163 lines
6.3 KiB
C
163 lines
6.3 KiB
C
/*
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* This file is part of libfftpack.
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*
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* libfftpack is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* libfftpack is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with libfftpack; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/*
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* libfftpack is being developed at the Max-Planck-Institut fuer Astrophysik
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* and financially supported by the Deutsches Zentrum fuer Luft- und Raumfahrt
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* (DLR).
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*/
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/*! \file ls_fft.h
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* Interface for the LevelS FFT package.
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*
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* Copyright (C) 2004 Max-Planck-Society
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* \author Martin Reinecke
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*/
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#ifndef PLANCK_LS_FFT_H
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#define PLANCK_LS_FFT_H
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#include "c_utils.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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/*!\defgroup fftgroup FFT interface
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This package is intended to calculate one-dimensional real or complex FFTs
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with high accuracy and good efficiency even for lengths containing large
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prime factors.
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The code is written in C, but a Fortran wrapper exists as well.
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Before any FFT is executed, a plan must be generated for it. Plan creation
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is designed to be fast, so that there is no significant overhead if the
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plan is only used once or a few times.
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The main component of the code is based on Paul N. Swarztrauber's FFTPACK in the
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double precision incarnation by Hugh C. Pumphrey
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(http://www.netlib.org/fftpack/dp.tgz).
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I replaced the iterative sine and cosine calculations in radfg() and radbg()
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by an exact calculation, which slightly improves the transform accuracy for
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real FFTs with lengths containing large prime factors.
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Since FFTPACK becomes quite slow for FFT lengths with large prime factors
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(in the worst case of prime lengths it reaches \f$\mathcal{O}(n^2)\f$
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complexity), I implemented Bluestein's algorithm, which computes a FFT of length
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\f$n\f$ by several FFTs of length \f$n_2\ge 2n-1\f$ and a convolution. Since
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\f$n_2\f$ can be chosen to be highly composite, this algorithm is more efficient
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if \f$n\f$ has large prime factors. The longer FFTs themselves are then computed
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using the FFTPACK routines.
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Bluestein's algorithm was implemented according to the description on Wikipedia
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(<a href="http://en.wikipedia.org/wiki/Bluestein%27s_FFT_algorithm">
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http://en.wikipedia.org/wiki/Bluestein%27s_FFT_algorithm</a>).
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\b Thread-safety:
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All routines can be called concurrently; all information needed by
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<tt>ls_fft</tt> is stored in the plan variable. However, using the same plan
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variable on multiple threads simultaneously is not supported and will lead to
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data corruption.
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*/
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/*! \{ */
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typedef struct
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{
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double *work;
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size_t length, worksize;
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int bluestein;
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} complex_plan_i;
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/*! The opaque handle type for complex-FFT plans. */
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typedef complex_plan_i * complex_plan;
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/*! Returns a plan for a complex FFT with \a length elements. */
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complex_plan make_complex_plan (size_t length);
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/*! Constructs a copy of \a plan. */
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complex_plan copy_complex_plan (complex_plan plan);
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/*! Destroys a plan for a complex FFT. */
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void kill_complex_plan (complex_plan plan);
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/*! Computes a complex forward FFT on \a data, using \a plan.
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\a Data has the form <tt>r0, i0, r1, i1, ...,
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r[length-1], i[length-1]</tt>. */
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void complex_plan_forward (complex_plan plan, double *data);
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/*! Computes a complex backward FFT on \a data, using \a plan.
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\a Data has the form <tt>r0, i0, r1, i1, ...,
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r[length-1], i[length-1]</tt>. */
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void complex_plan_backward (complex_plan plan, double *data);
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typedef struct
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{
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double *work;
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size_t length, worksize;
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int bluestein;
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} real_plan_i;
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/*! The opaque handle type for real-FFT plans. */
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typedef real_plan_i * real_plan;
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/*! Returns a plan for a real FFT with \a length elements. */
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real_plan make_real_plan (size_t length);
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/*! Constructs a copy of \a plan. */
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real_plan copy_real_plan (real_plan plan);
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/*! Destroys a plan for a real FFT. */
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void kill_real_plan (real_plan plan);
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/*! Computes a real forward FFT on \a data, using \a plan
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and assuming the FFTPACK storage scheme:
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- on entry, \a data has the form <tt>r0, r1, ..., r[length-1]</tt>;
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- on exit, it has the form <tt>r0, r1, i1, r2, i2, ...</tt>
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(a total of \a length values). */
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void real_plan_forward_fftpack (real_plan plan, double *data);
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/*! Computes a real forward FFT on \a data, using \a plan
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and assuming the FFTPACK storage scheme:
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- on entry, \a data has the form <tt>r0, r1, i1, r2, i2, ...</tt>
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(a total of \a length values);
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- on exit, it has the form <tt>r0, r1, ..., r[length-1]</tt>. */
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void real_plan_backward_fftpack (real_plan plan, double *data);
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/*! Computes a real forward FFT on \a data, using \a plan
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and assuming the FFTW halfcomplex storage scheme:
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- on entry, \a data has the form <tt>r0, r1, ..., r[length-1]</tt>;
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- on exit, it has the form <tt>r0, r1, r2, ..., i2, i1</tt>. */
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void real_plan_forward_fftw (real_plan plan, double *data);
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/*! Computes a real backward FFT on \a data, using \a plan
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and assuming the FFTW halfcomplex storage scheme:
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- on entry, \a data has the form <tt>r0, r1, r2, ..., i2, i1</tt>.
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- on exit, it has the form <tt>r0, r1, ..., r[length-1]</tt>. */
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void real_plan_backward_fftw (real_plan plan, double *data);
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/*! Computes a real forward FFT on \a data, using \a plan
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and assuming a full-complex storage scheme:
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- on entry, \a data has the form <tt>r0, [ignored], r1, [ignored], ...,
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r[length-1], [ignored]</tt>;
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- on exit, it has the form <tt>r0, i0, r1, i1, ...,
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r[length-1], i[length-1]</tt>.
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*/
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void real_plan_forward_c (real_plan plan, double *data);
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/*! Computes a real backward FFT on \a data, using \a plan
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and assuming a full-complex storage scheme:
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- on entry, \a data has the form <tt>r0, i0, r1, i1, ...,
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r[length-1], i[length-1]</tt>;
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- on exit, it has the form <tt>r0, 0, r1, 0, ..., r[length-1], 0</tt>. */
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void real_plan_backward_c (real_plan plan, double *data);
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/*! \} */
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#ifdef __cplusplus
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}
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#endif
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#endif
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