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add C++14 constexpr fft/ifft

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This commit is contained in:
bolero-MURAKAMI 2014-04-18 11:34:28 +09:00
parent 6a6fdd41ec
commit 07b5f69ebb
5 changed files with 205 additions and 4 deletions
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10
sprout/complex/complex.hpp
View file

@ -41,13 +41,19 @@ namespace sprout {
SPROUT_CONSTEXPR complex(complex<X> const& other) SPROUT_NOEXCEPT
: re_(other.real()), im_(other.imag())
{}
SPROUT_CONSTEXPR T real() const SPROUT_NOEXCEPT {
SPROUT_CONSTEXPR T const& real() const SPROUT_NOEXCEPT {
return re_;
}
SPROUT_CXX14_CONSTEXPR T& real() SPROUT_NOEXCEPT {
return re_;
}
SPROUT_CXX14_CONSTEXPR void real(T re) SPROUT_NOEXCEPT {
re_ = re;
}
SPROUT_CONSTEXPR T imag() const SPROUT_NOEXCEPT {
SPROUT_CONSTEXPR T const& imag() const SPROUT_NOEXCEPT {
return im_;
}
SPROUT_CXX14_CONSTEXPR T& imag() SPROUT_NOEXCEPT {
return im_;
}
SPROUT_CXX14_CONSTEXPR void imag(T im) SPROUT_NOEXCEPT {

14
sprout/complex/values.hpp
View file

@ -23,16 +23,26 @@ namespace sprout {
// 26.4.7, values:
template<typename T>
inline SPROUT_CONSTEXPR T
inline SPROUT_CONSTEXPR T const&
real(sprout::complex<T> const& x) {
return x.real();
}
template<typename T>
inline SPROUT_CONSTEXPR T
inline SPROUT_CONSTEXPR T const&
imag(sprout::complex<T> const& x) {
return x.imag();
}
template<typename T>
inline SPROUT_CXX14_CONSTEXPR T&
real(sprout::complex<T>& x) {
return x.real();
}
template<typename T>
inline SPROUT_CXX14_CONSTEXPR T&
imag(sprout::complex<T>& x) {
return x.imag();
}
template<typename T>
inline SPROUT_CONSTEXPR T
abs(sprout::complex<T> const& x) {
return sprout::sqrt(sprout::norm(x));

2
sprout/numeric/fft.hpp
View file

@ -9,6 +9,8 @@
#define SPROUT_NUMERIC_FFT_HPP
#include <sprout/config.hpp>
#include <sprout/numeric/fft/fft.hpp>
#include <sprout/numeric/fft/ifft.hpp>
#include <sprout/numeric/fft/bitrev_table.hpp>
#endif // #ifndef SPROUT_NUMERIC_FFT_HPP

