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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"><HTML><HEAD><!-- This HTML file has been created by texi2html 1.52 from fftw.texi on 24 March 2003 --><TITLE>FFTW - Footnotes</TITLE></HEAD><BODY TEXT="#000000" BGCOLOR="#FFFFFF"><H1>FFTW</H1><H2>For version 2.1.5, 16 March 2003</H2><P><P><HR><P><H3><A NAME="FOOT1" HREF="fftw_2.html#DOCF1">(1)</A></H3><P>The output for themulti-dimensional rfftw is a more-conventional array of<CODE>fftw_complex</CODE> values, but the format here permitted us greaterefficiency in one dimension.<H3><A NAME="FOOT2" HREF="fftw_3.html#DOCF2">(2)</A></H3><P>The basic problem is the resolution of the clock:FFTW needs to run for a certain time for the clock to be reliable.<H3><A NAME="FOOT3" HREF="fftw_3.html#DOCF3">(3)</A></H3><P><CODE>fftwnd</CODE> actually may use some temporarystorage (hidden in the plan), but this storage space is only the size ofthe largest dimension of the array, rather than being as big as theentire array. (Unless you use <CODE>fftwnd</CODE> to perform one-dimensionaltransforms, in which case the temporary storage required for in-placetransforms <EM>is</EM> as big as the entire array.)<H3><A NAME="FOOT4" HREF="fftw_3.html#DOCF4">(4)</A></H3><P>The etymologically-correct spelling would be<CODE>frftw_</CODE>, but it is hard to remember.<H3><A NAME="FOOT5" HREF="fftw_4.html#DOCF5">(5)</A></H3><P>There is one exception: when performingone-dimensional in-place transforms, the <CODE>out</CODE> parameter is alwaysignored by the multi-threaded routines, instead of being used as aworkspace if it is non-<CODE>NULL</CODE> as in the uniprocessor routines. Themulti-threaded routines always allocate their own workspace (the size ofwhich depends upon the number of threads).<H3><A NAME="FOOT6" HREF="fftw_4.html#DOCF6">(6)</A></H3><P>The 1Dtransforms require much more communication. All the communication inour FFT routines takes the form of an all-to-all communication: themulti-dimensional transforms require two all-to-all communications (orone, if you use <CODE>FFTW_TRANSPOSED_ORDER</CODE>), while the one-dimensionaltransforms require <EM>three</EM> (or two, if you use scrambled input oroutput).<H3><A NAME="FOOT7" HREF="fftw_4.html#DOCF7">(7)</A></H3><P>AnFFT is particularly hard on communications systems, as it requires an<EM>all-to-all</EM> communication, which is more or less the worst possiblecase.<H3><A NAME="FOOT8" HREF="fftw_5.html#DOCF8">(8)</A></H3><P>Technically, Fortran 77 identifiers arenot allowed to have more than 6 characters, nor may they containunderscores. Any compiler that enforces this limitation doesn't deserveto link to FFTW.<H3><A NAME="FOOT9" HREF="fftw_6.html#DOCF9">(9)</A></H3><P>Each version of <CODE>cc</CODE>seems to have its own magic incantation to get the fastest code most ofthe time--you'd think that people would have agreed upon someconvention, e.g. "<CODE>-Omax</CODE>", by now.<P><HR><P>This document was generated on 24 March 2003 using the<A HREF="http://wwwinfo.cern.ch/dis/texi2html/">texi2html</A>translator version 1.52. (properly hacked by athena@theory.lcs.mit.edu)</P></BODY></HTML>⌨️ 快捷键说明
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