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#ifndef KISSFFT_I32_CLASS_HH
#define KISSFFT_I32_CLASS_HH
#include <complex>
#include <utility>
#include <vector>
// TODO1: substitute complex<type> (behaviour not defined for nonfloats), should be faster
// TODO2: use std:: namespace
// TODO3: make unittests for all ffts (c, cpp, i32)
template <typename DType>
struct complex_s
{
DType real;
DType imag;
};
class kissfft_i32
{
private:
using scalar_type = int32_t;
using cpx_type = complex<int32_t>;
scalar_type _scale_factor;
std::size_t _nfft;
bool _inverse;
std::vector<cpx_type> _twiddles;
std::vector<std::size_t> _stageRadix;
std::vector<std::size_t> _stageRemainder;
public:
// scale_factor: upscale twiddle-factors otherwise they lie between 0..1 (out of range for integer) --> fixed point math
kissfft_i32(const std::size_t nfft, const bool inverse, const double scale_factor = 1024.0)
: _scale_factor(scalar_type(scale_factor)), _nfft(nfft), _inverse(inverse)
{
// fill twiddle factors
_twiddles.resize(_nfft);
const double phinc = (_inverse ? 2 : -2) * acos(-1.0) / _nfft;
for (std::size_t i = 0; i < _nfft; ++i)
{
_twiddles[i] = scale_factor * exp(complex<double>(0, i * phinc));
}
//factorize
//start factoring out 4's, then 2's, then 3,5,7,9,...
std::size_t n = _nfft;
std::size_t p = 4;
do
{
while (n % p)
{
switch (p)
{
case 4:
p = 2;
break;
case 2:
p = 3;
break;
default:
p += 2;
break;
}
if (p * p > n) p = n;// no more factors
}
n /= p;
_stageRadix.push_back(p);
_stageRemainder.push_back(n);
} while (n > 1);
}
/// Calculates the complex Discrete Fourier Transform.
///
/// The size of the passed arrays must be passed in the constructor.
/// The sum of the squares of the absolute values in the @c dst
/// array will be @c N times the sum of the squares of the absolute
/// values in the @c src array, where @c N is the size of the array.
/// In other words, the l_2 norm of the resulting array will be
/// @c sqrt(N) times as big as the l_2 norm of the input array.
/// This is also the case when the inverse flag is set in the
/// constructor. Hence when applying the same transform twice, but with
/// the inverse flag changed the second time, then the result will
/// be equal to the original input times @c N.
void transform(const cpx_type * FSrc,
cpx_type * FDst,
const std::size_t stage = 0,
const std::size_t fstride = 1,
const std::size_t in_stride = 1) const
{
const std::size_t p = _stageRadix[stage];
const std::size_t m = _stageRemainder[stage];
cpx_type *const Fout_beg = FDst;
cpx_type *const Fout_end = FDst + p * m;
if (m == 1)
{
do
{
*FDst = *FSrc;
FSrc += fstride * in_stride;
} while (++FDst != Fout_end);
}
else
{
do
{
// recursive call:
// DFT of size m*p performed by doing
// p instances of smaller DFTs of size m,
// each one takes a decimated version of the input
transform(FSrc, FDst, stage + 1, fstride * p, in_stride);
FSrc += fstride * in_stride;
} while ((FDst += m) != Fout_end);
}
FDst = Fout_beg;
// recombine the p smaller DFTs
switch (p)
{
case 2:
kf_bfly2(FDst, fstride, m);
break;
case 3:
kf_bfly3(FDst, fstride, m);
break;
case 4:
kf_bfly4(FDst, fstride, m);
break;
case 5:
kf_bfly5(FDst, fstride, m);
break;
default:
kf_bfly_generic(FDst, fstride, m, p);
break;
}
}
private:
void kf_bfly2(cpx_type *const Fout, const size_t fstride, const std::size_t m) const
{
for (std::size_t k = 0; k < m; ++k)
{
const cpx_type t = (Fout[m + k] * _twiddles[k * fstride]) / _scale_factor;
Fout[m + k] = Fout[k] - t;
Fout[k] += t;
}
}
void kf_bfly3(cpx_type *Fout, const std::size_t fstride, const std::size_t m) const
{
std::size_t k = m;
const std::size_t m2 = 2 * m;
const cpx_type *tw1, *tw2;
cpx_type scratch[5];
const cpx_type epi3 = _twiddles[fstride * m];
tw1 = tw2 = &_twiddles[0];
do
{
scratch[1] = (Fout[m] * *tw1) / _scale_factor;
scratch[2] = (Fout[m2] * *tw2) / _scale_factor;
scratch[3] = scratch[1] + scratch[2];
scratch[0] = scratch[1] - scratch[2];
tw1 += fstride;
tw2 += fstride * 2;
Fout[m] = Fout[0] - (scratch[3] / 2);
scratch[0] *= epi3.imag();
scratch[0] /= _scale_factor;
Fout[0] += scratch[3];
Fout[m2] = cpx_type(Fout[m].real() + scratch[0].imag(), Fout[m].imag() - scratch[0].real());
Fout[m] += cpx_type(-scratch[0].imag(), scratch[0].real());
++Fout;
} while (--k);
}
void kf_bfly4(cpx_type *const Fout, const std::size_t fstride, const std::size_t m) const
{
cpx_type scratch[7];
const scalar_type negative_if_inverse = _inverse ? -1 : +1;
for (std::size_t k = 0; k < m; ++k)
{
scratch[0] = (Fout[k + m] * _twiddles[k * fstride]) / _scale_factor;
scratch[1] = (Fout[k + 2 * m] * _twiddles[k * fstride * 2]) / _scale_factor;
scratch[2] = (Fout[k + 3 * m] * _twiddles[k * fstride * 3]) / _scale_factor;
scratch[5] = Fout[k] - scratch[1];
Fout[k] += scratch[1];
scratch[3] = scratch[0] + scratch[2];
scratch[4] = scratch[0] - scratch[2];
scratch[4] = cpx_type(scratch[4].imag() * negative_if_inverse,
-scratch[4].real() * negative_if_inverse);
Fout[k + 2 * m] = Fout[k] - scratch[3];
Fout[k] += scratch[3];
Fout[k + m] = scratch[5] + scratch[4];
Fout[k + 3 * m] = scratch[5] - scratch[4];
}
}
void kf_bfly5(cpx_type *const Fout, const std::size_t fstride, const std::size_t m) const
{
cpx_type *Fout0, *Fout1, *Fout2, *Fout3, *Fout4;
cpx_type scratch[13];
const cpx_type ya = _twiddles[fstride * m];
const cpx_type yb = _twiddles[fstride * 2 * m];
Fout0 = Fout;
Fout1 = Fout0 + m;
Fout2 = Fout0 + 2 * m;
Fout3 = Fout0 + 3 * m;
Fout4 = Fout0 + 4 * m;
for (std::size_t u = 0; u < m; ++u)
{
scratch[0] = *Fout0;
scratch[1] = (*Fout1 * _twiddles[u * fstride]) / _scale_factor;
scratch[2] = (*Fout2 * _twiddles[2 * u * fstride]) / _scale_factor;
scratch[3] = (*Fout3 * _twiddles[3 * u * fstride]) / _scale_factor;
scratch[4] = (*Fout4 * _twiddles[4 * u * fstride]) / _scale_factor;
scratch[7] = scratch[1] + scratch[4];
scratch[10] = scratch[1] - scratch[4];
scratch[8] = scratch[2] + scratch[3];
scratch[9] = scratch[2] - scratch[3];
*Fout0 += scratch[7];
*Fout0 += scratch[8];
scratch[5] = scratch[0] + (cpx_type(
scratch[7].real() * ya.real() + scratch[8].real() * yb.real(),
scratch[7].imag() * ya.real() + scratch[8].imag() * yb.real() ) / _scale_factor);
scratch[6] = cpx_type(
scratch[10].imag() * ya.imag() + scratch[9].imag() * yb.imag(),
-scratch[10].real() * ya.imag() - scratch[9].real() * yb.imag() ) / _scale_factor;
*Fout1 = scratch[5] - scratch[6];
*Fout4 = scratch[5] + scratch[6];
scratch[11] = scratch[0] + (cpx_type(
scratch[7].real() * yb.real() + scratch[8].real() * ya.real(),
scratch[7].imag() * yb.real() + scratch[8].imag() * ya.real() ) / _scale_factor);
scratch[12] = cpx_type(
-scratch[10].imag() * yb.imag() + scratch[9].imag() * ya.imag(),
scratch[10].real() * yb.imag() - scratch[9].real() * ya.imag() ) / _scale_factor;
*Fout2 = scratch[11] + scratch[12];
*Fout3 = scratch[11] - scratch[12];
++Fout0;
++Fout1;
++Fout2;
++Fout3;
++Fout4;
}
}
/* perform the butterfly for one stage of a mixed radix FFT */
void kf_bfly_generic(cpx_type * const Fout, const size_t fstride, const std::size_t m, const std::size_t p) const
{
const cpx_type *twiddles = &_twiddles[0];
cpx_type scratchbuf[p];
for (std::size_t u = 0; u < m; ++u)
{
std::size_t k = u;
for (std::size_t q1 = 0; q1 < p; ++q1)
{
scratchbuf[q1] = Fout[k];
k += m;
}
k = u;
for (std::size_t q1 = 0; q1 < p; ++q1)
{
std::size_t twidx = 0;
Fout[k] = scratchbuf[0];
for (std::size_t q = 1; q < p; ++q)
{
twidx += fstride * k;
if (twidx >= _nfft)
twidx -= _nfft;
Fout[k] += (scratchbuf[q] * twiddles[twidx]) / _scale_factor;
}
k += m;
}
}
}
};
#endif
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