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#include "config.h"
#include "alcomplex.h"
#include <algorithm>
#include <array>
#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>;
using complex_d = std::complex<double>;
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.");
std::array<ushort2,BitReverseCounter(N)> mData{};
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{idx};
revidx = ((revidx&0xaaaaaaaa) >> 1) | ((revidx&0x55555555) << 1);
revidx = ((revidx&0xcccccccc) >> 2) | ((revidx&0x33333333) << 2);
revidx = ((revidx&0xf0f0f0f0) >> 4) | ((revidx&0x0f0f0f0f) << 4);
revidx = ((revidx&0xff00ff00) >> 8) | ((revidx&0x00ff00ff) << 8);
revidx = (revidx >> 16) | ((revidx&0x0000ffff) << 16);
revidx >>= 32-N;
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 11-bit indices (2048 elements),
* which is large enough for the filters and effects in OpenAL Soft. Larger FFT
* requests 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 BitReverser<11> BitReverser11{};
constexpr std::array<al::span<const ushort2>,12> gBitReverses{{
{}, {},
BitReverser2.mData,
BitReverser3.mData,
BitReverser4.mData,
BitReverser5.mData,
BitReverser6.mData,
BitReverser7.mData,
BitReverser8.mData,
BitReverser9.mData,
BitReverser10.mData,
BitReverser11.mData
}};
/* Lookup table for std::polar(1, pi / (1<<index)); */
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)},
{static_cast<T>( 9.99995293809576172e-01), static_cast<T>(3.06795676296597627e-03)}
}};
} // namespace
void complex_fft(const al::span<std::complex<double>> buffer, const double 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{1_uz << i};
const size_t step{2_uz << i};
/* The first iteration of the inner loop would have u=1, which we
* can simplify to remove a number of complex multiplies.
*/
for(size_t k{0};k < fftsize;k+=step)
{
const complex_d temp{buffer[k+step2]};
buffer[k+step2] = buffer[k] - temp;
buffer[k] += temp;
}
const complex_d w{gArgAngle<double>[i].real(), gArgAngle<double>[i].imag()*sign};
complex_d u{w};
for(size_t j{1};j < step2;j++)
{
for(size_t k{j};k < fftsize;k+=step)
{
const complex_d temp{buffer[k+step2] * u};
buffer[k+step2] = buffer[k] - temp;
buffer[k] += temp;
}
u *= w;
}
}
}
else
{
assert(log2_size < 32);
for(size_t idx{1u};idx < fftsize-1;++idx)
{
size_t revidx{idx};
revidx = ((revidx&0xaaaaaaaa) >> 1) | ((revidx&0x55555555) << 1);
revidx = ((revidx&0xcccccccc) >> 2) | ((revidx&0x33333333) << 2);
revidx = ((revidx&0xf0f0f0f0) >> 4) | ((revidx&0x0f0f0f0f) << 4);
revidx = ((revidx&0xff00ff00) >> 8) | ((revidx&0x00ff00ff) << 8);
revidx = (revidx >> 16) | ((revidx&0x0000ffff) << 16);
revidx >>= 32-log2_size;
if(idx < revidx)
std::swap(buffer[idx], buffer[revidx]);
}
const double pi{al::numbers::pi * sign};
for(size_t i{0};i < log2_size;++i)
{
const size_t step2{1_uz << i};
const size_t step{2_uz << i};
for(size_t k{0};k < fftsize;k+=step)
{
const complex_d temp{buffer[k+step2]};
buffer[k+step2] = buffer[k] - temp;
buffer[k] += temp;
}
const double arg{pi / static_cast<double>(step2)};
const complex_d w{std::polar(1.0, arg)};
complex_d u{w};
for(size_t j{1};j < step2;j++)
{
for(size_t k{j};k < fftsize;k+=step)
{
const complex_d temp{buffer[k+step2] * u};
buffer[k+step2] = buffer[k] - temp;
buffer[k] += temp;
}
u *= w;
}
}
}
}
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);
}
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