Chris@42: FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS Chris@42: 30 Jul 2016 Chris@42: Matteo Frigo Chris@42: Steven G. Johnson Chris@42: Chris@42: Chris@42: This is the list of Frequently Asked Questions about FFTW, a collection of Chris@42: fast C routines for computing the Discrete Fourier Transform in one or Chris@42: more dimensions. Chris@42: Chris@42: =============================================================================== Chris@42: Chris@42: Index Chris@42: Chris@42: Section 1. Introduction and General Information Chris@42: Q1.1 What is FFTW? Chris@42: Q1.2 How do I obtain FFTW? Chris@42: Q1.3 Is FFTW free software? Chris@42: Q1.4 What is this about non-free licenses? Chris@42: Q1.5 In the West? I thought MIT was in the East? Chris@42: Chris@42: Section 2. Installing FFTW Chris@42: Q2.1 Which systems does FFTW run on? Chris@42: Q2.2 Does FFTW run on Windows? Chris@42: Q2.3 My compiler has trouble with FFTW. Chris@42: Q2.4 FFTW does not compile on Solaris, complaining about const. Chris@42: Q2.5 What's the difference between --enable-3dnow and --enable-k7? Chris@42: Q2.6 What's the difference between the fma and the non-fma versions? Chris@42: Q2.7 Which language is FFTW written in? Chris@42: Q2.8 Can I call FFTW from Fortran? Chris@42: Q2.9 Can I call FFTW from C++? Chris@42: Q2.10 Why isn't FFTW written in Fortran/C++? Chris@42: Q2.11 How do I compile FFTW to run in single precision? Chris@42: Q2.12 --enable-k7 does not work on x86-64 Chris@42: Chris@42: Section 3. Using FFTW Chris@42: Q3.1 Why not support the FFTW 2 interface in FFTW 3? Chris@42: Q3.2 Why do FFTW 3 plans encapsulate the input/output arrays and not ju Chris@42: Q3.3 FFTW seems really slow. Chris@42: Q3.4 FFTW slows down after repeated calls. Chris@42: Q3.5 An FFTW routine is crashing when I call it. Chris@42: Q3.6 My Fortran program crashes when calling FFTW. Chris@42: Q3.7 FFTW gives results different from my old FFT. Chris@42: Q3.8 FFTW gives different results between runs Chris@42: Q3.9 Can I save FFTW's plans? Chris@42: Q3.10 Why does your inverse transform return a scaled result? Chris@42: Q3.11 How can I make FFTW put the origin (zero frequency) at the center Chris@42: Q3.12 How do I FFT an image/audio file in *foobar* format? Chris@42: Q3.13 My program does not link (on Unix). Chris@42: Q3.14 I included your header, but linking still fails. Chris@42: Q3.15 My program crashes, complaining about stack space. Chris@42: Q3.16 FFTW seems to have a memory leak. Chris@42: Q3.17 The output of FFTW's transform is all zeros. Chris@42: Q3.18 How do I call FFTW from the Microsoft language du jour? Chris@42: Q3.19 Can I compute only a subset of the DFT outputs? Chris@42: Q3.20 Can I use FFTW's routines for in-place and out-of-place matrix tra Chris@42: Chris@42: Section 4. Internals of FFTW Chris@42: Q4.1 How does FFTW work? Chris@42: Q4.2 Why is FFTW so fast? Chris@42: Chris@42: Section 5. Known bugs Chris@42: Q5.1 FFTW 1.1 crashes in rfftwnd on Linux. Chris@42: Q5.2 The MPI transforms in FFTW 1.2 give incorrect results/leak memory. Chris@42: Q5.3 The test programs in FFTW 1.2.1 fail when I change FFTW to use sin Chris@42: Q5.4 The test program in FFTW 1.2.1 fails for n > 46340. Chris@42: Q5.5 The threaded code fails on Linux Redhat 5.0 Chris@42: Q5.6 FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dime Chris@42: Q5.7 FFTW 2.0's complex transforms give the wrong results with prime fa Chris@42: Q5.8 FFTW 2.1.1's MPI test programs crash with MPICH. Chris@42: Q5.9 FFTW 2.1.2's multi-threaded transforms don't work on AIX. Chris@42: Q5.10 FFTW 2.1.2's complex transforms give incorrect results for large p Chris@42: Q5.11 FFTW 2.1.3's multi-threaded transforms don't give any speedup on S Chris@42: Q5.12 FFTW 2.1.3 crashes on AIX. Chris@42: Chris@42: =============================================================================== Chris@42: Chris@42: Section 1. Introduction and General Information Chris@42: Chris@42: Q1.1 What is FFTW? Chris@42: Q1.2 How do I obtain FFTW? Chris@42: Q1.3 Is FFTW free software? Chris@42: Q1.4 What is this about non-free licenses? Chris@42: Q1.5 In the West? I thought MIT was in the East? Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 1.1. What is FFTW? Chris@42: Chris@42: FFTW is a free collection of fast C routines for computing the Discrete Chris@42: Fourier Transform in one or more dimensions. It includes complex, real, Chris@42: symmetric, and parallel transforms, and can handle arbitrary array sizes Chris@42: efficiently. FFTW is typically faster than other publically-available FFT Chris@42: implementations, and is even competitive with vendor-tuned libraries. Chris@42: (See our web page for extensive benchmarks.) To achieve this performance, Chris@42: FFTW uses novel code-generation and runtime self-optimization techniques Chris@42: (along with many other tricks). Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 1.2. How do I obtain FFTW? Chris@42: Chris@42: FFTW can be found at the FFTW web page. You can also retrieve it from Chris@42: ftp.fftw.org in /pub/fftw. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 1.3. Is FFTW free software? Chris@42: Chris@42: Starting with version 1.3, FFTW is Free Software in the technical sense Chris@42: defined by the Free Software Foundation (see Categories of Free and Chris@42: Non-Free Software), and is distributed under the terms of the GNU General Chris@42: Public License. Previous versions of FFTW were distributed without fee Chris@42: for noncommercial use, but were not technically ``free.'' Chris@42: Chris@42: Non-free licenses for FFTW are also available that permit different terms Chris@42: of use than the GPL. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 1.4. 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 (which Chris@42: would require them to release source code and allow free redistribution). Chris@42: Such users can purchase an unlimited-use license from MIT. Contact us for Chris@42: 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 copyright Chris@42: to FFTW and they only let us GPL it because we convinced them that it Chris@42: would neither affect their licensing revenue nor irritate existing Chris@42: licensees. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 1.5. 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 (with Chris@42: apologies to Sergio Leone). Chris@42: Chris@42: =============================================================================== Chris@42: Chris@42: Section 2. Installing FFTW Chris@42: Chris@42: Q2.1 Which systems does FFTW run on? Chris@42: Q2.2 Does FFTW run on Windows? Chris@42: Q2.3 My compiler has trouble with FFTW. Chris@42: Q2.4 FFTW does not compile on Solaris, complaining about const. Chris@42: Q2.5 What's the difference between --enable-3dnow and --enable-k7? Chris@42: Q2.6 What's the difference between the fma and the non-fma versions? Chris@42: Q2.7 Which language is FFTW written in? Chris@42: Q2.8 Can I call FFTW from Fortran? Chris@42: Q2.9 Can I call FFTW from C++? Chris@42: Q2.10 Why isn't FFTW written in Fortran/C++? Chris@42: Q2.11 How do I compile FFTW to run in single precision? Chris@42: Q2.12 --enable-k7 does not work on x86-64 Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.1. 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 C Chris@42: compiler. (See also Q2.2 `Does FFTW run on Windows?', Q2.3 `My compiler Chris@42: has trouble with FFTW.'.) FFTW can also take advantage of certain Chris@42: hardware-specific features, such as cycle counters and SIMD instructions, Chris@42: but this is optional. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.2. 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 code Chris@42: is essentially straight ANSI C. See also the FFTW Windows installation Chris@42: notes, Q2.3 `My compiler has trouble with FFTW.', and Q3.18 `How do I call Chris@42: FFTW from the Microsoft language du jour?'. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.3. 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 gcc 3.2.x on x86 and PPC, a recent Compaq C Chris@42: compiler for Alpha, version 6 of IBM's xlc compiler for AIX, Intel's icc Chris@42: versions 5-7, and Sun WorkShop 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: gcc 2.95.x for Solaris/SPARC produces incorrect code for the test program Chris@42: (workaround: recompile the libbench2 directory with -O2). Chris@42: Chris@42: NetBSD/macppc 1.6 comes with a gcc version that also miscompiles the test Chris@42: program. (Please report a workaround if you know one.) Chris@42: Chris@42: gcc 3.2.3 for ARM reportedly crashes during compilation. This bug is Chris@42: reportedly fixed in