\comment This is the source for the FFTW FAQ list, in
\comment the Bizarre Format With No Name.  It is turned into Lout
\comment input, HTML, plain ASCII and an Info document by a Perl script.
\comment
\comment The format and scripts come from the Linux FAQ, by
\comment Ian Jackson.
\set brieftitle FFTW FAQ
\set author     <A href="http://www.fftw.org">Matteo Frigo and Steven G. Johnson</A> / <A href="mailto:fftw@fftw.org">fftw@fftw.org</A>
\set authormail fftw@fftw.org
\set title      FFTW Frequently Asked Questions with Answers
\set copyholder Massachusetts Institute of Technology
\call-html startup html.refs
\copyto ASCII
            FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS
                            `date '+%d %h %Y'`
			     Matteo Frigo
			   Steven G. Johnson
 			    <fftw@fftw.org>

\endcopy
\copyto INFO
START-INFO-DIR-ENTRY
* FFTW FAQ: (fftw-faq). FFTW Frequently Asked Questions with Answers.
END-INFO-DIR-ENTRY


File: $prefix.info, Node: Top, Next: Question 1.1, Up: (dir)

            FFTW FREQUENTLY ASKED QUESTIONS WITH ANSWERS
                            `date '+%d %h %Y'`
			     Matteo Frigo
			   Steven G. Johnson
			    <fftw@fftw.org>

\endcopy

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.

\section  Index

\index

\comment ######################################################################

\section  Introduction and General Information

\question 26aug:whatisfftw  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, 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 26aug:whereisfftw  How do I obtain FFTW?

FFTW can be found at \docref{the FFTW web page\}.  You can also
retrieve it from \ftpon ftp.fftw.org in \ftpin /pub/fftw.

\question 26aug:isfftwfree  Is FFTW free software?

Starting with version 1.3, FFTW is Free Software in the technical
sense defined by the Free Software Foundation (see \docref{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 10apr:nonfree  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.

\comment ######################################################################

\section  Installing FFTW

\question 26aug:systems  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 \qref runOnDOS and 
\qref compilerCrashes.)

\question 26aug:runOnDOS  Does FFTW run on DOS/Windows?

It should.  FFTW was not developed on DOS or Windows, but the source
code is straight ANSI C.  Some users have reported using FFTW on
DOS/Windows using various compilers.  See also the \docref{FFTW Windows
installation notes\} and \qref compilerCrashes

\question 26aug:compilerCrashes  My compiler has trouble with FFTW.

Complain fiercely to the vendor of the compiler. 

FFTW is a heavily-optimized piece of software that is likely to push
compilers to their limits.  We had no problems with, for example,
\courier{gcc 2.7.2\}, \courier{egcs 1.1.x\}, Sun's \courier{SC4.0\},
and IBM's \courier{XLC\}.  Users have also reported successful
compilations of FFTW using Borland's C/C++ compilers on Windows.

The Portland Group PGCC compiler, version 4.0 for Linux/x86,
reportedly produces incorrect code for FFTW 2.1.3.

Visual C++ 4.0 crashes when compiling FFTW 1.2 with all optimizations
turned on.  Visual C++ 5.0 reportedly produces incorrect code for the
real transforms in FFTW 2.x when the option "Maximize speed" is set.
We are told that Service Pack 3 fixes the bug.

Metrowerks CodeWarrior Pro 4 reportedly generates incorrect code for
the PowerPC when compiling FFTW at optimization level 4.  Supposedly,
this bug is fixed in CW Pro 5 with all the latest updates applied.
(No problems were reported for previous versions.)

Various problems have also been observed with SGI's MIPSpro compilers,
versions 7.2.0 and 7.2.1 (you may have to lower the optimization level
for some files to get them to compile); the bug seems to be fixed in
version 7.3.  The test program in earlier versions of FFTW had
problems with the \courier{-xO5\} option in Sun's \courier{SC4.0\} C
compiler.  \courier{egcs 1.0.2\} produced incorrect code for FFTW on
the PowerPC (corrected in \courier{egcs 1.1\}).

