diff options
Diffstat (limited to 'src/loris')
| -rw-r--r-- | src/loris/Analyzer.C | 90 | ||||
| -rw-r--r-- | src/loris/Analyzer.h | 500 | ||||
| -rw-r--r-- | src/loris/FourierTransform.C | 5 | ||||
| -rw-r--r-- | src/loris/fftsg.c | 3331 |
4 files changed, 295 insertions, 3631 deletions
diff --git a/src/loris/Analyzer.C b/src/loris/Analyzer.C index 5b4996c..deaf178 100644 --- a/src/loris/Analyzer.C +++ b/src/loris/Analyzer.C @@ -89,78 +89,6 @@ static double compare2nd( const Pair & p1, const Pair & p2 ) return p1.second < p2.second; } -// --------------------------------------------------------------------------- -// LinearEnvelopeBuilder -// --------------------------------------------------------------------------- -// Base class for envelope builders that add a point (possibly) at each -// analysis frame. -// -// TODO: make a dictionary of these things and allow clients to add their -// own envelope builders and builder functions, and retrieve them after -// analysis. -class LinearEnvelopeBuilder -{ -public: - virtual ~LinearEnvelopeBuilder( void ) {} - virtual LinearEnvelopeBuilder * clone( void ) const = 0; - virtual void build( const Peaks & peaks, double frameTime ) = 0; - - const LinearEnvelope & envelope( void ) const { return mEnvelope; } - - // reset (clear) envelope, override if necesssary: - virtual void reset( void ) { mEnvelope.clear(); } - -protected: - - LinearEnvelope mEnvelope; // build this -}; - -// --------------------------------------------------------------------------- -// FundamentalBuilder - for constructing an F0 envelope during analysis -// --------------------------------------------------------------------------- -class FundamentalBuilder : public LinearEnvelopeBuilder -{ - std::auto_ptr< Envelope > mFminEnv; - std::auto_ptr< Envelope > mFmaxEnv; - - double mAmpThresh, mFreqThresh; - - std::vector< double > amplitudes, frequencies; - - const double mMinConfidence; // 0.9, this could be made a parameter, - // or raised to make estimates smoother - -public: - FundamentalBuilder( double fmin, double fmax, double threshDb = -60, double threshHz = 8000 ) : - mFminEnv( new LinearEnvelope( fmin ) ), - mFmaxEnv( new LinearEnvelope( fmax ) ), - mAmpThresh( std::pow( 10., 0.05*(threshDb) ) ), - mFreqThresh( threshHz ), - mMinConfidence( 0.9 ) - {} - - FundamentalBuilder( const Envelope & fmin, const Envelope & fmax, - double threshDb = -60, double threshHz = 8000 ) : - mFminEnv( fmin.clone() ), - mFmaxEnv( fmax.clone() ), - mAmpThresh( std::pow( 10., 0.05*(threshDb) ) ), - mFreqThresh( threshHz ), - mMinConfidence( 0.9 ) - {} - - FundamentalBuilder( const FundamentalBuilder & rhs ) : - mFminEnv( rhs.mFminEnv->clone() ), - mFmaxEnv( rhs.mFmaxEnv->clone() ), - mAmpThresh( rhs.mAmpThresh ), - mFreqThresh( rhs.mFreqThresh ), - mMinConfidence( rhs.mMinConfidence ) - {} - - - FundamentalBuilder * clone( void ) const { return new FundamentalBuilder(*this); } - - void build( const Peaks & peaks, double frameTime ); -}; // --------------------------------------------------------------------------- // FundamentalBuilder::build @@ -198,19 +126,6 @@ void FundamentalBuilder::build( const Peaks & peaks, double frameTime ) } -// --------------------------------------------------------------------------- -// AmpEnvBuilder - for constructing an amplitude envelope during analysis -// --------------------------------------------------------------------------- -class AmpEnvBuilder : public LinearEnvelopeBuilder -{ -public: - AmpEnvBuilder( void ) {} - - AmpEnvBuilder * clone( void ) const { return new AmpEnvBuilder(*this); } - - void build( const Peaks & peaks, double frameTime ); - -}; // --------------------------------------------------------------------------- // AmpEnvBuilder::build @@ -732,11 +647,6 @@ Analyzer::analyze( const double * bufBegin, const double * bufEnd, double srate, } } -void -Analyzer::analyze_peaks( const std::vector<double> & vec, double srate ) -{ - printf("analyze_peaks\n"); -} // -- parameter access -- // --------------------------------------------------------------------------- diff --git a/src/loris/Analyzer.h b/src/loris/Analyzer.h index 58ece87..9effdc5 100644 --- a/src/loris/Analyzer.h +++ b/src/loris/Analyzer.h @@ -1,8 +1,8 @@ #ifndef INCLUDE_ANALYZER_H #define INCLUDE_ANALYZER_H /* - * This is the Loris C++ Class Library, implementing analysis, - * manipulation, and synthesis of digitized sounds using the Reassigned + * This is the Loris C++ Class Library, implementing analysis, + * manipulation, and synthesis of digitized sounds using the Reassigned * Bandwidth-Enhanced Additive Sound Model. * * Loris is Copyright (c) 1999-2010 by Kelly Fitz and Lippold Haken @@ -34,6 +34,7 @@ */ #include <memory> #include <vector> +#include <cmath> #include "LinearEnvelope.h" #include "Partial.h" #include "PartialList.h" @@ -43,42 +44,127 @@ namespace Loris { class Envelope; -class LinearEnvelopeBuilder; -// oooo, this is nasty, need to fix it! -// class SpectralPeak; -// typedef std::vector< SpectralPeak > Peaks; + +// --------------------------------------------------------------------------- +// LinearEnvelopeBuilder +// --------------------------------------------------------------------------- +// Base class for envelope builders that add a point (possibly) at each +// analysis frame. +// +// TODO: make a dictionary of these things and allow clients to add their +// own envelope builders and builder functions, and retrieve them after +// analysis. +class LinearEnvelopeBuilder +{ +public: + virtual ~LinearEnvelopeBuilder( void ) {} + virtual LinearEnvelopeBuilder * clone( void ) const = 0; + virtual void build( const Peaks & peaks, double frameTime ) = 0; + + const LinearEnvelope & envelope( void ) const { return mEnvelope; } + + // reset (clear) envelope, override if necesssary: + virtual void reset( void ) { mEnvelope.clear(); } + +protected: + + LinearEnvelope mEnvelope; // build this +}; + + +// --------------------------------------------------------------------------- +// FundamentalBuilder - for constructing an F0 envelope during analysis +// --------------------------------------------------------------------------- +class FundamentalBuilder : public LinearEnvelopeBuilder +{ + std::auto_ptr< Envelope > mFminEnv; + std::auto_ptr< Envelope > mFmaxEnv; + + double mAmpThresh, mFreqThresh; + + std::vector< double > amplitudes, frequencies; + + const double mMinConfidence; // 0.9, this could be made a parameter, + // or raised to make estimates smoother + +public: + FundamentalBuilder( double fmin, double fmax, double threshDb = -60, double threshHz = 8000 ) : + mFminEnv( new LinearEnvelope( fmin ) ), + mFmaxEnv( new LinearEnvelope( fmax ) ), + mAmpThresh( std::pow( 10., 0.05*(threshDb) ) ), + mFreqThresh( threshHz ), + mMinConfidence( 0.9 ) + {} + + FundamentalBuilder( const Envelope & fmin, const Envelope & fmax, + double threshDb = -60, double threshHz = 8000 ) : + mFminEnv( fmin.clone() ), + mFmaxEnv( fmax.clone() ), + mAmpThresh( std::pow( 10., 0.05*(threshDb) ) ), + mFreqThresh( threshHz ), + mMinConfidence( 0.9 ) + {} + + FundamentalBuilder( const FundamentalBuilder & rhs ) : + mFminEnv( rhs.mFminEnv->clone() ), + mFmaxEnv( rhs.mFmaxEnv->clone() ), + mAmpThresh( rhs.mAmpThresh ), + mFreqThresh( rhs.mFreqThresh ), + mMinConfidence( rhs.mMinConfidence ) + {} + + + FundamentalBuilder * clone( void ) const { return new FundamentalBuilder(*this); } + + void build( const Peaks & peaks, double frameTime ); +}; + + +// --------------------------------------------------------------------------- +// AmpEnvBuilder - for constructing an amplitude envelope during analysis +// --------------------------------------------------------------------------- +class AmpEnvBuilder : public LinearEnvelopeBuilder +{ +public: + AmpEnvBuilder( void ) {} + + AmpEnvBuilder * clone( void ) const { return new AmpEnvBuilder(*this); } + + void build( const Peaks & peaks, double frameTime ); + +}; // --------------------------------------------------------------------------- // class Analyzer // //! Class Analyzer represents a configuration of parameters for //! performing Reassigned Bandwidth-Enhanced Additive Analysis -//! of sampled sounds. The analysis process yields a collection +//! of sampled sounds. The analysis process yields a collection //! of Partials, each having a trio of synchronous, non-uniformly- -//! sampled breakpoint envelopes representing the time-varying +//! sampled breakpoint envelopes representing the time-varying //! frequency, amplitude, and noisiness of a single bandwidth- //! enhanced sinusoid. These Partials are accumulated in the //! Analyzer. //! -//! The core analysis parameter is the frequency resolution, the -//! minimum instantaneous frequency spacing between partials. Most -//! other parameters are initially configured according to this +//! The core analysis parameter is the frequency resolution, the +//! minimum instantaneous frequency spacing between partials. Most +//! other parameters are initially configured according to this //! parameter (and the analysis window width, if specified). //! Subsequent parameter mutations are independent. -//! +//! //! Bandwidth enhancement: //! Two different strategies are available for computing bandwidth -//! (or noisiness) envelope: -//! +//! (or noisiness) envelope: +//! //! One strategy is to construct bandwidth envelopes during analysis -//! by associating residual energy in the spectrum (after peak -//! extraction) with the selected spectral peaks that are used +//! by associating residual energy in the spectrum (after peak +//! extraction) with the selected spectral peaks that are used //! to construct Partials. This is the original bandwidth enhancement //! algorithm, and bandwidth envelopes constructed in this way may -//! be suitable for use in bandwidth-enhanced synthesis. -//! -//! Another stategy is to construct bandwidth envelopes during -//! analysis by storing the mixed derivative of short-time phase, +//! be suitable for use in bandwidth-enhanced synthesis. +//! +//! Another stategy is to construct bandwidth envelopes during +//! analysis by storing the mixed derivative of short-time phase, //! scaled and shifted so that a value of 0 corresponds //! to a pure sinusoid, and a value of 1 corresponds to a //! bandwidth-enhanced sinusoid with maximal energy spread @@ -86,17 +172,17 @@ class LinearEnvelopeBuilder; //! are not suitable for bandwidth-enhanced synthesis, be sure //! to set the bandwidth to 0, or to disable bandwidth enhancement //! before rendering. -//! +//! //! The Analyzer may be configured to use either of these two //! strategies for bandwidth-enhanced analysis, or to construct //! no bandwidth envelopes at all. If unspecified, the default //! Analyzer configuration uses spectral residue to construct //! bandwidth envelopes. -//! +//! //! \sa storeResidueBandwidth, storeConvergenceBandwidth, storeNoBandwidth -//! -//! For more information about Reassigned Bandwidth-Enhanced -//! Analysis and the Reassigned Bandwidth-Enhanced Additive Sound +//! +//! For more information about Reassigned Bandwidth-Enhanced +//! Analysis and the Reassigned Bandwidth-Enhanced Additive Sound //! Model, refer to the Loris website: www.cerlsoundgroup.org/Loris/. // class Analyzer @@ -106,74 +192,74 @@ public: // -- construction -- - //! Construct a new Analyzer configured with the given - //! frequency resolution (minimum instantaneous frequency - //! difference between Partials). All other Analyzer parameters - //! are computed from the specified frequency resolution. - //! + //! Construct a new Analyzer configured with the given + //! frequency resolution (minimum instantaneous frequency + //! difference between Partials). All other Analyzer parameters + //! are computed from the specified frequency resolution. + //! //! \param resolutionHz is the frequency resolution in Hz. explicit Analyzer( double resolutionHz ); - - //! Construct a new Analyzer configured with the given - //! frequency resolution (minimum instantaneous frequency + + //! Construct a new Analyzer configured with the given + //! frequency resolution (minimum instantaneous frequency //! difference between Partials) and analysis window width - //! (main lobe, zero-to-zero). All other Analyzer parameters - //! are computed from the specified resolution and window width. - //! + //! (main lobe, zero-to-zero). All other Analyzer parameters + //! are computed from the specified resolution and window width. + //! //! \param resolutionHz is the frequency resolution in Hz. //! \param windowWidthHz is the main lobe width of the Kaiser //! analysis window in