later versions of gcc. Chris@42: Chris@42: Versions 8.0 and 8.1 of Intel's icc falsely claim to be gcc, so you should Chris@42: specify CC="icc -no-gcc"; this is automatic in FFTW 3.1. icc-8.0.066 Chris@42: reportely produces incorrect code for FFTW 2.1.5, but is fixed in version Chris@42: 8.1. icc-7.1 compiler build 20030402Z appears to produce incorrect Chris@42: dependencies, causing the compilation to fail. icc-7.1 build 20030307Z Chris@42: appears to work fine. (Use icc -V to check which build you have.) As of Chris@42: 2003/04/18, build 20030402Z appears not to be available any longer on Chris@42: Intel's website, whereas the older build 20030307Z is available. Chris@42: Chris@42: ranlib of GNU binutils 2.9.1 on Irix has been observed to corrupt the FFTW Chris@42: libraries, causing a link failure when FFTW is compiled. Since ranlib is Chris@42: completely superfluous on Irix, we suggest deleting it from your system Chris@42: and replacing it with a symbolic link to /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: gcc 3.4.[0123] for x86 produces incorrect SSE2 code for FFTW when -O2 (the Chris@42: best choice for FFTW) is used, causing FFTW to crash (make check crashes). Chris@42: This bug is fixed in gcc 3.4.4. On x86_64 (amd64/em64t), gcc 3.4.4 Chris@42: reportedly still has a similar problem, but this is fixed as of gcc 3.4.6. Chris@42: Chris@42: gcc-3.2 for x86 produces incorrect SIMD code if -O3 is used. The same Chris@42: compiler produces incorrect SIMD code if no optimization is used, too. Chris@42: When using gcc-3.2, it is a good idea not to change the default CFLAGS Chris@42: selected by the configure script. Chris@42: Chris@42: Some 3.0.x and 3.1.x versions of gcc on x86 may crash. gcc so-called 2.96 Chris@42: shipping with RedHat 7.3 crashes when compiling SIMD code. In both cases, Chris@42: please upgrade to gcc-3.2 or later. Chris@42: Chris@42: Intel's icc 6.0 misaligns SSE constants, but FFTW has a workaround. icc Chris@42: 8.x fails to compile FFTW 3.0.x because it falsely claims to be gcc; we Chris@42: believe this to be a bug in 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 reodft11e-r2hc-odd.c Chris@42: unless optimizations are disabled for that file. Chris@42: Chris@42: gcc 2.95 on MacOS X miscompiles AltiVec code (fixed in later versions). Chris@42: gcc 3.2.x miscompiles AltiVec permutations, but FFTW has a workaround. Chris@42: gcc 4.0.1 on MacOS for Intel crashes when compiling FFTW; a workaround is Chris@42: to compile one file without optimization: cd kernel; make CFLAGS=" " Chris@42: trig.lo. Chris@42: Chris@42: gcc 4.1.1 reportedly crashes when compiling FFTW for MIPS; the workaround Chris@42: is to compile the file it crashes on (t2_64.c) with a lower optimization Chris@42: level. Chris@42: Chris@42: gcc versions 4.1.2 to 4.2.0 for x86 reportedly miscompile FFTW 3.1's test Chris@42: program, causing make check to crash (gcc bug #26528). The bug was Chris@42: reportedly fixed in gcc version 4.2.1 and later. A workaround is to Chris@42: compile libbench2/verify-lib.c without optimization. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.4. FFTW does not compile on Solaris, complaining about const. Chris@42: Chris@42: We know that at least on Solaris 2.5.x with Sun's compilers 4.2 you might Chris@42: get error messages from make such as Chris@42: Chris@42: "./fftw.h", line 88: warning: const is a keyword in ANSI C Chris@42: Chris@42: This is the case when the configure script reports that const does not Chris@42: work: Chris@42: Chris@42: checking for working const... (cached) no Chris@42: Chris@42: You should be aware that Solaris comes with two compilers, namely, Chris@42: /opt/SUNWspro/SC4.2/bin/cc and /usr/ucb/cc. The latter compiler is Chris@42: non-ANSI. Indeed, it is a perverse shell script that calls the real Chris@42: compiler in non-ANSI mode. In order to compile FFTW, change your path so Chris@42: that the right cc is used. Chris@42: Chris@42: To know whether your compiler is the right one, type cc -V. If the Chris@42: compiler prints ``ucbcc'', as in Chris@42: Chris@42: 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: cc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2 Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.5. What's the difference between --enable-3dnow and --enable-k7? Chris@42: Chris@42: --enable-k7 enables 3DNow! instructions on K7 processors (AMD Athlon and Chris@42: its variants). K7 support is provided by assembly routines generated by a Chris@42: special purpose compiler. As of fftw-3.2, --enable-k7 is no longer Chris@42: supported. Chris@42: Chris@42: --enable-3dnow enables generic 3DNow! support using gcc builtin functions. Chris@42: This works on earlier AMD processors, but it is not as fast as our special Chris@42: assembly routines. As of fftw-3.1, --enable-3dnow is no longer supported. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.6. 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 two Chris@42: FFTW packages are otherwise identical. In FFTW 3.1, the fma and non-fma Chris@42: versions were merged together into a single package, and the configure Chris@42: script attempts to automatically guess which version to use. Chris@42: Chris@42: The FFTW 3.1 configure script enables fma by default on PowerPC, Itanium, Chris@42: and PA-RISC, and disables it otherwise. You can force one or the other by Chris@42: using the --enable-fma or --disable-fma flag for configure. Chris@42: Chris@42: Definitely use fma if you have a PowerPC-based system with gcc (or IBM Chris@42: xlc). This includes all GNU/Linux systems for PowerPC and the older Chris@42: PowerPC-based MacOS systems. Also use it on PA-RISC and Itanium with the Chris@42: 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 gcc-3.2 appears not to exploit Chris@42: it correctly. Other compilers may do the right thing, but we have not Chris@42: tried them. Please send us your feedback so that we can update this FAQ Chris@42: entry. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.7. Which language is FFTW written in? Chris@42: Chris@42: FFTW is written in ANSI C. Most of the code, however, was automatically Chris@42: generated by a program called genfft, written in the Objective Caml Chris@42: dialect of ML. You do not need to know ML or to have an Objective Caml Chris@42: compiler in order to use FFTW. Chris@42: Chris@42: genfft is provided with the FFTW sources, which means that you can play Chris@42: with the code generator if you want. In this case, you need a working Chris@42: Objective Caml system. Objective Caml is available from the Caml web Chris@42: page. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.8. Can I call FFTW from Fortran? Chris@42: Chris@42: Yes, FFTW (versions 1.3 and higher) contains a Fortran-callable interface, Chris@42: documented in the FFTW manual. Chris@42: Chris@42: By default, FFTW configures its Fortran interface to work with the first Chris@42: compiler it finds, e.g. g77. To configure for a different, incompatible Chris@42: Fortran compiler foobar, use ./configure F77=foobar when installing FFTW. Chris@42: (In the case of 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 at Chris@42: least.) Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.9. Can I call FFTW from C++? Chris@42: Chris@42: Most definitely. FFTW should compile and/or link under any C++ compiler. Chris@42: Moreover, it is likely that the C++ template class is Chris@42: bit-compatible with FFTW's complex-number format (see the FFTW manual for Chris@42: more details). Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.10. 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: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.11. How do I compile FFTW to run in single precision? Chris@42: Chris@42: On a Unix system: configure --enable-float. On a non-Unix system: edit Chris@42: config.h to #define the symbol FFTW_SINGLE (for FFTW 3.x). In both cases, Chris@42: you must then recompile FFTW. In FFTW 3, all FFTW identifiers will then Chris@42: begin with fftwf_ instead of fftw_. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 2.12. --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 and Chris@42: the AMD Opteron in 32-bit mode. --enable-k7 does not work on AMD Opteron Chris@42: 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 works Chris@42: in both 32-bit and 64-bit mode. Chris@42: Chris@42: =============================================================================== Chris@42: Chris@42: Section 3. Using FFTW Chris@42: Chris@42: Q3.1 Why not support the FFTW 2 interface in FFTW 3? Chris@42: Q3.2 Why do FFTW 3 plans encapsulate the input/output arrays and not ju Chris@42: Q3.3 FFTW seems really slow. Chris@42: Q3.4 FFTW slows down after repeated calls. Chris@42: Q3.5 An FFTW routine is crashing when I call it. Chris@42: Q3.6 My Fortran program crashes when calling FFTW. Chris@42: Q3.7 FFTW gives results different from my old FFT. Chris@42: Q3.8 FFTW gives different results between runs Chris@42: Q3.9 Can I save FFTW's plans? Chris@42: Q3.10 Why does your inverse transform return a scaled result? Chris@42: Q3.11 How can I make FFTW put the origin (zero frequency) at the center Chris@42: Q3.12 How do I FFT an image/audio file in *foobar* format? Chris@42: Q3.13 My program does not link (on Unix). Chris@42: Q3.14 I included your header, but linking still fails. Chris@42: Q3.15 My program crashes, complaining about stack space. Chris@42: Q3.16 FFTW seems to have a memory leak. Chris@42: Q3.17 The output of FFTW's transform is all zeros. Chris@42: Q3.18 How do I call FFTW from the Microsoft language du jour? Chris@42: Q3.19 Can I compute only a subset of the DFT outputs? Chris@42: Q3.20 Can I use FFTW's routines for in-place and out-of-place matrix tra Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.1. 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 characteristics Chris@42: of the input and output arrays; these stronger semantics are necessary for Chris@42: performance reasons. Thus, it is impossible to efficiently emulate the Chris@42: older interface (whose plans can be used for any transform of the same Chris@42: size). We believe that it should be possible to upgrade most programs Chris@42: without any difficulty, however. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.2. 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: * 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: * 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: * If you need to transform another array of the same size, creating a new Chris@42: plan once the first exists is a cheap operation. Chris@42: * If you need to transform many arrays of the same size at once, you Chris@42: should really use the plan_many routines in FFTW's "advanced" interface. 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 need Chris@42: to, we provide a "new-array execution" interface to apply a plan to a Chris@42: new array. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.3. FFTW seems really slow. Chris@42: Chris@42: You are probably recreating the plan before every transform, rather than Chris@42: creating it once and reusing it for all transforms of the same size. FFTW Chris@42: is designed to be used in the following way: Chris@42: Chris@42: * First, you create a plan. This will take several seconds. Chris@42: * Then, you reuse the plan many times to perform FFTs. These are fast. Chris@42: Chris@42: If you don't need to compute many transforms and the time for the planner Chris@42: is significant, you have two options. First, you can use the Chris@42: FFTW_ESTIMATE option in the planner, which uses heuristics instead of Chris@42: runtime measurements and produces a good plan in a short time. Second, Chris@42: you can use the wisdom feature to precompute the plan; see Q3.9 `Can I Chris@42: save FFTW's plans?' Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.4. FFTW slows down after repeated calls. Chris@42: Chris@42: Probably, NaNs or similar are creeping into your data, and the slowdown is Chris@42: due to the resulting floating-point exceptions. For example, be aware Chris@42: that repeatedly FFTing the same array is a diverging process (because FFTW Chris@42: computes the unnormalized transform). Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.5. An FFTW routine is crashing when I call it. Chris@42: Chris@42: Did the FFTW test programs pass (make check, or cd tests; make bigcheck if Chris@42: you want to be paranoid)? If so, you almost certainly have a bug in your Chris@42: own code. For example, you could be passing invalid arguments (such as Chris@42: wrongly-sized arrays) to FFTW, or you could simply have memory corruption Chris@42: elsewhere in your program that causes random crashes later on. Please Chris@42: don't complain to us unless you can come up with a minimal self-contained Chris@42: program (preferably under 30 lines) that illustrates the problem. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.6. My Fortran program crashes when calling FFTW. Chris@42: Chris@42: As described in the manual, on 64-bit machines you must store the plans in Chris@42: variables large enough to hold a pointer, for example integer*8. We Chris@42: recommend using integer*8 on 32-bit machines as well, to simplify porting. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.7. FFTW gives results different from my old FFT. Chris@42: Chris@42: People follow many different conventions for the DFT, and you should be Chris@42: sure to know the ones that we use (described in the FFTW manual). In Chris@42: particular, you should be aware that the FFTW_FORWARD/FFTW_BACKWARD Chris@42: directions correspond to signs of -1/+1 in the exponent of the DFT Chris@42: definition. (*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 Q3.10 `Why does your inverse transform return a scaled Chris@42: result?'. Chris@42: Chris@42: Finally, note that floating-point arithmetic is not exact, so different Chris@42: FFT algorithms will give slightly different results (on the order of the Chris@42: numerical accuracy; typically a fractional difference of 1e-15 or so in Chris@42: double precision). Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.8. FFTW gives different results between runs Chris@42: Chris@42: If you use FFTW_MEASURE or FFTW_PATIENT mode, then the algorithm FFTW Chris@42: employs is not deterministic: it depends on runtime performance Chris@42: measurements. This will cause the results to vary slightly from run to Chris@42: run. However, the differences should be slight, on the order of the Chris@42: floating-point precision, and therefore should have no practical impact on Chris@42: most applications. Chris@42: Chris@42: If you use saved plans (wisdom) or FFTW_ESTIMATE mode, however, then the Chris@42: algorithm is deterministic and the results should be identical between Chris@42: runs. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.9. Can I save FFTW's plans? Chris@42: Chris@42: Yes. Starting with version 1.2, FFTW provides the wisdom mechanism for Chris@42: saving plans; see the FFTW manual. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.10. 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 product of Chris@42: the dimensions.) We could, instead, have chosen a normalization that Chris@42: would have returned the unscaled array. Or, to accomodate the many Chris@42: conventions in this matter, the transform routines could have accepted a Chris@42: "scale factor" parameter. We did not do this, however, for two reasons. Chris@42: First, we didn't want to sacrifice performance in the common case where Chris@42: the scale factor is 1. Second, in real applications the FFT is followed or Chris@42: preceded by some computation on the data, into which the scale factor can Chris@42: typically be absorbed at little or no cost. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.11. 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 origin Chris@42: in frequency space at the center of the output array, rather than in the Chris@42: zero-th element (the default in FFTW). If all of the dimensions of your Chris@42: array are even, you can accomplish this by simply multiplying each element Chris@42: of the input array by (-1)^(i + j + ...), where i, j, etcetera are the Chris@42: indices of the element. (This trick is a general property of the DFT, and Chris@42: is not specific to FFTW.) Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.12. How do I FFT an image/audio file in *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, but Chris@42: you are responsible for figuring out your data format and converting it to Chris@42: the form FFTW requires. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.13. My program does not link (on Unix). Chris@42: Chris@42: The libraries must be listed in the correct order (-lfftw3 -lm for FFTW Chris@42: 3.x) and *after* your program sources/objects. (The general rule is that Chris@42: if *A* uses *B*, then *A* must be listed before *B* in the link command.). Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.14. 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 library Chris@42: and link it into your program, not just #include . (Yes, this is Chris@42: really a FAQ.) Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.15. My program crashes, complaining about stack space. Chris@42: Chris@42: You cannot declare large arrays with automatic storage (e.g. via Chris@42: fftw_complex array[N]); you should use fftw_malloc (or equivalent) to Chris@42: allocate the arrays you want to transform if they are larger than a few Chris@42: hundred elements. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.16. FFTW seems to have a memory leak. Chris@42: Chris@42: After you create a plan, FFTW caches the information required to quickly Chris@42: recreate the plan. (See Q3.9 `Can I save FFTW's plans?') It also Chris@42: maintains a small amount of other persistent memory. You can deallocate Chris@42: all of FFTW's internally allocated memory, if you wish, by calling Chris@42: fftw_cleanup(), as documented in the manual. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.17. The output of FFTW's transform is all zeros. Chris@42: Chris@42: You should initialize your input array *after* creating the plan, unless Chris@42: you use FFTW_ESTIMATE: planning with FFTW_MEASURE or FFTW_PATIENT Chris@42: overwrites the input/output arrays, as described in the manual. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.18. How do I call FFTW from the Microsoft language du jour? Chris@42: Chris@42: Please *do not* ask us Windows-specific questions. We do not use Windows. Chris@42: We know nothing about Visual Basic, Visual C++, or .NET. Please find the Chris@42: appropriate Usenet discussion group and ask your question there. See also Chris@42: Q2.2 `Does FFTW run on Windows?'. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.19. 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 inputs. Chris@42: In principle, there is something called a *pruned FFT* that can do what Chris@42: you want, but to compute K outputs out of N the complexity is in general Chris@42: O(N log K) instead of O(N log N), thus saving only a small additive factor Chris@42: in the log. (The same argument holds if you instead have only K nonzero Chris@42: 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 FFTs. Chris@42: In particular, the case where you want the first K outputs, where K Chris@42: divides N, can be handled by performing N/K transforms of size K and then Chris@42: summing the outputs multiplied by appropriate phase factors. For more Chris@42: details, see pruned FFTs with FFTW. Chris@42: Chris@42: There are also some algorithms that compute pruned transforms Chris@42: *approximately*, but they are beyond the scope of this FAQ. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 3.20. 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 vector Chris@42: rank 2 where the vector strides are transposed. (A rank-0 transform is Chris@42: equivalent to a 1D transform of size 1, which. just copies the input into Chris@42: the output.) Specifying the same location for the input and output makes Chris@42: the transpose in-place. Chris@42: Chris@42: For double-valued data stored in row-major format, plan creation looks Chris@42: like this: Chris@42: 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: (This entry was written by Rhys Ulerich.) Chris@42: Chris@42: =============================================================================== Chris@42: Chris@42: Section 4. Internals of FFTW Chris@42: Chris@42: Q4.1 How does FFTW work? Chris@42: Q4.2 Why is FFTW so fast? Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 4.1. 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 *solvers*, representing different FFT algorithms and Chris@42: implementation strategies, whose combination into a particular *plan* for Chris@42: a given size can be determined at runtime according to the characteristics Chris@42: of your machine/compiler. This peculiar software architecture allows FFTW Chris@42: to adapt itself to 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 S. G. Chris@42: Johnson, *Proc. ICASSP* 3, 1381 (1998), also available at the FFTW web Chris@42: page. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 4.2. Why is FFTW so fast? Chris@42: Chris@42: This is a complex question, and there is no simple answer. In fact, the Chris@42: authors do not fully know the answer, either. In addition to many small Chris@42: performance hacks throughout FFTW, there are three general reasons for Chris@42: FFTW's speed. Chris@42: Chris@42: * FFTW uses a variety of FFT algorithms and implementation styles that Chris@42: can be arbitrarily composed to adapt itself to a machine. See Q4.1 `How Chris@42: does FFTW work?'