125
sprout/numeric/fft/fft.hpp Normal file
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@ -0,0 +1,125 @@
/*=============================================================================
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_NUMERIC_FFT_FFT_HPP
#define SPROUT_NUMERIC_FFT_FFT_HPP
#include <iterator>
#include <sprout/config.hpp>
#include <sprout/complex.hpp>
#include <sprout/math/cos.hpp>
#include <sprout/math/sin.hpp>
#include <sprout/math/constants.hpp>
#include <sprout/utility/swap.hpp>
namespace sprout {
//
// fft
//
template<typename RandomAccessIterator>
inline SPROUT_CXX14_CONSTEXPR void
fft(RandomAccessIterator first, RandomAccessIterator last) {
typedef typename std::iterator_traits<RandomAccessIterator>::difference_type difference_type;
typedef typename std::iterator_traits<RandomAccessIterator>::value_type value_type;
typedef typename value_type::value_type elem_type;
using sprout::real;
using sprout::imag;
difference_type const size = last - first;
// scrambler
for (difference_type i = 0, j = 1; j < size - 1; ++j) {
for (difference_type k = size >> 1; k > (i ^= k); k >>= 1)
;
if (j < i) {
sprout::swap(first[i], first[j]);
}
}
// L shaped butterflies
elem_type const theta = -(sprout::math::half_pi<elem_type>() / size);
for (difference_type m = 4; m <= size; m <<= 1) {
difference_type mq = m >> 2;
// W == 1
for (difference_type k = mq; k >= 1; k >>= 2) {
for (difference_type j = mq - k; j < mq - (k >> 1); ++j) {
difference_type j1 = j + mq;
difference_type j2 = j1 + mq;
difference_type j3 = j2 + mq;
value_type x1 = first[j] - first[j1];
first[j] += first[j1];
value_type x3 = first[j3] - first[j2];
first[j2] += first[j3];
real(first[j1]) = real(x1) - imag(x3);
imag(first[j1]) = imag(x1) + real(x3);
real(first[j3]) = real(x1) + imag(x3);
imag(first[j3]) = imag(x1) - real(x3);
}
}
if (m == size) {
continue;
}
difference_type irev = size >> 1;
elem_type w1r = sprout::cos(theta * irev);
for (difference_type k = mq; k >= 1; k >>= 2) {
for (difference_type j = m + mq - k; j < m + mq - (k >> 1); ++j) {
difference_type j1 = j + mq;
difference_type j2 = j1 + mq;
difference_type j3 = j2 + mq;
value_type x1 = first[j] - first[j1];
first[j] += first[j1];
value_type x3 = first[j3] - first[j2];
first[j2] += first[j3];
elem_type x0r = real(x1) - imag(x3);
elem_type x0i = imag(x1) + real(x3);
real(first[j1]) = w1r * (x0r + x0i);
imag(first[j1]) = w1r * (x0i - x0r);
x0r = real(x1) + imag(x3);
x0i = imag(x1) - real(x3);
real(first[j3]) = w1r * (-x0r + x0i);
imag(first[j3]) = w1r * (-x0i - x0r);
}
}
for (difference_type i = 2 * m; i < size; i += m) {
for (difference_type k = size >> 1; k > (irev ^= k); k >>= 1)
;
elem_type w1r = sprout::cos(theta * irev);
elem_type w1i = sprout::sin(theta * irev);
elem_type w3r = sprout::cos(theta * 3 * irev);
elem_type w3i = sprout::sin(theta * 3 * irev);
for (difference_type k = mq; k >= 1; k >>= 2) {
for (difference_type j = i + mq - k; j < i + mq - (k >> 1); ++j) {
difference_type j1 = j + mq;
difference_type j2 = j1 + mq;
difference_type j3 = j2 + mq;
value_type x1 = first[j] - first[j1];
first[j] += first[j1];
value_type x3 = first[j3] - first[j2];
first[j2] += first[j3];
elem_type x0r = real(x1) - imag(x3);
elem_type x0i = imag(x1) + real(x3);
real(first[j1]) = w1r * x0r - w1i * x0i;
imag(first[j1]) = w1r * x0i + w1i * x0r;
x0r = real(x1) + imag(x3);
x0i = imag(x1) - real(x3);
real(first[j3]) = w3r * x0r - w3i * x0i;
imag(first[j3]) = w3r * x0i + w3i * x0r;
}
}
}
}
// radix 2 butterflies
difference_type mq = size >> 1;
for (difference_type k = mq; k >= 1; k >>= 2) {
for (difference_type j = mq - k; j < mq - (k >> 1); ++j) {
difference_type j1 = mq + j;
value_type x0 = first[j] - first[j1];
first[j] += first[j1];
first[j1] = x0;
}
}
}
} // namespace sprout
#endif // #ifndef SPROUT_NUMERIC_FFT_FFT_HPP

58
sprout/numeric/fft/ifft.hpp Normal file
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@ -0,0 +1,58 @@
/*=============================================================================
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_NUMERIC_FFT_IFFT_HPP
#define SPROUT_NUMERIC_FFT_IFFT_HPP
#include <iterator>
#include <sprout/config.hpp>
#include <sprout/complex.hpp>
#include <sprout/algorithm/cxx14/transform.hpp>
#include <sprout/numeric/fft/fft.hpp>
namespace sprout {
namespace detail {
struct conj_value {
public:
template<typename Complex>
SPROUT_CONSTEXPR Complex operator()(Complex const& x) const {
return conj(x);
}
};
template<typename Size>
struct conj_div_value {
private:
Size n_;
public:
explicit SPROUT_CONSTEXPR conj_div_value(Size n)
: n_(n)
{}
template<typename Complex>
SPROUT_CONSTEXPR Complex operator()(Complex const& x) const {
return conj(x) / typename Complex::value_type(n_);
}
};
template<typename Size>
SPROUT_CONSTEXPR sprout::detail::conj_div_value<Size>
conj_div(Size n) {
return sprout::detail::conj_div_value<Size>(n);
}
} // namespace detail
//
// ifft
//
template<typename RandomAccessIterator>
inline SPROUT_CXX14_CONSTEXPR void
ifft(RandomAccessIterator first, RandomAccessIterator last) {
sprout::transform(first, last, first, sprout::detail::conj_value());
sprout::fft(first, last);
sprout::transform(first, last, first, sprout::detail::conj_div(last - first));
}
} // namespace sprout
#endif // #ifndef SPROUT_NUMERIC_FFT_IFFT_HPP