Chris@42: \comment This is the source for the FFTW FAQ list, in
Chris@42: \comment the Bizarre Format With No Name. It is turned into Lout
Chris@42: \comment input, HTML, plain ASCII and an Info document by a Perl script.
Chris@42: \comment
Chris@42: \comment The format and scripts come from the Linux FAQ, by
Chris@42: \comment Ian Jackson.
Chris@42: \set brieftitle FFTW FAQ
Chris@42: \set author Matteo Frigo and Steven G. Johnson / fftw@fftw.org
Chris@42: \set authormail fftw@fftw.org
Chris@42: \set title FFTW Frequently Asked Questions with Answers
Chris@42: \set copyholder Matteo Frigo and Massachusetts Institute of Technology
Chris@42: \call-html startup html.refs2
Chris@42: \copyto ASCII
Chris@42: FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS
Chris@42: `date '+%d %h %Y'`
Chris@42: Matteo Frigo
Chris@42: Steven G. Johnson
Chris@42:
Chris@42:
Chris@42: \endcopy
Chris@42: \copyto INFO
Chris@42: INFO-DIR-SECTION Development
Chris@42: START-INFO-DIR-ENTRY
Chris@42: * FFTW FAQ: (fftw-faq). FFTW Frequently Asked Questions with Answers.
Chris@42: END-INFO-DIR-ENTRY
Chris@42:
Chris@42:
Chris@42: File: $prefix.info, Node: Top, Next: Question 1.1, Up: (dir)
Chris@42:
Chris@42: FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS
Chris@42: `date '+%d %h %Y'`
Chris@42: Matteo Frigo
Chris@42: Steven G. Johnson
Chris@42:
Chris@42:
Chris@42: \endcopy
Chris@42:
Chris@42: This is the list of Frequently Asked Questions about FFTW, a
Chris@42: collection of fast C routines for computing the Discrete Fourier
Chris@42: Transform in one or more dimensions.
Chris@42:
Chris@42: \section Index
Chris@42:
Chris@42: \index
Chris@42:
Chris@42: \comment ######################################################################
Chris@42:
Chris@42: \section Introduction and General Information
Chris@42:
Chris@42: \question 26aug:whatisfftw What is FFTW?
Chris@42:
Chris@42: FFTW is a free collection of fast C routines for computing the
Chris@42: Discrete Fourier Transform in one or more dimensions. It includes
Chris@42: complex, real, symmetric, and parallel transforms, and can handle
Chris@42: arbitrary array sizes efficiently. FFTW is typically faster than
Chris@42: other publically-available FFT implementations, and is even
Chris@42: competitive with vendor-tuned libraries. (See our web page for
Chris@42: extensive benchmarks.) To achieve this performance, FFTW uses novel
Chris@42: code-generation and runtime self-optimization techniques (along with
Chris@42: many other tricks).
Chris@42:
Chris@42: \question 26aug:whereisfftw How do I obtain FFTW?
Chris@42:
Chris@42: FFTW can be found at \docref{the FFTW web page\}. You can also
Chris@42: retrieve it from \ftpon ftp.fftw.org in \ftpin /pub/fftw.
Chris@42:
Chris@42: \question 26aug:isfftwfree Is FFTW free software?
Chris@42:
Chris@42: Starting with version 1.3, FFTW is Free Software in the technical
Chris@42: sense defined by the Free Software Foundation (see \docref{Categories
Chris@42: of Free and Non-Free Software\}), and is distributed under the terms
Chris@42: of the GNU General Public License. Previous versions of FFTW were
Chris@42: distributed without fee for noncommercial use, but were not
Chris@42: technically ``free.''
Chris@42:
Chris@42: Non-free licenses for FFTW are also available that permit different
Chris@42: terms of use than the GPL.
Chris@42:
Chris@42: \question 10apr:nonfree What is this about non-free licenses?
Chris@42:
Chris@42: The non-free licenses are for companies that wish to use FFTW in their
Chris@42: products but are unwilling to release their software under the GPL
Chris@42: (which would require them to release source code and allow free
Chris@42: redistribution). Such users can purchase an unlimited-use license
Chris@42: from MIT. Contact us for more details.
Chris@42:
Chris@42: We could instead have released FFTW under the LGPL, or even disallowed
Chris@42: non-Free usage. Suffice it to say, however, that MIT owns the
Chris@42: copyright to FFTW and they only let us GPL it because we convinced
Chris@42: them that it would neither affect their licensing revenue nor irritate
Chris@42: existing licensees.
Chris@42:
Chris@42: \question 24oct:west In the West? I thought MIT was in the East?
Chris@42:
Chris@42: Not to an Italian. You could say that we're a Spaghetti Western
Chris@42: (with apologies to Sergio Leone).
Chris@42:
Chris@42: \comment ######################################################################
Chris@42:
Chris@42: \section Installing FFTW
Chris@42:
Chris@42: \question 26aug:systems Which systems does FFTW run on?
Chris@42:
Chris@42: FFTW is written in ANSI C, and should work on any system with a decent
Chris@42: C compiler. (See also \qref runOnWindows, \qref compilerCrashes.)
