cannam@127: \comment This is the source for the FFTW FAQ list, in cannam@127: \comment the Bizarre Format With No Name. It is turned into Lout cannam@127: \comment input, HTML, plain ASCII and an Info document by a Perl script. cannam@127: \comment cannam@127: \comment The format and scripts come from the Linux FAQ, by cannam@127: \comment Ian Jackson. cannam@127: \set brieftitle FFTW FAQ cannam@127: \set author Matteo Frigo and Steven G. Johnson / fftw@fftw.org cannam@127: \set authormail fftw@fftw.org cannam@127: \set title FFTW Frequently Asked Questions with Answers cannam@127: \set copyholder Matteo Frigo and Massachusetts Institute of Technology cannam@127: \call-html startup html.refs2 cannam@127: \copyto ASCII cannam@127: FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS cannam@127: `date '+%d %h %Y'` cannam@127: Matteo Frigo cannam@127: Steven G. Johnson cannam@127: cannam@127: cannam@127: \endcopy cannam@127: \copyto INFO cannam@127: INFO-DIR-SECTION Development cannam@127: START-INFO-DIR-ENTRY cannam@127: * FFTW FAQ: (fftw-faq). FFTW Frequently Asked Questions with Answers. cannam@127: END-INFO-DIR-ENTRY cannam@127: cannam@127:  cannam@127: File: $prefix.info, Node: Top, Next: Question 1.1, Up: (dir) cannam@127: cannam@127: FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS cannam@127: `date '+%d %h %Y'` cannam@127: Matteo Frigo cannam@127: Steven G. Johnson cannam@127: cannam@127: cannam@127: \endcopy cannam@127: cannam@127: This is the list of Frequently Asked Questions about FFTW, a cannam@127: collection of fast C routines for computing the Discrete Fourier cannam@127: Transform in one or more dimensions. cannam@127: cannam@127: \section Index cannam@127: cannam@127: \index cannam@127: cannam@127: \comment ###################################################################### cannam@127: cannam@127: \section Introduction and General Information cannam@127: cannam@127: \question 26aug:whatisfftw What is FFTW? cannam@127: cannam@127: FFTW is a free collection of fast C routines for computing the cannam@127: Discrete Fourier Transform in one or more dimensions. It includes cannam@127: complex, real, symmetric, and parallel transforms, and can handle cannam@127: arbitrary array sizes efficiently. FFTW is typically faster than cannam@127: other publically-available FFT implementations, and is even cannam@127: competitive with vendor-tuned libraries. (See our web page for cannam@127: extensive benchmarks.) To achieve this performance, FFTW uses novel cannam@127: code-generation and runtime self-optimization techniques (along with cannam@127: many other tricks). cannam@127: cannam@127: \question 26aug:whereisfftw How do I obtain FFTW? cannam@127: cannam@127: FFTW can be found at \docref{the FFTW web page\}. You can also cannam@127: retrieve it from \ftpon ftp.fftw.org in \ftpin /pub/fftw. cannam@127: cannam@127: \question 26aug:isfftwfree Is FFTW free software? cannam@127: cannam@127: Starting with version 1.3, FFTW is Free Software in the technical cannam@127: sense defined by the Free Software Foundation (see \docref{Categories cannam@127: of Free and Non-Free Software\}), and is distributed under the terms cannam@127: of the GNU General Public License. Previous versions of FFTW were cannam@127: distributed without fee for noncommercial use, but were not cannam@127: technically ``free.'' cannam@127: cannam@127: Non-free licenses for FFTW are also available that permit different cannam@127: terms of use than the GPL. cannam@127: cannam@127: \question 10apr:nonfree What is this about non-free licenses? cannam@127: cannam@127: The non-free licenses are for companies that wish to use FFTW in their cannam@127: products but are unwilling to release their software under the GPL cannam@127: (which would require them to release source code and allow free cannam@127: redistribution). Such users can purchase an unlimited-use license cannam@127: from MIT. Contact us for more details. cannam@127: cannam@127: We could instead have released FFTW under the LGPL, or even disallowed cannam@127: non-Free usage. Suffice it to say, however, that MIT owns the cannam@127: copyright to FFTW and they only let us GPL it because we convinced cannam@127: them that it would neither affect their licensing revenue nor irritate cannam@127: existing licensees. cannam@127: cannam@127: \question 24oct:west In the West? I thought MIT was in the East? cannam@127: cannam@127: Not to an Italian. You could say that we're a Spaghetti Western cannam@127: (with apologies to Sergio Leone). cannam@127: cannam@127: \comment ###################################################################### cannam@127: cannam@127: \section Installing FFTW cannam@127: cannam@127: \question 26aug:systems Which systems does FFTW run on? cannam@127: cannam@127: FFTW is written in ANSI