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Serial-Studio/lib/QRealFourier/fftreal/FFTReal.hpp
Alex Spataru 87a8329c84 Move project to CMake
2024-08-10 12:58:21 -05:00

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/*****************************************************************************
FFTReal.hpp
By Laurent de Soras
--- Legal stuff ---
This program is free software. It comes without any warranty, to
the extent permitted by applicable law. You can redistribute it
and/or modify it under the terms of the Do What The Fuck You Want
To Public License, Version 2, as published by Sam Hocevar. See
http://sam.zoy.org/wtfpl/COPYING for more details.
*Tab=3***********************************************************************/
#if defined(ffft_FFTReal_CURRENT_CODEHEADER)
# error Recursive inclusion of FFTReal code header.
#endif
#define ffft_FFTReal_CURRENT_CODEHEADER
#if !defined(ffft_FFTReal_CODEHEADER_INCLUDED)
# define ffft_FFTReal_CODEHEADER_INCLUDED
/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
# include <cassert>
# include <cmath>
namespace ffft
{
static inline bool FFTReal_is_pow2(long x)
{
assert(x > 0);
return ((x & -x) == x);
}
static inline int FFTReal_get_next_pow2(long x)
{
--x;
int p = 0;
while ((x & ~0xFFFFL) != 0)
{
p += 16;
x >>= 16;
}
while ((x & ~0xFL) != 0)
{
p += 4;
x >>= 4;
}
while (x > 0)
{
++p;
x >>= 1;
}
return (p);
}
/*\\\ PUBLIC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
/*
==============================================================================
Name: ctor
Input parameters:
- length: length of the array on which we want to do a FFT. Range: power
of 2 only, > 0. Throws: std::bad_alloc
==============================================================================
*/
template<class DT>
FFTReal<DT>::FFTReal(long length)
: _length(length)
, _nbr_bits(FFTReal_get_next_pow2(length))
, _br_lut()
, _trigo_lut()
, _buffer(length)
, _trigo_osc()
{
assert(FFTReal_is_pow2(length));
assert(_nbr_bits <= MAX_BIT_DEPTH);
init_br_lut();
init_trigo_lut();
init_trigo_osc();
}
/*
==============================================================================
Name: get_length
Description:
Returns the number of points processed by this FFT object.
Returns: The number of points, power of 2, > 0.
Throws: Nothing
==============================================================================
*/
template<class DT>
long FFTReal<DT>::get_length() const
{
return (_length);
}
/*
==============================================================================
Name: do_fft
Description:
Compute the FFT of the array.
Input parameters:
- x: pointer on the source array (time).
Output parameters:
- f: pointer on the destination array (frequencies).
f [0...length(x)/2] = real values,
f [length(x)/2+1...length(x)-1] = negative imaginary values of
coefficents 1...length(x)/2-1.
Throws: Nothing
==============================================================================
*/
template<class DT>
void FFTReal<DT>::do_fft(DataType f[], const DataType x[]) const
{
assert(f != 0);
assert(f != use_buffer());
assert(x != 0);
assert(x != use_buffer());
assert(x != f);
// General case
if (_nbr_bits > 2)
{
compute_fft_general(f, x);
}
// 4-point FFT
else if (_nbr_bits == 2)
{
f[1] = x[0] - x[2];
f[3] = x[1] - x[3];
const DataType b_0 = x[0] + x[2];
const DataType b_2 = x[1] + x[3];
f[0] = b_0 + b_2;
f[2] = b_0 - b_2;
}
// 2-point FFT
else if (_nbr_bits == 1)
{
f[0] = x[0] + x[1];
f[1] = x[0] - x[1];
}
// 1-point FFT
else
{
f[0] = x[0];
}
}
/*
==============================================================================
Name: do_ifft
Description:
Compute the inverse FFT of the array. Note that data must be
post-scaled: IFFT (FFT (x)) = x * length (x). Input parameters:
- f: pointer on the source array (frequencies).
f [0...length(x)/2] = real values
f [length(x)/2+1...length(x)-1] = negative imaginary values of
coefficents 1...length(x)/2-1.