Hz. Analyzer( double resolutionHz, double windowWidthHz ); //! Construct a new Analyzer configured with the given time-varying - //! frequency resolution (minimum instantaneous frequency + //! frequency resolution (minimum instantaneous frequency //! difference between Partials) and analysis window width - //! (main lobe, zero-to-zero). All other Analyzer parameters - //! are computed from the specified resolution and window width. - //! + //! (main lobe, zero-to-zero). All other Analyzer parameters + //! are computed from the specified resolution and window width. + //! //! \param resolutionHz is the frequency resolution in Hz. //! \param windowWidthHz is the main lobe width of the Kaiser //! analysis window in Hz. Analyzer( const Envelope & resolutionEnv, double windowWidthHz ); //! Construct a new Analyzer having identical - //! parameter configuration to another Analyzer. - //! The list of collected Partials is not copied. - //! - //! \param other is the Analyzer to copy. + //! parameter configuration to another Analyzer. + //! The list of collected Partials is not copied. + //! + //! \param other is the Analyzer to copy. Analyzer( const Analyzer & other ); //! Destroy this Analyzer. ~Analyzer( void ); //! Construct a new Analyzer having identical - //! parameter configuration to another Analyzer. - //! The list of collected Partials is not copied. - //! - //! \param rhs is the Analyzer to copy. + //! parameter configuration to another Analyzer. + //! The list of collected Partials is not copied. + //! + //! \param rhs is the Analyzer to copy. Analyzer & operator=( const Analyzer & rhs ); // -- configuration -- - //! Configure this Analyzer with the given frequency resolution - //! (minimum instantaneous frequency difference between Partials, - //! in Hz). All other Analyzer parameters are (re-)computed from the + //! Configure this Analyzer with the given frequency resolution + //! (minimum instantaneous frequency difference between Partials, + //! in Hz). All other Analyzer parameters are (re-)computed from the //! frequency resolution, including the window width, which is - //! twice the resolution. - //! + //! twice the resolution. + //! //! \param resolutionHz is the frequency resolution in Hz. void configure( double resolutionHz ); - //! Configure this Analyzer with the given frequency resolution + //! Configure this Analyzer with the given frequency resolution //! (minimum instantaneous frequency difference between Partials) - //! and analysis window width (main lobe, zero-to-zero, in Hz). - //! All other Analyzer parameters are (re-)computed from the - //! frequency resolution and window width. - //! + //! and analysis window width (main lobe, zero-to-zero, in Hz). + //! All other Analyzer parameters are (re-)computed from the + //! frequency resolution and window width. + //! //! \param resolutionHz is the frequency resolution in Hz. //! \param windowWidthHz is the main lobe width of the Kaiser //! analysis window in Hz. - //! + //! //! There are three categories of analysis parameters: //! - the resolution, and params that are usually related to (or //! identical to) the resolution (frequency floor and drift) @@ -182,17 +268,17 @@ public: //! - independent parameters (bw region width and amp floor) void configure( double resolutionHz, double windowWidthHz ); - //! Configure this Analyzer with the given time-varying frequency resolution + //! Configure this Analyzer with the given time-varying frequency resolution //! (minimum instantaneous frequency difference between Partials) - //! and analysis window width (main lobe, zero-to-zero, in Hz). - //! All other Analyzer parameters are (re-)computed from the - //! frequency resolution and window width. - //! - //! \param resolutionEnv is the time-varying frequency resolution + //! and analysis window width (main lobe, zero-to-zero, in Hz). + //! All other Analyzer parameters are (re-)computed from the + //! frequency resolution and window width. + //! + //! \param resolutionEnv is the time-varying frequency resolution //! in Hz. //! \param windowWidthHz is the main lobe width of the Kaiser //! analysis window in Hz. - //! + //! //! There are three categories of analysis parameters: //! - the resolution, and params that are usually related to (or //! identical to) the resolution (frequency floor and drift) @@ -200,31 +286,31 @@ public: //! identical to) the window width (hop and crop times) //! - independent parameters (bw region width and amp floor) // - void configure( const Envelope & resolutionEnv, double windowWidthHz ); - + void configure( const Envelope & resolutionEnv, double windowWidthHz ); + // -- analysis -- - //! Analyze a vector of (mono) samples at the given sample rate - //! (in Hz) and store the extracted Partials in the Analyzer's - //! PartialList (std::list of Partials). - //! + //! Analyze a vector of (mono) samples at the given sample rate + //! (in Hz) and store the extracted Partials in the Analyzer's + //! PartialList (std::list of Partials). + //! //! \param vec is a vector of floating point samples - //! \param srate is the sample rate of the samples in the vector + //! \param srate is the sample rate of the samples in the vector void analyze( const std::vector<double> & vec, double srate ); - - //! Analyze a range of (mono) samples at the given sample rate + + //! Analyze a range of (mono) samples at the given sample rate //! (in Hz) and store the extracted Partials in the Analyzer's - //! PartialList (std::list of Partials). - //! + //! PartialList (std::list of Partials). + //! //! \param bufBegin is a pointer to a buffer of floating point samples - //! \param bufEnd is (one-past) the end of a buffer of floating point + //! \param bufEnd is (one-past) the end of a buffer of floating point //! samples //! \param srate is the sample rate of the samples in the buffer void analyze( const double * bufBegin, const double * bufEnd, double srate ); - + // -- tracking analysis -- - //! Analyze a vector of (mono) samples at the given sample rate + //! Analyze a vector of (mono) samples at the given sample rate //! (in Hz) and store the extracted Partials in the Analyzer's //! PartialList (std::list of Partials). Use the specified envelope //! as a frequency reference for Partial tracking. @@ -233,29 +319,27 @@ public: //! \param srate is the sample rate of the samples in the vector //! \param reference is an Envelope having the approximate //! frequency contour expected of the resulting Partials. - void analyze( const std::vector<double> & vec, double srate, + void analyze( const std::vector<double> & vec, double srate, const Envelope & reference ); - - //! Analyze a range of (mono) samples at the given sample rate + + //! Analyze a range of (mono) samples at the given sample rate //! (in Hz) and store the extracted Partials in the Analyzer's //! PartialList (std::list of Partials). Use the specified envelope //! as a frequency reference for Partial tracking. - //! + //! //! \param bufBegin is a pointer to a buffer of floating point samples - //! \param bufEnd is (one-past) the end of a buffer of floating point + //! \param bufEnd is (one-past) the end of a buffer of floating point //! samples //! \param srate is the sample rate of the samples in the buffer //! \param reference is an Envelope having the approximate //! frequency contour expected of the resulting Partials. - void analyze( const double * bufBegin, const double * bufEnd, double srate, - const Envelope & reference ); + virtual void analyze( const double * bufBegin, const double * bufEnd, double srate, + const Envelope & reference ); - void analyze_peaks( const std::vector<double> & vec, double srate ); - // -- parameter access -- - //! Return the amplitude floor (lowest detected spectral amplitude), - //! in (negative) dB, for this Analyzer. + //! Return the amplitude floor (lowest detected spectral amplitude), + //! in (negative) dB, for this Analyzer. double ampFloor( void ) const; //! Return the crop time (maximum temporal displacement of a time- @@ -264,40 +348,40 @@ public: //! for this Analyzer. double cropTime( void ) const; - //! Return the maximum allowable frequency difference between - //! consecutive Breakpoints in a Partial envelope for this Analyzer. + //! Return the maximum allowable frequency difference between + //! consecutive Breakpoints in a Partial envelope for this Analyzer. double freqDrift( void ) const; - //! Return the frequency floor (minimum instantaneous Partial - //! frequency), in Hz, for this Analyzer. + //! Return the frequency floor (minimum instantaneous Partial + //! frequency), in Hz, for this Analyzer. double freqFloor( void ) const; - - //! Return the frequency resolution (minimum instantaneous frequency + + //! Return the frequency resolution (minimum instantaneous frequency //! difference between Partials) for this Analyzer at the specified //! time in seconds. If no time is specified, then the initial resolution //! (at 0 seconds) is returned. - //! - //! \param time is the time in seconds at which to evaluate the + //! + //! \param time is the time in seconds at which to evaluate the //! frequency resolution - double freqResolution( double time = 0.0 ) const; + double freqResolution( double time = 0.0 ) const; - //! Return the hop time (which corresponds approximately to the - //! average density of Partial envelope Breakpoint data) for this + //! Return the hop time (which corresponds approximately to the + //! average density of Partial envelope Breakpoint data) for this //! Analyzer. double hopTime( void ) const; //! Return the sidelobe attenutation level for the Kaiser analysis window in - //! positive dB. Larger numbers (e.g. 90) give very good sidelobe - //! rejection but cause the window to be longer in time. Smaller numbers + //! positive dB. Larger numbers (e.g. 90) give very good sidelobe + //! rejection but cause the window to be longer in time. Smaller numbers //! (like 60) raise the level of the sidelobes, increasing the likelihood //! of frequency-domain interference, but allow the window to be shorter //! in time. double sidelobeLevel( void ) const; - //! Return the frequency-domain main lobe width (measured between - //! zero-crossings) of the analysis window used by this Analyzer. + //! Return the frequency-domain main lobe width (measured between + //! zero-crossings) of the analysis window used by this Analyzer. double windowWidth( void ) const; - + //! Return true if the phases and frequencies of the constructed //! partials should be modified to be consistent at the end of the //! analysis, and false otherwise. (Default is true.) @@ -306,66 +390,66 @@ public: // -- parameter mutation -- - //! Set the amplitude floor (lowest detected spectral amplitude), in - //! (negative) dB, for this Analyzer. - //! - //! \param x is the new value of this parameter. + //! Set the amplitude floor (lowest detected spectral amplitude), in + //! (negative) dB, for this Analyzer. + //! + //! \param x is the new value of this parameter. void setAmpFloor( double x ); //! Set the crop time (maximum temporal displacement of a time- //! frequency data point from the time-domain center of the analysis //! window, beyond which data points are considered "unreliable") //! for this Analyzer. - //! - //! \param x is the new value of this parameter. + //! + //! \param x is the new value of this parameter. void setCropTime( double x ); - //! Set the maximum allowable frequency difference between - //! consecutive Breakpoints in a Partial envelope for this Analyzer. - //! - //! \param x is the new value of this parameter. + //! Set the maximum allowable frequency difference between + //! consecutive Breakpoints in a Partial envelope for this Analyzer. + //! + //! \param x is the new value of this parameter. void setFreqDrift( double x ); - //! Set the frequency floor (minimum instantaneous Partial + //! Set the frequency floor (minimum instantaneous Partial //! frequency), in Hz, for this Analyzer. - //! - //! \param x is the new value of this parameter. + //! + //! \param x is the new value of this parameter. void setFreqFloor( double x ); - //! Set the frequency resolution (minimum instantaneous frequency - //! difference between Partials) for this Analyzer. (Does not cause - //! other parameters to be recomputed.) - //! - //! \param x is the new value of this parameter. + //! Set the frequency resolution (minimum instantaneous frequency + //! difference between Partials) for this Analyzer. (Does not cause + //! other parameters to be recomputed.) + //! + //! \param x is the new value of this parameter. void setFreqResolution( double