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\comment This is the source for the FFTW FAQ list, in
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\comment the Bizarre Format With No Name. It is turned into Lout
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\comment input, HTML, plain ASCII and an Info document by a Perl script.
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\comment
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\comment The format and scripts come from the Linux FAQ, by
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\comment Ian Jackson.
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\set brieftitle FFTW FAQ
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\set author <A href="http://www.fftw.org">Matteo Frigo and Steven G. Johnson</A> / <A href="mailto:fftw@fftw.org">fftw@fftw.org</A>
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\set authormail fftw@fftw.org
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\set title FFTW Frequently Asked Questions with Answers
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\set copyholder Matteo Frigo and Massachusetts Institute of Technology
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\call-html startup html.refs2
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\copyto ASCII
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FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS
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`date '+%d %h %Y'`
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Matteo Frigo
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Steven G. Johnson
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<fftw@fftw.org>
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\endcopy
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\copyto INFO
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INFO-DIR-SECTION Development
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START-INFO-DIR-ENTRY
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* FFTW FAQ: (fftw-faq). FFTW Frequently Asked Questions with Answers.
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END-INFO-DIR-ENTRY
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File: $prefix.info, Node: Top, Next: Question 1.1, Up: (dir)
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FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS
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`date '+%d %h %Y'`
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Matteo Frigo
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Steven G. Johnson
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<fftw@fftw.org>
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\endcopy
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This is the list of Frequently Asked Questions about FFTW, a
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collection of fast C routines for computing the Discrete Fourier
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Transform in one or more dimensions.
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\section Index
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\index
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\comment ######################################################################
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\section Introduction and General Information
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\question 26aug:whatisfftw What is FFTW?
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FFTW is a free collection of fast C routines for computing the
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Discrete Fourier Transform in one or more dimensions. It includes
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complex, real, symmetric, and parallel transforms, and can handle
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arbitrary array sizes efficiently. FFTW is typically faster than
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other publically-available FFT implementations, and is even
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competitive with vendor-tuned libraries. (See our web page for
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extensive benchmarks.) To achieve this performance, FFTW uses novel
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code-generation and runtime self-optimization techniques (along with
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many other tricks).
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\question 26aug:whereisfftw How do I obtain FFTW?
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FFTW can be found at \docref{the FFTW web page\}. You can also
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retrieve it from \ftpon ftp.fftw.org in \ftpin /pub/fftw.
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\question 26aug:isfftwfree Is FFTW free software?
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Starting with version 1.3, FFTW is Free Software in the technical
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sense defined by the Free Software Foundation (see \docref{Categories
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of Free and Non-Free Software\}), and is distributed under the terms
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of the GNU General Public License. Previous versions of FFTW were
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distributed without fee for noncommercial use, but were not
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technically ``free.''
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Non-free licenses for FFTW are also available that permit different
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terms of use than the GPL.
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\question 10apr:nonfree What is this about non-free licenses?
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The non-free licenses are for companies that wish to use FFTW in their
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products but are unwilling to release their software under the GPL
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(which would require them to release source code and allow free
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redistribution). Such users can purchase an unlimited-use license
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from MIT. Contact us for more details.
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We could instead have released FFTW under the LGPL, or even disallowed
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non-Free usage. Suffice it to say, however, that MIT owns the
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copyright to FFTW and they only let us GPL it because we convinced
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them that it would neither affect their licensing revenue nor irritate
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existing licensees.
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\question 24oct:west In the West? I thought MIT was in the East?
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Not to an Italian. You could say that we're a Spaghetti Western
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(with apologies to Sergio Leone).
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\comment ######################################################################
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\section Installing FFTW
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\question 26aug:systems Which systems does FFTW run on?
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FFTW is written in ANSI C, and should work on any system with a decent
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C compiler. (See also \qref runOnWindows, \qref compilerCrashes.)
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FFTW can also take advantage of certain hardware-specific features,
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such as cycle counters and SIMD instructions, but this is optional.
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\question 26aug:runOnWindows Does FFTW run on Windows?
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Yes, many people have reported successfully using FFTW on Windows with
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various compilers. FFTW was not developed on Windows, but the source
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code is essentially straight ANSI C. See also the \docref{FFTW
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Windows installation notes\}, \qref compilerCrashes, and \qref
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vbetalia.