. Chris@42: * FFTW uses a code generator to produce highly-optimized routines for Chris@42: computing small transforms. Chris@42: * FFTW uses explicit divide-and-conquer to take advantage of the memory Chris@42: hierarchy. 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 S. G. Chris@42: Johnson, *Proc. ICASSP* 3, 1381 (1998), available along with other Chris@42: references at the FFTW web page. Chris@42: Chris@42: =============================================================================== Chris@42: Chris@42: Section 5. Known bugs Chris@42: Chris@42: Q5.1 FFTW 1.1 crashes in rfftwnd on Linux. Chris@42: Q5.2 The MPI transforms in FFTW 1.2 give incorrect results/leak memory. Chris@42: Q5.3 The test programs in FFTW 1.2.1 fail when I change FFTW to use sin Chris@42: Q5.4 The test program in FFTW 1.2.1 fails for n > 46340. Chris@42: Q5.5 The threaded code fails on Linux Redhat 5.0 Chris@42: Q5.6 FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dime Chris@42: Q5.7 FFTW 2.0's complex transforms give the wrong results with prime fa Chris@42: Q5.8 FFTW 2.1.1's MPI test programs crash with MPICH. Chris@42: Q5.9 FFTW 2.1.2's multi-threaded transforms don't work on AIX. Chris@42: Q5.10 FFTW 2.1.2's complex transforms give incorrect results for large p Chris@42: Q5.11 FFTW 2.1.3's multi-threaded transforms don't give any speedup on S Chris@42: Q5.12 FFTW 2.1.3 crashes on AIX. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.1. 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 rfftwnd causing an Chris@42: incorrect amount of memory to be allocated. The bug showed up in Linux Chris@42: with libc-5.3.12 (and nowhere else that we know of). Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.2. 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, just Chris@42: the transpose routines) in FFTW 1.2 had bugs that could cause errors in Chris@42: some situations. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.3. 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 work in Chris@42: single precision, but the test programs didn't--the error tolerances in Chris@42: the tests were set for double precision.) Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.4. 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, but Chris@42: the test program was wrong. For large n, n*n in the naive transform that Chris@42: we used for comparison overflows 32 bit integer precision, breaking the Chris@42: test. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.5. 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 glibc-2.0.7. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.6. 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 Chris@42: due to a poorly-parenthesized expression.) Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.7. 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: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.8. 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 ch_p4 device (TCP/IP); Chris@42: the transforms themselves worked fine. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.9. 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 pthreads implementation, which Chris@42: idiosyncratically creates threads in detached (non-joinable) mode by Chris@42: default. Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.10. 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 for Chris@42: prime sizes (in versions 2.0 to 2.1.2) had an integer overflow problem Chris@42: that caused incorrect results for many primes greater than 32768 (on Chris@42: 32-bit machines). (Sizes without large prime factors are not affected.) Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.11. 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 threads Chris@42: that do not parallelize over multiple processors, so one has to request Chris@42: the proper behavior specifically.) Chris@42: Chris@42: ------------------------------------------------------------------------------- Chris@42: Chris@42: Question 5.12. FFTW 2.1.3 crashes on AIX. Chris@42: Chris@42: The FFTW 2.1.3 configure script picked incorrect compiler flags for the Chris@42: xlc compiler on newer IBM processors. This is fixed in FFTW 2.1.4. Chris@42: