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#include "config.h"
#include "alcomplex.h"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstddef>
#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>;
/* Because std::array doesn't have constexpr non-const accessors in C++14. */
template<typename T, size_t N>
struct our_array {
T mData[N];
};
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>
constexpr auto GetBitReverser() noexcept
{
static_assert(N <= sizeof(ushort)*8, "Too many bits for the bit-reversal table.");
our_array<ushort2, BitReverseCounter(N)> ret{};
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)
{
ret.mData[ret_i].first = static_cast<ushort>(idx);
ret.mData[ret_i].second = static_cast<ushort>(revidx);
++ret_i;
}
}
assert(ret_i == al::size(ret.mData));
return ret;
}
/* 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 auto BitReverser2 = GetBitReverser<2>();
constexpr auto BitReverser3 = GetBitReverser<3>();
constexpr auto BitReverser4 = GetBitReverser<4>();
constexpr auto BitReverser5 = GetBitReverser<5>();
constexpr auto BitReverser6 = GetBitReverser<6>();
constexpr auto BitReverser7 = GetBitReverser<7>();
constexpr auto BitReverser8 = GetBitReverser<8>();
constexpr auto BitReverser9 = GetBitReverser<9>();
constexpr auto BitReverser10 = GetBitReverser<10>();
constexpr al::span<const ushort2> gBitReverses[11]{
{}, {},
BitReverser2.mData,
BitReverser3.mData,
BitReverser4.mData,
BitReverser5.mData,
BitReverser6.mData,
BitReverser7.mData,
BitReverser8.mData,
BitReverser9.mData,
BitReverser10.mData
};
} // 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(unlikely(log2_size >= al::size(gBitReverses)))
{
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]);
}
}
else for(auto &rev : gBitReverses[log2_size])
std::swap(buffer[rev.first], buffer[rev.second]);
/* Iterative form of Danielson-Lanczos lemma */
const double pi{al::numbers::pi * sign};
size_t step2{1u};
for(size_t i{0};i < log2_size;++i)
{
const double arg{pi / static_cast<double>(step2)};
/* TODO: Would std::polar(1.0, arg) be any better? */
const std::complex<double> w{std::cos(arg), std::sin(arg)};
std::complex<double> 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<double> 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)
{
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,
[inverse_size](const std::complex<double> &c) -> std::complex<double>
{ return c * (2.0*inverse_size); });
*bufiter *= inverse_size; ++bufiter;
std::fill(bufiter, buffer.end(), std::complex<double>{});
forward_fft(buffer);
}
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