The DEC C compiler, V5.8-009 on Digital UNIX V4.0 (Rev. 1091) is known
to have bugs with its EV6 tuning.  Specifically, compiling FFTW with
\courier{-arch host\} (the default) or \courier{-arch ev6\} on an
Alpha EV6 can cause FFTW (e.g. \courier{fftw_test -s 256\}) to crash.

\question 26aug:solarisSucks FFTW does not compile on Solaris, complaining about \courier{const\}.

We know that at least on Solaris 2.5.x with Sun's compilers 4.2 you
might get error messages from \courier{make\} such as

\courier{"./fftw.h", line 88: warning: const is a keyword in ANSI C\}

This is the case when the \courier{configure\} script reports that
\courier{const\} does not work:

\courier{checking for working const... (cached) no\}

You should be aware that Solaris comes with two compilers, namely,
\courier{/opt/SUNWspro/SC4.2/bin/cc\} and \courier{/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 \courier{cc\}
is used.

To know whether your compiler is the right one,  type
\courier{cc -V\}.  If the compiler prints ``\courier{ucbcc\}'',
as in 

\courier{ucbcc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2\}

then the compiler is wrong.  The right message is something like

\courier{cc: WorkShop Compilers 4.2 30 Oct 1996 C 4.2\}


\question 26aug:languages  Which language is FFTW written in?

FFTW is written in ANSI C.  Most of the code, however, was
automatically generated by a program called \courier{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.

\courier{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 \ftpon ftp.inria.fr in the directory \ftpin /lang/caml-light.

\question 26aug:fortran  Can I call FFTW from FORTRAN?

Yes, but not directly.  The main problem is that Fortran cannot pass
parameters by value.  However, FFTW can be called indirectly from
Fortran through the use of special C "wrapper" routines.  Appropriate
wrapper code, documented in the FFTW manual, is included with FFTW
(versions 1.3 and higher).

By default, FFTW configures its wrapper routines to work with the
first compiler it finds, e.g. \courier{g77\}.  To configure for a
different, incompatible Fortran compiler \courier{foobar\}, use
\courier{./configure F77=foobar\} when installing FFTW.

\question 26aug:cplusplus  Can I call FFTW from C++?

Most definitely.  FFTW should compile and run under any C++ compiler.

\question 26aug:whynotfortran  Why isn't FFTW written in FORTRAN/C++?

Because we don't like those languages, and neither approaches the
portability of C.

\question 29mar:singleprec How do I compile FFTW to run in single precision?

On a Unix system: \courier{configure --enable-float\}.  On a non-Unix
system: edit \courier{fftw/fftw.h\} to \courier{#define\} the symbol
\courier{FFTW_ENABLE_FLOAT\}.  In both cases, you must then recompile
FFTW.

\comment ######################################################################

\section  Using FFTW

\question 25may:slow 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:

\call startlist
\call item
First, you create a plan.  This will take several seconds.
\call item
Then, you reuse the plan many times to perform FFTs.  These are fast.
\call endlist

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
\courier{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 \qref savePlans

\question 22oct:slows 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 22oct:segfault An FFTW routine is crashing when I call it.

You almost certainly have a bug in your 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.  Learn to debug, and don't
complain to us unless you can come up with a minimal program
(preferably under 30 lines) that illustrates the problem.

\question 22oct:fortran64 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
\courier{integer*8\}.

\question 24mar:conventions 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
\courier{FFTW_FORWARD\}/\courier{FFTW_BACKWARD\} directions correspond
to signs of -1/+1 in the exponent of the DFT definition.
(\italic{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 \qref whyscaled.

Finally, note that floating-point arithmetic is not exact, so
different FFT algorithms will give slightly different results (on the
order of the numerical accuracy; typically a fractional difference of
1e-15 or so).

\question 22oct:inplace Your in-place transform gives incorrect results.

As described in the FFTW manual, the output array argument has a
special meaning for \courier{FFTW_INPLACE\} transforms; you should not
pass the input array for this argument.

\question 26aug:savePlans Can I save FFTW's plans?

Yes. Starting with version 1.2, FFTW provides the 
\courier{wisdom\} mechanism for saving plans.  See \qref wisdom
and the FFTW manual.

\question 14sep:whyscaled Why does your inverse transform return a scaled result?

Computing the forward transform followed by the backward transform (or
vice versa) yields the original array scaled by the size of the array.
(For multi-dimensional transforms, the size of the array is the
product of the dimensions.)  We could, instead, have chosen a
normalization that would have returned the unscaled array. Or, to
accomodate the many conventions in this matter, the transform routines
could have accepted a "scale factor" parameter. We did not do this,
however, for two reasons. First, we didn't want to sacrifice
performance in the common case where the scale factor is 1. Second, in
real applications the FFT is followed or preceded by some computation
on the data, into which the scale factor can typically be absorbed at
little or no cost.

\question 02dec:centerorigin How can I make FFTW put the origin (zero frequency) at the center of its output?

For human viewing of a spectrum, it is often convenient to put the
origin in frequency space at the center of the output array, rather
than in the zero-th element (the default in FFTW).  If all of the
dimensions of your array are even, you can accomplish this by simply
multiplying each element of the input array by (-1)^(i + j + ...),
where i, j, etcetera are the indices of the element.  (This trick is a
general property of the DFT, and is not specific to FFTW.)

\question 08may:imageaudio How do I FFT an image/audio file in \italic{foobar\} format?

FFTW performs an FFT on an array of floating-point values.  You can
certainly use it to compute the transform of an image or audio stream,
but you are responsible for figuring out your data format and
converting it to the form FFTW requires.

\question 09apr:linkfails My program does not link (on Unix).

Please use the exact order in which libraries are specified by the
FFTW manual (e.g. \courier{-lrfftw -lfftw -lm\}).  Also, note that the
libraries must be listed after your program sources/objects.  (The
general rule is that if \italic{A\} uses \italic{B\}, then \italic{A\}
must be listed before \italic{B\} in the link command.).  For example,
switching the order to \courier{-lfftw -lrfftw -lm\} will fail.

\question 22oct:nostack My program crashes, complaining about stack space.

You cannot declare large arrays statically; you should use
\courier{malloc\} (or equivalent) to allocate the arrays you want to
transform if they are larger than a few hundred elements.

\comment ######################################################################

\section  Internals of FFTW

\question 26aug:howworks  How does FFTW work?

The innovation (if it can be so called) in FFTW consists in having an
interpreter execute the transform.  The program for the interpreter
(the \italic{plan\}) is computed 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, see the paper "The Fastest Fourier Transform in the
West", by M. Frigo and S. G. Johnson, available at \docref{the FFTW
web page\}.  See also "FFTW: An Adaptive Software Architecture for the
FFT", in ICASSP '98.

\question 26aug:whyfast Why is FFTW so fast?

This is a complex question, and there is no simple answer.  In fact,
the authors do not fully know the answer, either.  In addition to many
small performance hacks throughout FFTW, there are three general
reasons for FFTW's speed.

\call startlist
\call item
	FFTW uses an internal interpreter to adapt itself to
a machine.  See \qref howworks.
\call item
	FFTW uses a code generator to produce highly-optimized
routines for computing small transforms.
\call item
	FFTW uses explicit divide-and-conquer to take advantage
of the memory hierarchy.
\call endlist

For more details on these three topics, see the paper "The Fastest
Fourier Transform in the West", by M. Frigo and S. G. Johnson,
available at \docref{the FFTW web page\}.

\question 26aug:wisdom What is this \courier{wisdom\} thing?

\courier{wisdom\} is the name of the mechanism that FFTW uses to save
and restore plans.  Rather than just saving plans, FFTW remembers what
it learns about your machine, and becomes wiser and wiser as time
passes by.  You can save \courier{wisdom\} for later use.

\question 26aug:whywisdom Why do you use \courier{wisdom\}? I just wanted to save a plan.

\courier{wisdom\} could be implemented with less effort than a general
plan-saving mechanism would have required.  In addition,
\courier{wisdom\} provides additional benefits.  For example, if you
are planning transforms of size 1024, and later you want a transform
of size 2048, most of the calculations of the 1024 case can be reused.

In short, \courier{wisdom\} does more things with less effort, and
seemed like The Right Thing to do.

\comment ######################################################################

\section  Known bugs

\question 27aug:rfftwndbug  FFTW 1.1 crashes in rfftwnd on Linux.

This bug was fixed in FFTW 1.2.  There was a bug in \courier{rfftwnd\}
causing an incorrect amount of memory to be allocated.  The bug showed
up in Linux with libc-5.3.12 (and nowhere else that we know of).

\question 15oct:fftwmpibug The MPI transforms in FFTW 1.2 give incorrect results/leak memory.

These bugs were corrected in FFTW 1.2.1.  The MPI transforms (really,
just the transpose routines) in FFTW 1.2 had bugs that could cause
errors in some situations.

\question 05nov:testsingbug The test programs in FFTW 1.2.1 fail when I change FFTW to use single precision.

This bug was fixed in FFTW 1.3.  (Older versions of FFTW did
work in single precision, but the test programs didn't--the error
tolerances in the tests were set for double precision.)

\question 24mar:teststoobig The test program in FFTW 1.2.1 fails for n > 46340.

This bug was fixed in FFTW 1.3.  FFTW 1.2.1 produced the right answer,
but the test program was wrong.  For large n, n*n in the naive
transform that we used for comparison overflows 32 bit integer
precision, breaking the test.

\question 24aug:linuxthreads The threaded code fails on Linux Redhat 5.0

We had problems with glibc-2.0.5.  The code should work with
glibc-2.0.7.

\question 26sep:bigrfftwnd FFTW 2.0's rfftwnd fails for rank > 1 transforms with a final dimension >= 65536.

This bug was fixed in FFTW 2.0.1.  (There was a 32-bit integer overflow due
to a poorly-parenthesized expression.)

\question 26mar:primebug FFTW 2.0's complex transforms give the wrong results with prime factors 17 to 97.

There was a bug in the complex transforms that could cause incorrect
results under (hopefully rare) circumstances for lengths with
intermediate-size prime factors (17-97).  This bug was fixed in FFTW
2.1.1.

\question 05apr:mpichbug FFTW 2.1.1's MPI test programs crash with MPICH.

This bug was fixed in FFTW 2.1.2.  The 2.1/2.1.1 MPI test programs crashed
when using the MPICH implementation of MPI with the \courier{ch_p4\}
device (TCP/IP); the transforms themselves worked fine.

\question 25may:aixthreadbug FFTW 2.1.2's multi-threaded transforms don't work on AIX.

This bug was fixed in FFTW 2.1.3.  The multi-threaded transforms in
previous versions didn't work with AIX's \courier{pthreads\}
implementation, which idiosyncratically creates threads in detached
(non-joinable) mode by default.

\question 27sep:bigprimebug FFTW 2.1.2's complex transforms give incorrect results for large prime sizes.

This bug was fixed in FFTW 2.1.3.  FFTW's complex-transform algorithm
for prime sizes (in versions 2.0 to 2.1.2) had an integer overflow
problem that caused incorrect results for many primes greater than
32768 (on 32-bit machines).  (Sizes without large prime factors are
not affected.)

\question 03may:aixflags  FFTW 2.1.3 crashes on AIX

The FFTW 2.1.3 \courier{configure\} script picked incorrect compiler
flags for the \courier{xlc\} compiler on newer IBM processors.  This
is fixed in FFTW 2.1.4.

\comment Here it ends!