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\question 26aug:compilerCrashes My compiler has trouble with FFTW.
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Complain fiercely to the vendor of the compiler.
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We have successfully used \courier{gcc\} 3.2.x on x86 and PPC, a
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recent Compaq C compiler for Alpha, version 6 of IBM's \courier{xlc\}
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compiler for AIX, Intel's \courier{icc\} versions 5-7, and Sun
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WorkShop \courier{cc\} version 6.
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FFTW is likely to push compilers to their limits, however, and several
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compiler bugs have been exposed by FFTW. A partial list follows.
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\courier{gcc\} 2.95.x for Solaris/SPARC produces incorrect code for
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the test program (workaround: recompile the \courier{libbench2\}
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directory with \courier{-O2\}).
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NetBSD/macppc 1.6 comes with a \courier{gcc\} version that also
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miscompiles the test program. (Please report a workaround if you know
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one.)
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\courier{gcc\} 3.2.3 for ARM reportedly crashes during compilation.
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This bug is reportedly fixed in later versions of \courier{gcc\}.
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Versions 8.0 and 8.1 of Intel's \courier{icc\} falsely claim to be
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\courier{gcc\}, so you should specify \courier{CC="icc -no-gcc"\};
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this is automatic in FFTW 3.1. \courier{icc-8.0.066\} reportely
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produces incorrect code for FFTW 2.1.5, but is fixed in version 8.1.
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\courier{icc-7.1\} compiler build 20030402Z appears to produce
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incorrect dependencies, causing the compilation to fail.
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\courier{icc-7.1\} build 20030307Z appears to work fine. (Use
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\courier{icc -V\} to check which build you have.) As of 2003/04/18,
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build 20030402Z appears not to be available any longer on Intel's
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website, whereas the older build 20030307Z is available.
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\courier{ranlib\} of GNU \courier{binutils\} 2.9.1 on Irix has been
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observed to corrupt the FFTW libraries, causing a link failure when
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FFTW is compiled. Since \courier{ranlib\} is completely superfluous
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on Irix, we suggest deleting it from your system and replacing it with
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a symbolic link to \courier{/bin/echo\}.
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If support for SIMD instructions is enabled in FFTW, further compiler
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problems may appear:
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\courier{gcc\} 3.4.[0123] for x86 produces incorrect SSE2 code for
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FFTW when \courier{-O2\} (the best choice for FFTW) is used, causing
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FFTW to crash (\courier{make check\} crashes). This bug is fixed in
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\courier{gcc\} 3.4.4. On x86_64 (amd64/em64t), \courier{gcc\} 3.4.4
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reportedly still has a similar problem, but this is fixed as of
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\courier{gcc\} 3.4.6.
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\courier{gcc-3.2\} for x86 produces incorrect SIMD code if
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\courier{-O3\} is used. The same compiler produces incorrect SIMD
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code if no optimization is used, too. When using \courier{gcc-3.2\},
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it is a good idea not to change the default \courier{CFLAGS\} selected
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by the \courier{configure\} script.
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Some 3.0.x and 3.1.x versions of \courier{gcc\} on \courier{x86\} may
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crash. \courier{gcc\} so-called 2.96 shipping with RedHat 7.3 crashes
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when compiling SIMD code. In both cases, please upgrade to
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\courier{gcc-3.2\} or later.
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Intel's \courier{icc\} 6.0 misaligns SSE constants, but FFTW has a
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workaround. \courier{icc\} 8.x fails to compile FFTW 3.0.x because it
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falsely claims to be \courier{gcc\}; we believe this to be a bug in
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\courier{icc\}, but FFTW 3.1 has a workaround.
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Visual C++ 2003 reportedly produces incorrect code for SSE/SSE2 when
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compiling FFTW. This bug was reportedly fixed in VC++ 2005;
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alternatively, you could switch to the Intel compiler. VC++ 6.0 also
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reportedly produces incorrect code for the file
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\courier{reodft11e-r2hc-odd.c\} unless optimizations are disabled for
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that file.