Chris@42: FFTW can also take advantage of certain hardware-specific features,
Chris@42: such as cycle counters and SIMD instructions, but this is optional.
Chris@42:
Chris@42: \question 26aug:runOnWindows Does FFTW run on Windows?
Chris@42:
Chris@42: Yes, many people have reported successfully using FFTW on Windows with
Chris@42: various compilers. FFTW was not developed on Windows, but the source
Chris@42: code is essentially straight ANSI C. See also the \docref{FFTW
Chris@42: Windows installation notes\}, \qref compilerCrashes, and \qref
Chris@42: vbetalia.
Chris@42:
Chris@42: \question 26aug:compilerCrashes My compiler has trouble with FFTW.
Chris@42:
Chris@42: Complain fiercely to the vendor of the compiler.
Chris@42:
Chris@42: We have successfully used \courier{gcc\} 3.2.x on x86 and PPC, a
Chris@42: recent Compaq C compiler for Alpha, version 6 of IBM's \courier{xlc\}
Chris@42: compiler for AIX, Intel's \courier{icc\} versions 5-7, and Sun
Chris@42: WorkShop \courier{cc\} version 6.
Chris@42:
Chris@42: FFTW is likely to push compilers to their limits, however, and several
Chris@42: compiler bugs have been exposed by FFTW. A partial list follows.
Chris@42:
Chris@42: \courier{gcc\} 2.95.x for Solaris/SPARC produces incorrect code for
Chris@42: the test program (workaround: recompile the \courier{libbench2\}
Chris@42: directory with \courier{-O2\}).
Chris@42:
Chris@42: NetBSD/macppc 1.6 comes with a \courier{gcc\} version that also
Chris@42: miscompiles the test program. (Please report a workaround if you know
Chris@42: one.)
Chris@42:
Chris@42: \courier{gcc\} 3.2.3 for ARM reportedly crashes during compilation.
Chris@42: This bug is reportedly fixed in later versions of \courier{gcc\}.
Chris@42:
Chris@42: Versions 8.0 and 8.1 of Intel's \courier{icc\} falsely claim to be
Chris@42: \courier{gcc\}, so you should specify \courier{CC="icc -no-gcc"\};
Chris@42: this is automatic in FFTW 3.1. \courier{icc-8.0.066\} reportely
Chris@42: produces incorrect code for FFTW 2.1.5, but is fixed in version 8.1.
Chris@42: \courier{icc-7.1\} compiler build 20030402Z appears to produce
Chris@42: incorrect dependencies, causing the compilation to fail.
Chris@42: \courier{icc-7.1\} build 20030307Z appears to work fine. (Use
Chris@42: \courier{icc -V\} to check which build you have.) As of 2003/04/18,
Chris@42: build 20030402Z appears not to be available any longer on Intel's
Chris@42: website, whereas the older build 20030307Z is available.
Chris@42:
Chris@42: \courier{ranlib\} of GNU \courier{binutils\} 2.9.1 on Irix has been
Chris@42: observed to corrupt the FFTW libraries, causing a link failure when
Chris@42: FFTW is compiled. Since \courier{ranlib\} is completely superfluous
Chris@42: on Irix, we suggest deleting it from your system and replacing it with
Chris@42: a symbolic link to \courier{/bin/echo\}.
Chris@42:
Chris@42: If support for SIMD instructions is enabled in FFTW, further compiler
Chris@42: problems may appear:
Chris@42:
Chris@42: \courier{gcc\} 3.4.[0123] for x86 produces incorrect SSE2 code for
Chris@42: FFTW when \courier{-O2\} (the best choice for FFTW) is used, causing
Chris@42: FFTW to crash (\courier{make check\} crashes). This bug is fixed in
Chris@42: \courier{gcc\} 3.4.4. On x86_64 (amd64/em64t), \courier{gcc\} 3.4.4
Chris@42: reportedly still has a similar problem, but this is fixed as of
Chris@42: \courier{gcc\} 3.4.6.
Chris@42:
Chris@42: \courier{gcc-3.2\} for x86 produces incorrect SIMD code if
Chris@42: \courier{-O3\} is used. The same compiler produces incorrect SIMD
Chris@42: code if no optimization is used, too. When using \courier{gcc-3.2\},
Chris@42: it is a good idea not to change the default \courier{CFLAGS\} selected
Chris@42: by the \courier{configure\} script.
Chris@42:
Chris@42: Some 3.0.x and 3.1.x versions of \courier{gcc\} on \courier{x86\} may
Chris@42: crash. \courier{gcc\} so-called 2.96 shipping with RedHat 7.3 crashes
Chris@42: when compiling SIMD code. In both cases, please upgrade to
Chris@42: \courier{gcc-3.2\} or later.
Chris@42:
Chris@42: Intel's \courier{icc\} 6.0 misaligns SSE constants, but FFTW has a
Chris@42: workaround. \courier{icc\} 8.x fails to compile FFTW 3.0.x because it
Chris@42: falsely claims to be \courier{gcc\}; we believe this to be a bug in
Chris@42: \courier{icc\}, but FFTW 3.1 has a workaround.
