Mercurial > hg > sv-dependency-builds
diff src/fftw-3.3.5/doc/FAQ/fftw-faq.ascii @ 42:2cd0e3b3e1fd
Current fftw source
| author | Chris Cannam |
|---|---|
| date | Tue, 18 Oct 2016 13:40:26 +0100 |
| parents | |
| children |
line wrap: on
line diff
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/fftw-3.3.5/doc/FAQ/fftw-faq.ascii Tue Oct 18 13:40:26 2016 +0100 @@ -0,0 +1,842 @@ + FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS + 30 Jul 2016 + Matteo Frigo + Steven G. Johnson + <fftw@fftw.org> + +This is the list of Frequently Asked Questions about FFTW, a collection of +fast C routines for computing the Discrete Fourier Transform in one or +more dimensions. + +=============================================================================== + +Index + + Section 1. Introduction and General Information + Q1.1 What is FFTW? + Q1.2 How do I obtain FFTW? + Q1.3 Is FFTW free software? + Q1.4 What is this about non-free licenses? + Q1.5 In the West? I thought MIT was in the East? + + Section 2. Installing FFTW + Q2.1 Which systems does FFTW run on? + Q2.2 Does FFTW run on Windows? + Q2.3 My compiler has trouble with FFTW. + Q2.4 FFTW does not compile on Solaris, complaining about const. + Q2.5 What's the difference between --enable-3dnow and --enable-k7? + Q2.6 What's the difference between the fma and the non-fma versions? + Q2.7 Which language is FFTW written in? + Q2.8 Can I call FFTW from Fortran? + Q2.9 Can I call FFTW from C++? + Q2.10 Why isn't FFTW written in Fortran/C++? + Q2.11 How do I compile FFTW to run in single precision? + Q2.12 --enable-k7 does not work on x86-64 + + Section 3. Using FFTW + Q3.1 Why not support the FFTW 2 interface in FFTW 3? + Q3.2 Why do FFTW 3 plans encapsulate the input/output arrays and not ju + Q3.3 FFTW seems really slow. + Q3.4 FFTW slows down after repeated calls. + Q3.5 An FFTW routine is crashing when I call it. + Q3.6 My Fortran program crashes when calling FFTW. + Q3.7 FFTW gives results different from my old FFT. + Q3.8 FFTW gives different results between runs + Q3.9 Can I save FFTW's plans? + Q3.10 Why does your inverse transform return a scaled result? + Q3.11 How can I make FFTW put the origin (zero frequency) at the center + Q3.12 How do I FFT an image/audio file in *foobar* format? + Q3.13 My program does not link (on Unix). + Q3.14 I included your header, but linking still fails. + Q3.15 My program crashes, complaining about stack space. + Q3.16 FFTW seems to have a memory leak. + Q3.17 The output of FFTW's transform is all zeros. + Q3.18 How do I call FFTW from the Microsoft language du jour? + Q3.19 Can I compute only a subset of the DFT outputs? + Q3.20 Can I use FFTW's routines for in-place and out-of-place matrix tra + + Section 4. Internals of FFTW + Q4.1 How does FFTW work? + Q4.2 Why is FFTW so fast? + + Section 5. Known bugs + Q5.1 FFTW 1.1 crashes in rfftwnd on Linux. + Q5.2 The MPI transforms in FFTW 1.2 give incorrect results/leak memory. + Q5.3 The test programs in FFTW 1.2.1 fail when I change FFTW to use sin + Q5.4 The test program in FFTW 1.2.1 fails for n > 46340. + Q5.5 The threaded code fails on Linux Redhat 5.0 + Q5.6 FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dime + Q5.7 FFTW 2.0's complex transforms give the wrong results with prime fa + Q5.8 FFTW 2.1.1's MPI test programs crash with MPICH. + Q5.9 FFTW 2.1.2's multi-threaded transforms don't work on AIX. + Q5.10 FFTW 2.1.2's complex transforms give incorrect results for large p + Q5.11 FFTW 2.1.3's multi-threaded transforms don't give any speedup on S + Q5.12 FFTW 2.1.3 crashes on AIX. + +=============================================================================== + +Section 1. Introduction and General Information + + Q1.1 What is FFTW? + Q1.2 How do I obtain FFTW? + Q1.3 Is FFTW free software? + Q1.4 What is this about non-free licenses? + Q1.5 In the West? I thought MIT was in the East? + +------------------------------------------------------------------------------- + +Question 1.1. What is FFTW? + +FFTW is a free collection of fast C routines for computing the Discrete +Fourier Transform in one or more dimensions. It includes complex, real, +symmetric, and parallel transforms, and can handle arbitrary array sizes +efficiently. FFTW is typically faster than other publically-available FFT +implementations, and is even competitive with vendor-tuned libraries. +(See our web page for extensive benchmarks.) To achieve this performance, +FFTW uses novel code-generation and runtime self-optimization techniques +(along with many other tricks). + +------------------------------------------------------------------------------- + +Question 1.2. How do I obtain FFTW? + +FFTW can be found at the FFTW web page. You can also retrieve it from +ftp.fftw.org