Output parameters:
- x: pointer on the destination array (time).
Throws: Nothing
==============================================================================
*/
template<class DT>
void FFTReal<DT>::do_ifft(const DataType f[], DataType x[]) const
{
assert(f != 0);
assert(f != use_buffer());
assert(x != 0);
assert(x != use_buffer());
assert(x != f);
// General case
if (_nbr_bits > 2)
{
compute_ifft_general(f, x);
}
// 4-point IFFT
else if (_nbr_bits == 2)
{
const DataType b_0 = f[0] + f[2];
const DataType b_2 = f[0] - f[2];
x[0] = b_0 + f[1] * 2;
x[2] = b_0 - f[1] * 2;
x[1] = b_2 + f[3] * 2;
x[3] = b_2 - f[3] * 2;
}
// 2-point IFFT
else if (_nbr_bits == 1)
{
x[0] = f[0] + f[1];
x[1] = f[0] - f[1];
}
// 1-point IFFT
else
{
x[0] = f[0];
}
}
/*
==============================================================================
Name: rescale
Description:
Scale an array by divide each element by its length. This function
should be called after FFT + IFFT. Input parameters:
- x: pointer on array to rescale (time or frequency).
Throws: Nothing
==============================================================================
*/
template<class DT>
void FFTReal<DT>::rescale(DataType x[]) const
{
const DataType mul = DataType(1.0 / _length);
if (_length < 4)
{
long i = _length - 1;
do
{
x[i] *= mul;
--i;
} while (i >= 0);
}
else
{
assert((_length & 3) == 0);
// Could be optimized with SIMD instruction sets (needs alignment check)
long i = _length - 4;
do
{
x[i + 0] *= mul;
x[i + 1] *= mul;
x[i + 2] *= mul;
x[i + 3] *= mul;
i -= 4;
} while (i >= 0);
}
}
/*
==============================================================================
Name: use_buffer
Description:
Access the internal buffer, whose length is the FFT one.
Buffer content will be erased at each do_fft() / do_ifft() call!
This buffer cannot be used as:
- source for FFT or IFFT done with this object
- destination for FFT or IFFT done with this object
Returns:
Buffer start address
Throws: Nothing
==============================================================================
*/
template<class DT>
typename FFTReal<DT>::DataType *FFTReal<DT>::use_buffer() const
{
return (&_buffer[0]);
}
/*\\\ PROTECTED \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
/*\\\ PRIVATE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
template<class DT>
void FFTReal<DT>::init_br_lut()
{
const long length = 1L << _nbr_bits;
_br_lut.resize(length);
_br_lut[0] = 0;
long br_index = 0;
for (long cnt = 1; cnt < length; ++cnt)
{
// ++br_index (bit reversed)
long bit = length >> 1;
while (((br_index ^= bit) & bit) == 0)
{
bit >>= 1;
}
_br_lut[cnt] = br_index;
}
}
template<class DT>
void FFTReal<DT>::init_trigo_lut()
{
using namespace std;
if (_nbr_bits > 3)
{
const long total_len = (1L << (_nbr_bits - 1)) - 4;
_trigo_lut.resize(total_len);
for (int level = 3; level < _nbr_bits; ++level)
{
const long level_len = 1L << (level - 1);
DataType *const level_ptr = &_trigo_lut[get_trigo_level_index(level)];