x ); - - //! Set the time-varying frequency resolution (minimum instantaneous frequency - //! difference between Partials) for this Analyzer. (Does not cause - //! other parameters to be recomputed.) - //! - //! \param e is the envelope to copy for this parameter. - void setFreqResolution( const Envelope & e ); + + //! Set the time-varying frequency resolution (minimum instantaneous frequency + //! difference between Partials) for this Analyzer. (Does not cause + //! other parameters to be recomputed.) + //! + //! \param e is the envelope to copy for this parameter. + void setFreqResolution( const Envelope & e ); //! Set the hop time (which corresponds approximately to the average //! density of Partial envelope Breakpoint data) for this Analyzer. - //! - //! \param x is the new value of this parameter. + //! + //! \param x is the new value of this parameter. void setHopTime( double x ); //! Set the sidelobe attenutation level for the Kaiser analysis window in - //! positive dB. More negative numbers (e.g. -90) give very good sidelobe - //! rejection but cause the window to be longer in time. Less negative + //! positive dB. More negative numbers (e.g. -90) give very good sidelobe + //! rejection but cause the window to be longer in time. Less negative //! numbers raise the level of the sidelobes, increasing the likelihood //! of frequency-domain interference, but allow the window to be shorter //! in time. - //! - //! \param x is the new value of this parameter. + //! + //! \param x is the new value of this parameter. void setSidelobeLevel( double x ); - //! Set the frequency-domain main lobe width (measured between - //! zero-crossings) of the analysis window used by this Analyzer. - //! - //! \param x is the new value of this parameter. + //! Set the frequency-domain main lobe width (measured between + //! zero-crossings) of the analysis window used by this Analyzer. + //! + //! \param x is the new value of this parameter. void setWindowWidth( double x ); //! Indicate whether the phases and frequencies of the constructed @@ -375,54 +459,54 @@ public: //! \param TF is a flag indicating whether or not to construct //! phase-corrected Partials void setPhaseCorrect( bool TF = true ); - - + + // -- bandwidth envelope specification -- enum { Default_ResidueBandwidth_RegionWidth = 2000, Default_ConvergenceBandwidth_TolerancePct = 10 }; - + //! Construct Partial bandwidth envelopes during analysis //! by associating residual energy in the spectrum (after //! peak extraction) with the selected spectral peaks that - //! are used to construct Partials. + //! are used to construct Partials. //! //! This is the default bandwidth-enhancement strategy. - //! - //! \param regionWidth is the width (in Hz) of the bandwidth + //! + //! \param regionWidth is the width (in Hz) of the bandwidth //! association regions used by this process, must be positive. //! If unspecified, a default value is used. void storeResidueBandwidth( double regionWidth = Default_ResidueBandwidth_RegionWidth ); - + //! Construct Partial bandwidth envelopes during analysis - //! by storing the mixed derivative of short-time phase, + //! by storing the mixed derivative of short-time phase, //! scaled and shifted so that a value of 0 corresponds //! to a pure sinusoid, and a value of 1 corresponds to a //! bandwidth-enhanced sinusoid with maximal energy spread //! (minimum sinusoidal convergence). //! - //! \param tolerance is the amount of range over which the - //! mixed derivative indicator should be allowed to drift away + //! \param tolerance is the amount of range over which the + //! mixed derivative indicator should be allowed to drift away //! from a pure sinusoid before saturating. This range is mapped - //! to bandwidth values on the range [0,1]. Must be positive and + //! to bandwidth values on the range [0,1]. Must be positive and //! not greater than 1. If unspecified, a default value is used. - void storeConvergenceBandwidth( double tolerancePct = + void storeConvergenceBandwidth( double tolerancePct = 0.01 * (double)Default_ConvergenceBandwidth_TolerancePct ); - - //! Disable bandwidth envelope construction. Bandwidth + + //! Disable bandwidth envelope construction. Bandwidth //! will be zero for all Breakpoints in all Partials. void storeNoBandwidth( void ); - + //! Return true if this Analyzer is configured to compute //! bandwidth envelopes using the spectral residue after //! peaks have been identified, and false otherwise. bool bandwidthIsResidue( void ) const; - + //! Return true if this Analyzer is configured to compute //! bandwidth envelopes using the mixed derivative convergence //! indicator, and false otherwise. bool bandwidthIsConvergence( void ) const; - + //! Return the width (in Hz) of the Bandwidth Association regions //! used by this Analyzer, only if the spectral residue method is //! used to compute bandwidth envelopes. Return zero if the mixed @@ -436,45 +520,45 @@ public: double bwConvergenceTolerance( void ) const; //! Return true if bandwidth envelopes are to be constructed - //! by any means, that is, if either bandwidthIsResidue() or + //! by any means, that is, if either bandwidthIsResidue() or //! bandwidthIsConvergence() are true. Otherwise, return //! false. bool associateBandwidth( void ) const { return bandwidthIsResidue() || bandwidthIsConvergence(); } - //! Deprecated, use storeResidueBandwidth or storeNoBandwidth instead. - void setBwRegionWidth( double x ) - { + //! Deprecated, use storeResidueBandwidth or storeNoBandwidth instead. + void setBwRegionWidth( double x ) + { if ( x != 0 ) { - storeResidueBandwidth( x ); + storeResidueBandwidth( x ); } else { storeNoBandwidth(); } } - + // -- PartialList access -- - //! Return a mutable reference to this Analyzer's list of - //! analyzed Partials. + //! Return a mutable reference to this Analyzer's list of + //! analyzed Partials. PartialList & partials( void ); - //! Return an immutable (const) reference to this Analyzer's - //! list of analyzed Partials. + //! Return an immutable (const) reference to this Analyzer's + //! list of analyzed Partials. const PartialList & partials( void ) const; // -- envelope access -- - enum { Default_FundamentalEnv_ThreshDb = -60, + enum { Default_FundamentalEnv_ThreshDb = -60, Default_FundamentalEnv_ThreshHz = 8000 }; - //! Specify parameters for constructing a fundamental frequency - //! envelope for the analyzed sound during analysis. The fundamental - //! frequency estimate can be accessed by fundamentalEnv() after the - //! analysis is complete. + //! Specify parameters for constructing a fundamental frequency + //! envelope for the analyzed sound during analysis. The fundamental + //! frequency estimate can be accessed by fundamentalEnv() after the + //! analysis is complete. //! //! By default, a fundamental envelope is estimated during analysis //! between the frequency resolution and 1.5 times the resolution. @@ -488,9 +572,9 @@ public: //! \param threshHz is the upper bound on the frequency of a spectral //! peak that will constribute to the fundamental frequency estimate. //! Default is 8 kHz. - void buildFundamentalEnv( double fmin, double fmax, - double threshDb = Default_FundamentalEnv_ThreshDb, - double threshHz = Default_FundamentalEnv_ThreshHz ); + void buildFundamentalEnv( double fmin, double fmax, + double threshDb = Default_FundamentalEnv_ThreshDb, + double threshHz = Default_FundamentalEnv_ThreshHz ); //! Return the fundamental frequency estimate envelope constructed @@ -503,10 +587,10 @@ public: //! Return the overall amplitude estimate envelope constructed //! during the most recent analysis performed by this Analyzer. const LinearEnvelope & ampEnv( void ) const; - - + + // -- legacy support -- - + // Fundamental and amplitude envelopes are always constructed during // analysis, these members do nothing, and are retained for backwards // compatibility. @@ -515,51 +599,51 @@ public: // -- private member variables -- -private: +protected: - std::auto_ptr< Envelope > m_freqResolutionEnv; + std::auto_ptr< Envelope > m_freqResolutionEnv; //! in Hz, minimum instantaneous frequency distance; //! this is the core parameter, others are, by default, //! computed from this one - + double m_ampFloor; //! dB, relative to full amplitude sine wave, absolute //! amplitude threshold (negative) - + double m_windowWidth; //! in Hz, width of main lobe; this might be more //! conveniently presented as window length, but //! the main lobe width more explicitly highlights //! the critical interaction with resolution - - // std::auto_ptr< Envelope > m_freqFloorEnv; + + // std::auto_ptr< Envelope > m_freqFloorEnv; double m_freqFloor; //! lowest frequency (Hz) component extracted //! in spectral analysis - - double m_freqDrift; //! the maximum frequency (Hz) difference between two + + double m_freqDrift; //! the maximum frequency (Hz) difference between two //! consecutive Breakpoints that will be linked to //! form a Partial - + double m_hopTime; //! in seconds, time between analysis windows in //! successive spectral analyses - + double m_cropTime; //! in seconds, maximum time correction for a spectral //! component to be considered reliable, and to be eligible //! for extraction and for Breakpoint formation - - double m_bwAssocParam; //! formerly, width in Hz of overlapping bandwidth + + double m_bwAssocParam; //! formerly, width in Hz of overlapping bandwidth //! association regions, or zero if bandwidth association //! is disabled, now a catch-all bandwidth association //! parameter that, if negative, indicates the tolerance (%) //! level used to construct bandwidth envelopes from the //! mixed phase derivative indicator - - double m_sidelobeLevel; //! sidelobe attenutation level for the Kaiser analysis + + double m_sidelobeLevel; //! sidelobe attenutation level for the Kaiser analysis //! window, in positive dB - + bool m_phaseCorrect; //! flag indicating that phases/frequencies should be //! made consistent at the end of the analysis - + PartialList m_partials; //! collect Partials here - + //! builder object for constructing a fundamental frequency //! estimate during analysis std::auto_ptr< LinearEnvelopeBuilder > m_f0Builder; @@ -573,22 +657,22 @@ private: /* // These members make up the sequence of operations in an - // analysis. If analysis were ever to be made into a + // analysis. If analysis were ever to be made into a // template method, these would be the operations that // derived classes could override. Or each of these could // be represented by a strategy class. //! Compute the spectrum of the next sequence of samples. void computeSpectrum( void ); - + //! Identify and select the spectral components that will be - //! used to form Partials. + //! used to form Partials. void selectPeaks( void ); - + //! Compute the bandwidth coefficients for the Breakpoints - //! that are going to be used to form Partials. + //! that are going to be used to form Partials. void associateBandwidth( void ); - + //! Construct Partials from extracted spectral components. //! Partials are built up frame by frame by appending //! Breakpoints to Partials under construction, and giving @@ -598,21 +682,21 @@ private: // Reject peaks that are too close in frequency to a louder peak that is // being retained, and peaks that are too quiet. Peaks that are retained, // but are quiet enough to be in the specified fadeRange should be faded. - // + // // Rejected peaks are placed at the end of the peak collection. // Return the first position in the collection containing a rejected peak, // or the end of the collection if no peaks are rejected. Peaks::iterator thinPeaks( Peaks & peaks, double frameTime ); - - // Fix the bandwidth value stored in the specified Peaks. + + // Fix the bandwidth value stored in the specified Peaks. // This function is invoked if the spectral residue method is // not used to compute bandwidth (that method overwrites the - // bandwidth already). If the convergence method is used to + // bandwidth already). If the convergence method is used to // compute bandwidth, the appropriate scaling is applied // to the stored mixed phase derivative. Otherwise, the // Peak bandwidth is set to zero. void fixBandwidth( Peaks & peaks ); - + }; // end of class Analyzer } // end of namespace Loris diff --git a/src/loris/FourierTransform.C b/src/loris/FourierTransform.C index 2a29238..b67e6de 100644 --- a/src/loris/FourierTransform.C +++ b/src/loris/FourierTransform.C @@ -328,7 +328,7 @@ public: #define SORRY_NO_FFTW 1 // function prototype, definition in fftsg.c -extern "C" void cdft(int, int, double *, int *, double *); +/* extern "C" void cdft(int, int, double *, int *, double *); */ // function prototype, definition below static void slowDFT( double * in, double * out, int N ); @@ -444,7 +444,8 @@ public: { if ( mIsPO2 ) { - cdft( 2*N, -1, mTxInOut, mWorkspace, mTwiddle ); + /* cdft( 2*N, -1, mTxInOut, mWorkspace, mTwiddle ); */ + slowDFT( mTxInOut, mTwiddle, N ); } else { diff --git a/src/loris/fftsg.c b/src/loris/fftsg.c deleted file mode 100644 index dc3e237..0000000 --- a/src/loris/fftsg.c +++ /dev/null @@ -1,3331 +0,0 @@ -/* - double-precision floating point transform functions - adapted from the tranform library of Ooura. - http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html - - Identical to fftsg.c, wrapped in extern "C" - to prevent name-mangling by a C++ compiler. - - Kelly Fitz 21 July 2006 - kfitz@cerlsoundgroup.org -*/ -/* -Fast Fourier/Cosine/Sine Transform - dimension :one - data length :power of 2 - decimation :frequency - radix :split-radix - data :inplace - table :use -functions - cdft: Complex Discrete Fourier Transform - rdft: Real Discrete Fourier Transform - ddct: Discrete Cosine Transform - ddst: Discrete Sine Transform - dfct: Cosine Transform of RDFT (Real Symmetric DFT) - dfst: Sine Transform of RDFT (Real Anti-symmetric DFT) -function prototypes - void cdft(int, int, double *, int *, double *); - void rdft(int, int, double *, int *, double *); - void ddct(int, int, double *, int *, double *); - void ddst(int, int, double *, int *, double *); - void dfct(int, double *, double *, int *, double *); - void dfst(int, double *, double *, int *, double *); -macro definitions - USE_CDFT_PTHREADS : default=not defined - CDFT_THREADS_BEGIN_N : must be >= 512, default=8192 - CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536 - USE_CDFT_WINTHREADS : default=not defined - CDFT_THREADS_BEGIN_N : must be >= 512, default=32768 - CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288 - - --------- Complex DFT (Discrete Fourier Transform) -------- - [definition] - <case1> - X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n - <case2> - X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n - (notes: sum_j=0^n-1 is a summation from j=0 to n-1) - [usage] - <case1> - ip[0] = 0; // first time only - cdft(2*n, 1, a, ip, w); - <case2> - ip[0] = 0; // first time only - cdft(2*n, -1, a, ip, w); - [parameters] - 2*n :data length (int) - n >= 1, n = power of 2 - a[0...2*n-1] :input/output data (double *) - input data - a[2*j] = Re(x[j]), - a[2*j+1] = Im(x[j]), 0<=j<n - output data - a[2*k] = Re(X[k]), - a[2*k+1] = Im(X[k]), 0<=k<n - ip[0...*] :work area for bit reversal (int *) - length of ip >= 2+sqrt(n) - strictly, - length of ip >= - 2+(1<<(int)(log(n+0.5)/log(2))/2). - ip[0],ip[1] are pointers of the cos/sin table. - w[0...n/2-1] :cos/sin table (double *) - w[],ip[] are initialized if ip[0] == 0. - [remark] - Inverse of - cdft(2*n, -1, a, ip, w); - is - cdft(2*n, 1, a, ip, w); - for (j = 0; j <= 2 * n - 1; j++) { - a[j] *= 1.0 / n; - } - . - - --------- Real DFT / Inverse of Real DFT -------- - [definition] - <case1> RDFT - R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2 - I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2 - <case2> IRDFT (excluding scale) - a[k] = (R[0] + R[n/2]*cos(pi*k))/2 + - sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) + - sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n - [usage] - <case1> - ip[0] = 0; // first time only - rdft(n, 1, a, ip, w); - <case2> - ip[0] = 0; // first time only - rdft(n, -1, a, ip, w); - [parameters] - n :data length (int) - n >= 2, n = power of 2 - a[0...n-1] :input/output data (double *) - <case1> - output data - a[2*k] = R[k], 0<=k<n/2 - a[2*k+1] = I[k], 0<k<n/2 - a[1] = R[n/2] - <case2> - input data - a[2*j] = R[j], 0<=j<n/2 - a[2*j+1] = I[j], 0<j<n/2 - a[1] = R[n/2] - ip[0...*] :work area for bit reversal (int *) - length of ip >= 2+sqrt(n/2) - strictly, - length of ip >= - 2+(1<<(int)(log(n/2+0.5)/log(2))/2). - ip[0],ip[1] are pointers of the cos/sin table. - w[0...n/2-1] :cos/sin table (double *) - w[],ip[] are initialized if ip[0] == 0. - [remark] - Inverse of - rdft(n, 1, a, ip, w); - is - rdft(n, -1, a, ip, w); - for (j = 0; j <= n - 1; j++) { - a[j] *= 2.0 / n; - } - . - - --------- DCT (Discrete Cosine Transform) / Inverse of DCT -------- - [definition] - <case1> IDCT (excluding scale) - C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n - <case2> DCT - C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n - [usage] - <case1> - ip[0] = 0; // first time only - ddct(n, 1, a, ip, w); - <case2> - ip[0] = 0; // first time only - ddct(n, -1, a, ip, w); - [parameters] - n :data length (int) - n >= 2, n = power of 2 - a[0...n-1] :input/output data (double *) - output data - a[k] = C[k], 0<=k<n - ip[0...*] :work area for bit reversal (int *) - length of ip >= 2+sqrt(n/2) - strictly, - length of ip >= - 2+(1<<(int)(log(n/2+0.5)/log(2))/2). - ip[0],ip[1] are pointers of the cos/sin table. - w[0...n*5/4-1] :cos/sin table (double *) - w[],ip[] are initialized if ip[0] == 0. - [remark] - Inverse of - ddct(n, -1, a, ip, w); - is - a[0] *= 0.5; - ddct(n, 1, a, ip, w); - for (j = 0; j <= n - 1; j++) { - a[j] *= 2.0 / n; - } - . - - --------- DST (Discrete Sine Transform) / Inverse of DST -------- - [definition] - <case1> IDST (excluding scale) - S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n - <case2> DST - S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n - [usage] - <case1> - ip[0] = 0; // first time only - ddst(n, 1, a, ip, w); - <case2> - ip[0] = 0; // first time only - ddst(n, -1, a, ip, w); - [parameters] - n :data length (int) - n >= 2, n = power of 2 - a[0...n-1] :input/output data (double *) - <case1> - input data - a[j] = A[j], 0<j<n - a[0] = A[n] - output data - a[k] = S[k], 0<=k<n - <case2> - output data - a[k] = S[k], 0<k<n - a[0] = S[n] - ip[0...*] :work area for bit reversal (int *) - length of ip >= 2+sqrt(n/2) - strictly, - length of ip >= - 2+(1<<(int)(log(n/2+0.5)/log(2))/2). - ip[0],ip[1] are pointers of the cos/sin table. - w[0...n*5/4-1] :cos/sin table (double *) - w[],ip[] are initialized if ip[0] == 0. - [remark] - Inverse of - ddst(n, -1, a, ip, w); - is - a[0] *= 0.5; - ddst(n, 1, a, ip, w); - for (j = 0; j <= n - 1; j++) { - a[j] *= 2.0 / n; - } - . - - --------- Cosine Transform of RDFT (Real Symmetric DFT) -------- - [definition] - C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n - [usage] - ip[0] = 0; // first time only - dfct(n, a, t, ip, w); - [parameters] - n :data length - 1 (int) - n >= 2, n = power of 2 - a[0...n] :input/output data (double *) - output data - a[k] = C[k], 0<=k<=n - t[0...n/2] :work area (double *) - ip[0...*] :work area for bit reversal (int *) - length of ip >= 2+sqrt(n/4) - strictly, - length of ip >= - 2+(1<<(int)(log(n/4+0.5)/log(2))/2). - ip[0],ip[1] are pointers of the cos/sin table. - w[0...n*5/8-1] :cos/sin table (double *) - w[],ip[] are initialized if ip[0] == 0. - [remark] - Inverse of - a[0] *= 0.5; - a[n] *= 0.5; - dfct(n, a, t, ip, w); - is - a[0] *= 0.5; - a[n] *= 0.5; - dfct(n, a, t, ip, w); - for (j = 0; j <= n; j++) { - a[j] *= 2.0 / n; - } - . - - --------- Sine Transform of RDFT (Real Anti-symmetric DFT) -------- - [definition] - S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n - [usage] - ip[0] = 0; // first time only - dfst(n, a, t, ip, w); - [parameters] - n :data length + 1 (int) - n >= 2, n = power of 2 - a[0...n-1] :input/output data (double *) - output data - a[k] = S[k], 0<k<n - (a[0] is used for work area) - t[0...n/2-1] :work area (double *) - ip[0...*] :work area for bit reversal (int *) - length of ip >= 2+sqrt(n/4) - strictly, - length of ip >= - 2+(1<<(int)(log(n/4+0.5)/log(2))/2). - ip[0],ip[1] are pointers of the cos/sin table. - w[0...n*5/8-1] :cos/sin table (double *) - w[],ip[] are initialized if ip[0] == 0. - [remark] - Inverse of - dfst(n, a, t, ip, w); - is - dfst(n, a, t, ip, w); - for (j = 1; j <= n - 1; j++) { - a[j] *= 2.0 / n; - } - . - - -Appendix : - The cos/sin table is recalculated when the larger table required. - w[] and ip[] are compatible with all routines. -*/ - -#if defined(__cplusplus) -extern "C" { -#endif - -void cdft(int n, int isgn, double *a, int *ip, double *w) -{ - void makewt(int nw, int *ip, double *w); - void cftfsub(int n, double *a, int *ip, int nw, double *w); - void cftbsub(int n, double *a, int *ip, int nw, double *w); - int nw; - - nw = ip[0]; - if (n > (nw << 2)) { - nw = n >> 2; - makewt(nw, ip, w); - } - if (isgn >= 0) { - cftfsub(n, a, ip, nw, w); - } else { - cftbsub(n, a, ip, nw, w); - } -} - - -void rdft(int n, int isgn, double *a, int *ip, double *w) -{ - void makewt(int nw, int *ip, double *w); - void makect(int nc, int *ip, double *c); - void cftfsub(int n, double *a, int *ip, int nw, double *w); - void cftbsub(int n, double *a, int *ip, int nw, double *w); - void rftfsub(int n, double *a, int nc, double *c); - void rftbsub(int n, double *a, int nc, double *c); - int nw, nc; - double xi; - - nw = ip[0]; - if (n > (nw << 2)) { - nw = n >> 2; - makewt(nw, ip, w); - } - nc = ip[1]; - if (n > (nc << 2)) { - nc = n >> 2; - makect(nc, ip, w + nw); - } - if (isgn >= 0) { - if (n > 4) { - cftfsub(n, a, ip, nw, w); - rftfsub(n, a, nc, w + nw); - } else if (n == 4) { - cftfsub(n, a, ip, nw, w); - } - xi = a[0] - a[1]; - a[0] += a[1]; - a[1] = xi; - } else { - a[1] = 0.5 * (a[0] - a[1]); - a[0] -= a[1]; - if (n > 4) { - rftbsub(n, a, nc, w + nw); - cftbsub(n, a, ip, nw, w); - } else if (n == 4) { - cftbsub(n, a, ip, nw, w); - } - } -} - - -void ddct(int n, int isgn, double *a, int *ip, double *w) -{ - void makewt(int nw, int *ip, double *w); - void makect(int nc, int *ip, double *c); - void cftfsub(int n, double *a, int *ip, int nw, double *w); - void cftbsub(int n, double *a, int *ip, int nw, double *w); - void rftfsub(int n, double *a, int nc, double *c); - void rftbsub(int n, double *a, int nc, double *c); - void dctsub(int n, double *a, int nc, double *c); - int j, nw, nc; - double xr; - - nw = ip[0]; - if (n > (nw << 2)) { - nw = n >> 2; - makewt(nw, ip, w); - } - nc = ip[1]; - if (n > nc) { - nc = n; - makect(nc, ip, w + nw); - } - if (isgn < 0) { - xr = a[n - 1]; - for (j = n - 2; j >= 2; j -= 2) { - a[j + 1] = a[j] - a[j - 1]; - a[j] += a[j - 1]; - } - a[1] = a[0] - xr; - a[0] += xr; - if (n > 4) { - rftbsub(n, a, nc, w + nw); - cftbsub(n, a, ip, nw, w); - } else if (n == 4) { - cftbsub(n, a, ip, nw, w); - } - } - dctsub(n, a, nc, w + nw); - if (isgn >= 0) { - if (n > 4) { - cftfsub(n, a, ip, nw, w); - rftfsub(n, a, nc, w + nw); - } else if (n == 4) { - cftfsub(n, a, ip, nw, w); - } - xr = a[0] - a[1]; - a[0] += a[1]; - for (j = 2; j < n; j += 2) { - a[j - 1] = a[j] - a[j + 1]; - a[j] += a[j + 1]; - } - a[n - 1] = xr; - } -} - - -void ddst(int n, int isgn, double *a, int *ip, double *w) -{ - void makewt(int nw, int *ip, double *w); - void makect(int nc, int *ip, double *c); - void cftfsub(int n, double *a, int *ip, int nw, double *w); - void cftbsub(int n, double *a, int *ip, int nw, double *w); - void rftfsub(int n, double *a, int nc, double *c); - void rftbsub(int n, double *a, int nc, double *c); - void dstsub(int n, double *a, int nc, double *c); - int j, nw, nc; - double xr; - - nw = ip[0]; - if (n > (nw << 2)) { - nw = n >> 2; - makewt(nw, ip, w); - } - nc = ip[1]; - if (n > nc) { - nc = n; - makect(nc, ip, w + nw); - } - if (isgn < 0) { - xr = a[n - 1]; - for (j = n - 2; j >= 2; j -= 2) { - a[j + 1] = -a[j] - a[j - 1]; - a[j] -= a[j - 1]; - } - a[1] = a[0] + xr; - a[0] -= xr; - if (n > 4) { - rftbsub(n, a, nc, w + nw); - cftbsub(n, a, ip, nw, w); - } else if (n == 4) { - cftbsub(n, a, ip, nw, w); - } - } - dstsub(n, a, nc, w + nw); - if (isgn >= 0) { - if (n > 4) { - cftfsub(n, a, ip, nw, w); - rftfsub(n, a, nc, w + nw); - } else if (n == 4) { - cftfsub(n, a, ip, nw, w); - } - xr = a[0] - a[1]; - a[0] += a[1]; - for (j = 2; j < n; j += 2) { - a[j - 1] = -a[j] - a[j + 1]; - a[j] -= a[j + 1]; - } - a[n - 1] = -xr; - } -} - - -void dfct(int n, double *a, double *t, int *ip, double *w) -{ - void makewt(int nw, int *ip, double *w); - void makect(int nc, int *ip, double *c); - void cftfsub(int n, double *a, int *ip, int nw, double *w); - void rftfsub(int n, double *a, int nc, double *c); - void dctsub(int n, double *a, int nc, double *c); - int j, k, l, m, mh, nw, nc; - double xr, xi, yr, yi; - - nw = ip[0]; - if (n > (nw << 3)) { - nw = n >> 3; - makewt(nw, ip, w); - } - nc = ip[1]; - if (n > (nc << 1)) { - nc = n >> 1; - makect(nc, ip, w + nw); - } - m = n >> 1; - yi = a[m]; - xi = a[0] + a[n]; - a[0] -= a[n]; - t[0] = xi - yi; - t[m] = xi + yi; - if (n > 2) { - mh = m >> 1; - for (j = 1; j < mh; j++) { - k = m - j; - xr = a[j] - a[n - j]; - xi = a[j] + a[n - j]; - yr = a[k] - a[n - k]; - yi = a[k] + a[n - k]; - a[j] = xr; - a[k] = yr; - t[j] = xi - yi; - t[k] = xi + yi; - } - t[mh] = a[mh] + a[n - mh]; - a[mh] -= a[n - mh]; - dctsub(m, a, nc, w + nw); - if (m > 4) { - cftfsub(m, a, ip, nw, w); - rftfsub(m, a, nc, w + nw); - } else if (m == 4) { - cftfsub(m, a, ip, nw, w); - } - a[n - 1] = a[0] - a[1]; - a[1] = a[0] + a[1]; - for (j = m - 2; j >= 2; j -= 2) { - a[2 * j + 1] = a[j] + a[j + 1]; - a[2 * j - 1] = a[j] - a[j + 1]; - } - l = 2; - m = mh; - while (m >= 2) { - dctsub(m, t, nc, w + nw); - if (m > 4) { - cftfsub(m, t, ip, nw, w); - rftfsub(m, t, nc, w + nw); - } else if (m == 4) { - cftfsub(m, t, ip, nw, w); - } - a[n - l] = t[0] - t[1]; - a[l] = t[0] + t[1]; - k = 0; - for (j = 2; j < m; j += 2) { - k += l << 2; - a[k - l] = t[j] - t[j + 1]; - a[k + l] = t[j] + t[j + 1]; - } - l <<= 1; - mh = m >> 1; - for (j = 0; j < mh; j++) { - k = m - j; - t[j] = t[m + k] - t[m + j]; - t[k] = t[m + k] + t[m + j]; - } - t[mh] = t[m + mh]; - m = mh; - } - a[l] = t[0]; - a[n] = t[2] - t[1]; - a[0] = t[2] + t[1]; - } else { - a[1] = a[0]; - a[2] = t[0]; - a[0] = t[1]; - } -} - - -void dfst(int n, double *a, double *t, int *ip, double *w) -{ - void makewt(int nw, int *ip, double *w); - void makect(int nc, int *ip, double *c); - void cftfsub(int n, double *a, int *ip, int nw, double *w); - void rftfsub(int n, double *a, int nc, double *c); - void dstsub(int n, double *a, int nc, double *c); - int j, k, l, m, mh, nw, nc; - double xr, xi, yr, yi; - - nw = ip[0]; - if (n > (nw << 3)) { - nw = n >> 3; - makewt(nw, ip, w); - } - nc = ip[1]; - if (n > (nc << 1)) { - nc = n >> 1; - makect(nc, ip, w + nw); - } - if (n > 2) { - m = n >> 1; - mh = m >> 1; - for (j = 1; j < mh; j++) { - k = m - j; - xr = a[j] + a[n - j]; - xi = a[j] - a[n - j]; - yr = a[k] + a[n - k]; - yi = a[k] - a[n - k]; - a[j] = xr; - a[k] = yr; - t[j] = xi + yi; - t[k] = xi - yi; - } - t[0] = a[mh] - a[n - mh]; - a[mh] += a[n - mh]; - a[0] = a[m]; - dstsub(m, a, nc, w + nw); - if (m > 4) { - cftfsub(m, a, ip, nw, w); - rftfsub(m, a, nc, w + nw); - } else if (m == 4) { - cftfsub(m, a, ip, nw, w); - } - a[n - 1] = a[1] - a[0]; - a[1] = a[0] + a[1]; - for (j = m - 2; j >= 2; j -= 2) { - a[2 * j + 1] = a[j] - a[j + 1]; - a[2 * j - 1] = -a[j] - a[j + 1]; - } - l = 2; - m = mh; - while (m >= 2) { - dstsub(m, t, nc, w + nw); - if (m > 4) { - cftfsub(m, t, ip, nw, w); - rftfsub(m, t, nc, w + nw); - } else if (m == 4) { - cftfsub(m, t, ip, nw, w); - } - a[n - l] = t[1] - t[0]; - a[l] = t[0] + t[1]; - k = 0; - for (j = 2; j < m; j += 2) { - k += l << 2; - a[k - l] = -t[j] - t[j + 1]; - a[k + l] = t[j] - t[j + 1]; - } - l <<= 1; - mh = m >> 1; - for (j = 1; j < mh; j++) { - k = m - j; - t[j] = t[m + k] + t[m + j]; - t[k] = t[m + k] - t[m + j]; - } - t[0] = t[m + mh]; - m = mh; - } - a[l] = t[0]; - } - a[0] = 0; -} - - -/* -------- initializing routines -------- */ - - -#include <math.h> - -void makewt(int nw, int *ip, double *w) -{ - void makeipt(int nw, int *ip); - int j, nwh, nw0, nw1; - double delta, wn4r, wk1r, wk1i, wk3r, wk3i; - - ip[0] = nw; - ip[1] = 1; - if (nw > 2) { - nwh = nw >> 1; - delta = atan(1.0) / nwh; - wn4r = cos(delta * nwh); - w[0] = 1; - w[1] = wn4r; - if (nwh == 4) { - w[2] = cos(delta * 2); - w[3] = sin(delta * 2); - } else if (nwh > 4) { - makeipt(nw, ip); - w[2] = 0.5 / cos(delta * 2); - w[3] = 0.5 / cos(delta * 6); - for (j = 4; j < nwh; j += 4) { - w[j] = cos(delta * j); - w[j + 1] = sin(delta * j); - w[j + 2] = cos(3 * delta * j); - w[j + 3] = -sin(3 * delta * j); - } - } - nw0 = 0; - while (nwh > 2) { - nw1 = nw0 + nwh; - nwh >>= 1; - w[nw1] = 1; - w[nw1 + 1] = wn4r; - if (nwh == 4) { - wk1r = w[nw0 + 4]; - wk1i = w[nw0 + 5]; - w[nw1 + 2] = wk1r; - w[nw1 + 3] = wk1i; - } else if (nwh > 4) { - wk1r = w[nw0 + 4]; - wk3r = w[nw0 + 6]; - w[nw1 + 2] = 0.5 / wk1r; - w[nw1 + 3] = 0.5 / wk3r; - for (j = 4; j < nwh; j += 4) { - wk1r = w[nw0 + 2 * j]; - wk1i = w[nw0 + 2 * j + 1]; - wk3r = w[nw0 + 2 * j + 2]; - wk3i = w[nw0 + 2 * j + 3]; - w[nw1 + j] = wk1r; - w[nw1 + j + 1] = wk1i; - w[nw1 + j + 2] = wk3r; - w[nw1 + j + 3] = wk3i; - } - } - nw0 = nw1; - } - } -} - - -void makeipt(int nw, int *ip) -{ - int j, l, m, m2, p, q; - - ip[2] = 0; - ip[3] = 16; - m = 2; - for (l = nw; l > 32; l >>= 2) { - m2 = m << 1; - q = m2 << 3; - for (j = m; j < m2; j++) { - p = ip[j] << 2; - ip[m + j] = p; - ip[m2 + j] = p + q; - } - m = m2; - } -} - - -void makect(int nc, int *ip, double *c) -{ - int j, nch; - double delta; - - ip[1] = nc; - if (nc > 1) { - nch = nc >> 1; - delta = atan(1.0) / nch; - c[0] = cos(delta * nch); - c[nch] = 0.5 * c[0]; - for (j = 1; j < nch; j++) { - c[j] = 0.5 * cos(delta * j); - c[nc - j] = 0.5 * sin(delta * j); - } - } -} - - -/* -------- child routines -------- */ - - -#ifdef USE_CDFT_PTHREADS -#define USE_CDFT_THREADS -#ifndef CDFT_THREADS_BEGIN_N -#define CDFT_THREADS_BEGIN_N 8192 -#endif -#ifndef CDFT_4THREADS_BEGIN_N -#define CDFT_4THREADS_BEGIN_N 65536 -#endif -#include <pthread.h> -#include <stdio.h> -#include <stdlib.h> -#define cdft_thread_t pthread_t -#define cdft_thread_create(thp,func,argp) { \ - if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \ - fprintf(stderr, "cdft thread error\n"); \ - exit(1); \ - } \ -} -#define cdft_thread_wait(th) { \ - if (pthread_join(th, NULL) != 0) { \ - fprintf(stderr, "cdft thread error\n"); \ - exit(1); \ - } \ -} -#endif /* USE_CDFT_PTHREADS */ - - -#ifdef USE_CDFT_WINTHREADS -#define USE_CDFT_THREADS -#ifndef CDFT_THREADS_BEGIN_N -#define CDFT_THREADS_BEGIN_N 32768 -#endif -#ifndef CDFT_4THREADS_BEGIN_N -#define CDFT_4THREADS_BEGIN_N 524288 -#endif -#include <windows.h> -#include <stdio.h> -#include <stdlib.h> -#define cdft_thread_t HANDLE -#define cdft_thread_create(thp,func,argp) { \ - DWORD thid; \ - *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \ - if (*(thp) == 0) { \ - fprintf(stderr, "cdft thread error\n"); \ - exit(1); \ - } \ -} -#define cdft_thread_wait(th) { \ - WaitForSingleObject(th, INFINITE); \ - CloseHandle(th); \ -} -#endif /* USE_CDFT_WINTHREADS */ - - -void cftfsub(int n, double *a, int *ip, int nw, double *w) -{ - void bitrv2(int n, int *ip, double *a); - void bitrv216(double *a); - void bitrv208(double *a); - void cftf1st(int n, double *a, double *w); - void cftrec4(int n, double *a, int nw, double *w); - void cftleaf(int n, int isplt, double *a, int nw, double *w); - void cftfx41(int n, double *a, int nw, double *w); - void cftf161(double *a, double *w); - void cftf081(double *a, double *w); - void cftf040(double *a); - void cftx020(double *a); -#ifdef USE_CDFT_THREADS - void cftrec4_th(int n, double *a, int nw, double *w); -#endif /* USE_CDFT_THREADS */ - - if (n > 8) { - if (n > 32) { - cftf1st(n, a, &w[nw - (n >> 2)]); -#ifdef USE_CDFT_THREADS - if (n > CDFT_THREADS_BEGIN_N) { - cftrec4_th(n, a, nw, w); - } else -#endif /* USE_CDFT_THREADS */ - if (n > 512) { - cftrec4(n, a, nw, w); - } else if (n > 128) { - cftleaf(n, 1, a, nw, w); - } else { - cftfx41(n, a, nw, w); - } - bitrv2(n, ip, a); - } else if (n == 32) { - cftf161(a, &w[nw - 8]); - bitrv216(a); - } else { - cftf081(a, w); - bitrv208(a); - } - } else if (n == 8) { - cftf040(a); - } else if (n == 4) { - cftx020(a); - } -} - - -void cftbsub(int n, double *a, int *ip, int nw, double *w) -{ - void bitrv2conj(int n, int *ip, double *a); - void bitrv216neg(double *a); - void bitrv208neg(double *a); - void cftb1st(int n, double *a, double *w); - void cftrec4(int n, double *a, int nw, double *w); - void cftleaf(int n, int isplt, double *a, int nw, double *w); - void cftfx41(int n, double *a, int nw, double *w); - void cftf161(double *a, double *w); - void cftf081(double *a, double *w); - void cftb040(double *a); - void cftx020(double *a); -#ifdef USE_CDFT_THREADS - void cftrec4_th(int n, double *a, int nw, double *w); -#endif /* USE_CDFT_THREADS */ - - if (n > 8) { - if (n > 32) { - cftb1st(n, a, &w[nw - (n >> 2)]); -#ifdef USE_CDFT_THREADS - if (n > CDFT_THREADS_BEGIN_N) { - cftrec4_th(n, a, nw, w); - } else -#endif /* USE_CDFT_THREADS */ - if (n > 512) { - cftrec4(n, a, nw, w); - } else if (n > 128) { - cftleaf(n, 1, a, nw, w); - } else { - cftfx41(n, a, nw, w); - } - bitrv2conj(n, ip, a); - } else if (n == 32) { - cftf161(a, &w[nw - 8]); - bitrv216neg(a); - } else { - cftf081(a, w); - bitrv208neg(a); - } - } else if (n == 8) { - cftb040(a); - } else if (n == 4) { - cftx020(a); - } -} - - -void bitrv2(int n, int *ip, double *a) -{ - int j, j1, k, k1, l, m, nh, nm; - double xr, xi, yr, yi; - - m = 1; - for (l = n >> 2; l > 8; l >>= 2) { - m <<= 1; - } - nh = n >> 1; - nm = 4 * m; - if (l == 8) { - for (k = 0; k < m; k++) { - for (j = 0; j < k; j++) { - j1 = 4 * j + 2 * ip[m + k]; - k1 = 4 * k + 2 * ip[m + j]; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 -= nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nh; - k1 += 2; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 += nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += 2; - k1 += nh; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 -= nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nh; - k1 -= 2; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 += nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - } - k1 = 4 * k + 2 * ip[m + k]; - j1 = k1 + 2; - k1 += nh; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 -= nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= 2; - k1 -= nh; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nh + 2; - k1 += nh + 2; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nh - nm; - k1 += 2 * nm - 2; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - } - } else { - for (k = 0; k < m; k++) { - for (j = 0; j < k; j++) { - j1 = 4 * j + ip[m + k]; - k1 = 4 * k + ip[m + j]; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nh; - k1 += 2; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += 2; - k1 += nh; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nh; - k1 -= 2; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - } - k1 = 4 * k + ip[m + k]; - j1 = k1 + 2; - k1 += nh; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += nm; - xr = a[j1]; - xi = a[j1 + 1]; - yr = a[k1]; - yi = a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - } - } -} - - -void bitrv2conj(int n, int *ip, double *a) -{ - int j, j1, k, k1, l, m, nh, nm; - double xr, xi, yr, yi; - - m = 1; - for (l = n >> 2; l > 8; l >>= 2) { - m <<= 1; - } - nh = n >> 1; - nm = 4 * m; - if (l == 8) { - for (k = 0; k < m; k++) { - for (j = 0; j < k; j++) { - j1 = 4 * j + 2 * ip[m + k]; - k1 = 4 * k + 2 * ip[m + j]; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 -= nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nh; - k1 += 2; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 += nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += 2; - k1 += nh; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 -= nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nh; - k1 -= 2; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 += nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - } - k1 = 4 * k + 2 * ip[m + k]; - j1 = k1 + 2; - k1 += nh; - a[j1 - 1] = -a[j1 - 1]; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - a[k1 + 3] = -a[k1 + 3]; - j1 += nm; - k1 += 2 * nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 -= nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= 2; - k1 -= nh; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nh + 2; - k1 += nh + 2; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nh - nm; - k1 += 2 * nm - 2; - a[j1 - 1] = -a[j1 - 1]; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - a[k1 + 3] = -a[k1 + 3]; - } - } else { - for (k = 0; k < m; k++) { - for (j = 0; j < k; j++) { - j1 = 4 * j + ip[m + k]; - k1 = 4 * k + ip[m + j]; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nh; - k1 += 2; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += 2; - k1 += nh; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 += nm; - k1 += nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nh; - k1 -= 2; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - j1 -= nm; - k1 -= nm; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - } - k1 = 4 * k + ip[m + k]; - j1 = k1 + 2; - k1 += nh; - a[j1 - 1] = -a[j1 - 1]; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - a[k1 + 3] = -a[k1 + 3]; - j1 += nm; - k1 += nm; - a[j1 - 1] = -a[j1 - 1]; - xr = a[j1]; - xi = -a[j1 + 1]; - yr = a[k1]; - yi = -a[k1 + 1]; - a[j1] = yr; - a[j1 + 1] = yi; - a[k1] = xr; - a[k1 + 1] = xi; - a[k1 + 3] = -a[k1 + 3]; - } - } -} - - -void