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+/*****************************************************************************
+
+ FFTReal.hpp
+ Copyright (c) 2005 Laurent de Soras
+
+--- Legal stuff ---
+
+This library is free software; you can redistribute it and/or
+modify it under the terms of the GNU Lesser General Public
+License as published by the Free Software Foundation; either
+version 2.1 of the License, or (at your option) any later version.
+
+This library is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+Lesser General Public License for more details.
+
+You should have received a copy of the GNU Lesser General Public
+License along with this library; if not, write to the Free Software
+Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+*Tab=3***********************************************************************/
+
+
+
+#if defined (FFTReal_CURRENT_CODEHEADER)
+ #error Recursive inclusion of FFTReal code header.
+#endif
+#define FFTReal_CURRENT_CODEHEADER
+
+#if ! defined (FFTReal_CODEHEADER_INCLUDED)
+#define FFTReal_CODEHEADER_INCLUDED
+
+
+
+/*\\\ INCLUDE FILES \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
+
+#include <cassert>
+#include <cmath>
+
+
+
+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);
+}
+
+
+
+#endif // FFTReal_CODEHEADER_INCLUDED
+
+#undef FFTReal_CURRENT_CODEHEADER
+
+
+
+/*\\\ EOF \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/
generated by cgit v0.12 at 2024-12-27 12:39:50 (GMT)