C, and should work on any system with a decent cannam@127: C compiler. (See also \qref runOnWindows, \qref compilerCrashes.) cannam@127: FFTW can also take advantage of certain hardware-specific features, cannam@127: such as cycle counters and SIMD instructions, but this is optional. cannam@127: cannam@127: \question 26aug:runOnWindows Does FFTW run on Windows? cannam@127: cannam@127: Yes, many people have reported successfully using FFTW on Windows with cannam@127: various compilers. FFTW was not developed on Windows, but the source cannam@127: code is essentially straight ANSI C. See also the \docref{FFTW cannam@127: Windows installation notes\}, \qref compilerCrashes, and \qref cannam@127: vbetalia. cannam@127: cannam@127: \question 26aug:compilerCrashes My compiler has trouble with FFTW. cannam@127: cannam@127: Complain fiercely to the vendor of the compiler. cannam@127: cannam@127: We have successfully used \courier{gcc\} 3.2.x on x86 and PPC, a cannam@127: recent Compaq C compiler for Alpha, version 6 of IBM's \courier{xlc\} cannam@127: compiler for AIX, Intel's \courier{icc\} versions 5-7, and Sun cannam@127: WorkShop \courier{cc\} version 6. cannam@127: cannam@127: FFTW is likely to push compilers to their limits, however, and several cannam@127: compiler bugs have been exposed by FFTW. A partial list follows. cannam@127: cannam@127: \courier{gcc\} 2.95.x for Solaris/SPARC produces incorrect code for cannam@127: the test program (workaround: recompile the \courier{libbench2\} cannam@127: directory with \courier{-O2\}). cannam@127: cannam@127: NetBSD/macppc 1.6 comes with a \courier{gcc\} version that also cannam@127: miscompiles the test program. (Please report a workaround if you know cannam@127: one.) cannam@127: cannam@127: \courier{gcc\} 3.2.3 for ARM reportedly crashes during compilation. cannam@127: This bug is reportedly fixed in later versions of \courier{gcc\}. cannam@127: cannam@127: Versions 8.0 and 8.1 of Intel's \courier{icc\} falsely claim to be cannam@127: \courier{gcc\}, so you should specify \courier{CC="icc -no-gcc"\}; cannam@127: this is automatic in FFTW 3.1. \courier{icc-8.0.066\} reportely cannam@127: produces incorrect code for FFTW 2.1.5, but is fixed in version 8.1. cannam@127: \courier{icc-7.1\} compiler build 20030402Z appears to produce cannam@127: incorrect dependencies, causing the compilation to fail. cannam@127: \courier{icc-7.1\} build 20030307Z appears to work fine. (Use cannam@127: \courier{icc -V\} to check which build you have.) As of 2003/04/18, cannam@127: build 20030402Z appears not to be available any longer on Intel's cannam@127: website, whereas the older build 20030307Z is available. cannam@127: cannam@127: \courier{ranlib\} of GNU \courier{binutils\} 2.9.1 on Irix has been cannam@127: observed to corrupt the FFTW libraries, causing a link failure when cannam@127: FFTW is compiled. Since \courier{ranlib\} is completely superfluous cannam@127: on Irix, we suggest deleting it from your system and replacing it with cannam@127: a symbolic link to \courier{/bin/echo\}. cannam@127: cannam@127: If support for SIMD instructions is enabled in FFTW, further compiler cannam@127: problems may appear: cannam@127: cannam@127: \courier{gcc\} 3.4.[0123] for x86 produces incorrect SSE2 code for cannam@127: FFTW when \courier{-O2\} (the best choice for FFTW) is used, causing cannam@127: FFTW to crash (\courier{make check\} crashes). This bug is fixed in cannam@127: \courier{gcc\} 3.4.4. On x86_64 (amd64/em64t), \courier{gcc\} 3.4.4 cannam@127: reportedly still has a similar problem, but this is fixed as of cannam@127: \courier{gcc\} 3.4.6. cannam@127: cannam@127: \courier{gcc-3.2\} for x86 produces incorrect SIMD code if cannam@127: \courier{-O3\} is used. The same compiler produces incorrect SIMD cannam@127: code if no optimization is used, too. When using \courier{gcc-3.2\}, cannam@127: it is a good idea not to change the default \courier{CFLAGS\} selected cannam@127: by the \courier{configure\} script. cannam@127: cannam@127: Some 3.0.x and 3.1.x versions of \courier{gcc\} on \courier{x86\} may cannam@127: crash. \courier{gcc\} so-called 2.96 shipping with RedHat 7.3 crashes cannam@127: when compiling SIMD code. In both cases, please upgrade to cannam@127: \courier{gcc-3.2\} or later. cannam@127: cannam@127: Intel's \courier{icc\} 6.0 misaligns SSE constants, but FFTW has a cannam@127: workaround. \courier{icc\} 8.x fails to compile FFTW 3.0.x because it cannam@127: falsely claims to be \courier{gcc\}; we believe this to be a bug in cannam@127: \courier{icc\}, but FFTW 3.1 has a workaround. cannam@127: cannam@127: Visual C++ 2003 reportedly produces incorrect code for SSE/SSE2 when cannam@127: compiling FFTW. This bug was reportedly fixed in VC++ 2005; cannam@127: alternatively, you could switch to the Intel