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Sergey Lapin
2025-07-12 12:17:44 +03:00
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fftw-3.3.10/doc/fftw3.texi Normal file
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\input texinfo @c -*-texinfo-*-
@c Update by C-x C-e on: (texinfo-multiple-files-update "fftw3.texi" nil t)
@setfilename fftw3.info
@include version.texi
@finalout
@settitle FFTW @value{VERSION}
@setchapternewpage odd
@c define constant index (ct)
@defcodeindex ct
@syncodeindex ct fn
@syncodeindex vr fn
@syncodeindex pg fn
@syncodeindex tp fn
@c define foreign function index (ff)
@defcodeindex ff
@syncodeindex ff cp
@c define foreign constant index (fc)
@defcodeindex fc
@syncodeindex fc cp
@c define foreign program index (fp)
@defcodeindex fp
@syncodeindex fp cp
@comment %**end of header
@iftex
@paragraphindent 0
@parskip=@medskipamount
@end iftex
@c
@c The following macros are coded in a weird way:
@c @macro FOO
@c @noindent
@c <STUFF>
@c @refill
@c @end macro
@c The @noindent/@refill stuff is not necessary in texinfo up to version
@c 4, but it is a hack necessary to make texinfo-5 work.
@c Texinfo has been stable for the first 15 years of FFTW's history.
@c Then some genius, with too much time in his hands and on a mission to
@c deliver the world from the evil of the C language, decided to rewrite
@c makeinfo in Perl, the old C version of makeinfo being, as I said,
@c evil. The official excuse for the rewrite was that now I can have my
@c manual in XML format, as if XML were a feature.
@c The result of this stroke of genius is that texinfo-5 has different
@c rules for macro expansion than texinfo-4 does, specifically regarding
@c whether or not spaces after a macro are ignored. Texinfo-4 had weird
@c rules, but at least they were constant and internally more or less
@c consistent. Texinfo-5 has different rules, and even worse the rules
@c in texinfo-5 are inconsistent between the TeX and HTML output
@c processors. This situation makes it almost impossible for us to
@c produce a manual that works with both texinfo 4 and 5 in all modes
@c (TeX, info, and html). The @noindent/@refill hack is my best shot at
@c patching this situation.
@c "@noindent" has two effects: First, it makes texinfo-5 believe that
@c the next "@ifinfo" is on a new line, otherwise texinfo-5 complains
@c that it is not (even though it obviously is). Second, "@noindent" is
@c a macro that eats extra space, and we want this effect because somehow
@c macro expansion in texinfo-5 inserts extra spaces that were not there
@c in texinfo-4.
@c "@refill" stops texinfo-5 from interpreting the rest of the line after
@c a macro invocation as an argument to "@end tex". For example, in
@c "FFTW uses @Onlogn algorithms", somehow texinfo-5 thinks that
@c "algorithms" is an argument to "@end tex". "@noindent" would have the
@c same effect (as would any other macro invocation, I think), but,
@c unlike "@noindent", "@refill" does not eat spaces and does not scan
@c the rest of the input file for macro arguments. However, "@refill" is
@c deemed "obsolete" in the texinfo-5 source code, so expect this to
@c break at some point.
@c This situation is wholly unsatisfactory, and the GNU project is
@c obviously out of control. If this nonsense persists, we will abandon
@c texinfo and produce a latex-only version of the manual.
@macro Onlogn
@noindent
@ifinfo
O(n log n)
@end ifinfo
@html
<i>O</i>(<i>n</i>&nbsp;log&nbsp;<i>n</i>)
@end html
@tex
$O(n \\log n)$
@end tex
@refill
@end macro
@macro ndims
@noindent
@ifinfo
n[0] x n[1] x n[2] x ... x n[d-1]
@end ifinfo
@html
n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;n<sub>d-1</sub>
@end html
@tex
$n_0 \\times n_1 \\times n_2 \\times \\cdots \\times n_{d-1}$
@end tex
@refill
@end macro
@macro ndimshalf
@noindent
@ifinfo
n[0] x n[1] x n[2] x ... x (n[d-1]/2 + 1)
@end ifinfo
@html
n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;(n<sub>d-1</sub>/2 + 1)
@end html
@tex
$n_0 \\times n_1 \\times n_2 \\times \\cdots \\times (n_{d-1}/2 + 1)$
@end tex
@refill
@end macro
@macro ndimspad
@noindent
@ifinfo
n[0] x n[1] x n[2] x ... x [2 (n[d-1]/2 + 1)]
@end ifinfo
@html
n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&nbsp;&hellip;&nbsp;&times;&nbsp;[2&nbsp;(n<sub>d-1</sub>/2 + 1)]
@end html
@tex
$n_0 \\times n_1 \\times n_2 \\times \\cdots \\times [2(n_{d-1}/2 + 1)]$
@end tex
@refill
@end macro
@macro twodims{d1, d2}
@noindent
@ifinfo
\d1\ x \d2\
@end ifinfo
@html
\d1\&nbsp;&times;&nbsp;\d2\
@end html
@tex
$\d1\ \\times \d2\$
@end tex
@refill
@end macro
@macro threedims{d1, d2, d3}
@noindent
@ifinfo
\d1\ x \d2\ x \d3\
@end ifinfo
@html
\d1\&nbsp;&times;&nbsp;\d2\&nbsp;&times;&nbsp;\d3\
@end html
@tex
$\d1\ \\times \d2\ \\times \d3\$
@end tex
@refill
@end macro
@macro dimk{k}
@noindent
@ifinfo
n[\k\]
@end ifinfo
@html
n<sub>\k\</sub>
@end html
@tex
$n_\k\$
@end tex
@refill
@end macro
@macro ndimstrans
@noindent
@ifinfo
n[1] x n[0] x n[2] x ... x n[d-1]
@end ifinfo
@html
n<sub>1</sub>&nbsp;&times;&nbsp;n<sub>0</sub>&nbsp;&times;&nbsp;n<sub>2</sub>&nbsp;&times;&hellip;&times;&nbsp;n<sub>d-1</sub>
@end html
@tex
$n_1 \\times n_0 \\times n_2 \\times \\cdots \\times n_{d-1}$
@end tex
@refill
@end macro
@copying
This manual is for FFTW
(version @value{VERSION}, @value{UPDATED}).
Copyright @copyright{} 2003 Matteo Frigo.
Copyright @copyright{} 2003 Massachusetts Institute of Technology.
@quotation
Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.
Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided that the
entire resulting derived work is distributed under the terms of a
permission notice identical to this one.
Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that this permission notice may be stated in a translation
approved by the Free Software Foundation.
@end quotation
@end copying
@dircategory Development
@direntry
* fftw3: (fftw3). FFTW User's Manual.
@end direntry
@titlepage
@title FFTW
@subtitle for version @value{VERSION}, @value{UPDATED}
@author Matteo Frigo
@author Steven G. Johnson
@page
@vskip 0pt plus 1filll
@insertcopying
@end titlepage
@contents
@ifnottex
@node Top, Introduction, (dir), (dir)
@top FFTW User Manual
Welcome to FFTW, the Fastest Fourier Transform in the West. FFTW is a
collection of fast C routines to compute the discrete Fourier transform.
This manual documents FFTW version @value{VERSION}.
@end ifnottex
@menu
* Introduction::
* Tutorial::
* Other Important Topics::
* FFTW Reference::
* Multi-threaded FFTW::
* Distributed-memory FFTW with MPI::
* Calling FFTW from Modern Fortran::
* Calling FFTW from Legacy Fortran::
* Upgrading from FFTW version 2::
* Installation and Customization::
* Acknowledgments::
* License and Copyright::
* Concept Index::
* Library Index::
@end menu
@c ************************************************************
@include intro.texi
@include tutorial.texi
@include other.texi
@include reference.texi
@include threads.texi
@include mpi.texi
@include modern-fortran.texi
@include legacy-fortran.texi
@include upgrading.texi
@include install.texi
@include acknowledgements.texi
@include license.texi
@include cindex.texi
@include findex.texi
@c ************************************************************
@bye