mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
synced 2024-11-14 10:39:05 +00:00
137 lines
4.4 KiB
C++
137 lines
4.4 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_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];
|
|
first[j1] = value_type(
|
|
real(x1) - imag(x3),
|
|
imag(x1) + real(x3)
|
|
);
|
|
first[j3] = value_type(
|
|
real(x1) + imag(x3),
|
|
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);
|
|
first[j1] = value_type(
|
|
w1r * (x0r + x0i),
|
|
w1r * (x0i - x0r)
|
|
);
|
|
x0r = real(x1) + imag(x3);
|
|
x0i = imag(x1) - real(x3);
|
|
first[j3] = value_type(
|
|
w1r * (-x0r + x0i),
|
|
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);
|
|
first[j1] = value_type(
|
|
w1r * x0r - w1i * x0i,
|
|
w1r * x0i + w1i * x0r
|
|
);
|
|
x0r = real(x1) + imag(x3);
|
|
x0i = imag(x1) - real(x3);
|
|
first[j3] = value_type(
|
|
w3r * x0r - w3i * x0i,
|
|
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
|