compiler. VC++ 6.0 also cannam@127: reportedly produces incorrect code for the file cannam@127: \courier{reodft11e-r2hc-odd.c\} unless optimizations are disabled for cannam@127: that file. cannam@127: cannam@127: \courier{gcc\} 2.95 on MacOS X miscompiles AltiVec code (fixed in cannam@127: later versions). \courier{gcc\} 3.2.x miscompiles AltiVec cannam@127: permutations, but FFTW has a workaround. \courier{gcc\} 4.0.1 on cannam@127: MacOS for Intel crashes when compiling FFTW; a workaround is to cannam@127: compile one file without optimization: \courier{cd kernel; make cannam@127: CFLAGS=" " trig.lo\}. cannam@127: cannam@127: \courier{gcc\} 4.1.1 reportedly crashes when compiling FFTW for MIPS; cannam@127: the workaround is to compile the file it crashes on cannam@127: (\courier{t2_64.c\}) with a lower optimization level. cannam@127: cannam@127: \courier{gcc\} versions 4.1.2 to 4.2.0 for x86 reportedly miscompile cannam@127: FFTW 3.1's test program, causing \courier{make check\} to crash cannam@127: (\courier{gcc\} bug #26528). The bug was reportedly fixed in cannam@127: \courier{gcc\} version 4.2.1 and later. A workaround is to compile cannam@127: \courier{libbench2/verify-lib.c\} without optimization. cannam@127: cannam@127: \question 26aug:solarisSucks FFTW does not compile on Solaris, complaining about \courier{const\}. cannam@127: cannam@127: We know that at least on Solaris 2.5.x with Sun's compilers 4.2 you cannam@127: might get error messages from \courier{make\} such as cannam@127: cannam@127: \courier{"./fftw.h", line 88: warning: const is a keyword in ANSI C\} cannam@127: cannam@127: This is the case when the \courier{configure\} script reports that cannam@127: \courier{const\} does not work: cannam@127: cannam@127: \courier{checking for working const... (cached) no\} cannam@127: cannam@127: You should be aware that Solaris comes with two compilers, namely, cannam@127: \courier{/opt/SUNWspro/SC4.2/bin/cc\} and \courier{/usr/ucb/cc\}. The cannam@127: latter compiler is non-ANSI. Indeed, it is a perverse shell script cannam@127: that calls the real compiler in non-ANSI mode. In order cannam@127: to compile FFTW, change your path so that the right \courier{cc\} cannam@127: is used. cannam@127: cannam@127: To know whether your compiler is the right one, type cannam@127: \courier{cc -V\}. If the compiler prints ``\courier{ucbcc\}'', cannam@127: as in cannam@127: cannam@127: \courier{ucbcc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2\} cannam@127: cannam@127: then the compiler is wrong. The right message is something like cannam@127: cannam@127: \courier{cc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2\} cannam@127: cannam@127: \question 19mar:3dnow What's the difference between \courier{--enable-3dnow\} and \courier{--enable-k7\}? cannam@127: cannam@127: \courier{--enable-k7\} enables 3DNow! instructions on K7 processors cannam@127: (AMD Athlon and its variants). K7 support is provided by assembly cannam@127: routines generated by a special purpose compiler. cannam@127: As of fftw-3.2, --enable-k7 is no longer supported. cannam@127: cannam@127: \courier{--enable-3dnow\} enables generic 3DNow! support using cannam@127: \courier{gcc\} builtin functions. This works on earlier AMD cannam@127: processors, but it is not as fast as our special assembly routines. cannam@127: As of fftw-3.1, --enable-3dnow is no longer supported. cannam@127: cannam@127: \question 18apr:fma What's the difference between the fma and the non-fma versions? cannam@127: cannam@127: The fma version tries to exploit the fused multiply-add instructions cannam@127: implemented in many processors such as PowerPC, ia-64, and MIPS. The cannam@127: two FFTW packages are otherwise identical. In FFTW 3.1, the fma and cannam@127: non-fma versions were merged together into a single package, and the cannam@127: \courier{configure\} script attempts to automatically guess which cannam@127: version to use. cannam@127: cannam@127: The FFTW 3.1 \courier{configure\} script enables fma by default on cannam@127: PowerPC, Itanium, and PA-RISC, and disables it otherwise. You can cannam@127: force one or the other by using the \courier{--enable-fma\} or cannam@127: \courier{--disable-fma\} flag for \courier{configure\}. cannam@127: cannam@127: Definitely use fma if you have a PowerPC-based system with cannam@127: \courier{gcc\} (or IBM \courier{xlc\}). This includes all GNU/Linux cannam@127: systems for PowerPC and the older PowerPC-based MacOS systems. Also cannam@127: use it on PA-RISC and Itanium with the HP/UX compiler. cannam@127: cannam@127: Definitely do not use the fma version if you have an ia-32 processor cannam@127: (Intel, AMD, MacOS on Intel, etcetera). cannam@127: cannam@127: For other architectures/compilers, the situation is not so clear. For cannam@127: example, ia-64 