Chris@42:
Chris@42: Visual C++ 2003 reportedly produces incorrect code for SSE/SSE2 when
Chris@42: compiling FFTW. This bug was reportedly fixed in VC++ 2005;
Chris@42: alternatively, you could switch to the Intel compiler. VC++ 6.0 also
Chris@42: reportedly produces incorrect code for the file
Chris@42: \courier{reodft11e-r2hc-odd.c\} unless optimizations are disabled for
Chris@42: that file.
Chris@42:
Chris@42: \courier{gcc\} 2.95 on MacOS X miscompiles AltiVec code (fixed in
Chris@42: later versions). \courier{gcc\} 3.2.x miscompiles AltiVec
Chris@42: permutations, but FFTW has a workaround. \courier{gcc\} 4.0.1 on
Chris@42: MacOS for Intel crashes when compiling FFTW; a workaround is to
Chris@42: compile one file without optimization: \courier{cd kernel; make
Chris@42: CFLAGS=" " trig.lo\}.
Chris@42:
Chris@42: \courier{gcc\} 4.1.1 reportedly crashes when compiling FFTW for MIPS;
Chris@42: the workaround is to compile the file it crashes on
Chris@42: (\courier{t2_64.c\}) with a lower optimization level.
Chris@42:
Chris@42: \courier{gcc\} versions 4.1.2 to 4.2.0 for x86 reportedly miscompile
Chris@42: FFTW 3.1's test program, causing \courier{make check\} to crash
Chris@42: (\courier{gcc\} bug #26528). The bug was reportedly fixed in
Chris@42: \courier{gcc\} version 4.2.1 and later. A workaround is to compile
Chris@42: \courier{libbench2/verify-lib.c\} without optimization.
Chris@42:
Chris@42: \question 26aug:solarisSucks FFTW does not compile on Solaris, complaining about \courier{const\}.
Chris@42:
Chris@42: We know that at least on Solaris 2.5.x with Sun's compilers 4.2 you
Chris@42: might get error messages from \courier{make\} such as
Chris@42:
Chris@42: \courier{"./fftw.h", line 88: warning: const is a keyword in ANSI C\}
Chris@42:
Chris@42: This is the case when the \courier{configure\} script reports that
Chris@42: \courier{const\} does not work:
Chris@42:
Chris@42: \courier{checking for working const... (cached) no\}
Chris@42:
Chris@42: You should be aware that Solaris comes with two compilers, namely,
Chris@42: \courier{/opt/SUNWspro/SC4.2/bin/cc\} and \courier{/usr/ucb/cc\}. The
Chris@42: latter compiler is non-ANSI. Indeed, it is a perverse shell script
Chris@42: that calls the real compiler in non-ANSI mode. In order
Chris@42: to compile FFTW, change your path so that the right \courier{cc\}
Chris@42: is used.
Chris@42:
Chris@42: To know whether your compiler is the right one, type
Chris@42: \courier{cc -V\}. If the compiler prints ``\courier{ucbcc\}'',
Chris@42: as in
Chris@42:
Chris@42: \courier{ucbcc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2\}
Chris@42:
Chris@42: then the compiler is wrong. The right message is something like
Chris@42:
Chris@42: \courier{cc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2\}
Chris@42:
Chris@42: \question 19mar:3dnow What's the difference between \courier{--enable-3dnow\} and \courier{--enable-k7\}?
Chris@42:
Chris@42: \courier{--enable-k7\} enables 3DNow! instructions on K7 processors
Chris@42: (AMD Athlon and its variants). K7 support is provided by assembly
Chris@42: routines generated by a special purpose compiler.
Chris@42: As of fftw-3.2, --enable-k7 is no longer supported.
Chris@42:
Chris@42: \courier{--enable-3dnow\} enables generic 3DNow! support using
Chris@42: \courier{gcc\} builtin functions. This works on earlier AMD
Chris@42: processors, but it is not as fast as our special assembly routines.
Chris@42: As of fftw-3.1, --enable-3dnow is no longer supported.
Chris@42:
Chris@42: \question 18apr:fma What's the difference between the fma and the non-fma versions?
Chris@42:
Chris@42: The fma version tries to exploit the fused multiply-add instructions
Chris@42: implemented in many processors such as PowerPC, ia-64, and MIPS. The
Chris@42: two FFTW packages are otherwise identical. In FFTW 3.1, the fma and
Chris@42: non-fma versions were merged together into a single package, and the
Chris@42: \courier{configure\} script attempts to automatically guess which
Chris@42: version to use.
Chris@42:
Chris@42: The FFTW 3.1 \courier{configure\} script enables fma by default on
Chris@42: PowerPC, Itanium, and PA-RISC, and disables it otherwise. You can
Chris@42: force one or the other by using the \courier{--enable-fma\} or
Chris@42: \courier{--disable-fma\} flag for \courier{configure\}.
