t) {
|
|||
|
|
return sprout::detail::sqrt_impl_2_1(x, t, t / T(2));
|
|||
|
|
}
|
|||
|
|
} // namespace detail
|
|||
|
|
template<typename T>
|
|||
|
|
inline SPROUT_CONSTEXPR sprout::complex<T>
|
|||
|
|
sqrt(sprout::complex<T> const& x) {
|
|||
|
|
typedef sprout::complex<T> type;
|
|||
|
|
return sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), x.imag())
|
|||
|
|
: sprout::math::isnan(x.real())
|
|||
|
|
? sprout::math::isnan(x.imag()) ? type(sprout::numeric_limits<T>::quiet_NaN(), sprout::numeric_limits<T>::quiet_NaN())
|
|||
|
|
: type(sprout::numeric_limits<T>::quiet_NaN(), sprout::numeric_limits<T>::quiet_NaN())
|
|||
|
|
: sprout::math::isnan(x.imag())
|
|||
|
|
? x.real() == sprout::numeric_limits<T>::infinity()
|
|||
|
|
? type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::numeric_limits<T>::quiet_NaN(), x.imag()))
|
|||
|
|
: x.real() == -sprout::numeric_limits<T>::infinity()
|
|||
|
|
? type(
|
|||
|
|
sprout::math::copysign(sprout::numeric_limits<T>::quiet_NaN(), x.imag()),
|
|||
|
|
sprout::math::copysign(sprout::numeric_limits<T>::infinity(), x.imag())
|
|||
|
|
)
|
|||
|
|
: type(sprout::numeric_limits<T>::quiet_NaN(), sprout::numeric_limits<T>::quiet_NaN())
|
|||
|
|
: x.real() == sprout::numeric_limits<T>::infinity()
|
|||
|
|
? type(sprout::numeric_limits<T>::infinity(), (x.imag() == 0 ? x.imag() : sprout::math::copysign(T(0), x.imag())))
|
|||
|
|
: x.real() == -sprout::numeric_limits<T>::infinity()
|
|||
|
|
? type(T(0), sprout::math::copysign(T(0), x.imag()))
|
|||
|
|
: x.real() == 0 && x.imag() == 0 ? type(T(0), x.imag())
|
|||
|
|
: x.real() == 0 ? sprout::detail::sqrt_impl_1(x, sprout::math::sqrt(sprout::math::abs(x.imag()) / T(2)))
|
|||
|
|
: sprout::detail::sqrt_impl_2(x, sprout::math::sqrt(T(2) * (sprout::abs(x) + sprout::math::abs(x.real()))))
|
|||
|
|
;
|
|||
|
|
}
|
|||
|
|
} // namespace sprout
|
|||
|
|
|
|||
|
|
#endif // #ifndef SPROUT_COMPLEX_SQRT_HPP
|