has the fma instruction, but \courier{gcc-3.2\} appears cannam@127: not to exploit it correctly. Other compilers may do the right thing, cannam@127: but we have not tried them. Please send us your feedback so that we cannam@127: can update this FAQ entry. cannam@127: cannam@127: \question 26aug:languages Which language is FFTW written in? cannam@127: cannam@127: FFTW is written in ANSI C. Most of the code, however, was cannam@127: automatically generated by a program called \courier{genfft\}, written cannam@127: in the Objective Caml dialect of ML. You do not need to know ML or to cannam@127: have an Objective Caml compiler in order to use FFTW. cannam@127: cannam@127: \courier{genfft\} is provided with the FFTW sources, which means that cannam@127: you can play with the code generator if you want. In this case, you cannam@127: need a working Objective Caml system. Objective Caml is available cannam@127: from \docref{the Caml web page\}. cannam@127: cannam@127: \question 26aug:fortran Can I call FFTW from Fortran? cannam@127: cannam@127: Yes, FFTW (versions 1.3 and higher) contains a Fortran-callable cannam@127: interface, documented in the FFTW manual. cannam@127: cannam@127: By default, FFTW configures its Fortran interface to work with the cannam@127: first compiler it finds, e.g. \courier{g77\}. To configure for a cannam@127: different, incompatible Fortran compiler \courier{foobar\}, use cannam@127: \courier{./configure F77=foobar\} when installing FFTW. (In the case cannam@127: of \courier{g77\}, however, FFTW 3.x also includes an extra set of cannam@127: Fortran-callable routines with one less underscore at the end of cannam@127: identifiers, which should cover most other Fortran compilers on Linux cannam@127: at least.) cannam@127: cannam@127: \question 26aug:cplusplus Can I call FFTW from C++? cannam@127: cannam@127: Most definitely. FFTW should compile and/or link under any C++ cannam@127: compiler. Moreover, it is likely that the C++ \courier{\} cannam@127: template class is bit-compatible with FFTW's complex-number format cannam@127: (see the FFTW manual for more details). cannam@127: cannam@127: \question 26aug:whynotfortran Why isn't FFTW written in Fortran/C++? cannam@127: cannam@127: Because we don't like those languages, and neither approaches the cannam@127: portability of C. cannam@127: cannam@127: \question 29mar:singleprec How do I compile FFTW to run in single precision? cannam@127: cannam@127: On a Unix system: \courier{configure --enable-float\}. On a non-Unix cannam@127: system: edit \courier{config.h\} to \courier{#define\} the symbol cannam@127: \courier{FFTW_SINGLE\} (for FFTW 3.x). In both cases, you must then cannam@127: recompile FFTW. In FFTW 3, all FFTW identifiers will then begin with cannam@127: \courier{fftwf_\} instead of \courier{fftw_\}. cannam@127: cannam@127: \question 28mar:64bitk7 --enable-k7 does not work on x86-64 cannam@127: cannam@127: Support for --enable-k7 was discontinued in fftw-3.2. cannam@127: cannam@127: The fftw-3.1 release supports --enable-k7. This option only works on cannam@127: 32-bit x86 machines that implement 3DNow!, including the AMD Athlon cannam@127: and the AMD Opteron in 32-bit mode. --enable-k7 does not work on AMD cannam@127: Opteron in 64-bit mode. Use --enable-sse for x86-64 machines. cannam@127: cannam@127: FFTW supports 3DNow! by means of assembly code generated by a cannam@127: special-purpose compiler. It is hard to produce assembly code that cannam@127: works in both 32-bit and 64-bit mode. cannam@127: cannam@127: \comment ###################################################################### cannam@127: cannam@127: \section Using FFTW cannam@127: cannam@127: \question 15mar:fftw2to3 Why not support the FFTW 2 interface in FFTW 3? cannam@127: cannam@127: FFTW 3 has semantics incompatible with earlier versions: its plans can cannam@127: only be used for a given stride, multiplicity, and other cannam@127: characteristics of the input and output arrays; these stronger cannam@127: semantics are necessary for performance reasons. Thus, it is cannam@127: impossible to efficiently emulate the older interface (whose plans can cannam@127: be used for any transform of the same size). We believe that it cannam@127: should be possible to upgrade most programs without any difficulty, cannam@127: however. cannam@127: cannam@127: \question 20mar:planperarray Why do FFTW 3 plans encapsulate the input/output arrays and not just the algorithm? cannam@127: cannam@127: There are several reasons: cannam@127: cannam@127: \call startlist cannam@127: \call item cannam@127: It was important for performance reasons that the plan be specific to cannam@127: array characteristics like the stride (and alignment, for SIMD), and cannam@127: requiring that the user maintain these invariants is