in /pub/fftw. + +------------------------------------------------------------------------------- + +Question 1.3. Is FFTW free software? + +Starting with version 1.3, FFTW is Free Software in the technical sense +defined by the Free Software Foundation (see Categories of Free and +Non-Free Software), and is distributed under the terms of the GNU General +Public License. Previous versions of FFTW were distributed without fee +for noncommercial use, but were not technically ``free.'' + +Non-free licenses for FFTW are also available that permit different terms +of use than the GPL. + +------------------------------------------------------------------------------- + +Question 1.4. What is this about non-free licenses? + +The non-free licenses are for companies that wish to use FFTW in their +products but are unwilling to release their software under the GPL (which +would require them to release source code and allow free redistribution). +Such users can purchase an unlimited-use license from MIT. Contact us for +more details. + +We could instead have released FFTW under the LGPL, or even disallowed +non-Free usage. Suffice it to say, however, that MIT owns the copyright +to FFTW and they only let us GPL it because we convinced them that it +would neither affect their licensing revenue nor irritate existing +licensees. + +------------------------------------------------------------------------------- + +Question 1.5. In the West? I thought MIT was in the East? + +Not to an Italian. You could say that we're a Spaghetti Western (with +apologies to Sergio Leone). + +=============================================================================== + +Section 2. Installing FFTW + + Q2.1 Which systems does FFTW run on? + Q2.2 Does FFTW run on Windows? + Q2.3 My compiler has trouble with FFTW. + Q2.4 FFTW does not compile on Solaris, complaining about const. + Q2.5 What's the difference between --enable-3dnow and --enable-k7? + Q2.6 What's the difference between the fma and the non-fma versions? + Q2.7 Which language is FFTW written in? + Q2.8 Can I call FFTW from Fortran? + Q2.9 Can I call FFTW from C++? + Q2.10 Why isn't FFTW written in Fortran/C++? + Q2.11 How do I compile FFTW to run in single precision? + Q2.12 --enable-k7 does not work on x86-64 + +------------------------------------------------------------------------------- + +Question 2.1. Which systems does FFTW run on? + +FFTW is written in ANSI C, and should work on any system with a decent C +compiler. (See also Q2.2 `Does FFTW run on Windows?', Q2.3 `My compiler +has trouble with FFTW.'.) FFTW can also take advantage of certain +hardware-specific features, such as cycle counters and SIMD instructions, +but this is optional. + +------------------------------------------------------------------------------- + +Question 2.2. Does FFTW run on Windows? + +Yes, many people have reported successfully using FFTW on Windows with +various compilers. FFTW was not developed on Windows, but the source code +is essentially straight ANSI C. See also the FFTW Windows installation +notes, Q2.3 `My compiler has trouble with FFTW.', and Q3.18 `How do I call +FFTW from the Microsoft language du jour?'. + +------------------------------------------------------------------------------- + +Question 2.3. My compiler has trouble with FFTW. + +Complain fiercely to the vendor of the compiler. + +We have successfully used gcc 3.2.x on x86 and PPC, a recent Compaq C +compiler for Alpha, version 6 of IBM's xlc compiler for AIX, Intel's icc +versions 5-7, and Sun WorkShop cc version 6. + +FFTW is likely to push compilers to their limits, however, and several +compiler bugs have been exposed by FFTW. A partial list follows. + +gcc 2.95.x for Solaris/SPARC produces incorrect code for the test program +(workaround: recompile the libbench2 directory with -O2). + +NetBSD/macppc 1.6 comes with a gcc version that also miscompiles the test +program. (Please report a workaround if you know one.) + +gcc 3.2.3 for ARM reportedly crashes during compilation. This bug is +reportedly fixed in later versions of gcc. + +Versions 8.0 and 8.1 of Intel's icc falsely claim to be gcc, so you should +specify CC="icc -no-gcc"; this is automatic in FFTW 3.1. icc-8.0.066 +reportely produces incorrect code for FFTW 2.1.5, but is fixed in version +8.1. icc-7.1 compiler build 20030402Z appears to produce incorrect +dependencies, causing the compilation to fail. icc-7.1 build 20030307Z +appears to work fine. (Use icc -V to check which build you have.) As of +2003/04/18, build 20030402Z appears not to be available any longer on +Intel's website, whereas the older build 20030307Z is available. + +ranlib of GNU binutils 2.9.1 on Irix has been observed to corrupt the FFTW +libraries, causing a link failure when FFTW is compiled. Since ranlib is +completely superfluous on Irix, we suggest deleting it from your system +and replacing it with a symbolic link to /bin/echo. + +If support for SIMD instructions is enabled in FFTW, further compiler +problems may appear: + +gcc 3.4.