bitrv216(double *a) -{ - double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, - x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i, - x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i; - - x1r = a[2]; - x1i = a[3]; - x2r = a[4]; - x2i = a[5]; - x3r = a[6]; - x3i = a[7]; - x4r = a[8]; - x4i = a[9]; - x5r = a[10]; - x5i = a[11]; - x7r = a[14]; - x7i = a[15]; - x8r = a[16]; - x8i = a[17]; - x10r = a[20]; - x10i = a[21]; - x11r = a[22]; - x11i = a[23]; - x12r = a[24]; - x12i = a[25]; - x13r = a[26]; - x13i = a[27]; - x14r = a[28]; - x14i = a[29]; - a[2] = x8r; - a[3] = x8i; - a[4] = x4r; - a[5] = x4i; - a[6] = x12r; - a[7] = x12i; - a[8] = x2r; - a[9] = x2i; - a[10] = x10r; - a[11] = x10i; - a[14] = x14r; - a[15] = x14i; - a[16] = x1r; - a[17] = x1i; - a[20] = x5r; - a[21] = x5i; - a[22] = x13r; - a[23] = x13i; - a[24] = x3r; - a[25] = x3i; - a[26] = x11r; - a[27] = x11i; - a[28] = x7r; - a[29] = x7i; -} - - -void bitrv216neg(double *a) -{ - double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, - x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i, - x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i, - x13r, x13i, x14r, x14i, x15r, x15i; - - x1r = a[2]; - x1i = a[3]; - x2r = a[4]; - x2i = a[5]; - x3r = a[6]; - x3i = a[7]; - x4r = a[8]; - x4i = a[9]; - x5r = a[10]; - x5i = a[11]; - x6r = a[12]; - x6i = a[13]; - x7r = a[14]; - x7i = a[15]; - x8r = a[16]; - x8i = a[17]; - x9r = a[18]; - x9i = a[19]; - x10r = a[20]; - x10i = a[21]; - x11r = a[22]; - x11i = a[23]; - x12r = a[24]; - x12i = a[25]; - x13r = a[26]; - x13i = a[27]; - x14r = a[28]; - x14i = a[29]; - x15r = a[30]; - x15i = a[31]; - a[2] = x15r; - a[3] = x15i; - a[4] = x7r; - a[5] = x7i; - a[6] = x11r; - a[7] = x11i; - a[8] = x3r; - a[9] = x3i; - a[10] = x13r; - a[11] = x13i; - a[12] = x5r; - a[13] = x5i; - a[14] = x9r; - a[15] = x9i; - a[16] = x1r; - a[17] = x1i; - a[18] = x14r; - a[19] = x14i; - a[20] = x6r; - a[21] = x6i; - a[22] = x10r; - a[23] = x10i; - a[24] = x2r; - a[25] = x2i; - a[26] = x12r; - a[27] = x12i; - a[28] = x4r; - a[29] = x4i; - a[30] = x8r; - a[31] = x8i; -} - - -void bitrv208(double *a) -{ - double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i; - - x1r = a[2]; - x1i = a[3]; - x3r = a[6]; - x3i = a[7]; - x4r = a[8]; - x4i = a[9]; - x6r = a[12]; - x6i = a[13]; - a[2] = x4r; - a[3] = x4i; - a[6] = x6r; - a[7] = x6i; - a[8] = x1r; - a[9] = x1i; - a[12] = x3r; - a[13] = x3i; -} - - -void bitrv208neg(double *a) -{ - double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, - x5r, x5i, x6r, x6i, x7r, x7i; - - x1r = a[2]; - x1i = a[3]; - x2r = a[4]; - x2i = a[5]; - x3r = a[6]; - x3i = a[7]; - x4r = a[8]; - x4i = a[9]; - x5r = a[10]; - x5i = a[11]; - x6r = a[12]; - x6i = a[13]; - x7r = a[14]; - x7i = a[15]; - a[2] = x7r; - a[3] = x7i; - a[4] = x3r; - a[5] = x3i; - a[6] = x5r; - a[7] = x5i; - a[8] = x1r; - a[9] = x1i; - a[10] = x6r; - a[11] = x6i; - a[12] = x2r; - a[13] = x2i; - a[14] = x4r; - a[15] = x4i; -} - - -void cftf1st(int n, double *a, double *w) -{ - int j, j0, j1, j2, j3, k, m, mh; - double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, - wd1r, wd1i, wd3r, wd3i; - double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, - y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i; - - mh = n >> 3; - m = 2 * mh; - j1 = m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[0] + a[j2]; - x0i = a[1] + a[j2 + 1]; - x1r = a[0] - a[j2]; - x1i = a[1] - a[j2 + 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - a[0] = x0r + x2r; - a[1] = x0i + x2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i - x2i; - a[j2] = x1r - x3i; - a[j2 + 1] = x1i + x3r; - a[j3] = x1r + x3i; - a[j3 + 1] = x1i - x3r; - wn4r = w[1]; - csc1 = w[2]; - csc3 = w[3]; - wd1r = 1; - wd1i = 0; - wd3r = 1; - wd3i = 0; - k = 0; - for (j = 2; j < mh - 2; j += 4) { - k += 4; - wk1r = csc1 * (wd1r + w[k]); - wk1i = csc1 * (wd1i + w[k + 1]); - wk3r = csc3 * (wd3r + w[k + 2]); - wk3i = csc3 * (wd3i + w[k + 3]); - wd1r = w[k]; - wd1i = w[k + 1]; - wd3r = w[k + 2]; - wd3i = w[k + 3]; - j1 = j + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j] + a[j2]; - x0i = a[j + 1] + a[j2 + 1]; - x1r = a[j] - a[j2]; - x1i = a[j + 1] - a[j2 + 1]; - y0r = a[j + 2] + a[j2 + 2]; - y0i = a[j + 3] + a[j2 + 3]; - y1r = a[j + 2] - a[j2 + 2]; - y1i = a[j + 3] - a[j2 + 3]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - y2r = a[j1 + 2] + a[j3 + 2]; - y2i = a[j1 + 3] + a[j3 + 3]; - y3r = a[j1 + 2] - a[j3 + 2]; - y3i = a[j1 + 3] - a[j3 + 3]; - a[j] = x0r + x2r; - a[j + 1] = x0i + x2i; - a[j + 2] = y0r + y2r; - a[j + 3] = y0i + y2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i - x2i; - a[j1 + 2] = y0r - y2r; - a[j1 + 3] = y0i - y2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - a[j2] = wk1r * x0r - wk1i * x0i; - a[j2 + 1] = wk1r * x0i + wk1i * x0r; - x0r = y1r - y3i; - x0i = y1i + y3r; - a[j2 + 2] = wd1r * x0r - wd1i * x0i; - a[j2 + 3] = wd1r * x0i + wd1i * x0r; - x0r = x1r + x3i; - x0i = x1i - x3r; - a[j3] = wk3r * x0r + wk3i * x0i; - a[j3 + 1] = wk3r * x0i - wk3i * x0r; - x0r = y1r + y3i; - x0i = y1i - y3r; - a[j3 + 2] = wd3r * x0r + wd3i * x0i; - a[j3 + 3] = wd3r * x0i - wd3i * x0r; - j0 = m - j; - j1 = j0 + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j0] + a[j2]; - x0i = a[j0 + 1] + a[j2 + 1]; - x1r = a[j0] - a[j2]; - x1i = a[j0 + 1] - a[j2 + 1]; - y0r = a[j0 - 2] + a[j2 - 2]; - y0i = a[j0 - 1] + a[j2 - 1]; - y1r = a[j0 - 2] - a[j2 - 2]; - y1i = a[j0 - 1] - a[j2 - 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - y2r = a[j1 - 2] + a[j3 - 2]; - y2i = a[j1 - 1] + a[j3 - 1]; - y3r = a[j1 - 2] - a[j3 - 2]; - y3i = a[j1 - 1] - a[j3 - 1]; - a[j0] = x0r + x2r; - a[j0 + 1] = x0i + x2i; - a[j0 - 2] = y0r + y2r; - a[j0 - 1] = y0i + y2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i - x2i; - a[j1 - 2] = y0r - y2r; - a[j1 - 1] = y0i - y2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - a[j2] = wk1i * x0r - wk1r * x0i; - a[j2 + 1] = wk1i * x0i + wk1r * x0r; - x0r = y1r - y3i; - x0i = y1i + y3r; - a[j2 - 2] = wd1i * x0r - wd1r * x0i; - a[j2 - 1] = wd1i * x0i + wd1r * x0r; - x0r = x1r + x3i; - x0i = x1i - x3r; - a[j3] = wk3i * x0r + wk3r * x0i; - a[j3 + 1] = wk3i * x0i - wk3r * x0r; - x0r = y1r + y3i; - x0i = y1i - y3r; - a[j3 - 2] = wd3i * x0r + wd3r * x0i; - a[j3 - 1] = wd3i * x0i - wd3r * x0r; - } - wk1r = csc1 * (wd1r + wn4r); - wk1i = csc1 * (wd1i + wn4r); - wk3r = csc3 * (wd3r - wn4r); - wk3i = csc3 * (wd3i - wn4r); - j0 = mh; - j1 = j0 + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j0 - 2] + a[j2 - 2]; - x0i = a[j0 - 1] + a[j2 - 1]; - x1r = a[j0 - 2] - a[j2 - 2]; - x1i = a[j0 - 1] - a[j2 - 1]; - x2r = a[j1 - 2] + a[j3 - 2]; - x2i = a[j1 - 1] + a[j3 - 1]; - x3r = a[j1 - 2] - a[j3 - 2]; - x3i = a[j1 - 1] - a[j3 - 1]; - a[j0 - 2] = x0r + x2r; - a[j0 - 1] = x0i + x2i; - a[j1 - 2] = x0r - x2r; - a[j1 - 1] = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - a[j2 - 2] = wk1r * x0r - wk1i * x0i; - a[j2 - 1] = wk1r * x0i + wk1i * x0r; - x0r = x1r + x3i; - x0i = x1i - x3r; - a[j3 - 2] = wk3r * x0r + wk3i * x0i; - a[j3 - 1] = wk3r * x0i - wk3i * x0r; - x0r = a[j0] + a[j2]; - x0i = a[j0 + 1] + a[j2 + 1]; - x1r = a[j0] - a[j2]; - x1i = a[j0 + 1] - a[j2 + 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - a[j0] = x0r + x2r; - a[j0 + 1] = x0i + x2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - a[j2] = wn4r * (x0r - x0i); - a[j2 + 1] = wn4r * (x0i + x0r); - x0r = x1r + x3i; - x0i = x1i - x3r; - a[j3] = -wn4r * (x0r + x0i); - a[j3 + 1] = -wn4r * (x0i - x0r); - x0r = a[j0 + 2] + a[j2 + 2]; - x0i = a[j0 + 3] + a[j2 + 3]; - x1r = a[j0 + 2] - a[j2 + 2]; - x1i = a[j0 + 3] - a[j2 + 3]; - x2r = a[j1 + 2] + a[j3 + 2]; - x2i = a[j1 + 3] + a[j3 + 3]; - x3r = a[j1 + 2] - a[j3 + 2]; - x3i = a[j1 + 3] - a[j3 + 3]; - a[j0 + 2] = x0r + x2r; - a[j0 + 3] = x0i + x2i; - a[j1 + 2] = x0r - x2r; - a[j1 + 3] = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - a[j2 + 2] = wk1i * x0r - wk1r * x0i; - a[j2 + 3] = wk1i * x0i + wk1r * x0r; - x0r = x1r + x3i; - x0i = x1i - x3r; - a[j3 + 2] = wk3i * x0r + wk3r * x0i; - a[j3 + 3] = wk3i * x0i - wk3r * x0r; -} - - -void cftb1st(int n, double *a, double *w) -{ - int j, j0, j1, j2, j3, k, m, mh; - double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, - wd1r, wd1i, wd3r, wd3i; - double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, - y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i; - - mh = n >> 3; - m = 2 * mh; - j1 = m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[0] + a[j2]; - x0i = -a[1] - a[j2 + 1]; - x1r = a[0] - a[j2]; - x1i = -a[1] + a[j2 + 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - a[0] = x0r + x2r; - a[1] = x0i - x2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i + x2i; - a[j2] = x1r + x3i; - a[j2 + 1] = x1i + x3r; - a[j3] = x1r - x3i; - a[j3 + 1] = x1i - x3r; - wn4r = w[1]; - csc1 = w[2]; - csc3 = w[3]; - wd1r = 1; - wd1i = 0; - wd3r = 1; - wd3i = 0; - k = 0; - for (j = 2; j < mh - 2; j += 4) { - k += 4; - wk1r = csc1 * (wd1r + w[k]); - wk1i = csc1 * (wd1i + w[k + 1]); - wk3r = csc3 * (wd3r + w[k + 2]); - wk3i = csc3 * (wd3i + w[k + 3]); - wd1r = w[k]; - wd1i = w[k + 1]; - wd3r = w[k + 2]; - wd3i = w[k + 3]; - j1 = j + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j] + a[j2]; - x0i = -a[j + 1] - a[j2 + 1]; - x1r = a[j] - a[j2]; - x1i = -a[j + 1] + a[j2 + 1]; - y0r = a[j + 2] + a[j2 + 2]; - y0i = -a[j + 3] - a[j2 + 3]; - y1r = a[j + 2] - a[j2 + 2]; - y1i = -a[j + 3] + a[j2 + 3]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - y2r = a[j1 + 2] + a[j3 + 2]; - y2i = a[j1 + 3] + a[j3 + 3]; - y3r = a[j1 + 2] - a[j3 + 2]; - y3i = a[j1 + 3] - a[j3 + 3]; - a[j] = x0r + x2r; - a[j + 1] = x0i - x2i; - a[j + 2] = y0r + y2r; - a[j + 3] = y0i - y2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i + x2i; - a[j1 + 2] = y0r - y2r; - a[j1 + 3] = y0i + y2i; - x0r = x1r + x3i; - x0i = x1i + x3r; - a[j2] = wk1r * x0r - wk1i * x0i; - a[j2 + 1] = wk1r * x0i + wk1i * x0r; - x0r = y1r + y3i; - x0i = y1i + y3r; - a[j2 + 2] = wd1r * x0r - wd1i * x0i; - a[j2 + 3] = wd1r * x0i + wd1i * x0r; - x0r = x1r - x3i; - x0i = x1i - x3r; - a[j3] = wk3r * x0r + wk3i * x0i; - a[j3 + 1] = wk3r * x0i - wk3i * x0r; - x0r = y1r - y3i; - x0i = y1i - y3r; - a[j3 + 2] = wd3r * x0r + wd3i * x0i; - a[j3 + 3] = wd3r * x0i - wd3i * x0r; - j0 = m - j; - j1 = j0 + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j0] + a[j2]; - x0i = -a[j0 + 1] - a[j2 + 1]; - x1r = a[j0] - a[j2]; - x1i = -a[j0 + 1] + a[j2 + 1]; - y0r = a[j0 - 2] + a[j2 - 2]; - y0i = -a[j0 - 1] - a[j2 - 1]; - y1r = a[j0 - 2] - a[j2 - 2]; - y1i = -a[j0 - 1] + a[j2 - 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - y2r = a[j1 - 2] + a[j3 - 2]; - y2i = a[j1 - 1] + a[j3 - 1]; - y3r = a[j1 - 2] - a[j3 - 2]; - y3i = a[j1 - 1] - a[j3 - 1]; - a[j0] = x0r + x2r; - a[j0 + 1] = x0i - x2i; - a[j0 - 2] = y0r + y2r; - a[j0 - 1] = y0i - y2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i + x2i; - a[j1 - 2] = y0r - y2r; - a[j1 - 1] = y0i + y2i; - x0r = x1r + x3i; - x0i = x1i + x3r; - a[j2] = wk1i * x0r - wk1r * x0i; - a[j2 + 1] = wk1i * x0i + wk1r * x0r; - x0r = y1r + y3i; - x0i = y1i + y3r; - a[j2 - 2] = wd1i * x0r - wd1r * x0i; - a[j2 - 1] = wd1i * x0i + wd1r * x0r; - x0r = x1r - x3i; - x0i = x1i - x3r; - a[j3] = wk3i * x0r + wk3r * x0i; - a[j3 + 1] = wk3i * x0i - wk3r * x0r; - x0r = y1r - y3i; - x0i = y1i - y3r; - a[j3 - 2] = wd3i * x0r + wd3r * x0i; - a[j3 - 1] = wd3i * x0i - wd3r * x0r; - } - wk1r = csc1 * (wd1r + wn4r); - wk1i = csc1 * (wd1i + wn4r); - wk3r = csc3 * (wd3r - wn4r); - wk3i = csc3 * (wd3i - wn4r); - j0 = mh; - j1 = j0 + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j0 - 2] + a[j2 - 2]; - x0i = -a[j0 - 1] - a[j2 - 1]; - x1r = a[j0 - 2] - a[j2 - 2]; - x1i = -a[j0 - 1] + a[j2 - 1]; - x2r = a[j1 - 2] + a[j3 - 2]; - x2i = a[j1 - 1] + a[j3 - 1]; - x3r = a[j1 - 2] - a[j3 - 2]; - x3i = a[j1 - 1] - a[j3 - 1]; - a[j0 - 2] = x0r + x2r; - a[j0 - 1] = x0i - x2i; - a[j1 - 2] = x0r - x2r; - a[j1 - 1] = x0i + x2i; - x0r = x1r + x3i; - x0i = x1i + x3r; - a[j2 - 2] = wk1r * x0r - wk1i * x0i; - a[j2 - 1] = wk1r * x0i + wk1i * x0r; - x0r = x1r - x3i; - x0i = x1i - x3r; - a[j3 - 2] = wk3r * x0r + wk3i * x0i; - a[j3 - 1] = wk3r * x0i - wk3i * x0r; - x0r = a[j0] + a[j2]; - x0i = -a[j0 + 1] - a[j2 + 1]; - x1r = a[j0] - a[j2]; - x1i = -a[j0 + 1] + a[j2 + 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - a[j0] = x0r + x2r; - a[j0 + 1] = x0i - x2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i + x2i; - x0r = x1r + x3i; - x0i = x1i + x3r; - a[j2] = wn4r * (x0r - x0i); - a[j2 + 1] = wn4r * (x0i + x0r); - x0r = x1r - x3i; - x0i = x1i - x3r; - a[j3] = -wn4r * (x0r + x0i); - a[j3 + 1] = -wn4r * (x0i - x0r); - x0r = a[j0 + 2] + a[j2 + 2]; - x0i = -a[j0 + 3] - a[j2 + 3]; - x1r = a[j0 + 2] - a[j2 + 2]; - x1i = -a[j0 + 3] + a[j2 + 3]; - x2r = a[j1 + 2] + a[j3 + 2]; - x2i = a[j1 + 3] + a[j3 + 3]; - x3r = a[j1 + 2] - a[j3 + 2]; - x3i = a[j1 + 3] - a[j3 + 3]; - a[j0 + 2] = x0r + x2r; - a[j0 + 3] = x0i - x2i; - a[j1 + 2] = x0r - x2r; - a[j1 + 3] = x0i + x2i; - x0r = x1r + x3i; - x0i = x1i + x3r; - a[j2 + 2] = wk1i * x0r - wk1r * x0i; - a[j2 + 3] = wk1i * x0i + wk1r * x0r; - x0r = x1r - x3i; - x0i = x1i - x3r; - a[j3 + 2] = wk3i * x0r + wk3r * x0i; - a[j3 + 3] = wk3i * x0i - wk3r * x0r; -} - - -#ifdef USE_CDFT_THREADS -struct cdft_arg_st { - int n0; - int n; - double *a; - int nw; - double *w; -}; -typedef struct cdft_arg_st cdft_arg_t; - - -void cftrec4_th(int n, double *a, int nw, double *w) -{ - void *cftrec1_th(void *p); - void *cftrec2_th(void *p); - int i, idiv4, m, nthread; - cdft_thread_t th[4]; - cdft_arg_t ag[4]; - - nthread = 2; - idiv4 = 0; - m = n >> 1; - if (n > CDFT_4THREADS_BEGIN_N) { - nthread = 4; - idiv4 = 1; - m >>= 1; - } - for (i = 0; i < nthread; i++) { - ag[i].n0 = n; - ag[i].n = m; - ag[i].a = &a[i * m]; - ag[i].nw = nw; - ag[i].w = w; - if (i != idiv4) { - cdft_thread_create(&th[i], cftrec1_th, &ag[i]); - } else { - cdft_thread_create(&th[i], cftrec2_th, &ag[i]); - } - } - for (i = 0; i < nthread; i++) { - cdft_thread_wait(th[i]); - } -} - - -void *cftrec1_th(void *p) -{ - int cfttree(int n, int j, int k, double *a, int nw, double *w); - void cftleaf(int n, int isplt, double *a, int nw, double *w); - void cftmdl1(int n, double *a, double *w); - int isplt, j, k, m, n, n0, nw; - double *a, *w; - - n0 = ((cdft_arg_t *) p)->n0; - n = ((cdft_arg_t *) p)->n; - a = ((cdft_arg_t *) p)->a; - nw = ((cdft_arg_t *) p)->nw; - w = ((cdft_arg_t *) p)->w; - m = n0; - while (m > 512) { - m >>= 2; - cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]); - } - cftleaf(m, 1, &a[n - m], nw, w); - k = 0; - for (j = n - m; j > 0; j -= m) { - k++; - isplt = cfttree(m, j, k, a, nw, w); - cftleaf(m, isplt, &a[j - m], nw, w); - } - return (void *) 0; -} - - -void *cftrec2_th(void *p) -{ - int cfttree(int n, int j, int k, double *a, int nw, double *w); - void cftleaf(int n, int isplt, double *a, int nw, double *w); - void cftmdl2(int n, double *a, double *w); - int isplt, j, k, m, n, n0, nw; - double *a, *w; - - n0 = ((cdft_arg_t *) p)->n0; - n = ((cdft_arg_t *) p)->n; - a = ((cdft_arg_t *) p)->a; - nw = ((cdft_arg_t *) p)->nw; - w = ((cdft_arg_t *) p)->w; - k = 1; - m = n0; - while (m > 512) { - m >>= 2; - k <<= 2; - cftmdl2(m, &a[n - m], &w[nw - m]); - } - cftleaf(m, 0, &a[n - m], nw, w); - k >>= 1; - for (j = n - m; j > 0; j -= m) { - k++; - isplt = cfttree(m, j, k, a, nw, w); - cftleaf(m, isplt, &a[j - m], nw, w); - } - return (void *) 0; -} -#endif /* USE_CDFT_THREADS */ - - -void cftrec4(int n, double *a, int nw, double *w) -{ - int cfttree(int n, int j, int k, double *a, int nw, double *w); - void cftleaf(int n, int isplt, double *a, int nw, double *w); - void cftmdl1(int n, double *a, double *w); - int isplt, j, k, m; - - m = n; - while (m > 512) { - m >>= 2; - cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]); - } - cftleaf(m, 1, &a[n - m], nw, w); - k = 0; - for (j = n - m; j > 0; j -= m) { - k++; - isplt = cfttree(m, j, k, a, nw, w); - cftleaf(m, isplt, &a[j - m], nw, w); - } -} - - -int cfttree(int n, int j, int k, double *a, int nw, double *w) -{ - void cftmdl1(int n, double *a, double *w); - void cftmdl2(int n, double *a, double *w); - int i, isplt, m; - - if ((k & 3) != 0) { - isplt = k & 1; - if (isplt != 0) { - cftmdl1(n, &a[j - n], &w[nw - (n >> 1)]); - } else { - cftmdl2(n, &a[j - n], &w[nw - n]); - } - } else { - m = n; - for (i = k; (i & 3) == 0; i >>= 2) { - m <<= 2; - } - isplt = i & 1; - if (isplt != 0) { - while (m > 128) { - cftmdl1(m, &a[j - m], &w[nw - (m >> 1)]); - m >>= 2; - } - } else { - while (m > 128) { - cftmdl2(m, &a[j - m], &w[nw - m]); - m >>= 2; - } - } - } - return isplt; -} - - -void cftleaf(int n, int isplt, double *a, int nw, double *w) -{ - void cftmdl1(int n, double *a, double *w); - void cftmdl2(int n, double *a, double *w); - void cftf161(double *a, double *w); - void cftf162(double *a, double *w); - void cftf081(double *a, double *w); - void cftf082(double *a, double *w); - - if (n == 512) { - cftmdl1(128, a, &w[nw - 64]); - cftf161(a, &w[nw - 8]); - cftf162(&a[32], &w[nw - 32]); - cftf161(&a[64], &w[nw - 8]); - cftf161(&a[96], &w[nw - 8]); - cftmdl2(128, &a[128], &w[nw - 128]); - cftf161(&a[128], &w[nw - 8]); - cftf162(&a[160], &w[nw - 32]); - cftf161(&a[192], &w[nw - 8]); - cftf162(&a[224], &w[nw - 32]); - cftmdl1(128, &a[256], &w[nw - 64]); - cftf161(&a[256], &w[nw - 8]); - cftf162(&a[288], &w[nw - 32]); - cftf161(&a[320], &w[nw - 8]); - cftf161(&a[352], &w[nw - 8]); - if (isplt != 0) { - cftmdl1(128, &a[384], &w[nw - 64]); - cftf161(&a[480], &w[nw - 8]); - } else { - cftmdl2(128, &a[384], &w[nw - 128]); - cftf162(&a[480], &w[nw - 32]); - } - cftf161(&a[384], &w[nw - 8]); - cftf162(&a[416], &w[nw - 32]); - cftf161(&a[448], &w[nw - 8]); - } else { - cftmdl1(64, a, &w[nw - 32]); - cftf081(a, &w[nw - 8]); - cftf082(&a[16], &w[nw - 8]); - cftf081(&a[32], &w[nw - 8]); - cftf081(&a[48], &w[nw - 8]); - cftmdl2(64, &a[64], &w[nw - 64]); - cftf081(&a[64], &w[nw - 8]); - cftf082(&a[80], &w[nw - 8]); - cftf081(&a[96], &w[nw - 8]); - cftf082(&a[112], &w[nw - 8]); - cftmdl1(64, &a[128], &w[nw - 32]); - cftf081(&a[128], &w[nw - 8]); - cftf082(&a[144], &w[nw - 8]); - cftf081(&a[160], &w[nw - 8]); - cftf081(&a[176], &w[nw - 8]); - if (isplt != 0) { - cftmdl1(64, &a[192], &w[nw - 32]); - cftf081(&a[240], &w[nw - 8]); - } else { - cftmdl2(64, &a[192], &w[nw - 64]); - cftf082(&a[240], &w[nw - 8]); - } - cftf081(&a[192], &w[nw - 8]); - cftf082(&a[208], &w[nw - 8]); - cftf081(&a[224], &w[nw - 8]); - } -} - - -void cftmdl1(int n, double *a, double *w) -{ - int j, j0, j1, j2, j3, k, m, mh; - double wn4r, wk1r, wk1i, wk3r, wk3i; - double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; - - mh = n >> 3; - m = 2 * mh; - j1 = m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[0] + a[j2]; - x0i = a[1] + a[j2 + 1]; - x1r = a[0] - a[j2]; - x1i = a[1] - a[j2 + 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - a[0] = x0r + x2r; - a[1] = x0i + x2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i - x2i; - a[j2] = x1r - x3i; - a[j2 + 1] = x1i + x3r; - a[j3] = x1r + x3i; - a[j3 + 1] = x1i - x3r; - wn4r = w[1]; - k = 0; - for (j = 2; j < mh; j += 2) { - k += 4; - wk1r = w[k]; - wk1i = w[k + 1]; - wk3r = w[k + 2]; - wk3i = w[k + 3]; - j1 = j + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j] + a[j2]; - x0i = a[j + 1] + a[j2 + 1]; - x1r = a[j] - a[j2]; - x1i = a[j + 1] - a[j2 + 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - a[j] = x0r + x2r; - a[j + 1] = x0i + x2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - a[j2] = wk1r * x0r - wk1i * x0i; - a[j2 + 1] = wk1r * x0i + wk1i * x0r; - x0r = x1r + x3i; - x0i = x1i - x3r; - a[j3] = wk3r * x0r + wk3i * x0i; - a[j3 + 1] = wk3r * x0i - wk3i * x0r; - j0 = m - j; - j1 = j0 + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j0] + a[j2]; - x0i = a[j0 + 1] + a[j2 + 1]; - x1r = a[j0] - a[j2]; - x1i = a[j0 + 1] - a[j2 + 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - a[j0] = x0r + x2r; - a[j0 + 1] = x0i + x2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - a[j2] = wk1i * x0r - wk1r * x0i; - a[j2 + 1] = wk1i * x0i + wk1r * x0r; - x0r = x1r + x3i; - x0i = x1i - x3r; - a[j3] = wk3i * x0r + wk3r * x0i; - a[j3 + 1] = wk3i * x0i - wk3r * x0r; - } - j0 = mh; - j1 = j0 + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j0] + a[j2]; - x0i = a[j0 + 1] + a[j2 + 1]; - x1r = a[j0] - a[j2]; - x1i = a[j0 + 1] - a[j2 + 1]; - x2r = a[j1] + a[j3]; - x2i = a[j1 + 1] + a[j3 + 1]; - x3r = a[j1] - a[j3]; - x3i = a[j1 + 1] - a[j3 + 1]; - a[j0] = x0r + x2r; - a[j0 + 1] = x0i + x2i; - a[j1] = x0r - x2r; - a[j1 + 1] = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - a[j2] = wn4r * (x0r - x0i); - a[j2 + 1] = wn4r * (x0i + x0r); - x0r = x1r + x3i; - x0i = x1i - x3r; - a[j3] = -wn4r * (x0r + x0i); - a[j3 + 1] = -wn4r * (x0i - x0r); -} - - -void cftmdl2(int n, double *a, double *w) -{ - int j, j0, j1, j2, j3, k, kr, m, mh; - double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i; - double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i; - - mh = n >> 3; - m = 2 * mh; - wn4r = w[1]; - j1 = m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[0] - a[j2 + 1]; - x0i = a[1] + a[j2]; - x1r = a[0] + a[j2 + 1]; - x1i = a[1] - a[j2]; - x2r = a[j1] - a[j3 + 1]; - x2i = a[j1 + 1] + a[j3]; - x3r = a[j1] + a[j3 + 1]; - x3i = a[j1 + 1] - a[j3]; - y0r = wn4r * (x2r - x2i); - y0i = wn4r * (x2i + x2r); - a[0] = x0r + y0r; - a[1] = x0i + y0i; - a[j1] = x0r - y0r; - a[j1 + 1] = x0i - y0i; - y0r = wn4r * (x3r - x3i); - y0i = wn4r * (x3i + x3r); - a[j2] = x1r - y0i; - a[j2 + 1] = x1i + y0r; - a[j3] = x1r + y0i; - a[j3 + 1] = x1i - y0r; - k = 0; - kr = 2 * m; - for (j = 2; j < mh; j += 2) { - k += 4; - wk1r = w[k]; - wk1i = w[k + 1]; - wk3r = w[k + 2]; - wk3i = w[k + 3]; - kr -= 4; - wd1i = w[kr]; - wd1r = w[kr + 1]; - wd3i = w[kr + 2]; - wd3r = w[kr + 3]; - j1 = j + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j] - a[j2 + 1]; - x0i = a[j + 1] + a[j2]; - x1r = a[j] + a[j2 + 1]; - x1i = a[j + 1] - a[j2]; - x2r = a[j1] - a[j3 + 1]; - x2i = a[j1 + 1] + a[j3]; - x3r = a[j1] + a[j3 + 1]; - x3i = a[j1 + 1] - a[j3]; - y0r = wk1r * x0r - wk1i * x0i; - y0i = wk1r * x0i + wk1i * x0r; - y2r = wd1r * x2r - wd1i * x2i; - y2i = wd1r * x2i + wd1i * x2r; - a[j] = y0r + y2r; - a[j + 1] = y0i + y2i; - a[j1] = y0r - y2r; - a[j1 + 1] = y0i - y2i; - y0r = wk3r * x1r + wk3i * x1i; - y0i = wk3r * x1i - wk3i * x1r; - y2r = wd3r * x3r + wd3i * x3i; - y2i = wd3r * x3i - wd3i * x3r; - a[j2] = y0r + y2r; - a[j2 + 1] = y0i + y2i; - a[j3] = y0r - y2r; - a[j3 + 1] = y0i - y2i; - j0 = m - j; - j1 = j0 + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j0] - a[j2 + 1]; - x0i = a[j0 + 1] + a[j2]; - x1r = a[j0] + a[j2 + 1]; - x1i = a[j0 + 1] - a[j2]; - x2r = a[j1] - a[j3 + 1]; - x2i = a[j1 + 1] + a[j3]; - x3r = a[j1] + a[j3 + 1]; - x3i = a[j1 + 1] - a[j3]; - y0r = wd1i * x0r - wd1r * x0i; - y0i = wd1i * x0i + wd1r * x0r; - y2r = wk1i * x2r - wk1r * x2i; - y2i = wk1i * x2i + wk1r * x2r; - a[j0] = y0r + y2r; - a[j0 + 1] = y0i + y2i; - a[j1] = y0r - y2r; - a[j1 + 1] = y0i - y2i; - y0r = wd3i * x1r + wd3r * x1i; - y0i = wd3i * x1i - wd3r * x1r; - y2r = wk3i * x3r + wk3r * x3i; - y2i = wk3i * x3i - wk3r * x3r; - a[j2] = y0r + y2r; - a[j2 + 1] = y0i + y2i; - a[j3] = y0r - y2r; - a[j3 + 1] = y0i - y2i; - } - wk1r = w[m]; - wk1i = w[m + 1]; - j0 = mh; - j1 = j0 + m; - j2 = j1 + m; - j3 = j2 + m; - x0r = a[j0] - a[j2 + 1]; - x0i = a[j0 + 1] + a[j2]; - x1r = a[j0] + a[j2 + 1]; - x1i = a[j0 + 1] - a[j2]; - x2r = a[j1] - a[j3 + 1]; - x2i = a[j1 + 1] + a[j3]; - x3r = a[j1] + a[j3 + 1]; - x3i = a[j1 + 1] - a[j3]; - y0r = wk1r * x0r - wk1i * x0i; - y0i = wk1r * x0i + wk1i * x0r; - y2r = wk1i * x2r - wk1r * x2i; - y2i = wk1i * x2i + wk1r * x2r; - a[j0] = y0r + y2r; - a[j0 + 1] = y0i + y2i; - a[j1] = y0r - y2r; - a[j1 + 1] = y0i - y2i; - y0r = wk1i * x1r - wk1r * x1i; - y0i = wk1i * x1i + wk1r * x1r; - y2r = wk1r * x3r - wk1i * x3i; - y2i = wk1r * x3i + wk1i * x3r; - a[j2] = y0r - y2r; - a[j2 + 1] = y0i - y2i; - a[j3] = y0r + y2r; - a[j3 + 1] = y0i + y2i; -} - - -void cftfx41(int n, double *a, int nw, double *w) -{ - void cftf161(double *a, double *w); - void cftf162(double *a, double *w); - void cftf081(double *a, double *w); - void cftf082(double *a, double *w); - - if (n == 128) { - cftf161(a, &w[nw - 8]); - cftf162(&a[32], &w[nw - 32]); - cftf161(&a[64], &w[nw - 8]); - cftf161(&a[96], &w[nw - 8]); - } else { - cftf081(a, &w[nw - 8]); - cftf082(&a[16], &w[nw - 8]); - cftf081(&a[32], &w[nw - 8]); - cftf081(&a[48], &w[nw - 8]); - } -} - - -void cftf161(double *a, double *w) -{ - double wn4r, wk1r, wk1i, - x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, - y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, - y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, - y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, - y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i; - - wn4r = w[1]; - wk1r = w[2]; - wk1i = w[3]; - x0r = a[0] + a[16]; - x0i = a[1] + a[17]; - x1r = a[0] - a[16]; - x1i = a[1] - a[17]; - x2r = a[8] + a[24]; - x2i = a[9] + a[25]; - x3r = a[8] - a[24]; - x3i = a[9] - a[25]; - y0r = x0r + x2r; - y0i = x0i + x2i; - y4r = x0r - x2r; - y4i = x0i - x2i; - y8r = x1r - x3i; - y8i = x1i + x3r; - y12r = x1r + x3i; - y12i = x1i - x3r; - x0r = a[2] + a[18]; - x0i = a[3] + a[19]; - x1r = a[2] - a[18]; - x1i = a[3] - a[19]; - x2r = a[10] + a[26]; - x2i = a[11] + a[27]; - x3r = a[10] - a[26]; - x3i = a[11] - a[27]; - y1r = x0r + x2r; - y1i = x0i + x2i; - y5r = x0r - x2r; - y5i = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - y9r = wk1r * x0r - wk1i * x0i; - y9i = wk1r * x0i + wk1i * x0r; - x0r = x1r + x3i; - x0i = x1i - x3r; - y13r = wk1i * x0r - wk1r * x0i; - y13i = wk1i * x0i + wk1r * x0r; - x0r = a[4] + a[20]; - x0i = a[5] + a[21]; - x1r = a[4] - a[20]; - x1i = a[5] - a[21]; - x2r = a[12] + a[28]; - x2i = a[13] + a[29]; - x3r = a[12] - a[28]; - x3i = a[13] - a[29]; - y2r = x0r + x2r; - y2i = x0i + x2i; - y6r = x0r - x2r; - y6i = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - y10r = wn4r * (x0r - x0i); - y10i = wn4r * (x0i + x0r); - x0r = x1r + x3i; - x0i = x1i - x3r; - y14r = wn4r * (x0r + x0i); - y14i = wn4r * (x0i - x0r); - x0r = a[6] + a[22]; - x0i = a[7] + a[23]; - x1r = a[6] - a[22]; - x1i = a[7] - a[23]; - x2r = a[14] + a[30]; - x2i = a[15] + a[31]; - x3r = a[14] - a[30]; - x3i = a[15] - a[31]; - y3r = x0r + x2r; - y3i = x0i + x2i; - y7r = x0r - x2r; - y7i = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - y11r = wk1i * x0r - wk1r * x0i; - y11i = wk1i * x0i + wk1r * x0r; - x0r = x1r + x3i; - x0i = x1i - x3r; - y15r = wk1r * x0r - wk1i * x0i; - y15i = wk1r * x0i + wk1i * x0r; - x0r = y12r - y14r; - x0i = y12i - y14i; - x1r = y12r + y14r; - x1i = y12i + y14i; - x2r = y13r - y15r; - x2i = y13i - y15i; - x3r = y13r + y15r; - x3i = y13i + y15i; - a[24] = x0r + x2r; - a[25] = x0i + x2i; - a[26] = x0r - x2r; - a[27] = x0i - x2i; - a[28] = x1r - x3i; - a[29] = x1i + x3r; - a[30] = x1r + x3i; - a[31] = x1i - x3r; - x0r = y8r + y10r; - x0i = y8i + y10i; - x1r = y8r - y10r; - x1i = y8i - y10i; - x2r = y9r + y11r; - x2i = y9i + y11i; - x3r = y9r - y11r; - x3i = y9i - y11i; - a[16] = x0r + x2r; - a[17] = x0i + x2i; - a[18] = x0r - x2r; - a[19] = x0i - x2i; - a[20] = x1r - x3i; - a[21] = x1i + x3r; - a[22] = x1r + x3i; - a[23] = x1i - x3r; - x0r = y5r - y7i; - x0i = y5i + y7r; - x2r = wn4r * (x0r - x0i); - x2i = wn4r * (x0i + x0r); - x0r = y5r + y7i; - x0i = y5i - y7r; - x3r = wn4r * (x0r - x0i); - x3i = wn4r * (x0i + x0r); - x0r = y4r - y6i; - x0i = y4i + y6r; - x1r = y4r + y6i; - x1i = y4i - y6r; - a[8] = x0r + x2r; - a[9] = x0i + x2i; - a[10] = x0r - x2r; - a[11] = x0i - x2i; - a[12] = x1r - x3i; - a[13] = x1i + x3r; - a[14] = x1r + x3i; - a[15] = x1i - x3r; - x0r = y0r + y2r; - x0i = y0i + y2i; - x1r = y0r - y2r; - x1i = y0i - y2i; - x2r = y1r + y3r; - x2i = y1i + y3i; - x3r = y1r - y3r; - x3i = y1i - y3i; - a[0] = x0r + x2r; - a[1] = x0i + x2i; - a[2] = x0r - x2r; - a[3] = x0i - x2i; - a[4] = x1r - x3i; - a[5] = x1i + x3r; - a[6] = x1r + x3i; - a[7] = x1i - x3r; -} - - -void cftf162(double *a, double *w) -{ - double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, - x0r, x0i, x1r, x1i, x2r, x2i, - y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, - y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, - y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, - y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i; - - wn4r = w[1]; - wk1r = w[4]; - wk1i = w[5]; - wk3r = w[6]; - wk3i = -w[7]; - wk2r = w[8]; - wk2i = w[9]; - x1r = a[0] - a[17]; - x1i = a[1] + a[16]; - x0r = a[8] - a[25]; - x0i = a[9] + a[24]; - x2r = wn4r * (x0r - x0i); - x2i = wn4r * (x0i + x0r); - y0r = x1r + x2r; - y0i = x1i + x2i; - y4r = x1r - x2r; - y4i = x1i - x2i; - x1r = a[0] + a[17]; - x1i = a[1] - a[16]; - x0r = a[8] + a[25]; - x0i = a[9] - a[24]; - x2r = wn4r * (x0r - x0i); - x2i = wn4r * (x0i + x0r); - y8r = x1r - x2i; - y8i = x1i + x2r; - y12r = x1r + x2i; - y12i = x1i - x2r; - x0r = a[2] - a[19]; - x0i = a[3] + a[18]; - x1r = wk1r * x0r - wk1i * x0i; - x1i = wk1r * x0i + wk1i * x0r; - x0r = a[10] - a[27]; - x0i = a[11] + a[26]; - x2r = wk3i * x0r - wk3r * x0i; - x2i = wk3i * x0i + wk3r * x0r; - y1r = x1r + x2r; - y1i = x1i + x2i; - y5r = x1r - x2r; - y5i = x1i - x2i; - x0r = a[2] + a[19]; - x0i = a[3] - a[18]; - x1r = wk3r * x0r - wk3i * x0i; - x1i = wk3r * x0i + wk3i * x0r; - x0r = a[10] + a[27]; - x0i = a[11] - a[26]; - x2r = wk1r * x0r + wk1i * x0i; - x2i = wk1r * x0i - wk1i * x0r; - y9r = x1r - x2r; - y9i = x1i - x2i; - y13r = x1r + x2r; - y13i = x1i + x2i; - x0r = a[4] - a[21]; - x0i = a[5] + a[20]; - x1r = wk2r * x0r - wk2i * x0i; - x1i = wk2r * x0i + wk2i * x0r; - x0r = a[12] - a[29]; - x0i = a[13] + a[28]; - x2r = wk2i * x0r - wk2r * x0i; - x2i = wk2i * x0i + wk2r * x0r; - y2r = x1r + x2r; - y2i = x1i + x2i; - y6r = x1r - x2r; - y6i = x1i - x2i; - x0r = a[4] + a[21]; - x0i = a[5] - a[20]; - x1r = wk2i * x0r - wk2r * x0i; - x1i = wk2i * x0i + wk2r * x0r; - x0r = a[12] + a[29]; - x0i = a[13] - a[28]; - x2r = wk2r * x0r - wk2i * x0i; - x2i = wk2r * x0i + wk2i * x0r; - y10r = x1r - x2r; - y10i = x1i - x2i; - y14r = x1r + x2r; - y14i = x1i + x2i; - x0r = a[6] - a[23]; - x0i = a[7] + a[22]; - x1r = wk3r * x0r - wk3i * x0i; - x1i = wk3r * x0i + wk3i * x0r; - x0r = a[14] - a[31]; - x0i = a[15] + a[30]; - x2r = wk1i * x0r - wk1r * x0i; - x2i = wk1i * x0i + wk1r * x0r; - y3r = x1r + x2r; - y3i = x1i + x2i; - y7r = x1r - x2r; - y7i = x1i - x2i; - x0r = a[6] + a[23]; - x0i = a[7] - a[22]; - x1r = wk1i * x0r + wk1r * x0i; - x1i = wk1i * x0i - wk1r * x0r; - x0r = a[14] + a[31]; - x0i = a[15] - a[30]; - x2r = wk3i * x0r - wk3r * x0i; - x2i = wk3i * x0i + wk3r * x0r; - y11r = x1r + x2r; - y11i = x1i + x2i; - y15r = x1r - x2r; - y15i = x1i - x2i; - x1r = y0r + y2r; - x1i = y0i + y2i; - x2r = y1r + y3r; - x2i = y1i + y3i; - a[0] = x1r + x2r; - a[1] = x1i + x2i; - a[2] = x1r - x2r; - a[3] = x1i - x2i; - x1r = y0r - y2r; - x1i = y0i - y2i; - x2r = y1r - y3r; - x2i = y1i - y3i; - a[4] = x1r - x2i; - a[5] = x1i + x2r; - a[6] = x1r + x2i; - a[7] = x1i - x2r; - x1r = y4r - y6i; - x1i = y4i + y6r; - x0r = y5r - y7i; - x0i = y5i + y7r; - x2r = wn4r * (x0r - x0i); - x2i = wn4r * (x0i + x0r); - a[8] = x1r + x2r; - a[9] = x1i + x2i; - a[10] = x1r - x2r; - a[11] = x1i - x2i; - x1r = y4r + y6i; - x1i = y4i - y6r; - x0r = y5r + y7i; - x0i = y5i - y7r; - x2r = wn4r * (x0r - x0i); - x2i = wn4r * (x0i + x0r); - a[12] = x1r - x2i; - a[13] = x1i + x2r; - a[14] = x1r + x2i; - a[15] = x1i - x2r; - x1r = y8r + y10r; - x1i = y8i + y10i; - x2r = y9r - y11r; - x2i = y9i - y11i; - a[16] = x1r + x2r; - a[17] = x1i + x2i; - a[18] = x1r - x2r; - a[19] = x1i - x2i; - x1r = y8r - y10r; - x1i = y8i - y10i; - x2r = y9r + y11r; - x2i = y9i + y11i; - a[20] = x1r - x2i; - a[21] = x1i + x2r; - a[22] = x1r + x2i; - a[23] = x1i - x2r; - x1r = y12r - y14i; - x1i = y12i + y14r; - x0r = y13r + y15i; - x0i = y13i - y15r; - x2r = wn4r * (x0r - x0i); - x2i = wn4r * (x0i + x0r); - a[24] = x1r + x2r; - a[25] = x1i + x2i; - a[26] = x1r - x2r; - a[27] = x1i - x2i; - x1r = y12r + y14i; - x1i = y12i - y14r; - x0r = y13r - y15i; - x0i = y13i + y15r; - x2r = wn4r * (x0r - x0i); - x2i = wn4r * (x0i + x0r); - a[28] = x1r - x2i; - a[29] = x1i + x2r; - a[30] = x1r + x2i; - a[31] = x1i - x2r; -} - - -void cftf081(double *a, double *w) -{ - double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, - y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, - y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i; - - wn4r = w[1]; - x0r = a[0] + a[8]; - x0i = a[1] + a[9]; - x1r = a[0] - a[8]; - x1i = a[1] - a[9]; - x2r = a[4] + a[12]; - x2i = a[5] + a[13]; - x3r = a[4] - a[12]; - x3i = a[5] - a[13]; - y0r = x0r + x2r; - y0i = x0i + x2i; - y2r = x0r - x2r; - y2i = x0i - x2i; - y1r = x1r - x3i; - y1i = x1i + x3r; - y3r = x1r + x3i; - y3i = x1i - x3r; - x0r = a[2] + a[10]; - x0i = a[3] + a[11]; - x1r = a[2] - a[10]; - x1i = a[3] - a[11]; - x2r = a[6] + a[14]; - x2i = a[7] + a[15]; - x3r = a[6] - a[14]; - x3i = a[7] - a[15]; - y4r = x0r + x2r; - y4i = x0i + x2i; - y6r = x0r - x2r; - y6i = x0i - x2i; - x0r = x1r - x3i; - x0i = x1i + x3r; - x2r = x1r + x3i; - x2i = x1i - x3r; - y5r = wn4r * (x0r - x0i); - y5i = wn4r * (x0r + x0i); - y7r = wn4r * (x2r - x2i); - y7i = wn4r * (x2r + x2i); - a[8] = y1r + y5r; - a[9] = y1i + y5i; - a[10] = y1r - y5r; - a[11] = y1i - y5i; - a[12] = y3r - y7i; - a[13] = y3i + y7r; - a[14] = y3r + y7i; - a[15] = y3i - y7r; - a[0] = y0r + y4r; - a[1] = y0i + y4i; - a[2] = y0r - y4r; - a[3] = y0i - y4i; - a[4] = y2r - y6i; - a[5] = y2i + y6r; - a[6] = y2r + y6i; - a[7] = y2i - y6r; -} - - -void cftf082(double *a, double *w) -{ - double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, - y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, - y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i; - - wn4r = w[1]; - wk1r = w[2]; - wk1i = w[3]; - y0r = a[0] - a[9]; - y0i = a[1] + a[8]; - y1r = a[0] + a[9]; - y1i = a[1] - a[8]; - x0r = a[4] - a[13]; - x0i = a[5] + a[12]; - y2r = wn4r * (x0r - x0i); - y2i = wn4r * (x0i + x0r); - x0r = a[4] + a[13]; - x0i = a[5] - a[12]; - y3r = wn4r * (x0r - x0i); - y3i = wn4r * (x0i + x0r); - x0r = a[2] - a[11]; - x0i = a[3] + a[10]; - y4r = wk1r * x0r - wk1i * x0i; - y4i = wk1r * x0i + wk1i * x0r; - x0r = a[2] + a[11]; - x0i = a[3] - a[10]; - y5r = wk1i * x0r - wk1r * x0i; - y5i = wk1i * x0i + wk1r * x0r; - x0r = a[6] - a[15]; - x0i = a[7] + a[14]; - y6r = wk1i * x0r - wk1r * x0i; - y6i = wk1i * x0i + wk1r * x0r; - x0r = a[6] + a[15]; - x0i = a[7] - a[14]; - y7r = wk1r * x0r - wk1i * x0i; - y7i = wk1r * x0i + wk1i * x0r; - x0r = y0r + y2r; - x0i = y0i + y2i; - x1r = y4r + y6r; - x1i = y4i + y6i; - a[0] = x0r + x1r; - a[1] = x0i + x1i; - a[2] = x0r - x1r; - a[3] = x0i - x1i; - x0r = y0r - y2r; - x0i = y0i - y2i; - x1r = y4r - y6r; - x1i = y4i - y6i; - a[4] = x0r - x1i; - a[5] = x0i + x1r; - a[6] = x0r + x1i; - a[7] = x0i - x1r; - x0r = y1r - y3i; - x0i = y1i + y3r; - x1r = y5r - y7r; - x1i = y5i - y7i; - a[8] = x0r + x1r; - a[9] = x0i + x1i; - a[10] = x0r - x1r; - a[11] = x0i - x1i; - x0r = y1r + y3i; - x0i = y1i - y3r; - x1r = y5r + y7r; - x1i = y5i + y7i; - a[12] = x0r - x1i; - a[13] = x0i + x1r; - a[14] = x0r + x1i; - a[15] = x0i - x1r; -} - - -void cftf040(double *a) -{ - double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; - - x0r = a[0] + a[4]; - x0i = a[1] + a[5]; - x1r = a[0] - a[4]; - x1i = a[1] - a[5]; - x2r = a[2] + a[6]; - x2i = a[3] + a[7]; - x3r = a[2] - a[6]; - x3i = a[3] - a[7]; - a[0] = x0r + x2r; - a[1] = x0i + x2i; - a[2] = x1r - x3i; - a[3] = x1i + x3r; - a[4] = x0r - x2r; - a[5] = x0i - x2i; - a[6] = x1r + x3i; - a[7] = x1i - x3r; -} - - -void cftb040(double *a) -{ - double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; - - x0r = a[0] + a[4]; - x0i = a[1] + a[5]; - x1r = a[0] - a[4]; - x1i = a[1] - a[5]; - x2r = a[2] + a[6]; - x2i = a[3] + a[7]; - x3r = a[2] - a[6]; - x3i = a[3] - a[7]; - a[0] = x0r + x2r; - a[1] = x0i + x2i; - a[2] = x1r + x3i; - a[3] = x1i - x3r; - a[4] = x0r - x2r; - a[5] = x0i - x2i; - a[6] = x1r - x3i; - a[7] = x1i + x3r; -} - - -void cftx020(double *a) -{ - double x0r, x0i; - - x0r = a[0] - a[2]; - x0i = a[1] - a[3]; - a[0] += a[2]; - a[1] += a[3]; - a[2] = x0r; - a[3] = x0i; -} - - -void rftfsub(int n, double *a, int nc, double *c) -{ - int j, k, kk, ks, m; - double wkr, wki, xr, xi, yr, yi; - - m = n >> 1; - ks = 2 * nc / m; - kk = 0; - for (j = 2; j < m; j += 2) { - k = n - j; - kk += ks; - wkr = 0.5 - c[nc - kk]; - wki = c[kk]; - xr = a[j] - a[k]; - xi = a[j + 1] + a[k + 1]; - yr = wkr * xr - wki * xi; - yi = wkr * xi + wki * xr; - a[j] -= yr; - a[j + 1] -= yi; - a[k] += yr; - a[k + 1] -= yi; - } -} - - -void rftbsub(int n, double *a, int nc, double *c) -{ - int j, k, kk, ks, m; - double wkr, wki, xr, xi, yr, yi; - - m = n >> 1; - ks = 2 * nc / m; - kk = 0; - for (j = 2; j < m; j += 2) { - k = n - j; - kk += ks; - wkr = 0.5 - c[nc - kk]; - wki = c[kk]; - xr = a[j] - a[k]; - xi = a[j + 1] + a[k + 1]; - yr = wkr * xr + wki * xi; - yi = wkr * xi - wki * xr; - a[j] -= yr; - a[j + 1] -= yi; - a[k] += yr; - a[k + 1] -= yi; - } -} - - -void dctsub(int n, double *a, int nc, double *c) -{ - int j, k, kk, ks, m; - double wkr, wki, xr; - - m = n >> 1; - ks = nc / n; - kk = 0; - for (j = 1; j < m; j++) { - k = n - j; - kk += ks; - wkr = c[kk] - c[nc - kk]; - wki = c[kk] + c[nc - kk]; - xr = wki * a[j] - wkr * a[k]; - a[j] = wkr * a[j] + wki * a[k]; - a[k] = xr; - } - a[m] *= c[0]; -} - - -void dstsub(int n, double *a, int nc, double *c) -{ - int j, k, kk, ks, m; - double wkr, wki, xr; - - m = n >> 1; - ks = nc / n; - kk = 0; - for (j = 1; j < m; j++) { - k = n - j; - kk += ks; - wkr = c[kk] - c[nc - kk]; - wki = c[kk] + c[nc - kk]; - xr = wki * a[k] - wkr * a[j]; - a[k] = wkr * a[k] + wki * a[j]; - a[j] = xr; - } - a[m] *= c[0]; -} - -#if defined(__cplusplus) -} // end of extern "C" -#endif |