Chris@42:
Chris@42: Definitely use fma if you have a PowerPC-based system with
Chris@42: \courier{gcc\} (or IBM \courier{xlc\}). This includes all GNU/Linux
Chris@42: systems for PowerPC and the older PowerPC-based MacOS systems. Also
Chris@42: use it on PA-RISC and Itanium with the HP/UX compiler.
Chris@42:
Chris@42: Definitely do not use the fma version if you have an ia-32 processor
Chris@42: (Intel, AMD, MacOS on Intel, etcetera).
Chris@42:
Chris@42: For other architectures/compilers, the situation is not so clear. For
Chris@42: example, ia-64 has the fma instruction, but \courier{gcc-3.2\} appears
Chris@42: not to exploit it correctly. Other compilers may do the right thing,
Chris@42: but we have not tried them. Please send us your feedback so that we
Chris@42: can update this FAQ entry.
Chris@42:
Chris@42: \question 26aug:languages Which language is FFTW written in?
Chris@42:
Chris@42: FFTW is written in ANSI C. Most of the code, however, was
Chris@42: automatically generated by a program called \courier{genfft\}, written
Chris@42: in the Objective Caml dialect of ML. You do not need to know ML or to
Chris@42: have an Objective Caml compiler in order to use FFTW.
Chris@42:
Chris@42: \courier{genfft\} is provided with the FFTW sources, which means that
Chris@42: you can play with the code generator if you want. In this case, you
Chris@42: need a working Objective Caml system. Objective Caml is available
Chris@42: from \docref{the Caml web page\}.
Chris@42:
Chris@42: \question 26aug:fortran Can I call FFTW from Fortran?
Chris@42:
Chris@42: Yes, FFTW (versions 1.3 and higher) contains a Fortran-callable
Chris@42: interface, documented in the FFTW manual.
Chris@42:
Chris@42: By default, FFTW configures its Fortran interface to work with the
Chris@42: first compiler it finds, e.g. \courier{g77\}. To configure for a
Chris@42: different, incompatible Fortran compiler \courier{foobar\}, use
Chris@42: \courier{./configure F77=foobar\} when installing FFTW. (In the case
Chris@42: of \courier{g77\}, however, FFTW 3.x also includes an extra set of
Chris@42: Fortran-callable routines with one less underscore at the end of
Chris@42: identifiers, which should cover most other Fortran compilers on Linux
Chris@42: at least.)
Chris@42:
Chris@42: \question 26aug:cplusplus Can I call FFTW from C++?
Chris@42:
Chris@42: Most definitely. FFTW should compile and/or link under any C++
Chris@42: compiler. Moreover, it is likely that the C++ \courier{\}
Chris@42: template class is bit-compatible with FFTW's complex-number format
Chris@42: (see the FFTW manual for more details).
Chris@42:
Chris@42: \question 26aug:whynotfortran Why isn't FFTW written in Fortran/C++?
Chris@42:
Chris@42: Because we don't like those languages, and neither approaches the
Chris@42: portability of C.
Chris@42:
Chris@42: \question 29mar:singleprec How do I compile FFTW to run in single precision?
Chris@42:
Chris@42: On a Unix system: \courier{configure --enable-float\}. On a non-Unix
Chris@42: system: edit \courier{config.h\} to \courier{#define\} the symbol
Chris@42: \courier{FFTW_SINGLE\} (for FFTW 3.x). In both cases, you must then
Chris@42: recompile FFTW. In FFTW 3, all FFTW identifiers will then begin with
Chris@42: \courier{fftwf_\} instead of \courier{fftw_\}.
Chris@42:
Chris@42: \question 28mar:64bitk7 --enable-k7 does not work on x86-64
Chris@42:
Chris@42: Support for --enable-k7 was discontinued in fftw-3.2.
Chris@42:
Chris@42: The fftw-3.1 release supports --enable-k7. This option only works on
Chris@42: 32-bit x86 machines that implement 3DNow!, including the AMD Athlon
Chris@42: and the AMD Opteron in 32-bit mode. --enable-k7 does not work on AMD
Chris@42: Opteron in 64-bit mode. Use --enable-sse for x86-64 machines.
Chris@42:
Chris@42: FFTW supports 3DNow! by means of assembly code generated by a
Chris@42: special-purpose compiler. It is hard to produce assembly code that
Chris@42: works in both 32-bit and 64-bit mode.
Chris@42:
Chris@42: \comment ######################################################################
Chris@42:
Chris@42: \section Using FFTW
Chris@42:
Chris@42: \question 15mar:fftw2to3 Why not support the FFTW 2 interface in FFTW 3?
Chris@42:
Chris@42: FFTW 3 has semantics incompatible with earlier versions: its plans can
Chris@42: only be used for a given stride, multiplicity, and other
Chris@42: characteristics of the input and output arrays; these stronger
Chris@42: semantics are necessary for performance reasons. Thus, it is
Chris@42: impossible to efficiently emulate the older interface (whose plans can
Chris@42: be used for any transform of the same size). We believe that it
Chris@42: should be possible to upgrade most programs without any difficulty,
Chris@42: however.
