Move the QtMultimedia spectrum demo to QtMultimediaKit

Change-Id: I60d7897eb84dfbe2ce5af5adeb23b33270aa7d7c
Reviewed-on: http://codereview.qt.nokia.com/1483
Reviewed-by: Jonas Rabbe <jonas.rabbe@nokia.com>

examples/spectrum/3rdparty/fftreal/FFTReal.hpp

@@ -0,0 +1,916 @@
+/*****************************************************************************
+
+        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 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*/