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| 2 | pj | 1 | <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> |
| 2 | <HTML> |
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| 3 | <HEAD> |
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| 4 | <!-- This HTML file has been created by texi2html 1.52 |
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| 5 | from fftw.texi on 18 May 1999 --> |
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| 6 | |||
| 7 | <TITLE>FFTW - Footnotes</TITLE> |
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| 8 | </HEAD> |
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| 9 | <BODY TEXT="#000000" BGCOLOR="#FFFFFF"> |
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| 10 | <H1>FFTW</H1> |
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| 11 | <H2>For version 2.1.2, 18 May 1999</H2> |
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| 12 | <P> |
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| 13 | <P><HR><P> |
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| 14 | <H3><A NAME="FOOT1" HREF="fftw_2.html#DOCF1">(1)</A></H3> |
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| 15 | <P>The output for the |
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| 16 | multi-dimensional rfftw is a more-conventional array of |
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| 17 | <CODE>fftw_complex</CODE> values, but the format here permitted us greater |
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| 18 | efficiency in one dimension. |
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| 19 | <H3><A NAME="FOOT2" HREF="fftw_3.html#DOCF2">(2)</A></H3> |
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| 20 | <P>The basic problem is the resolution of the clock: |
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| 21 | FFTW needs to run for a certain time for the clock to be reliable. |
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| 22 | <H3><A NAME="FOOT3" HREF="fftw_3.html#DOCF3">(3)</A></H3> |
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| 23 | <P><CODE>fftwnd</CODE> actually may use some temporary |
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| 24 | storage (hidden in the plan), but this storage space is only the size of |
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| 25 | the largest dimension of the array, rather than being as big as the |
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| 26 | entire array. (Unless you use <CODE>fftwnd</CODE> to perform one-dimensional |
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| 27 | transforms, in which case the temporary storage required for in-place |
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| 28 | transforms <EM>is</EM> as big as the entire array.) |
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| 29 | <H3><A NAME="FOOT4" HREF="fftw_3.html#DOCF4">(4)</A></H3> |
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| 30 | <P>The etymologically-correct spelling would be |
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| 31 | <CODE>frftw_</CODE>, but it is hard to remember. |
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| 32 | <H3><A NAME="FOOT5" HREF="fftw_4.html#DOCF5">(5)</A></H3> |
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| 33 | <P>There is one exception: when performing |
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| 34 | one-dimensional in-place transforms, the <CODE>out</CODE> parameter is always |
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| 35 | ignored by the multi-threaded routines, instead of being used as a |
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| 36 | workspace if it is non-<CODE>NULL</CODE> as in the uniprocessor routines. The |
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| 37 | multi-threaded routines always allocate their own workspace (the size of |
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| 38 | which depends upon the number of threads). |
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| 39 | <H3><A NAME="FOOT6" HREF="fftw_4.html#DOCF6">(6)</A></H3> |
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| 40 | <P>The 1D |
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| 41 | transforms require much more communication. All the communication in |
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| 42 | our FFT routines takes the form of an all-to-all communication: the |
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| 43 | multi-dimensional transforms require two all-to-all communications (or |
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| 44 | one, if you use <CODE>FFTW_TRANSPOSED_ORDER</CODE>), while the one-dimensional |
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| 45 | transforms require <EM>three</EM> (or two, if you use scrambled input or |
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| 46 | output). |
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| 47 | <H3><A NAME="FOOT7" HREF="fftw_4.html#DOCF7">(7)</A></H3> |
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| 48 | <P>An |
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| 49 | FFT is particularly hard on communications systems, as it requires an |
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| 50 | <EM>all-to-all</EM> communication, which is more or less the worst possible |
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| 51 | case. |
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| 52 | <H3><A NAME="FOOT8" HREF="fftw_5.html#DOCF8">(8)</A></H3> |
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| 53 | <P>Technically, Fortran 77 identifiers are |
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| 54 | not allowed to have more than 6 characters, nor may they contain |
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| 55 | underscores. Any compiler that enforces this limitation doesn't deserve |
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| 56 | to link to FFTW. |
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| 57 | <H3><A NAME="FOOT9" HREF="fftw_6.html#DOCF9">(9)</A></H3> |
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| 58 | <P>Each version of <CODE>cc</CODE> |
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| 59 | seems to have its own magic incantation to get the fastest code most of |
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| 60 | the time--you'd think that people would have agreed upon some |
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| 61 | convention, e.g. "<CODE>-Omax</CODE>", by now. |
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| 62 | <P><HR><P> |
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| 63 | This document was generated on 18 May 1999 using the |
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| 64 | <A HREF="http://wwwinfo.cern.ch/dis/texi2html/">texi2html</A> |
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| 65 | translator version 1.52. (properly hacked by athena@theory.lcs.mit.edu)</P> |
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| 66 | </BODY> |
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| 67 | </HTML> |