Chris@42:
Chris@42: \question 20mar:planperarray Why do FFTW 3 plans encapsulate the input/output arrays and not just the algorithm?
Chris@42:
Chris@42: There are several reasons:
Chris@42:
Chris@42: \call startlist
Chris@42: \call item
Chris@42: It was important for performance reasons that the plan be specific to
Chris@42: array characteristics like the stride (and alignment, for SIMD), and
Chris@42: requiring that the user maintain these invariants is error prone.
Chris@42: \call item
Chris@42: In most high-performance applications, as far as we can tell, you are
Chris@42: usually transforming the same array over and over, so FFTW's semantics
Chris@42: should not be a burden.
Chris@42: \call item
Chris@42: If you need to transform another array of the same size, creating a
Chris@42: new plan once the first exists is a cheap operation.
Chris@42: \call item
Chris@42: If you need to transform many arrays of the same size at once, you
Chris@42: should really use the \courier{plan_many\} routines in FFTW's "advanced"
Chris@42: interface.
Chris@42: \call item
Chris@42: If the abovementioned array characteristics are the same, you are
Chris@42: willing to pay close attention to the documentation, and you really
Chris@42: need to, we provide a "new-array execution" interface to apply a plan
Chris@42: to a new array.
Chris@42: \call endlist
Chris@42:
Chris@42: \question 25may:slow FFTW seems really slow.
Chris@42:
Chris@42: You are probably recreating the plan before every transform, rather
Chris@42: than creating it once and reusing it for all transforms of the same
Chris@42: size. FFTW is designed to be used in the following way:
Chris@42:
Chris@42: \call startlist
Chris@42: \call item
Chris@42: First, you create a plan. This will take several seconds.
Chris@42: \call item
Chris@42: Then, you reuse the plan many times to perform FFTs. These are fast.
Chris@42: \call endlist
Chris@42:
Chris@42: If you don't need to compute many transforms and the time for the
Chris@42: planner is significant, you have two options. First, you can use the
Chris@42: \courier{FFTW_ESTIMATE\} option in the planner, which uses heuristics
Chris@42: instead of runtime measurements and produces a good plan in a short
Chris@42: time. Second, you can use the wisdom feature to precompute the plan;
Chris@42: see \qref savePlans
Chris@42:
Chris@42: \question 22oct:slows FFTW slows down after repeated calls.
Chris@42:
Chris@42: Probably, NaNs or similar are creeping into your data, and the
Chris@42: slowdown is due to the resulting floating-point exceptions. For
Chris@42: example, be aware that repeatedly FFTing the same array is a diverging
Chris@42: process (because FFTW computes the unnormalized transform).
Chris@42:
Chris@42: \question 22oct:segfault An FFTW routine is crashing when I call it.
Chris@42:
Chris@42: Did the FFTW test programs pass (\courier{make check\}, or \courier{cd
Chris@42: tests; make bigcheck\} if you want to be paranoid)? If so, you almost
Chris@42: certainly have a bug in your own code. For example, you could be
Chris@42: passing invalid arguments (such as wrongly-sized arrays) to FFTW, or
Chris@42: you could simply have memory corruption elsewhere in your program that
Chris@42: causes random crashes later on. Please don't complain to us unless
Chris@42: you can come up with a minimal self-contained program (preferably
Chris@42: under 30 lines) that illustrates the problem.
Chris@42:
Chris@42: \question 22oct:fortran64 My Fortran program crashes when calling FFTW.
Chris@42:
Chris@42: As described in the manual, on 64-bit machines you must store the
Chris@42: plans in variables large enough to hold a pointer, for example
Chris@42: \courier{integer*8\}. We recommend using \courier{integer*8\} on
Chris@42: 32-bit machines as well, to simplify porting.
Chris@42:
Chris@42: \question 24mar:conventions FFTW gives results different from my old FFT.
Chris@42:
Chris@42: People follow many different conventions for the DFT, and you should
Chris@42: be sure to know the ones that we use (described in the FFTW manual).
Chris@42: In particular, you should be aware that the
Chris@42: \courier{FFTW_FORWARD\}/\courier{FFTW_BACKWARD\} directions correspond
Chris@42: to signs of -1/+1 in the exponent of the DFT definition.
Chris@42: (\italic{Numerical Recipes\} uses the opposite convention.)
Chris@42:
Chris@42: You should also know that we compute an unnormalized transform. In
Chris@42: contrast, Matlab is an example of program that computes a normalized
Chris@42: transform. See \qref whyscaled.
Chris@42:
Chris@42: Finally, note that floating-point arithmetic is not exact, so
Chris@42: different FFT algorithms will give slightly different results (on the
Chris@42: order of the numerical accuracy; typically a fractional difference of
Chris@42: 1e-15 or so in double precision).
Chris@42:
Chris@42: \question 31aug:nondeterministic FFTW gives different results between runs
Chris@42:
Chris@42: If you use \courier{FFTW_MEASURE\} or \courier{FFTW_PATIENT\} mode,
Chris@42: then the algorithm FFTW employs is not deterministic: it depends on
Chris@42: runtime performance measurements. This will cause the results to vary
Chris@42: slightly from run to run. However, the differences should be slight,
Chris@42: on the order of the floating-point precision, and therefore should
Chris@42: have no practical impact on most applications.
Chris@42:
Chris@42: If you use saved plans (wisdom) or \courier{FFTW_ESTIMATE\} mode,
Chris@42: however, then the algorithm is deterministic and the results should be
Chris@42: identical between runs.
Chris@42:
Chris@42: \question 26aug:savePlans Can I save FFTW's plans?
Chris@42:
Chris@42: Yes. Starting with version 1.2, FFTW provides the \courier{wisdom\}
Chris@42: mechanism for saving plans; see the FFTW manual.
Chris@42:
Chris@42: \question 14sep:whyscaled Why does your inverse transform return a scaled result?
Chris@42:
Chris@42: Computing the forward transform followed by the backward transform (or
Chris@42: vice versa) yields the original array scaled by the size of the array.
Chris@42: (For multi-dimensional transforms, the size of the array is the
Chris@42: product of the dimensions.) We could, instead, have chosen a
Chris@42: normalization that would have returned the unscaled array. Or, to
Chris@42: accomodate the many conventions in this matter, the transform routines
Chris@42: could have accepted a "scale factor" parameter. We did not do this,
Chris@42: however, for two reasons. First, we didn't want to sacrifice
Chris@42: performance in the common case where the scale factor is 1. Second, in
Chris@42: real applications the FFT is followed or preceded by some computation
Chris@42: on the data, into which the scale factor can typically be absorbed at
Chris@42: little or no cost.
Chris@42:
Chris@42: \question 02dec:centerorigin How can I make FFTW put the origin (zero frequency) at the center of its output?
Chris@42:
Chris@42: For human viewing of a spectrum, it is often convenient to put the
Chris@42: origin in frequency space at the center of the output array, rather
Chris@42: than in the zero-th element (the default in FFTW). If all of the
Chris@42: dimensions of your array are even, you can accomplish this by simply
Chris@42: multiplying each element of the input array by (-1)^(i + j + ...),
Chris@42: where i, j, etcetera are the indices of the element. (This trick is a
Chris@42: general property of the DFT, and is not specific to FFTW.)
Chris@42:
Chris@42: \question 08may:imageaudio How do I FFT an image/audio file in \italic{foobar\} format?
Chris@42:
Chris@42: FFTW performs an FFT on an array of floating-point values. You can
Chris@42: certainly use it to compute the transform of an image or audio stream,
Chris@42: but you are responsible for figuring out your data format and
Chris@42: converting it to the form FFTW requires.
Chris@42:
Chris@42: \question 09apr:linkfails My program does not link (on Unix).
Chris@42:
Chris@42: The libraries must be listed in the correct order (\courier{-lfftw3
Chris@42: -lm\} for FFTW 3.x) and \italic{after\} your program sources/objects.
Chris@42: (The general rule is that if \italic{A\} uses \italic{B\}, then
Chris@42: \italic{A\} must be listed before \italic{B\} in the link command.).
Chris@42:
Chris@42: \question 15mar:linkheader I included your header, but linking still fails.
Chris@42:
Chris@42: You're a C++ programmer, aren't you? You have to compile the FFTW
Chris@42: library and link it into your program, not just \courier{#include
Chris@42: \}. (Yes, this is really a FAQ.)
Chris@42:
Chris@42: \question 22oct:nostack My program crashes, complaining about stack space.
Chris@42:
Chris@42: You cannot declare large arrays with automatic storage (e.g. via
Chris@42: \courier{fftw_complex array[N]\}); you should use
Chris@42: \courier{fftw_malloc\} (or equivalent) to allocate the arrays you want
Chris@42: to transform if they are larger than a few hundred elements.
Chris@42:
Chris@42: \question 13may:leaks FFTW seems to have a memory leak.
Chris@42:
Chris@42: After you create a plan, FFTW caches the information required to
Chris@42: quickly recreate the plan. (See \qref savePlans) It also maintains a
Chris@42: small amount of other persistent memory. You can deallocate all of
Chris@42: FFTW's internally allocated memory, if you wish, by calling
Chris@42: \courier{fftw_cleanup()\}, as documented in the manual.
Chris@42:
Chris@42: \question 16may:allzero The output of FFTW's transform is all zeros.
Chris@42:
Chris@42: You should initialize your input array \italic{after\} creating the
Chris@42: plan, unless you use \courier{FFTW_ESTIMATE\}: planning with
Chris@42: \courier{FFTW_MEASURE\} or \courier{FFTW_PATIENT\} overwrites the
Chris@42: input/output arrays, as described in the manual.
Chris@42:
Chris@42: \question 05sep:vbetalia How do I call FFTW from the Microsoft language du jour?
Chris@42:
Chris@42: Please \italic{do not\} ask us Windows-specific questions. We do not
Chris@42: use Windows. We know nothing about Visual Basic, Visual C++, or .NET.