error prone. cannam@127: \call item cannam@127: In most high-performance applications, as far as we can tell, you are cannam@127: usually transforming the same array over and over, so FFTW's semantics cannam@127: should not be a burden. cannam@127: \call item cannam@127: If you need to transform another array of the same size, creating a cannam@127: new plan once the first exists is a cheap operation. cannam@127: \call item cannam@127: If you need to transform many arrays of the same size at once, you cannam@127: should really use the \courier{plan_many\} routines in FFTW's "advanced" cannam@127: interface. cannam@127: \call item cannam@127: If the abovementioned array characteristics are the same, you are cannam@127: willing to pay close attention to the documentation, and you really cannam@127: need to, we provide a "new-array execution" interface to apply a plan cannam@127: to a new array. cannam@127: \call endlist cannam@127: cannam@127: \question 25may:slow FFTW seems really slow. cannam@127: cannam@127: You are probably recreating the plan before every transform, rather cannam@127: than creating it once and reusing it for all transforms of the same cannam@127: size. FFTW is designed to be used in the following way: cannam@127: cannam@127: \call startlist cannam@127: \call item cannam@127: First, you create a plan. This will take several seconds. cannam@127: \call item cannam@127: Then, you reuse the plan many times to perform FFTs. These are fast. cannam@127: \call endlist cannam@127: cannam@127: If you don't need to compute many transforms and the time for the cannam@127: planner is significant, you have two options. First, you can use the cannam@127: \courier{FFTW_ESTIMATE\} option in the planner, which uses heuristics cannam@127: instead of runtime measurements and produces a good plan in a short cannam@127: time. Second, you can use the wisdom feature to precompute the plan; cannam@127: see \qref savePlans cannam@127: cannam@127: \question 22oct:slows FFTW slows down after repeated calls. cannam@127: cannam@127: Probably, NaNs or similar are creeping into your data, and the cannam@127: slowdown is due to the resulting floating-point exceptions. For cannam@127: example, be aware that repeatedly FFTing the same array is a diverging cannam@127: process (because FFTW computes the unnormalized transform). cannam@127: cannam@127: \question 22oct:segfault An FFTW routine is crashing when I call it. cannam@127: cannam@127: Did the FFTW test programs pass (\courier{make check\}, or \courier{cd cannam@127: tests; make bigcheck\} if you want to be paranoid)? If so, you almost cannam@127: certainly have a bug in your own code. For example, you could be cannam@127: passing invalid arguments (such as wrongly-sized arrays) to FFTW, or cannam@127: you could simply have memory corruption elsewhere in your program that cannam@127: causes random crashes later on. Please don't complain to us unless cannam@127: you can come up with a minimal self-contained program (preferably cannam@127: under 30 lines) that illustrates the problem. cannam@127: cannam@127: \question 22oct:fortran64 My Fortran program crashes when calling FFTW. cannam@127: cannam@127: As described in the manual, on 64-bit machines you must store the cannam@127: plans in variables large enough to hold a pointer, for example cannam@127: \courier{integer*8\}. We recommend using \courier{integer*8\} on cannam@127: 32-bit machines as well, to simplify porting. cannam@127: cannam@127: \question 24mar:conventions FFTW gives results different from my old FFT. cannam@127: cannam@127: People follow many different conventions for the DFT, and you should cannam@127: be sure to know the ones that we use (described in the FFTW manual). cannam@127: In particular, you should be aware that the cannam@127: \courier{FFTW_FORWARD\}/\courier{FFTW_BACKWARD\} directions correspond cannam@127: to signs of -1/+1 in the exponent of the DFT definition. cannam@127: (\italic{Numerical Recipes\} uses the opposite convention.) cannam@127: cannam@127: You should also know that we compute an unnormalized transform. In cannam@127: contrast, Matlab is an example of program that computes a normalized cannam@127: transform. See \qref whyscaled. cannam@127: cannam@127: Finally, note that floating-point arithmetic is not exact, so cannam@127: different FFT algorithms will give slightly different results (on the cannam@127: order of the numerical accuracy; typically a fractional difference of cannam@127: 1e-15 or so in double precision). cannam@127: cannam@127: \question 31aug:nondeterministic FFTW gives different results between runs cannam@127: cannam@127: If you use \courier{FFTW_MEASURE\} or \courier{FFTW_PATIENT\} mode, cannam@127: then the algorithm FFTW employs is not deterministic: it depends on cannam@127: runtime performance measurements. This will cause the results to vary cannam@127: slightly from run to run. However, the differences should be slight, cannam@127: on the order of the floating-point precision, and therefore should cannam@127: have no practical impact on most applications. cannam@127: cannam@127: If you use saved plans (wisdom) or \courier{FFTW_ESTIMATE\} mode, cannam@127: however, then the algorithm is deterministic and the results should be cannam@127: identical between runs. cannam@127: cannam@127: \question 26aug:savePlans Can I save FFTW's plans? cannam@127: cannam@127: Yes. Starting with version 1.2, FFTW provides the \courier{wisdom\} cannam@127: mechanism for saving plans; see the FFTW manual. cannam@127: cannam@127: \question 14sep:whyscaled Why does your inverse transform return a scaled result? cannam@127: cannam@127: Computing the forward transform followed by the backward transform (or cannam@127: vice versa) yields the original array scaled by the size of the array. cannam@127: (For multi-dimensional transforms, the size of the array is the cannam@127: product of the dimensions.) We could, instead, have chosen a cannam@127: normalization that would have returned the unscaled array. Or, to cannam@127: accomodate the many conventions in this matter, the transform routines cannam@127: could have accepted a "scale factor" parameter. We did not do this, cannam@127: however, for two reasons. First, we didn't want to sacrifice cannam@127: performance in the common case where the scale factor is 1. Second, in cannam@127: real applications the FFT is followed or preceded by some computation cannam@127: on the data, into which the scale factor can typically be absorbed at cannam@127: little or no cost. cannam@127: cannam@127: \question 02dec:centerorigin How can I make FFTW put the origin (zero frequency) at the center of its output? cannam@127: cannam@127: For human viewing of a spectrum, it is often convenient to put the cannam@127: origin in frequency space at the center of the output array, rather cannam@127: than in the zero-th element (the default in FFTW). If all of the cannam@127: dimensions of your array are even, you can accomplish this by simply cannam@127: multiplying each element of the input array by (-1)^(i + j + ...), cannam@127: where i, j, etcetera are the indices of the element. (This trick is a cannam@127: general property of the DFT, and is not specific to FFTW.) cannam@127: cannam@127: \question 08may:imageaudio How do I FFT an image/audio file in \italic{foobar\} format? cannam@127: cannam@127: FFTW performs an FFT on an array of floating-point values. You can cannam@127: certainly use it to compute the transform of an image or audio stream, cannam@127: but you are responsible for figuring out your data format and cannam@127: converting it to the form FFTW requires. cannam@127: cannam@127: \question 09apr:linkfails My program does not link (on Unix). cannam@127: cannam@127: The libraries must be listed in the correct order (\courier{-lfftw3 cannam@127: -lm\} for FFTW 3.x) and \italic{after\} your program sources/objects. cannam@127: (The general rule is that if \italic{A\} uses \italic{B\}, then cannam@127: \italic{A\} must be listed before \italic{B\} in the link command.). cannam@127: cannam@127: \question 15mar:linkheader I included your header, but linking still fails. cannam@127: cannam@127: You're a C++ programmer, aren't you? You have to compile the FFTW cannam@127: library and link it into your program, not just \courier{#include cannam@127: \}. (Yes, this is really a FAQ.) cannam@127: cannam@127: \question 22oct:nostack My program crashes, complaining about stack space. cannam@127: cannam@127: You cannot declare large arrays with automatic storage (e.g. via cannam@127: \courier{fftw_complex array[N]\}); you should use cannam@127: \courier{fftw_malloc\} (or equivalent) to allocate the arrays you want cannam@127: to transform if they are larger than a few hundred elements. cannam@127: cannam@127: \question 13may:leaks FFTW seems to have a memory leak. cannam@127: cannam@127: After you create a plan, FFTW caches the information required to cannam@127: quickly recreate the plan. (See \qref savePlans) It also maintains a cannam@127: small amount of other persistent memory. You can deallocate all of cannam@127: FFTW's internally allocated memory, if you wish, by calling cannam@127: \courier{fftw_cleanup()\}, as documented in the manual. cannam@127: cannam@127: \question 16may:allzero The output of FFTW's transform is all zeros. cannam@127: cannam@127: You should initialize your input array \italic{after\} creating the cannam@127: plan, unless you use \courier{FFTW_ESTIMATE\}: planning with cannam@127: \courier{FFTW_MEASURE\} or \courier{FFTW_PATIENT\} overwrites the cannam@127: input/output arrays, as described in the