[0123] for x86 produces incorrect SSE2 code for FFTW when -O2 (the +best choice for FFTW) is used, causing FFTW to crash (make check crashes). +This bug is fixed in gcc 3.4.4. On x86_64 (amd64/em64t), gcc 3.4.4 +reportedly still has a similar problem, but this is fixed as of gcc 3.4.6. + +gcc-3.2 for x86 produces incorrect SIMD code if -O3 is used. The same +compiler produces incorrect SIMD code if no optimization is used, too. +When using gcc-3.2, it is a good idea not to change the default CFLAGS +selected by the configure script. + +Some 3.0.x and 3.1.x versions of gcc on x86 may crash. gcc so-called 2.96 +shipping with RedHat 7.3 crashes when compiling SIMD code. In both cases, +please upgrade to gcc-3.2 or later. + +Intel's icc 6.0 misaligns SSE constants, but FFTW has a workaround. icc +8.x fails to compile FFTW 3.0.x because it falsely claims to be gcc; we +believe this to be a bug in icc, but FFTW 3.1 has a workaround. + +Visual C++ 2003 reportedly produces incorrect code for SSE/SSE2 when +compiling FFTW. This bug was reportedly fixed in VC++ 2005; +alternatively, you could switch to the Intel compiler. VC++ 6.0 also +reportedly produces incorrect code for the file reodft11e-r2hc-odd.c +unless optimizations are disabled for that file. + +gcc 2.95 on MacOS X miscompiles AltiVec code (fixed in later versions). +gcc 3.2.x miscompiles AltiVec permutations, but FFTW has a workaround. +gcc 4.0.1 on MacOS for Intel crashes when compiling FFTW; a workaround is +to compile one file without optimization: cd kernel; make CFLAGS=" " +trig.lo. + +gcc 4.1.1 reportedly crashes when compiling FFTW for MIPS; the workaround +is to compile the file it crashes on (t2_64.c) with a lower optimization +level. + +gcc versions 4.1.2 to 4.2.0 for x86 reportedly miscompile FFTW 3.1's test +program, causing make check to crash (gcc bug #26528). The bug was +reportedly fixed in gcc version 4.2.1 and later. A workaround is to +compile libbench2/verify-lib.c without optimization. + +------------------------------------------------------------------------------- + +Question 2.4. FFTW does not compile on Solaris, complaining about const. + +We know that at least on Solaris 2.5.x with Sun's compilers 4.2 you might +get error messages from make such as + +"./fftw.h", line 88: warning: const is a keyword in ANSI C + +This is the case when the configure script reports that const does not +work: + +checking for working const... (cached) no + +You should be aware that Solaris comes with two compilers, namely, +/opt/SUNWspro/SC4.2/bin/cc and /usr/ucb/cc. The latter compiler is +non-ANSI. Indeed, it is a perverse shell script that calls the real +compiler in non-ANSI mode. In order to compile FFTW, change your path so +that the right cc is used. + +To know whether your compiler is the right one, type cc -V. If the +compiler prints ``ucbcc'', as in + +ucbcc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2 + +then the compiler is wrong. The right message is something like + +cc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2 + +------------------------------------------------------------------------------- + +Question 2.5. What's the difference between --enable-3dnow and --enable-k7? + +--enable-k7 enables 3DNow! instructions on K7 processors (AMD Athlon and +its variants). K7 support is provided by assembly routines generated by a +special purpose compiler. As of fftw-3.2, --enable-k7 is no longer +supported. + +--enable-3dnow enables generic 3DNow! support using gcc builtin functions. +This works on earlier AMD processors, but it is not as fast as our special +assembly routines. As of fftw-3.1, --enable-3dnow is no longer supported. + +------------------------------------------------------------------------------- + +Question 2.6. What's the difference between the fma and the non-fma versions? + +The fma version tries to exploit the fused multiply-add instructions +implemented in many processors such as PowerPC, ia-64, and MIPS. The two +FFTW packages are otherwise identical. In FFTW 3.1, the fma and non-fma +versions were merged together into a single package, and the configure +script attempts to automatically guess which version to use. + +The FFTW 3.1 configure script enables fma by default on PowerPC, Itanium, +and PA-RISC, and disables it otherwise. You can force one or the other by +using the --enable-fma or --disable-fma flag for configure. + +Definitely use fma if you have a PowerPC-based system with gcc (or IBM +xlc). This includes all GNU/Linux systems for PowerPC and the older +PowerPC-based MacOS systems. Also use it on PA-RISC and Itanium with the +HP/UX compiler. + +Definitely do not use the fma version if you have an ia-32 processor +(Intel, AMD, MacOS on Intel, etcetera). + +For other architectures/compilers, the situation is not so clear. For +example, ia-64 has the fma instruction, but gcc-3.2 appears not to exploit +it correctly. Other compilers may do the right thing, but we have not +tried them. Please send us your feedback so that we can update this FAQ +entry. + +------------------------------------------------------------------------------- + +Question 2.7. Which language is FFTW written in? + +FFTW is written in ANSI C. Most of the code, however, was automatically +generated by a program called genfft, written in the Objective Caml +dialect of ML. You do not need to know ML or to have an Objective Caml +compiler in order to use FFTW. + +genfft is provided with the FFTW sources, which means that you can play +with the code generator if you want. In this case, you need a working +Objective Caml system. Objective Caml is available from the Caml web +page. + +------------------------------------------------------------------------------- + +Question 2.8. Can I call FFTW from Fortran? + +Yes, FFTW (versions 1.3 and higher) contains a Fortran-callable interface, +documented in the FFTW manual. + +By default, FFTW configures its Fortran interface to work with the first +compiler it finds, e.g. g77. To configure for a different, incompatible +Fortran compiler foobar, use ./configure F77=foobar when installing FFTW. +(In the case of g77, however, FFTW 3.x also includes an extra set of +Fortran-callable routines with one less underscore at the end of +identifiers, which should cover most other Fortran compilers on Linux at +least.) + +------------------------------------------------------------------------------- + +Question 2.9. Can I call FFTW from C++? + +Most definitely. FFTW should compile and/or link under any C++ compiler. +Moreover, it is likely that the C++ <complex> template class is +bit-compatible with FFTW's complex-number format (see the FFTW manual for +more details). + +------------------------------------------------------------------------------- + +Question 2.10. Why isn't FFTW written in Fortran/C++? + +Because we don't like those languages, and neither approaches the +portability of C. + +------------------------------------------------------------------------------- + +Question 2.11. How do I compile FFTW to run in single precision? + +On a Unix system: configure --enable-float. On a non-Unix system: edit +config.h to #define the symbol FFTW_SINGLE (for FFTW 3.x). In both cases, +you must then recompile FFTW. In FFTW 3, all FFTW identifiers will then +begin with fftwf_ instead of fftw_. + +------------------------------------------------------------------------------- + +Question 2.12. --enable-k7 does not work on x86-64 + +Support for --enable-k7 was discontinued in fftw-3.2. + +The fftw-3.1 release supports --enable-k7. This option only works on +32-bit x86 machines that implement 3DNow!, including the AMD Athlon and +the AMD Opteron in 32-bit mode. --enable-k7 does not work on AMD Opteron +in 64-bit mode. Use --enable-sse for x86-64 machines. + +FFTW supports 3DNow! by means of assembly code generated by a +special-purpose compiler. It is hard to produce assembly code that works +in both 32-bit and 64-bit mode. + +=============================================================================== + +Section 3. Using FFTW + + Q3.1 Why not support the FFTW 2 interface in FFTW 3? + Q3.2 Why do FFTW 3 plans encapsulate the input/output arrays and not ju + Q3.3 FFTW seems really slow. + Q3.4 FFTW slows down after repeated calls. + Q3.5 An FFTW routine is crashing when I call it. + Q3.6 My Fortran program crashes when calling FFTW. + Q3.7 FFTW gives results different from my old FFT. + Q3.8 FFTW gives different results between runs + Q3.9 Can I save FFTW's plans? + Q3.10 Why does your inverse transform return a scaled result? + Q3.11 How can I make FFTW put the origin (zero frequency) at the center + Q3.12 How do I FFT an image/audio file in *foobar* format? + Q3.13 My program does not link (on Unix). + Q3.14 I included your header, but linking still fails. + Q3.15 My program crashes, complaining about stack space. + Q3.16 FFTW seems to have a memory leak. + Q3.17 The output of FFTW's transform is all zeros. + Q3.18 How do I call FFTW from the Microsoft language du jour? + Q3.19 Can I compute only a subset of the DFT outputs? + Q3.20 Can I use FFTW's routines for in-place and out-of-place matrix tra + +------------------------------------------------------------------------------- + +Question 3.1. Why not support the FFTW 2 interface in FFTW 3? + +FFTW 3 has semantics incompatible with earlier versions: its plans can +only be used for a given stride, multiplicity, and other characteristics +of the input and output arrays; these stronger semantics are necessary for +performance reasons. Thus, it is impossible to efficiently emulate the +older interface (whose plans can be used for any transform of the same +size). We believe that it should be possible to upgrade most programs +without any difficulty, however. + +------------------------------------------------------------------------------- + +Question 3.2. Why do FFTW 3 plans encapsulate the input/output arrays and not just the algorithm? + +There are several reasons: + +* It was important for performance reasons that the plan be specific to + array characteristics like the stride (and alignment, for SIMD), and + requiring that the user maintain these invariants is error prone. +* In most high-performance applications, as far as we can tell, you are + usually transforming the same array over and over, so FFTW's semantics + should not be a burden. +* If you need to transform another array of the same size, creating a new + plan once the first exists is a cheap operation. +* If you need to transform many arrays of the same size at once, you + should really use the plan_many routines in FFTW's "advanced" interface. +* If the abovementioned array characteristics are the same, you are + willing to pay close attention to the documentation, and you really need + to, we provide a "new-array execution" interface to apply a plan to a + new array. + +------------------------------------------------------------------------------- + +Question 3.3. FFTW seems really slow. + +You are probably recreating the plan before every transform, rather than +creating it once and reusing it for all transforms of the same size. FFTW +is designed to be used in the following way: + +* First, you create a plan. This will take several seconds. +* Then, you reuse the plan many times to perform FFTs. These are fast. + +If you don't need to compute many transforms and the time for the planner +is significant, you have two options. First, you can use the +FFTW_ESTIMATE option in the planner, which uses heuristics instead of +runtime measurements and produces a good plan in a short time. Second, +you can use the wisdom feature to precompute the plan; see Q3.9 `Can I +save FFTW's plans?' + +------------------------------------------------------------------------------- + +Question 3.4. FFTW slows down after repeated calls. + +Probably, NaNs or similar are creeping into your data, and the slowdown is +due to the resulting floating-point exceptions. For example, be aware +that repeatedly FFTing the same array is a diverging process (because FFTW +computes the unnormalized transform). + +------------------------------------------------------------------------------- + +Question 3.5. An FFTW routine is crashing when I call it. + +Did the FFTW test programs pass (make check, or cd tests; make bigcheck if +you want to be paranoid)? If so, you almost certainly have a bug in your +own code. For example, you could be passing invalid arguments (such as +wrongly-sized arrays) to FFTW, or you could simply have memory corruption +elsewhere in your program that causes random crashes later on. Please +don't complain to us unless you can come up with a minimal self-contained +program (preferably under 30 lines) that illustrates the problem. + +------------------------------------------------------------------------------- + +Question 3.6. My Fortran program crashes when calling FFTW. + +As described in the manual, on 64-bit machines you must store the plans in +variables large enough to hold a pointer, for example integer*8. We +recommend using integer*8 on 32-bit machines as well, to simplify porting. + +------------------------------------------------------------------------------- + +Question 3.7. FFTW gives results different from my old FFT. + +People follow many different conventions for the DFT, and you should be +sure to know the ones that we use (described in the FFTW manual). In +particular, you should be aware that the FFTW_FORWARD/FFTW_BACKWARD +directions correspond to signs of -1/+1 in the exponent of the DFT +definition. (*Numerical Recipes* uses the opposite convention.) + +You should also know that we compute an unnormalized transform. In +contrast, Matlab is an example of program that computes a normalized +transform. See Q3.10 `Why does your inverse transform return a scaled +result?'. + +Finally, note that floating-point arithmetic is not exact, so different +FFT algorithms will give slightly different results (on the order of the +numerical accuracy; typically a fractional difference of 1e-15 or so in +double precision). + +------------------------------------------------------------------------------- + +Question 3.8. FFTW gives different results between runs + +If you use FFTW_MEASURE or FFTW_PATIENT mode, then the algorithm FFTW +employs is not deterministic: it depends on runtime performance +measurements. This will cause the results to vary slightly from run to +run. However, the differences should be slight, on the order of the +floating-point precision, and therefore should have no practical impact on +most applications. + +If you use saved plans (wisdom) or FFTW_ESTIMATE mode, however, then the +algorithm is deterministic and the results should be identical between +runs. + +------------------------------------------------------------------------------- + +Question 3.9. Can I save FFTW's plans? + +Yes. Starting with version 1.2, FFTW provides the wisdom mechanism for +saving plans; see the FFTW manual. + +------------------------------------------------------------------------------- + +Question 3.10. Why does your inverse transform return a scaled result? + +Computing the forward transform followed by the backward transform (or +vice versa) yields the original array scaled by the size of the array. +(For multi-dimensional transforms, the size of the array is the product of +the dimensions.) We could, instead, have chosen a normalization that +would have returned the unscaled array. Or, to accomodate the many +conventions in this matter, the transform routines could have accepted a +"scale factor" parameter. We did not do this, however, for two reasons. +First, we didn't want to sacrifice performance in the common case where +the scale factor is 1. Second, in real applications the FFT is followed or +preceded by some computation on the data, into which the scale factor can +typically be absorbed at little or no cost. + +------------------------------------------------------------------------------- + +Question 3.11. How can I make FFTW put the origin (zero frequency) at the center of its output? + +For human viewing of a spectrum, it is often convenient to put the origin +in frequency space at the center of the output array, rather than in the +zero-th element (the default in FFTW). If all of the dimensions of your +array are even, you can accomplish this by simply multiplying each element +of the input array by (-1)^(i + j + ...), where i, j, etcetera are the +indices of the element. (This trick is a general property of the DFT, and +is not specific to FFTW.) + +------------------------------------------------------------------------------- + +Question 3.12. How do I FFT an image/audio file in *foobar* format? + +FFTW performs an FFT on an array of floating-point values. You can +certainly use it to compute the transform of an image or audio stream, but +you are responsible for figuring out your data format and converting it to +the form FFTW requires. + +------------------------------------------------------------------------------- + +Question 3.13. My program does not link (on Unix). + +The libraries must be listed in the correct order (-lfftw3 -lm for FFTW +3.x) and *after* your program sources/objects. (The general rule is that +if *A* uses *B*, then *A* must be listed before *B* in the link command.). + +------------------------------------------------------------------------------- + +Question 3.14. I included your header, but linking still fails. + +You're a C++ programmer, aren't you? You have to compile the FFTW library +and link it into your program, not just #include <fftw3.h>. (Yes, this is +really a FAQ.) + +------------------------------------------------------------------------------- + +Question 3.15. My program crashes, complaining about stack space. + +You cannot declare large arrays with automatic storage (e.g. via +fftw_complex array[N]); you should use fftw_malloc (or equivalent) to +allocate the arrays you want to transform if they are larger than a few +hundred elements. + +------------------------------------------------------------------------------- + +Question 3.16. FFTW seems to have a memory leak. + +After you create a plan, FFTW caches the information required to quickly +recreate the plan. (See Q3.9 `Can I save FFTW's plans?') It also +maintains a small amount of other persistent memory. You can deallocate +all of FFTW's internally allocated memory, if you wish, by calling +fftw_cleanup(), as documented in the manual. + +------------------------------------------------------------------------------- + +Question 3.17. The output of FFTW's transform is all zeros. + +You should initialize your input array *after* creating the plan, unless +you use FFTW_ESTIMATE: planning with FFTW_MEASURE or FFTW_PATIENT +overwrites the input/output arrays, as described in the manual. + +------------------------------------------------------------------------------- + +Question 3.18. How do I call FFTW from the Microsoft language du jour? + +Please *do not* ask us Windows-specific questions. We do not use Windows. +We know nothing about Visual Basic, Visual C++, or .NET. Please find the +appropriate Usenet discussion group and ask your question there. See also +Q2.2 `Does FFTW run on Windows?'