Chris@42: Please find the appropriate Usenet discussion group and ask your
Chris@42: question there. See also \qref runOnWindows.
Chris@42:
Chris@42: \question 15oct:pruned Can I compute only a subset of the DFT outputs?
Chris@42:
Chris@42: In general, no, an FFT intrinsically computes all outputs from all
Chris@42: inputs. In principle, there is something called a \italic{pruned
Chris@42: FFT\} that can do what you want, but to compute K outputs out of N the
Chris@42: complexity is in general O(N log K) instead of O(N log N), thus saving
Chris@42: only a small additive factor in the log. (The same argument holds if
Chris@42: you instead have only K nonzero inputs.)
Chris@42:
Chris@42: There are some specific cases in which you can get the O(N log K)
Chris@42: performance benefits easily, however, by combining a few ordinary
Chris@42: FFTs. In particular, the case where you want the first K outputs,
Chris@42: where K divides N, can be handled by performing N/K transforms of size
Chris@42: K and then summing the outputs multiplied by appropriate phase
Chris@42: factors. For more details, see \docref{pruned FFTs with FFTW\}.
Chris@42:
Chris@42: There are also some algorithms that compute pruned transforms
Chris@42: \italic{approximately\}, but they are beyond the scope of this FAQ.
Chris@42:
Chris@42: \question 21jan:transpose Can I use FFTW's routines for in-place and out-of-place matrix transposition?
Chris@42:
Chris@42: You can use the FFTW guru interface to create a rank-0 transform of
Chris@42: vector rank 2 where the vector strides are transposed. (A rank-0
Chris@42: transform is equivalent to a 1D transform of size 1, which. just
Chris@42: copies the input into the output.) Specifying the same location for
Chris@42: the input and output makes the transpose in-place.
Chris@42:
Chris@42: For double-valued data stored in row-major format, plan creation looks like
Chris@42: this:
Chris@42:
Chris@42: \verbatim
Chris@42: fftw_plan plan_transpose(int rows, int cols, double *in, double *out)
Chris@42: {
Chris@42: const unsigned flags = FFTW_ESTIMATE; /* other flags are possible */
Chris@42: fftw_iodim howmany_dims[2];
Chris@42:
Chris@42: howmany_dims[0].n = rows;
Chris@42: howmany_dims[0].is = cols;
Chris@42: howmany_dims[0].os = 1;
Chris@42:
Chris@42: howmany_dims[1].n = cols;
Chris@42: howmany_dims[1].is = 1;
Chris@42: howmany_dims[1].os = rows;
Chris@42:
Chris@42: return fftw_plan_guru_r2r(/*rank=*/ 0, /*dims=*/ NULL,
Chris@42: /*howmany_rank=*/ 2, howmany_dims,
Chris@42: in, out, /*kind=*/ NULL, flags);
Chris@42: }
Chris@42: \endverbatim
Chris@42:
Chris@42: (This entry was written by Rhys Ulerich.)
Chris@42:
Chris@42: \comment ######################################################################
Chris@42:
Chris@42: \section Internals of FFTW
Chris@42:
Chris@42: \question 26aug:howworks How does FFTW work?
Chris@42:
Chris@42: The innovation (if it can be so called) in FFTW consists in having a
Chris@42: variety of composable \italic{solvers\}, representing different FFT
Chris@42: algorithms and implementation strategies, whose combination into a
Chris@42: particular \italic{plan\} for a given size can be determined at
Chris@42: runtime according to the characteristics of your machine/compiler.
Chris@42: This peculiar software architecture allows FFTW to adapt itself to
Chris@42: almost any machine.
Chris@42:
Chris@42: For more details (albeit somewhat outdated), see the paper "FFTW: An
Chris@42: Adaptive Software Architecture for the FFT", by M. Frigo and
Chris@42: S. G. Johnson, \italic{Proc. ICASSP\} 3, 1381 (1998), also
Chris@42: available at \docref{the FFTW web page\}.
Chris@42:
Chris@42: \question 26aug:whyfast Why is FFTW so fast?
Chris@42:
Chris@42: This is a complex question, and there is no simple answer. In fact,
Chris@42: the authors do not fully know the answer, either. In addition to many
Chris@42: small performance hacks throughout FFTW, there are three general
Chris@42: reasons for FFTW's speed.
Chris@42:
Chris@42: \call startlist
Chris@42: \call item
Chris@42: FFTW uses a variety of FFT algorithms and implementation styles
Chris@42: that can be arbitrarily composed to adapt itself to
Chris@42: a machine. See \qref howworks.
Chris@42: \call item
Chris@42: FFTW uses a code generator to produce highly-optimized
Chris@42: routines for computing small transforms.
Chris@42: \call item
Chris@42: FFTW uses explicit divide-and-conquer to take advantage
Chris@42: of the memory hierarchy.