manual. cannam@127: cannam@127: \question 05sep:vbetalia How do I call FFTW from the Microsoft language du jour? cannam@127: cannam@127: Please \italic{do not\} ask us Windows-specific questions. We do not cannam@127: use Windows. We know nothing about Visual Basic, Visual C++, or .NET. cannam@127: Please find the appropriate Usenet discussion group and ask your cannam@127: question there. See also \qref runOnWindows. cannam@127: cannam@127: \question 15oct:pruned Can I compute only a subset of the DFT outputs? cannam@127: cannam@127: In general, no, an FFT intrinsically computes all outputs from all cannam@127: inputs. In principle, there is something called a \italic{pruned cannam@127: FFT\} that can do what you want, but to compute K outputs out of N the cannam@127: complexity is in general O(N log K) instead of O(N log N), thus saving cannam@127: only a small additive factor in the log. (The same argument holds if cannam@127: you instead have only K nonzero inputs.) cannam@127: cannam@127: There are some specific cases in which you can get the O(N log K) cannam@127: performance benefits easily, however, by combining a few ordinary cannam@127: FFTs. In particular, the case where you want the first K outputs, cannam@127: where K divides N, can be handled by performing N/K transforms of size cannam@127: K and then summing the outputs multiplied by appropriate phase cannam@127: factors. For more details, see \docref{pruned FFTs with FFTW\}. cannam@127: cannam@127: There are also some algorithms that compute pruned transforms cannam@127: \italic{approximately\}, but they are beyond the scope of this FAQ. cannam@127: cannam@127: \question 21jan:transpose Can I use FFTW's routines for in-place and out-of-place matrix transposition? cannam@127: cannam@127: You can use the FFTW guru interface to create a rank-0 transform of cannam@127: vector rank 2 where the vector strides are transposed. (A rank-0 cannam@127: transform is equivalent to a 1D transform of size 1, which. just cannam@127: copies the input into the output.) Specifying the same location for cannam@127: the input and output makes the transpose in-place. cannam@127: cannam@127: For double-valued data stored in row-major format, plan creation looks like cannam@127: this: cannam@127: cannam@127: \verbatim cannam@127: fftw_plan plan_transpose(int rows, int cols, double *in, double *out) cannam@127: { cannam@127: const unsigned flags = FFTW_ESTIMATE; /* other flags are possible */ cannam@127: fftw_iodim howmany_dims[2]; cannam@127: cannam@127: howmany_dims[0].n = rows; cannam@127: howmany_dims[0].is = cols; cannam@127: howmany_dims[0].os = 1; cannam@127: cannam@127: howmany_dims[1].n = cols; cannam@127: howmany_dims[1].is = 1; cannam@127: howmany_dims[1].os = rows; cannam@127: cannam@127: return fftw_plan_guru_r2r(/*rank=*/ 0, /*dims=*/ NULL, cannam@127: /*howmany_rank=*/ 2, howmany_dims, cannam@127: in, out, /*kind=*/ NULL, flags); cannam@127: } cannam@127: \endverbatim cannam@127: cannam@127: (This entry was written by Rhys Ulerich.) cannam@127: cannam@127: \comment ###################################################################### cannam@127: cannam@127: \section Internals of FFTW cannam@127: cannam@127: \question 26aug:howworks How does FFTW work? cannam@127: cannam@127: The innovation (if it can be so called) in FFTW consists in having a cannam@127: variety of composable \italic{solvers\}, representing different FFT cannam@127: algorithms and implementation strategies, whose combination into a cannam@127: particular \italic{plan\} for a given size can be determined at cannam@127: runtime according to the characteristics of your machine/compiler. cannam@127: This peculiar software architecture allows FFTW to adapt itself to cannam@127: almost any machine. cannam@127: cannam@127: For more details (albeit somewhat outdated), see the paper "FFTW: An cannam@127: Adaptive Software Architecture for the FFT", by M. Frigo and cannam@127: S. G. Johnson, \italic{Proc. ICASSP\} 3, 1381 (1998), also cannam@127: available at \docref{the FFTW web page\}. cannam@127: cannam@127: \question 26aug:whyfast Why is FFTW so fast? cannam@127: cannam@127: This is a complex question, and there is no simple answer. In fact, cannam@127: the authors do not fully know the answer, either. In addition to many cannam@127: small performance hacks throughout FFTW, there are three general cannam@127: reasons for FFTW's speed. cannam@127: cannam@127: \call startlist cannam@127: \call item cannam@127: FFTW uses a variety of FFT algorithms and implementation styles cannam@127: that can be arbitrarily composed to adapt itself to cannam@127: a machine. See \qref howworks. cannam@127: \call item cannam@127: FFTW uses a code generator to produce highly-optimized cannam@127: routines for computing small transforms. cannam@127: \call item cannam@127: FFTW uses explicit divide-and-conquer to take advantage cannam@127: of the memory hierarchy. cannam@127: \call endlist cannam@127: cannam@127: For more details (albeit somewhat outdated), see the paper "FFTW: An cannam@127: Adaptive Software Architecture for the FFT", by M. Frigo and cannam@127: S. G. Johnson, \italic{Proc. ICASSP\} 3, 1381 (1998), cannam@127: available along with other references at \docref{the FFTW web page\}. cannam@127: cannam@127: \comment ###################################################################### cannam@127: cannam@127: \section Known bugs cannam@127: cannam@127: \question 27aug:rfftwndbug FFTW 1.1 crashes in rfftwnd on Linux. cannam@127: cannam@127: This bug was fixed in FFTW 1.2. There was a bug in \courier{rfftwnd\} cannam@127: causing an incorrect amount of memory to be allocated. The bug showed cannam@127: up in Linux with libc-5.3.12 (and nowhere else that we know of). cannam@127: cannam@127: \question 15oct:fftwmpibug The MPI transforms in FFTW 1.2 give incorrect results/leak memory. cannam@127: cannam@127: These bugs were corrected in FFTW 1.2.1. The MPI transforms (really, cannam@127: just the transpose routines) in FFTW 1.2 had bugs that could cause cannam@127: errors in some situations. cannam@127: cannam@127: \question 05nov:testsingbug The test programs in FFTW 1.2.1 fail when I change FFTW to use single precision. cannam@127: cannam@127: This bug was fixed in FFTW 1.3. (Older versions of FFTW did cannam@127: work in single precision, but the test programs didn't--the error cannam@127: tolerances in the tests were set for double precision.) cannam@127: cannam@127: \question 24mar:teststoobig The test program in FFTW 1.2.1 fails for n > 46340. cannam@127: cannam@127: This bug was fixed in FFTW 1.3. FFTW 1.2.1 produced the right answer, cannam@127: but the test program was wrong. For large n, n*n in the naive cannam@127: transform that we used for comparison overflows 32 bit integer cannam@127: precision, breaking the test. cannam@127: cannam@127: \question 24aug:linuxthreads The threaded code fails on Linux Redhat 5.0 cannam@127: cannam@127: We had problems with glibc-2.0.5. The code should work with cannam@127: glibc-2.0.7. cannam@127: cannam@127: \question 26sep:bigrfftwnd FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dimension >= 65536. cannam@127: cannam@127: This bug was fixed in FFTW 2.0.1. (There was a 32-bit integer overflow due cannam@127: to a poorly-parenthesized expression.) cannam@127: cannam@127: \question 26mar:primebug FFTW 2.0's complex transforms give the wrong results with prime factors 17 to 97. cannam@127: cannam@127: There was a bug in the complex transforms that could cause incorrect cannam@127: results under (hopefully rare) circumstances for lengths with cannam@127: intermediate-size prime factors (17-97). This bug was fixed in FFTW cannam@127: 2.1.1. cannam@127: cannam@127: \question 05apr:mpichbug FFTW 2.1.1's MPI test programs crash with MPICH. cannam@127: cannam@127: This bug was fixed in FFTW 2.1.2. The 2.1/2.1.1 MPI test programs crashed cannam@127: when using the MPICH implementation of MPI with the \courier{ch_p4\} cannam@127: device (TCP/IP); the transforms themselves worked fine. cannam@127: cannam@127: \question 25may:aixthreadbug FFTW 2.1.2's multi-threaded transforms don't work on AIX. cannam@127: cannam@127: This bug was fixed in FFTW 2.1.3. The multi-threaded transforms in cannam@127: previous versions didn't work with AIX's \courier{pthreads\} cannam@127: implementation, which idiosyncratically creates threads in detached cannam@127: (non-joinable) mode by default. cannam@127: cannam@127: \question 27sep:bigprimebug FFTW 2.1.2's complex transforms give incorrect results for large prime sizes. cannam@127: cannam@127: This bug was fixed in FFTW 2.1.3. FFTW's complex-transform algorithm cannam@127: for prime sizes (in versions 2.0 to 2.1.2) had an integer overflow cannam@127: problem that caused incorrect results for many primes greater than cannam@127: 32768 (on 32-bit machines). (Sizes without large prime factors are cannam@127: not affected.) cannam@127: cannam@127: \question 25may:solaristhreadbug FFTW 2.1.3's multi-threaded transforms don't give any speedup on Solaris. cannam@127: cannam@127: This bug was fixed in FFTW 2.1.4. (By default, Solaris creates cannam@127: threads that do not parallelize over multiple processors, so one has cannam@127: to request the proper behavior specifically.) cannam@127: cannam@127: \question 03may:aixflags FFTW 2.1.3 crashes on AIX. cannam@127: cannam@127: The FFTW 2.1.3 \courier{configure\} script picked incorrect compiler cannam@127: flags for the \courier{xlc\} compiler on newer IBM processors. This cannam@127: is fixed in FFTW 2.1.4. cannam@127: cannam@127: \comment Here it ends! cannam@127: