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<!-- This HTML file has been created by texi2html 1.52
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     from fftw.texi on 18 May 1999 -->
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<TITLE>FFTW - Footnotes</TITLE>
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<H1>FFTW</H1>
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<H2>For version 2.1.2, 18 May 1999</H2>
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<P>
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<P><HR><P>
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<H3><A NAME="FOOT1" HREF="fftw_2.html#DOCF1">(1)</A></H3>
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<P>The output for the
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multi-dimensional rfftw is a more-conventional array of
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<CODE>fftw_complex</CODE> values, but the format here permitted us greater
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efficiency in one dimension.
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<H3><A NAME="FOOT2" HREF="fftw_3.html#DOCF2">(2)</A></H3>
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<P>The basic problem is the resolution of the clock:
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FFTW needs to run for a certain time for the clock to be reliable.
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<H3><A NAME="FOOT3" HREF="fftw_3.html#DOCF3">(3)</A></H3>
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<P><CODE>fftwnd</CODE> actually may use some temporary
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storage (hidden in the plan), but this storage space is only the size of
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the largest dimension of the array, rather than being as big as the
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entire array.  (Unless you use <CODE>fftwnd</CODE> to perform one-dimensional
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transforms, in which case the temporary storage required for in-place
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transforms <EM>is</EM> as big as the entire array.)
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<H3><A NAME="FOOT4" HREF="fftw_3.html#DOCF4">(4)</A></H3>
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<P>The etymologically-correct spelling would be
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<CODE>frftw_</CODE>, but it is hard to remember.
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<H3><A NAME="FOOT5" HREF="fftw_4.html#DOCF5">(5)</A></H3>
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<P>There is one exception: when performing
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one-dimensional in-place transforms, the <CODE>out</CODE> parameter is always
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ignored by the multi-threaded routines, instead of being used as a
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workspace if it is non-<CODE>NULL</CODE> as in the uniprocessor routines.  The
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multi-threaded routines always allocate their own workspace (the size of
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which depends upon the number of threads).
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<H3><A NAME="FOOT6" HREF="fftw_4.html#DOCF6">(6)</A></H3>
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<P>The 1D
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transforms require much more communication.  All the communication in
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our FFT routines takes the form of an all-to-all communication: the
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multi-dimensional transforms require two all-to-all communications (or
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one, if you use <CODE>FFTW_TRANSPOSED_ORDER</CODE>), while the one-dimensional
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transforms require <EM>three</EM> (or two, if you use scrambled input or
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output).
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<H3><A NAME="FOOT7" HREF="fftw_4.html#DOCF7">(7)</A></H3>
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<P>An
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FFT is particularly hard on communications systems, as it requires an
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<EM>all-to-all</EM> communication, which is more or less the worst possible
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case.
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<H3><A NAME="FOOT8" HREF="fftw_5.html#DOCF8">(8)</A></H3>
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<P>Technically, Fortran 77 identifiers are
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not allowed to have more than 6 characters, nor may they contain
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underscores.  Any compiler that enforces this limitation doesn't deserve
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to link to FFTW.
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<H3><A NAME="FOOT9" HREF="fftw_6.html#DOCF9">(9)</A></H3>
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<P>Each version of <CODE>cc</CODE>
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seems to have its own magic incantation to get the fastest code most of
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the time--you'd think that people would have agreed upon some
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convention, e.g. "<CODE>-Omax</CODE>", by now.
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<P><HR><P>
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This document was generated on 18 May 1999 using the
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<A HREF="http://wwwinfo.cern.ch/dis/texi2html/">texi2html</A>
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translator version 1.52. (properly hacked by athena@theory.lcs.mit.edu)</P>
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