. + +------------------------------------------------------------------------------- + +Question 3.19. Can I compute only a subset of the DFT outputs? + +In general, no, an FFT intrinsically computes all outputs from all inputs. +In principle, there is something called a *pruned FFT* that can do what +you want, but to compute K outputs out of N the complexity is in general +O(N log K) instead of O(N log N), thus saving only a small additive factor +in the log. (The same argument holds if you instead have only K nonzero +inputs.) + +There are some specific cases in which you can get the O(N log K) +performance benefits easily, however, by combining a few ordinary FFTs. +In particular, the case where you want the first K outputs, where K +divides N, can be handled by performing N/K transforms of size K and then +summing the outputs multiplied by appropriate phase factors. For more +details, see pruned FFTs with FFTW. + +There are also some algorithms that compute pruned transforms +*approximately*, but they are beyond the scope of this FAQ. + +------------------------------------------------------------------------------- + +Question 3.20. Can I use FFTW's routines for in-place and out-of-place matrix transposition? + +You can use the FFTW guru interface to create a rank-0 transform of vector +rank 2 where the vector strides are transposed. (A rank-0 transform is +equivalent to a 1D transform of size 1, which. just copies the input into +the output.) Specifying the same location for the input and output makes +the transpose in-place. + +For double-valued data stored in row-major format, plan creation looks +like this: + +fftw_plan plan_transpose(int rows, int cols, double *in, double *out) +{ + const unsigned flags = FFTW_ESTIMATE; /* other flags are possible */ + fftw_iodim howmany_dims[2]; + + howmany_dims[0].n = rows; + howmany_dims[0].is = cols; + howmany_dims[0].os = 1; + + howmany_dims[1].n = cols; + howmany_dims[1].is = 1; + howmany_dims[1].os = rows; + + return fftw_plan_guru_r2r(/*rank=*/ 0, /*dims=*/ NULL, + /*howmany_rank=*/ 2, howmany_dims, + in, out, /*kind=*/ NULL, flags); +} +(This entry was written by Rhys Ulerich.) + +=============================================================================== + +Section 4. Internals of FFTW + + Q4.1 How does FFTW work? + Q4.2 Why is FFTW so fast? + +------------------------------------------------------------------------------- + +Question 4.1. How does FFTW work? + +The innovation (if it can be so called) in FFTW consists in having a +variety of composable *solvers*, representing different FFT algorithms and +implementation strategies, whose combination into a particular *plan* for +a given size can be determined at runtime according to the characteristics +of your machine/compiler. This peculiar software architecture allows FFTW +to adapt itself to almost any machine. + +For more details (albeit somewhat outdated), see the paper "FFTW: An +Adaptive Software Architecture for the FFT", by M. Frigo and S. G. +Johnson, *Proc. ICASSP* 3, 1381 (1998), also available at the FFTW web +page. + +------------------------------------------------------------------------------- + +Question 4.2. Why is FFTW so fast? + +This is a complex question, and there is no simple answer. In fact, the +authors do not fully know the answer, either. In addition to many small +performance hacks throughout FFTW, there are three general reasons for +FFTW's speed. + +* FFTW uses a variety of FFT algorithms and implementation styles that + can be arbitrarily composed to adapt itself to a machine. See Q4.1 `How + does FFTW work?'