const double mul = PI / (level_len << 1);
for (long i = 0; i < level_len; ++i)
{
level_ptr[i] = static_cast<DataType>(cos(i * mul));
}
}
}
}
template<class DT>
void FFTReal<DT>::init_trigo_osc()
{
const int nbr_osc = _nbr_bits - TRIGO_BD_LIMIT;
if (nbr_osc > 0)
{
_trigo_osc.resize(nbr_osc);
for (int osc_cnt = 0; osc_cnt < nbr_osc; ++osc_cnt)
{
OscType &osc = _trigo_osc[osc_cnt];
const long len = 1L << (TRIGO_BD_LIMIT + osc_cnt);
const double mul = (0.5 * PI) / len;
osc.set_step(mul);
}
}
}
template<class DT>
const long *FFTReal<DT>::get_br_ptr() const
{
return (&_br_lut[0]);
}
template<class DT>
const typename FFTReal<DT>::DataType *
FFTReal<DT>::get_trigo_ptr(int level) const
{
assert(level >= 3);
return (&_trigo_lut[get_trigo_level_index(level)]);
}
template<class DT>
long FFTReal<DT>::get_trigo_level_index(int level) const
{
assert(level >= 3);
return ((1L << (level - 1)) - 4);
}
// Transform in several passes
template<class DT>
void FFTReal<DT>::compute_fft_general(DataType f[], const DataType x[]) const
{
assert(f != 0);
assert(f != use_buffer());
assert(x != 0);
assert(x != use_buffer());
assert(x != f);
DataType *sf;
DataType *df;
if ((_nbr_bits & 1) != 0)
{
df = use_buffer();
sf = f;
}
else
{
df = f;
sf = use_buffer();
}
compute_direct_pass_1_2(df, x);
compute_direct_pass_3(sf, df);
for (int pass = 3; pass < _nbr_bits; ++pass)
{
compute_direct_pass_n(df, sf, pass);
DataType *const temp_ptr = df;
df = sf;
sf = temp_ptr;
}
}
template<class DT>
void FFTReal<DT>::compute_direct_pass_1_2(DataType df[],
const DataType x[]) const
{
assert(df != 0);
assert(x != 0);
assert(df != x);
const long *const bit_rev_lut_ptr = get_br_ptr();
long coef_index = 0;
do
{
const long rev_index_0 = bit_rev_lut_ptr[coef_index];
const long rev_index_1 = bit_rev_lut_ptr[coef_index + 1];
const long rev_index_2 = bit_rev_lut_ptr[coef_index + 2];
const long rev_index_3 = bit_rev_lut_ptr[coef_index + 3];
DataType *const df2 = df + coef_index;
df2[1] = x[rev_index_0] - x[rev_index_1];
df2[3] = x[rev_index_2] - x[rev_index_3];
const DataType sf_0 = x[rev_index_0] + x[rev_index_1];
const DataType sf_2 = x[rev_index_2] + x[rev_index_3];
df2[0] = sf_0 + sf_2;
df2[2] = sf_0 - sf_2;
coef_index += 4;
} while (coef_index < _length);
}
template<class DT>
void FFTReal<DT>::compute_direct_pass_3(DataType df[],
const DataType sf[]) const
{
assert(df != 0);
assert(sf != 0);
assert(df != sf);
const DataType sqrt2_2 = DataType(SQRT2 * 0.5);
long coef_index = 0;
do
{
DataType v;
df[coef_index] = sf[coef_index] + sf[coef_index + 4];
df[coef_index + 4] = sf[coef_index] - sf[coef_index + 4];
df[coef_index + 2] = sf[coef_index + 2];
df[coef_index + 6] = sf[coef_index + 6];
v = (sf[coef_index + 5] - sf[coef_index + 7]) * sqrt2_2;
df[coef_index + 1] = sf[coef_index + 1] + v;
df[coef_index + 3] = sf[coef_index + 1] - v;
v = (sf[coef_index + 5] + sf[coef_index + 7]) * sqrt2_2;