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\courier{gcc\} 2.95 on MacOS X miscompiles AltiVec code (fixed in
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later versions). \courier{gcc\} 3.2.x miscompiles AltiVec
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permutations, but FFTW has a workaround. \courier{gcc\} 4.0.1 on
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MacOS for Intel crashes when compiling FFTW; a workaround is to
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compile one file without optimization: \courier{cd kernel; make
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CFLAGS=" " trig.lo\}.
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\courier{gcc\} 4.1.1 reportedly crashes when compiling FFTW for MIPS;
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the workaround is to compile the file it crashes on
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(\courier{t2_64.c\}) with a lower optimization level.
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\courier{gcc\} versions 4.1.2 to 4.2.0 for x86 reportedly miscompile
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FFTW 3.1's test program, causing \courier{make check\} to crash
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(\courier{gcc\} bug #26528). The bug was reportedly fixed in
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\courier{gcc\} version 4.2.1 and later. A workaround is to compile
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\courier{libbench2/verify-lib.c\} without optimization.
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\question 26aug:solarisSucks FFTW does not compile on Solaris, complaining about \courier{const\}.
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We know that at least on Solaris 2.5.x with Sun's compilers 4.2 you
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might get error messages from \courier{make\} such as
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\courier{"./fftw.h", line 88: warning: const is a keyword in ANSI C\}
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This is the case when the \courier{configure\} script reports that
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\courier{const\} does not work:
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\courier{checking for working const... (cached) no\}
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You should be aware that Solaris comes with two compilers, namely,
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\courier{/opt/SUNWspro/SC4.2/bin/cc\} and \courier{/usr/ucb/cc\}. The
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latter compiler is non-ANSI. Indeed, it is a perverse shell script
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that calls the real compiler in non-ANSI mode. In order
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to compile FFTW, change your path so that the right \courier{cc\}
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is used.
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To know whether your compiler is the right one, type
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\courier{cc -V\}. If the compiler prints ``\courier{ucbcc\}'',
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as in
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\courier{ucbcc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2\}
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then the compiler is wrong. The right message is something like
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\courier{cc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2\}
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\question 19mar:3dnow What's the difference between \courier{--enable-3dnow\} and \courier{--enable-k7\}?
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\courier{--enable-k7\} enables 3DNow! instructions on K7 processors
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(AMD Athlon and its variants). K7 support is provided by assembly
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routines generated by a special purpose compiler.
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As of fftw-3.2, --enable-k7 is no longer supported.
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\courier{--enable-3dnow\} enables generic 3DNow! support using
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\courier{gcc\} builtin functions. This works on earlier AMD
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processors, but it is not as fast as our special assembly routines.
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As of fftw-3.1, --enable-3dnow is no longer supported.
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\question 18apr:fma What's the difference between the fma and the non-fma versions?
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The fma version tries to exploit the fused multiply-add instructions
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implemented in many processors such as PowerPC, ia-64, and MIPS. The
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two FFTW packages are otherwise identical. In FFTW 3.1, the fma and
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non-fma versions were merged together into a single package, and the
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\courier{configure\} script attempts to automatically guess which
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version to use.
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The FFTW 3.1 \courier{configure\} script enables fma by default on
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PowerPC, Itanium, and PA-RISC, and disables it otherwise. You can
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force one or the other by using the \courier{--enable-fma\} or
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\courier{--disable-fma\} flag for \courier{configure\}.
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Definitely use fma if you have a PowerPC-based system with
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\courier{gcc\} (or IBM \courier{xlc\}). This includes all GNU/Linux
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systems for PowerPC and the older PowerPC-based MacOS systems. Also
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use it on PA-RISC and Itanium with the HP/UX compiler.
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Definitely do not use the fma version if you have an ia-32 processor
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(Intel, AMD, MacOS on Intel, etcetera).
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For other architectures/compilers, the situation is not so clear. For
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example, ia-64 has the fma instruction, but \courier{gcc-3.2\} appears
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not to exploit it correctly. Other compilers may do the right thing,
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but we have not tried them. Please send us your feedback so that we
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can update this FAQ entry.
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\question 26aug:languages Which language is FFTW written in?
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FFTW is written in ANSI C. Most of the code, however, was
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automatically generated by a program called \courier{genfft\}, written
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in the Objective Caml dialect of ML. You do not need to know ML or to
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have an Objective Caml compiler in order to use FFTW.
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\courier{genfft\} is provided with the FFTW sources, which means that
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you can play with the code generator if you want. In this case, you
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need a working Objective Caml system. Objective Caml is available
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from \docref{the Caml web page\}.
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\question 26aug:fortran Can I call FFTW from Fortran?
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Yes, FFTW (versions 1.3 and higher) contains a Fortran-callable
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interface, documented in the FFTW manual.
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By default, FFTW configures its Fortran interface to work with the
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first compiler it finds, e.g. \courier{g77\}. To configure for a
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different, incompatible Fortran compiler \courier{foobar\}, use
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\courier{./configure F77=foobar\} when installing FFTW. (In the case
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of \courier{g77\}, however, FFTW 3.x also includes an extra set of
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Fortran-callable routines with one less underscore at the end of
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identifiers, which should cover most other Fortran compilers on Linux
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at least.)
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\question 26aug:cplusplus Can I call FFTW from C++?
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Most definitely. FFTW should compile and/or link under any C++
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compiler. Moreover, it is likely that the C++ \courier{<complex>\}
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template class is bit-compatible with FFTW's complex-number format
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(see the FFTW manual for more details).
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\question 26aug:whynotfortran Why isn't FFTW written in Fortran/C++?
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Because we don't like those languages, and neither approaches the
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portability of C.
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\question 29mar:singleprec How do I compile FFTW to run in single precision?
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On a Unix system: \courier{configure --enable-float\}. On a non-Unix
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system: edit \courier{config.h\} to \courier{#define\} the symbol
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\courier{FFTW_SINGLE\} (for FFTW 3.x). In both cases, you must then
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recompile FFTW. In FFTW 3, all FFTW identifiers will then begin with
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\courier{fftwf_\} instead of \courier{fftw_\}.
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\question 28mar:64bitk7 --enable-k7 does not work on x86-64
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Support for --enable-k7 was discontinued in fftw-3.2.
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The fftw-3.1 release supports --enable-k7. This option only works on
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32-bit x86 machines that implement 3DNow!, including the AMD Athlon
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and the AMD Opteron in 32-bit mode. --enable-k7 does not work on AMD
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Opteron in 64-bit mode. Use --enable-sse for x86-64 machines.
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FFTW supports 3DNow! by means of assembly code generated by a
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special-purpose compiler. It is hard to produce assembly code that
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works in both 32-bit and 64-bit mode.
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\comment ######################################################################
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\section Using FFTW
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\question 15mar:fftw2to3 Why not support the FFTW 2 interface in FFTW 3?
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FFTW 3 has semantics incompatible with earlier versions: its plans can
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only be used for a given stride, multiplicity, and other
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characteristics of the input and output arrays; these stronger
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semantics are necessary for performance reasons. Thus, it is
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impossible to efficiently emulate the older interface (whose plans can
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be used for any transform of the same size). We believe that it
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should be possible to upgrade most programs without any difficulty,
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however.
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\question 20mar:planperarray Why do FFTW 3 plans encapsulate the input/output arrays and not just the algorithm?
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There are several reasons:
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\call startlist
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\call item
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It was important for performance reasons that the plan be specific to
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array characteristics like the stride (and alignment, for SIMD), and
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requiring that the user maintain these invariants is error prone.
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\call item
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In most high-performance applications, as far as we can tell, you are
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usually transforming the same array over and over, so FFTW's semantics
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should not be a burden.
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\call item
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If you need to transform another array of the same size, creating a
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new plan once the first exists is a cheap operation.
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\call item
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If you need to transform many arrays of the same size at once, you
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should really use the \courier{plan_many\} routines in FFTW's "advanced"
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interface.
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\call item
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If the abovementioned array characteristics are the same, you are
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willing to pay close attention to the documentation, and you really
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need to, we provide a "new-array execution" interface to apply a plan
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to a new array.
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\call endlist
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\question 25may:slow FFTW seems really slow.
|
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|
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You are probably recreating the plan before every transform, rather
|
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than creating it once and reusing it for all transforms of the same
|
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size. FFTW is designed to be used in the following way:
|
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|
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\call startlist
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\call item
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First, you create a plan. This will take several seconds.
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\call item
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Then, you reuse the plan many times to perform FFTs. These are fast.
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\call endlist
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If you don't need to compute many transforms and the time for the
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planner is significant, you have two options. First, you can use the
|
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\courier{FFTW_ESTIMATE\} option in the planner, which uses heuristics
|
||
instead of runtime measurements and produces a good plan in a short
|
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time. Second, you can use the wisdom feature to precompute the plan;
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see \qref savePlans
|
||
|
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\question 22oct:slows FFTW slows down after repeated calls.
|
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|
||
Probably, NaNs or similar are creeping into your data, and the
|
||
slowdown is due to the resulting floating-point exceptions. For
|
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example, be aware that repeatedly FFTing the same array is a diverging
|
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process (because FFTW computes the unnormalized transform).
|
||
|
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\question 22oct:segfault An FFTW routine is crashing when I call it.
|
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|
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Did the FFTW test programs pass (\courier{make check\}, or \courier{cd
|
||
tests; make bigcheck\} if you want to be paranoid)? If so, you almost
|
||
certainly have a bug in your own code. For example, you could be
|
||
passing invalid arguments (such as wrongly-sized arrays) to FFTW, or
|
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you could simply have memory corruption elsewhere in your program that
|
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causes random crashes later on. Please don't complain to us unless
|
||
you can come up with a minimal self-contained program (preferably
|
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under 30 lines) that illustrates the problem.
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|
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\question 22oct:fortran64 My Fortran program crashes when calling FFTW.
|
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|
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As described in the manual, on 64-bit machines you must store the
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plans in variables large enough to hold a pointer, for example
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\courier{integer*8\}. We recommend using \courier{integer*8\} on
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32-bit machines as well, to simplify porting.
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||
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\question 24mar:conventions FFTW gives results different from my old FFT.
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People follow many different conventions for the DFT, and you should
|
||
be sure to know the ones that we use (described in the FFTW manual).
|
||
In particular, you should be aware that the
|
||
\courier{FFTW_FORWARD\}/\courier{FFTW_BACKWARD\} directions correspond
|
||
to signs of -1/+1 in the exponent of the DFT definition.
|
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(\italic{Numerical Recipes\} uses the opposite convention.)
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You should also know that we compute an unnormalized transform. In
|
||
contrast, Matlab is an example of program that computes a normalized
|
||
transform. See \qref whyscaled.
|
||
|
||
Finally, note that floating-point arithmetic is not exact, so
|
||
different FFT algorithms will give slightly different results (on the
|
||
order of the numerical accuracy; typically a fractional difference of
|
||
1e-15 or so in double precision).
|
||
|
||
\question 31aug:nondeterministic FFTW gives different results between runs
|
||
|
||
If you use \courier{FFTW_MEASURE\} or \courier{FFTW_PATIENT\} mode,
|
||
then the algorithm FFTW employs is not deterministic: it depends on
|
||
runtime performance measurements. This will cause the results to vary
|
||
slightly from run to run. However, the differences should be slight,
|
||
on the order of the floating-point precision, and therefore should
|
||
have no practical impact on most applications.
|
||
|
||
If you use saved plans (wisdom) or \courier{FFTW_ESTIMATE\} mode,
|
||
however, then the algorithm is deterministic and the results should be
|
||
identical between runs.
|
||
|
||
\question 26aug:savePlans Can I save FFTW's plans?
|
||
|
||
Yes. Starting with version 1.2, FFTW provides the \courier{wisdom\}
|
||
mechanism for saving plans; see the FFTW manual.
|
||
|
||
\question 14sep:whyscaled Why does your inverse transform return a scaled result?
|
||
|
||
Computing the forward transform followed by the backward transform (or
|
||
vice versa) yields the original array scaled by the size of the array.
|
||
(For multi-dimensional transforms, the size of the array is the
|
||
product of the dimensions.) We could, instead, have chosen a
|
||
normalization that would have returned the unscaled array. Or, to
|
||
accomodate the many conventions in this matter, the transform routines
|
||
could have accepted a "scale factor" parameter. We did not do this,
|
||
however, for two reasons. First, we didn't want to sacrifice
|
||
performance in the common case where the scale factor is 1. Second, in
|
||
real applications the FFT is followed or preceded by some computation
|
||
on the data, into which the scale factor can typically be absorbed at
|
||
little or no cost.
|
||
|
||
\question 02dec:centerorigin How can I make FFTW put the origin (zero frequency) at the center of its output?
|
||
|
||
For human viewing of a spectrum, it is often convenient to put the
|
||
origin in frequency space at the center of the output array, rather
|
||
than in the zero-th element (the default in FFTW). If all of the
|
||
dimensions of your array are even, you can accomplish this by simply
|
||
multiplying each element of the input array by (-1)^(i + j + ...),
|
||
where i, j, etcetera are the indices of the element. (This trick is a
|
||
general property of the DFT, and is not specific to FFTW.)
|
||
|
||
\question 08may:imageaudio How do I FFT an image/audio file in \italic{foobar\} format?
|
||
|
||
FFTW performs an FFT on an array of floating-point values. You can
|
||
certainly use it to compute the transform of an image or audio stream,
|
||
but you are responsible for figuring out your data format and
|
||
converting it to the form FFTW requires.
|
||
|
||
\question 09apr:linkfails My program does not link (on Unix).
|
||
|
||
The libraries must be listed in the correct order (\courier{-lfftw3
|
||
-lm\} for FFTW 3.x) and \italic{after\} your program sources/objects.
|
||
(The general rule is that if \italic{A\} uses \italic{B\}, then
|
||
\italic{A\} must be listed before \italic{B\} in the link command.).
|
||
|
||
\question 15mar:linkheader I included your header, but linking still fails.
|
||
|
||
You're a C++ programmer, aren't you? You have to compile the FFTW
|
||
library and link it into your program, not just \courier{#include
|
||
<fftw3.h>\}. (Yes, this is really a FAQ.)
|
||
|
||
\question 22oct:nostack My program crashes, complaining about stack space.
|
||
|
||
You cannot declare large arrays with automatic storage (e.g. via
|
||
\courier{fftw_complex array[N]\}); you should use
|
||
\courier{fftw_malloc\} (or equivalent) to allocate the arrays you want
|
||
to transform if they are larger than a few hundred elements.
|
||
|
||
\question 13may:leaks FFTW seems to have a memory leak.
|
||
|
||
After you create a plan, FFTW caches the information required to
|
||
quickly recreate the plan. (See \qref savePlans) It also maintains a
|
||
small amount of other persistent memory. You can deallocate all of
|
||
FFTW's internally allocated memory, if you wish, by calling
|
||
\courier{fftw_cleanup()\}, as documented in the manual.
|
||
|
||
\question 16may:allzero The output of FFTW's transform is all zeros.
|
||
|
||
You should initialize your input array \italic{after\} creating the
|
||
plan, unless you use \courier{FFTW_ESTIMATE\}: planning with
|
||
\courier{FFTW_MEASURE\} or \courier{FFTW_PATIENT\} overwrites the
|
||
input/output arrays, as described in the manual.
|
||
|
||
\question 05sep:vbetalia How do I call FFTW from the Microsoft language du jour?
|
||
|
||
Please \italic{do not\} ask us Windows-specific questions. We do not
|
||
use Windows. We know nothing about Visual Basic, Visual C++, or .NET.
|
||
Please find the appropriate Usenet discussion group and ask your
|
||
question there. See also \qref runOnWindows.
|
||
|
||
\question 15oct:pruned Can I compute only a subset of the DFT outputs?
|
||
|
||
In general, no, an FFT intrinsically computes all outputs from all
|
||
inputs. In principle, there is something called a \italic{pruned
|
||
FFT\} that can do what you want, but to compute K outputs out of N the
|
||
complexity is in general O(N log K) instead of O(N log N), thus saving
|
||
only a small additive factor in the log. (The same argument holds if
|
||
you instead have only K nonzero inputs.)
|
||
|
||
There are some specific cases in which you can get the O(N log K)
|
||
performance benefits easily, however, by combining a few ordinary
|
||
FFTs. In particular, the case where you want the first K outputs,
|
||
where K divides N, can be handled by performing N/K transforms of size
|
||
K and then summing the outputs multiplied by appropriate phase
|
||
factors. For more details, see \docref{pruned FFTs with FFTW\}.
|
||
|
||
There are also some algorithms that compute pruned transforms
|
||
\italic{approximately\}, but they are beyond the scope of this FAQ.
|
||
|
||
\question 21jan:transpose Can I use FFTW's routines for in-place and out-of-place matrix transposition?
|
||
|
||
You can use the FFTW guru interface to create a rank-0 transform of
|
||
vector rank 2 where the vector strides are transposed. (A rank-0
|
||
transform is equivalent to a 1D transform of size 1, which. just
|
||
copies the input into the output.) Specifying the same location for
|
||
the input and output makes the transpose in-place.
|
||
|
||
For double-valued data stored in row-major format, plan creation looks like
|
||
this:
|
||
|
||
\verbatim
|
||
fftw_plan plan_transpose(int rows, int cols, double *in, double *out)
|
||
{
|
||
const unsigned flags = FFTW_ESTIMATE; /* other flags are possible */
|
||
fftw_iodim howmany_dims[2];
|
||
|
||
howmany_dims[0].n = rows;
|
||
howmany_dims[0].is = cols;
|
||
howmany_dims[0].os = 1;
|
||
|
||
howmany_dims[1].n = cols;
|
||
howmany_dims[1].is = 1;
|
||
howmany_dims[1].os = rows;
|
||
|
||
return fftw_plan_guru_r2r(/*rank=*/ 0, /*dims=*/ NULL,
|
||
/*howmany_rank=*/ 2, howmany_dims,
|
||
in, out, /*kind=*/ NULL, flags);
|
||
}
|
||
\endverbatim
|
||
|
||
(This entry was written by Rhys Ulerich.)
|
||
|
||
\comment ######################################################################
|
||
|
||
\section Internals of FFTW
|
||
|
||
\question 26aug:howworks How does FFTW work?
|
||
|
||
The innovation (if it can be so called) in FFTW consists in having a
|
||
variety of composable \italic{solvers\}, representing different FFT
|
||
algorithms and implementation strategies, whose combination into a
|
||
particular \italic{plan\} for a given size can be determined at
|
||
runtime according to the characteristics of your machine/compiler.
|
||
This peculiar software architecture allows FFTW to adapt itself to
|
||
almost any machine.
|
||
|
||
For more details (albeit somewhat outdated), see the paper "FFTW: An
|
||
Adaptive Software Architecture for the FFT", by M. Frigo and
|
||
S. G. Johnson, \italic{Proc. ICASSP\} 3, 1381 (1998), also
|
||
available at \docref{the FFTW web page\}.
|
||
|
||
\question 26aug:whyfast Why is FFTW so fast?
|
||
|
||
This is a complex question, and there is no simple answer. In fact,
|
||
the authors do not fully know the answer, either. In addition to many
|
||
small performance hacks throughout FFTW, there are three general
|
||
reasons for FFTW's speed.
|
||
|
||
\call startlist
|
||
\call item
|
||
FFTW uses a variety of FFT algorithms and implementation styles
|
||
that can be arbitrarily composed to adapt itself to
|
||
a machine. See \qref howworks.
|
||
\call item
|
||
FFTW uses a code generator to produce highly-optimized
|
||
routines for computing small transforms.
|
||
\call item
|
||
FFTW uses explicit divide-and-conquer to take advantage
|
||
of the memory hierarchy.
|
||
\call endlist
|
||
|
||
For more details (albeit somewhat outdated), see the paper "FFTW: An
|
||
Adaptive Software Architecture for the FFT", by M. Frigo and
|
||
S. G. Johnson, \italic{Proc. ICASSP\} 3, 1381 (1998),
|
||
available along with other references at \docref{the FFTW web page\}.
|
||
|
||
\comment ######################################################################
|
||
|
||
\section Known bugs
|
||
|
||
\question 27aug:rfftwndbug FFTW 1.1 crashes in rfftwnd on Linux.
|
||
|
||
This bug was fixed in FFTW 1.2. There was a bug in \courier{rfftwnd\}
|
||
causing an incorrect amount of memory to be allocated. The bug showed
|
||
up in Linux with libc-5.3.12 (and nowhere else that we know of).
|
||
|
||
\question 15oct:fftwmpibug The MPI transforms in FFTW 1.2 give incorrect results/leak memory.
|
||
|
||
These bugs were corrected in FFTW 1.2.1. The MPI transforms (really,
|
||
just the transpose routines) in FFTW 1.2 had bugs that could cause
|
||
errors in some situations.
|
||
|
||
\question 05nov:testsingbug The test programs in FFTW 1.2.1 fail when I change FFTW to use single precision.
|
||
|
||
This bug was fixed in FFTW 1.3. (Older versions of FFTW did
|
||
work in single precision, but the test programs didn't--the error
|
||
tolerances in the tests were set for double precision.)
|
||
|
||
\question 24mar:teststoobig The test program in FFTW 1.2.1 fails for n > 46340.
|
||
|
||
This bug was fixed in FFTW 1.3. FFTW 1.2.1 produced the right answer,
|
||
but the test program was wrong. For large n, n*n in the naive
|
||
transform that we used for comparison overflows 32 bit integer
|
||
precision, breaking the test.
|
||
|
||
\question 24aug:linuxthreads The threaded code fails on Linux Redhat 5.0
|
||
|
||
We had problems with glibc-2.0.5. The code should work with
|
||
glibc-2.0.7.
|
||
|
||
\question 26sep:bigrfftwnd FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dimension >= 65536.
|
||
|
||
This bug was fixed in FFTW 2.0.1. (There was a 32-bit integer overflow due
|
||
to a poorly-parenthesized expression.)
|
||
|
||
\question 26mar:primebug FFTW 2.0's complex transforms give the wrong results with prime factors 17 to 97.
|
||
|
||
There was a bug in the complex transforms that could cause incorrect
|
||
results under (hopefully rare) circumstances for lengths with
|
||
intermediate-size prime factors (17-97). This bug was fixed in FFTW
|
||
2.1.1.
|
||
|
||
\question 05apr:mpichbug FFTW 2.1.1's MPI test programs crash with MPICH.
|
||
|
||
This bug was fixed in FFTW 2.1.2. The 2.1/2.1.1 MPI test programs crashed
|
||
when using the MPICH implementation of MPI with the \courier{ch_p4\}
|
||
device (TCP/IP); the transforms themselves worked fine.
|
||
|
||
\question 25may:aixthreadbug FFTW 2.1.2's multi-threaded transforms don't work on AIX.
|
||
|
||
This bug was fixed in FFTW 2.1.3. The multi-threaded transforms in
|
||
previous versions didn't work with AIX's \courier{pthreads\}
|
||
implementation, which idiosyncratically creates threads in detached
|
||
(non-joinable) mode by default.
|
||
|
||
\question 27sep:bigprimebug FFTW 2.1.2's complex transforms give incorrect results for large prime sizes.
|
||
|
||
This bug was fixed in FFTW 2.1.3. FFTW's complex-transform algorithm
|
||
for prime sizes (in versions 2.0 to 2.1.2) had an integer overflow
|
||
problem that caused incorrect results for many primes greater than
|
||
32768 (on 32-bit machines). (Sizes without large prime factors are
|
||
not affected.)
|
||
|
||
\question 25may:solaristhreadbug FFTW 2.1.3's multi-threaded transforms don't give any speedup on Solaris.
|
||
|
||
This bug was fixed in FFTW 2.1.4. (By default, Solaris creates
|
||
threads that do not parallelize over multiple processors, so one has
|
||
to request the proper behavior specifically.)
|
||
|
||
\question 03may:aixflags FFTW 2.1.3 crashes on AIX.
|
||
|
||
The FFTW 2.1.3 \courier{configure\} script picked incorrect compiler
|
||
flags for the \courier{xlc\} compiler on newer IBM processors. This
|
||
is fixed in FFTW 2.1.4.
|
||
|
||
\comment Here it ends!
|
||
|