. +* FFTW uses a code generator to produce highly-optimized routines for + computing small transforms. +* FFTW uses explicit divide-and-conquer to take advantage of the memory + hierarchy. + +For more details (albeit somewhat outdated), see the paper "FFTW: An +Adaptive Software Architecture for the FFT", by M. Frigo and S. G. +Johnson, *Proc. ICASSP* 3, 1381 (1998), available along with other +references at the FFTW web page. + +=============================================================================== + +Section 5. Known bugs + + Q5.1 FFTW 1.1 crashes in rfftwnd on Linux. + Q5.2 The MPI transforms in FFTW 1.2 give incorrect results/leak memory. + Q5.3 The test programs in FFTW 1.2.1 fail when I change FFTW to use sin + Q5.4 The test program in FFTW 1.2.1 fails for n > 46340. + Q5.5 The threaded code fails on Linux Redhat 5.0 + Q5.6 FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dime + Q5.7 FFTW 2.0's complex transforms give the wrong results with prime fa + Q5.8 FFTW 2.1.1's MPI test programs crash with MPICH. + Q5.9 FFTW 2.1.2's multi-threaded transforms don't work on AIX. + Q5.10 FFTW 2.1.2's complex transforms give incorrect results for large p + Q5.11 FFTW 2.1.3's multi-threaded transforms don't give any speedup on S + Q5.12 FFTW 2.1.3 crashes on AIX. + +------------------------------------------------------------------------------- + +Question 5.1. FFTW 1.1 crashes in rfftwnd on Linux. + +This bug was fixed in FFTW 1.2. There was a bug in rfftwnd causing an +incorrect amount of memory to be allocated. The bug showed up in Linux +with libc-5.3.12 (and nowhere else that we know of). + +------------------------------------------------------------------------------- + +Question 5.2. The MPI transforms in FFTW 1.2 give incorrect results/leak memory. + +These bugs were corrected in FFTW 1.2.1. The MPI transforms (really, just +the transpose routines) in FFTW 1.2 had bugs that could cause errors in +some situations. + +------------------------------------------------------------------------------- + +Question 5.3. The test programs in FFTW 1.2.1 fail when I change FFTW to use single precision. + +This bug was fixed in FFTW 1.3. (Older versions of FFTW did work in +single precision, but the test programs didn't--the error tolerances in +the tests were set for double precision.) + +------------------------------------------------------------------------------- + +Question 5.4. The test program in FFTW 1.2.1 fails for n > 46340. + +This bug was fixed in FFTW 1.3. FFTW 1.2.1 produced the right answer, but +the test program was wrong. For large n, n*n in the naive transform that +we used for comparison overflows 32 bit integer precision, breaking the +test. + +------------------------------------------------------------------------------- + +Question 5.5. The threaded code fails on Linux Redhat 5.0 + +We had problems with glibc-2.0.5. The code should work with glibc-2.0.7. + +------------------------------------------------------------------------------- + +Question 5.6. FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dimension >= 65536. + +This bug was fixed in FFTW 2.0.1. (There was a 32-bit integer overflow +due to a poorly-parenthesized expression.) + +------------------------------------------------------------------------------- + +Question 5.7. FFTW 2.0's complex transforms give the wrong results with prime factors 17 to 97. + +There was a bug in the complex transforms that could cause incorrect +results under (hopefully rare) circumstances for lengths with +intermediate-size prime factors (17-97). This bug was fixed in FFTW +2.1.1. + +------------------------------------------------------------------------------- + +Question 5.8. FFTW 2.1.1's MPI test programs crash with MPICH. + +This bug was fixed in FFTW 2.1.2. The 2.1/2.1.1 MPI test programs crashed +when using the MPICH implementation of MPI with the ch_p4 device (TCP/IP); +the transforms themselves worked fine. + +------------------------------------------------------------------------------- + +Question 5.9. FFTW 2.1.2's multi-threaded transforms don't work on AIX. + +This bug was fixed in FFTW 2.1.3. The multi-threaded transforms in +previous versions didn't work with AIX's pthreads implementation, which +idiosyncratically creates threads in detached (non-joinable) mode by +default. + +------------------------------------------------------------------------------- + +Question 5.10. FFTW 2.1.2's complex transforms give incorrect results for large prime sizes. + +This bug was fixed in FFTW 2.1.3. FFTW's complex-transform algorithm for +prime sizes (in versions 2.0 to 2.1.2) had an integer overflow problem +that caused incorrect results for many primes greater than 32768 (on +32-bit machines). (Sizes without large prime factors are not affected.) + +------------------------------------------------------------------------------- + +Question 5.11. FFTW 2.1.3's multi-threaded transforms don't give any speedup on Solaris. + +This bug was fixed in FFTW 2.1.4. (By default, Solaris creates threads +that do not parallelize over multiple processors, so one has to request +the proper behavior specifically.) + +------------------------------------------------------------------------------- + +Question 5.12. FFTW 2.1.3 crashes on AIX. + +The FFTW 2.1.3 configure script picked incorrect compiler flags for the +xlc compiler on newer IBM processors. This is fixed in FFTW 2.1.4. +