df[coef_index + 5] = v + sf[coef_index + 3];
df[coef_index + 7] = v - sf[coef_index + 3];
coef_index += 8;
} while (coef_index < _length);
}
template<class DT>
void FFTReal<DT>::compute_direct_pass_n(DataType df[], const DataType sf[],
int pass) const
{
assert(df != 0);
assert(sf != 0);
assert(df != sf);
assert(pass >= 3);
assert(pass < _nbr_bits);
if (pass <= TRIGO_BD_LIMIT)
{
compute_direct_pass_n_lut(df, sf, pass);
}
else
{
compute_direct_pass_n_osc(df, sf, pass);
}
}
template<class DT>
void FFTReal<DT>::compute_direct_pass_n_lut(DataType df[], const DataType sf[],
int pass) const
{
assert(df != 0);
assert(sf != 0);
assert(df != sf);
assert(pass >= 3);
assert(pass < _nbr_bits);
const long nbr_coef = 1 << pass;
const long h_nbr_coef = nbr_coef >> 1;
const long d_nbr_coef = nbr_coef << 1;
long coef_index = 0;
const DataType *const cos_ptr = get_trigo_ptr(pass);
do
{
const DataType *const sf1r = sf + coef_index;
const DataType *const sf2r = sf1r + nbr_coef;
DataType *const dfr = df + coef_index;
DataType *const dfi = dfr + nbr_coef;
// Extreme coefficients are always real
dfr[0] = sf1r[0] + sf2r[0];
dfi[0] = sf1r[0] - sf2r[0]; // dfr [nbr_coef] =
dfr[h_nbr_coef] = sf1r[h_nbr_coef];
dfi[h_nbr_coef] = sf2r[h_nbr_coef];
// Others are conjugate complex numbers
const DataType *const sf1i = sf1r + h_nbr_coef;
const DataType *const sf2i = sf1i + nbr_coef;
for (long i = 1; i < h_nbr_coef; ++i)
{
const DataType c = cos_ptr[i]; // cos (i*PI/nbr_coef);
const DataType s = cos_ptr[h_nbr_coef - i]; // sin (i*PI/nbr_coef);
DataType v;
v = sf2r[i] * c - sf2i[i] * s;
dfr[i] = sf1r[i] + v;
dfi[-i] = sf1r[i] - v; // dfr [nbr_coef - i] =
v = sf2r[i] * s + sf2i[i] * c;
dfi[i] = v + sf1i[i];
dfi[nbr_coef - i] = v - sf1i[i];
}
coef_index += d_nbr_coef;
} while (coef_index < _length);
}
template<class DT>
void FFTReal<DT>::compute_direct_pass_n_osc(DataType df[], const DataType sf[],
int pass) const
{
assert(df != 0);
assert(sf != 0);
assert(df != sf);
assert(pass > TRIGO_BD_LIMIT);
assert(pass < _nbr_bits);
const long nbr_coef = 1 << pass;
const long h_nbr_coef = nbr_coef >> 1;
const long d_nbr_coef = nbr_coef << 1;
long coef_index = 0;
OscType &osc = _trigo_osc[pass - (TRIGO_BD_LIMIT + 1)];
do
{
const DataType *const sf1r = sf + coef_index;
const DataType *const sf2r = sf1r + nbr_coef;
DataType *const dfr = df + coef_index;
DataType *const dfi = dfr + nbr_coef;
osc.clear_buffers();
// Extreme coefficients are always real
dfr[0] = sf1r[0] + sf2r[0];
dfi[0] = sf1r[0] - sf2r[0]; // dfr [nbr_coef] =
dfr[h_nbr_coef] = sf1r[h_nbr_coef];
dfi[h_nbr_coef] = sf2r[h_nbr_coef];
// Others are conjugate complex numbers
const DataType *const sf1i = sf1r + h_nbr_coef;
const DataType *const sf2i = sf1i + nbr_coef;
for (long i = 1; i < h_nbr_coef; ++i)
{
osc.step();
const DataType c = osc.get_cos();
const DataType s = osc.get_sin();
DataType v;
v = sf2r[i] * c - sf2i[i] * s;
dfr[i] = sf1r[i] + v;
dfi[-i] = sf1r[i] - v; // dfr [nbr_coef - i] =
v = sf2r[i] * s + sf2i[i] * c;
dfi[i] = v + sf1i[i];
dfi[nbr_coef - i] = v - sf1i[i];
}
coef_index += d_nbr_coef;
} while (coef_index < _length);
}
// Transform in several pass
template<class DT>
void FFTReal<DT>::compute_ifft_general(const DataType f[], DataType x[]) const
{
assert(f != 0);
assert(f != use_buffer());
assert(x != 0);
assert(x != use_buffer());
assert(x != f);
DataType *sf = const_cast<DataType *>(f);
DataType *df;
DataType *df_temp;
if (_nbr_bits & 1)
{
df = use_buffer();
df_temp = x;
}
else
{
df = x;
df_temp = use_buffer();
}
for (int pass = _nbr_bits - 1; pass >= 3; --pass)
{
compute_inverse_pass_n(df, sf, pass);
if (pass < _nbr_bits - 1)
{
DataType *const temp_ptr = df;
df = sf;
sf = temp_ptr;
}
else
{
sf = df;
df = df_temp;
}
}
compute_inverse_pass_3(df, sf);
compute_inverse_pass_1_2(x, df);
}
template<class DT>
void FFTReal<DT>::compute_inverse_pass_n(DataType df[], const DataType sf[],
int pass) const
{
assert(df != 0);
assert(sf != 0);
assert(df != sf);
assert(pass >= 3);
assert(pass < _nbr_bits);
if (pass <= TRIGO_BD_LIMIT)
{
compute_inverse_pass_n_lut(df, sf, pass);
}
else
{
compute_inverse_pass_n_osc(df, sf, pass);
}
}
template<class DT>
void FFTReal<DT>::compute_inverse_pass_n_lut(DataType df[], const DataType sf[],
int pass) const
{
assert(df != 0);
assert(sf != 0);
assert(df != sf);
assert(pass >= 3);
assert(pass < _nbr_bits);
const long nbr_coef = 1 << pass;
const long h_nbr_coef = nbr_coef >> 1;
const long d_nbr_coef = nbr_coef << 1;
long coef_index = 0;
const DataType *const cos_ptr = get_trigo_ptr(pass);
do
{
const DataType *const sfr = sf + coef_index;
const DataType *const sfi = sfr + nbr_coef;
DataType *const df1r = df + coef_index;
DataType *const df2r = df1r + nbr_coef;
// Extreme coefficients are always real
df1r[0] = sfr[0] + sfi[0]; // + sfr [nbr_coef]
df2r[0] = sfr[0] - sfi[0]; // - sfr [nbr_coef]
df1r[h_nbr_coef] = sfr[h_nbr_coef] * 2;
df2r[h_nbr_coef] = sfi[h_nbr_coef] * 2;
// Others are conjugate complex numbers
DataType *const df1i = df1r + h_nbr_coef;
DataType *const df2i = df1i + nbr_coef;
for (long i = 1; i < h_nbr_coef; ++i)
{
df1r[i] = sfr[i] + sfi[-i]; // + sfr [nbr_coef - i]
df1i[i] = sfi[i] - sfi[nbr_coef - i];
const DataType c = cos_ptr[i]; // cos (i*PI/nbr_coef);
const DataType s = cos_ptr[h_nbr_coef - i]; // sin (i*PI/nbr_coef);
const DataType vr = sfr[i] - sfi[-i]; // - sfr [nbr_coef - i]
const DataType vi = sfi[i] + sfi[nbr_coef - i];
df2r[i] = vr * c + vi * s;
df2i[i] = vi * c - vr * s;
}
coef_index += d_nbr_coef;
} while (coef_index < _length);
}
template<class DT>
void FFTReal<DT>::compute_inverse_pass_n_osc(DataType df[], const DataType sf[],
int pass) const
{
assert(df != 0);
assert(sf != 0);
assert(df != sf);
assert(pass > TRIGO_BD_LIMIT);
assert(pass < _nbr_bits);
const long nbr_coef = 1 << pass;
const long h_nbr_coef = nbr_coef >> 1;
const long d_nbr_coef = nbr_coef << 1;
long coef_index = 0;
OscType &osc = _trigo_osc[pass - (TRIGO_BD_LIMIT + 1)];
do
{
const DataType *const sfr = sf + coef_index;
const DataType *const sfi = sfr + nbr_coef;
DataType *const df1r = df + coef_index;
DataType *const df2r = df1r + nbr_coef;
osc.clear_buffers();
// Extreme coefficients are always real
df1r[0] = sfr[0] + sfi[0]; // + sfr [nbr_coef]
df2r[0] = sfr[0] - sfi[0]; // - sfr [nbr_coef]
df1r[h_nbr_coef] = sfr[h_nbr_coef] * 2;
df2r[h_nbr_coef] = sfi[h_nbr_coef] * 2;
// Others are conjugate complex numbers
DataType *const df1i = df1r + h_nbr_coef;
DataType *const df2i = df1i + nbr_coef;
for (long i = 1; i < h_nbr_coef; ++i)
{
df1r[i] = sfr[i] + sfi[-i]; // + sfr [nbr_coef - i]
df1i[i] = sfi[i] - sfi[nbr_coef - i];
osc.step();
const DataType c = osc.get_cos();
const DataType s = osc.get_sin();
const DataType vr = sfr[i] - sfi[-i]; // - sfr [nbr_coef - i]
const DataType vi = sfi[i] + sfi[nbr_coef - i];
df2r[i] = vr * c + vi * s;
df2i[i] = vi * c - vr * s;
}
coef_index += d_nbr_coef;
} while (coef_index < _length);
}
template<class DT>
void FFTReal<DT>::compute_inverse_pass_3(DataType df[],
const DataType sf[]) const
{
assert(df != 0);
assert(sf != 0);
assert(df != sf);
const DataType sqrt2_2 = DataType(SQRT2 * 0.5);
long coef_index = 0;
do
{
df[coef_index] = sf[coef_index] + sf[coef_index + 4];
df[coef_index + 4] = sf[coef_index] - sf[coef_index + 4];
df[coef_index + 2] = sf[coef_index + 2] * 2;
df[coef_index + 6] = sf[coef_index + 6] * 2;
df[coef_index + 1] = sf[coef_index + 1] + sf[coef_index + 3];
df[coef_index + 3] = sf[coef_index + 5] - sf[coef_index + 7];
const DataType vr = sf[coef_index + 1] - sf[coef_index + 3];
const DataType vi = sf[coef_index + 5] + sf[coef_index + 7];
df[coef_index + 5] = (vr + vi) * sqrt2_2;
df[coef_index + 7] = (vi - vr) * sqrt2_2;
coef_index += 8;
} while (coef_index < _length);
}
template<class DT>
void FFTReal<DT>::compute_inverse_pass_1_2(DataType x[],
const DataType sf[]) const
{
assert(x != 0);
assert(sf != 0);
assert(x != sf);
const long *bit_rev_lut_ptr = get_br_ptr();
const DataType *sf2 = sf;
long coef_index = 0;
do
{
{
const DataType b_0 = sf2[0] + sf2[2];
const DataType b_2 = sf2[0] - sf2[2];
const DataType b_1 = sf2[1] * 2;
const DataType b_3 = sf2[3] * 2;
x[bit_rev_lut_ptr[0]] = b_0 + b_1;
x[bit_rev_lut_ptr[1]] = b_0 - b_1;
x[bit_rev_lut_ptr[2]] = b_2 + b_3;
x[bit_rev_lut_ptr[3]] = b_2 - b_3;
}
{
const DataType b_0 = sf2[4] + sf2[6];
const DataType b_2 = sf2[4] - sf2[6];
const DataType b_1 = sf2[5] * 2;
const DataType b_3 = sf2[7] * 2;
x[bit_rev_lut_ptr[4]] = b_0 + b_1;
x[bit_rev_lut_ptr[5]] = b_0 - b_1;
x[bit_rev_lut_ptr[6]] = b_2 + b_3;
x[bit_rev_lut_ptr[7]] = b_2 - b_3;
}
sf2 += 8;
coef_index += 8;
bit_rev_lut_ptr += 8;
} while (coef_index < _length);
}
} // namespace ffft
#endif // ffft_FFTReal_CODEHEADER_INCLUDED
#undef ffft_FFTReal_CURRENT_CODEHEADER
/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
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