Chris@42: \call endlist
Chris@42:
Chris@42: For more details (albeit somewhat outdated), see the paper "FFTW: An
Chris@42: Adaptive Software Architecture for the FFT", by M. Frigo and
Chris@42: S. G. Johnson, \italic{Proc. ICASSP\} 3, 1381 (1998),
Chris@42: available along with other references at \docref{the FFTW web page\}.
Chris@42:
Chris@42: \comment ######################################################################
Chris@42:
Chris@42: \section Known bugs
Chris@42:
Chris@42: \question 27aug:rfftwndbug FFTW 1.1 crashes in rfftwnd on Linux.
Chris@42:
Chris@42: This bug was fixed in FFTW 1.2. There was a bug in \courier{rfftwnd\}
Chris@42: causing an incorrect amount of memory to be allocated. The bug showed
Chris@42: up in Linux with libc-5.3.12 (and nowhere else that we know of).
Chris@42:
Chris@42: \question 15oct:fftwmpibug The MPI transforms in FFTW 1.2 give incorrect results/leak memory.
Chris@42:
Chris@42: These bugs were corrected in FFTW 1.2.1. The MPI transforms (really,
Chris@42: just the transpose routines) in FFTW 1.2 had bugs that could cause
Chris@42: errors in some situations.
Chris@42:
Chris@42: \question 05nov:testsingbug The test programs in FFTW 1.2.1 fail when I change FFTW to use single precision.
Chris@42:
Chris@42: This bug was fixed in FFTW 1.3. (Older versions of FFTW did
Chris@42: work in single precision, but the test programs didn't--the error
Chris@42: tolerances in the tests were set for double precision.)
Chris@42:
Chris@42: \question 24mar:teststoobig The test program in FFTW 1.2.1 fails for n > 46340.
Chris@42:
Chris@42: This bug was fixed in FFTW 1.3. FFTW 1.2.1 produced the right answer,
Chris@42: but the test program was wrong. For large n, n*n in the naive
Chris@42: transform that we used for comparison overflows 32 bit integer
Chris@42: precision, breaking the test.
Chris@42:
Chris@42: \question 24aug:linuxthreads The threaded code fails on Linux Redhat 5.0
Chris@42:
Chris@42: We had problems with glibc-2.0.5. The code should work with
Chris@42: glibc-2.0.7.
Chris@42:
Chris@42: \question 26sep:bigrfftwnd FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dimension >= 65536.
Chris@42:
Chris@42: This bug was fixed in FFTW 2.0.1. (There was a 32-bit integer overflow due
Chris@42: to a poorly-parenthesized expression.)
Chris@42:
Chris@42: \question 26mar:primebug FFTW 2.0's complex transforms give the wrong results with prime factors 17 to 97.
Chris@42:
Chris@42: There was a bug in the complex transforms that could cause incorrect
Chris@42: results under (hopefully rare) circumstances for lengths with
Chris@42: intermediate-size prime factors (17-97). This bug was fixed in FFTW
Chris@42: 2.1.1.
Chris@42:
Chris@42: \question 05apr:mpichbug FFTW 2.1.1's MPI test programs crash with MPICH.
Chris@42:
Chris@42: This bug was fixed in FFTW 2.1.2. The 2.1/2.1.1 MPI test programs crashed
Chris@42: when using the MPICH implementation of MPI with the \courier{ch_p4\}
Chris@42: device (TCP/IP); the transforms themselves worked fine.
Chris@42:
Chris@42: \question 25may:aixthreadbug FFTW 2.1.2's multi-threaded transforms don't work on AIX.
Chris@42:
Chris@42: This bug was fixed in FFTW 2.1.3. The multi-threaded transforms in
Chris@42: previous versions didn't work with AIX's \courier{pthreads\}
Chris@42: implementation, which idiosyncratically creates threads in detached
Chris@42: (non-joinable) mode by default.
Chris@42:
Chris@42: \question 27sep:bigprimebug FFTW 2.1.2's complex transforms give incorrect results for large prime sizes.
Chris@42:
Chris@42: This bug was fixed in FFTW 2.1.3. FFTW's complex-transform algorithm
Chris@42: for prime sizes (in versions 2.0 to 2.1.2) had an integer overflow
Chris@42: problem that caused incorrect results for many primes greater than
Chris@42: 32768 (on 32-bit machines). (Sizes without large prime factors are
Chris@42: not affected.)
Chris@42:
Chris@42: \question 25may:solaristhreadbug FFTW 2.1.3's multi-threaded transforms don't give any speedup on Solaris.
Chris@42:
Chris@42: This bug was fixed in FFTW 2.1.4. (By default, Solaris creates
Chris@42: threads that do not parallelize over multiple processors, so one has
Chris@42: to request the proper behavior specifically.)
Chris@42:
Chris@42: \question 03may:aixflags FFTW 2.1.3 crashes on AIX.
Chris@42:
Chris@42: The FFTW 2.1.3 \courier{configure\} script picked incorrect compiler
Chris@42: flags for the \courier{xlc\} compiler on newer IBM processors. This
Chris@42: is fixed in FFTW 2.1.4.
Chris@42:
Chris@42: \comment Here it ends!
Chris@42: