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#include "config.h"
#include "alcomplex.h"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstddef>
#include <functional>
#include <utility>
#include "albit.h"
#include "alnumbers.h"
#include "alnumeric.h"
#include "opthelpers.h"
namespace {
using ushort = unsigned short;
using ushort2 = std::pair<ushort,ushort>;
constexpr size_t BitReverseCounter(size_t log2_size) noexcept
{
/* Some magic math that calculates the number of swaps needed for a
* sequence of bit-reversed indices when index < reversed_index.
*/
return (1u<<(log2_size-1)) - (1u<<((log2_size-1u)/2u));
}
template<size_t N>
struct BitReverser {
static_assert(N <= sizeof(ushort)*8, "Too many bits for the bit-reversal table.");
ushort2 mData[BitReverseCounter(N)]{};
constexpr BitReverser()
{
const size_t fftsize{1u << N};
size_t ret_i{0};
/* Bit-reversal permutation applied to a sequence of fftsize items. */
for(size_t idx{1u};idx < fftsize-1;++idx)
{
size_t revidx{0u}, imask{idx};
for(size_t i{0};i < N;++i)
{
revidx = (revidx<<1) | (imask&1);
imask >>= 1;
}
if(idx < revidx)
{
mData[ret_i].first = static_cast<ushort>(idx);
mData[ret_i].second = static_cast<ushort>(revidx);
++ret_i;
}
}
assert(ret_i == std::size(mData));
}
};
/* These bit-reversal swap tables support up to 10-bit indices (1024 elements),
* which is the largest used by OpenAL Soft's filters and effects. Larger FFT
* requests, used by some utilities where performance is less important, will
* use a slower table-less path.
*/
constexpr BitReverser<2> BitReverser2{};
constexpr BitReverser<3> BitReverser3{};
constexpr BitReverser<4> BitReverser4{};
constexpr BitReverser<5> BitReverser5{};
constexpr BitReverser<6> BitReverser6{};
constexpr BitReverser<7> BitReverser7{};
constexpr BitReverser<8> BitReverser8{};
constexpr BitReverser<9> BitReverser9{};
constexpr BitReverser<10> BitReverser10{};
constexpr std::array<al::span<const ushort2>,11> gBitReverses{{
{}, {},
BitReverser2.mData,
BitReverser3.mData,
BitReverser4.mData,
BitReverser5.mData,
BitReverser6.mData,
BitReverser7.mData,
BitReverser8.mData,
BitReverser9.mData,
BitReverser10.mData
}};
template<typename T>
constexpr std::array<std::complex<T>,gBitReverses.size()-1> gArgAngle{{
{static_cast<T>(-1.00000000000000000e+00), static_cast<T>(0.00000000000000000e+00)},
{static_cast<T>( 0.00000000000000000e+00), static_cast<T>(1.00000000000000000e+00)},
{static_cast<T>( 7.07106781186547524e-01), static_cast<T>(7.07106781186547524e-01)},
{static_cast<T>( 9.23879532511286756e-01), static_cast<T>(3.82683432365089772e-01)},
{static_cast<T>( 9.80785280403230449e-01), static_cast<T>(1.95090322016128268e-01)},
{static_cast<T>( 9.95184726672196886e-01), static_cast<T>(9.80171403295606020e-02)},
{static_cast<T>( 9.98795456205172393e-01), static_cast<T>(4.90676743274180143e-02)},
{static_cast<T>( 9.99698818696204220e-01), static_cast<T>(2.45412285229122880e-02)},
{static_cast<T>( 9.99924701839144541e-01), static_cast<T>(1.22715382857199261e-02)},
{static_cast<T>( 9.99981175282601143e-01), static_cast<T>(6.13588464915447536e-03)},
}};
} // namespace
template<typename Real>
std::enable_if_t<std::is_floating_point<Real>::value>
complex_fft(const al::span<std::complex<Real>> buffer, const al::type_identity_t<Real> sign)
{
const size_t fftsize{buffer.size()};
/* Get the number of bits used for indexing. Simplifies bit-reversal and
* the main loop count.
*/
const size_t log2_size{static_cast<size_t>(al::countr_zero(fftsize))};
if(log2_size < gBitReverses.size()) LIKELY
{
for(auto &rev : gBitReverses[log2_size])
std::swap(buffer[rev.first], buffer[rev.second]);
/* Iterative form of Danielson-Lanczos lemma */
for(size_t i{0};i < log2_size;++i)
{
const size_t step2{1u << i};
const size_t step{2u << i};
for(size_t k{0};k < fftsize;k+=step)
{
std::complex<Real> temp{buffer[k+step2]};
buffer[k+step2] = buffer[k] - temp;
buffer[k] += temp;
}
const std::complex<Real> w{gArgAngle<Real>[i].real(), gArgAngle<Real>[i].imag()*sign};
std::complex<Real> u{w};
for(size_t j{1};j < step2;j++)
{
for(size_t k{j};k < fftsize;k+=step)
{
std::complex<Real> temp{buffer[k+step2] * u};
buffer[k+step2] = buffer[k] - temp;
buffer[k] += temp;
}
u *= w;
}
}
}
else
{
for(size_t idx{1u};idx < fftsize-1;++idx)
{
size_t revidx{0u}, imask{idx};
for(size_t i{0};i < log2_size;++i)
{
revidx = (revidx<<1) | (imask&1);
imask >>= 1;
}
if(idx < revidx)
std::swap(buffer[idx], buffer[revidx]);
}
const Real pi{al::numbers::pi_v<Real> * sign};
size_t step2{1u};
for(size_t i{0};i < log2_size;++i)
{
const Real arg{pi / static_cast<Real>(step2)};
const std::complex<Real> w{std::polar(Real{1}, arg)};
std::complex<Real> u{1.0, 0.0};
const size_t step{step2 << 1};
for(size_t j{0};j < step2;j++)
{
for(size_t k{j};k < fftsize;k+=step)
{
std::complex<Real> temp{buffer[k+step2] * u};
buffer[k+step2] = buffer[k] - temp;
buffer[k] += temp;
}
u *= w;
}
step2 <<= 1;
}
}
}
void complex_hilbert(const al::span<std::complex<double>> buffer)
{
using namespace std::placeholders;
inverse_fft(buffer);
const double inverse_size = 1.0/static_cast<double>(buffer.size());
auto bufiter = buffer.begin();
const auto halfiter = bufiter + (buffer.size()>>1);
*bufiter *= inverse_size; ++bufiter;
bufiter = std::transform(bufiter, halfiter, bufiter,
[scale=inverse_size*2.0](std::complex<double> d){ return d * scale; });
*bufiter *= inverse_size; ++bufiter;
std::fill(bufiter, buffer.end(), std::complex<double>{});
forward_fft(buffer);
}
template void complex_fft<>(const al::span<std::complex<float>> buffer, const float sign);
template void complex_fft<>(const al::span<std::complex<double>> buffer, const double sign);
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