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/* Copyright (c) 2011 Julien Pommier ( pommier@modartt.com )
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Based on original fortran 77 code from FFTPACKv4 from NETLIB,
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authored by Dr Paul Swarztrauber of NCAR, in 1985.
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As confirmed by the NCAR fftpack software curators, the following
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FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
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released under the same terms.
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http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
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Copyright (c) 2004 the University Corporation for Atmospheric
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Research ("UCAR"). All rights reserved. Developed by NCAR's
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Computational and Information Systems Laboratory, UCAR,
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Redistribution and use of the Software in source and binary forms,
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with or without modification, is permitted provided that the
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following conditions are met:
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- Neither the names of NCAR's Computational and Information Systems
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Laboratory, the University Corporation for Atmospheric Research,
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nor the names of its sponsors or contributors may be used to
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endorse or promote products derived from this Software without
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specific prior written permission.
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- Redistributions of source code must retain the above copyright
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notices, this list of conditions, and the disclaimer below.
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- Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions, and the disclaimer below in the
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documentation and/or other materials provided with the
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THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
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MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
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HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
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ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
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PFFFT : a Pretty Fast FFT.
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This is basically an adaptation of the single precision fftpack
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(v4) as found on netlib taking advantage of SIMD instruction found
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on cpus such as intel x86 (SSE1), powerpc (Altivec), and arm (NEON).
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For architectures where no SIMD instruction is available, the code
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falls back to a scalar version.
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- 1D transforms only, with 32-bit single precision.
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- supports only transforms for inputs of length N of the form
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N=(2^a)*(3^b), a >= 5 and b >=0 (32, 48, 64, 96, 128, 144 etc
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are all acceptable lengths). Performance is best for 128<=N<=8192.
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- all (float*) pointers in the functions below are expected to
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have an "simd-compatible" alignment, that is 16 bytes on x86 and
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You can allocate such buffers with the functions
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pffft_aligned_malloc / pffft_aligned_free (or with stuff like
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/* opaque struct holding internal stuff (precomputed twiddle factors)
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this struct can be shared by many threads as it contains only
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typedef struct PFFFT_Setup PFFFT_Setup;
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/* direction of the transform */
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typedef enum { PFFFT_FORWARD, PFFFT_BACKWARD } pffft_direction_t;
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/* type of transform */
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typedef enum { PFFFT_REAL, PFFFT_COMPLEX } pffft_transform_t;
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prepare for performing transforms of size N -- the returned
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PFFFT_Setup structure is read-only so it can safely be shared by
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multiple concurrent threads.
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static PFFFT_Setup *pffft_new_setup(int N, pffft_transform_t transform);
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static void pffft_destroy_setup(PFFFT_Setup *);
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Perform a Fourier transform , The z-domain data is stored in the
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most efficient order for transforming it back, or using it for
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convolution. If you need to have its content sorted in the
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"usual" way, that is as an array of interleaved complex numbers,
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either use pffft_transform_ordered , or call pffft_zreorder after
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the forward fft, and before the backward fft.
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Transforms are not scaled: PFFFT_BACKWARD(PFFFT_FORWARD(x)) = N*x.
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Typically you will want to scale the backward transform by 1/N.
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The 'work' pointer should point to an area of N (2*N for complex
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fft) floats, properly aligned. [del]If 'work' is NULL, then stack will
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be used instead (this is probably the beest strategy for small
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FFTs, say for N < 16384).[/del]
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input and output may alias.
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static void pffft_transform(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction);
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Similar to pffft_transform, but makes sure that the output is
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ordered as expected (interleaved complex numbers). This is
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similar to calling pffft_transform and then pffft_zreorder.
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input and output may alias.
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static void pffft_transform_ordered(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction);
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call pffft_zreorder(.., PFFFT_FORWARD) after pffft_transform(...,
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PFFFT_FORWARD) if you want to have the frequency components in
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the correct "canonical" order, as interleaved complex numbers.
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(for real transforms, both 0-frequency and half frequency
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components, which are real, are assembled in the first entry as
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F(0)+i*F(n/2+1). Note that the original fftpack did place
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F(n/2+1) at the end of the arrays).
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input and output should not alias.
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static void pffft_zreorder(PFFFT_Setup *setup, const float *input, float *output, pffft_direction_t direction);
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Perform a multiplication of the frequency components of dft_a and
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dft_b and accumulate them into dft_ab. The arrays should have
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been obtained with pffft_transform(.., PFFFT_FORWARD) and should
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*not* have been reordered with pffft_zreorder (otherwise just
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perform the operation yourself as the dft coefs are stored as
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interleaved complex numbers).
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the operation performed is: dft_ab += (dft_a * fdt_b)*scaling
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The dft_a, dft_b and dft_ab pointers may alias.
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void pffft_zconvolve_accumulate(PFFFT_Setup *setup, const float *dft_a, const float *dft_b, float *dft_ab, float scaling);
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the operation performed is: dft_ab = (dft_a * fdt_b)
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The dft_a, dft_b and dft_ab pointers may alias.
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static void pffft_zconvolve(PFFFT_Setup *setup, const float *dft_a, const float *dft_b, float *dft_ab);
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/* return 4 or 1 wether support SSE/Altivec instructions was enable when building pffft.c */
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int pffft_simd_size(void);
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static void pffft_reorder_back(int length, void * setup, float * data, float * work);
added
removed
src/pffft.h
