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121 lines
5.4 KiB
Plaintext
121 lines
5.4 KiB
Plaintext
Brief Description of chkfft, by K1JT
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------------------------------------
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Discrete Fourier transforms (DFTs) are found at the root of most
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digital signal processing tasks. In WSJT and its sister programs the
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transforms are done using the FFTW library, and subroutine four2
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provides a convenient interface to the library. Program chkfft is a
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command-line utility offering a convenient way to test FFT execution
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times under a variety of circumstances.
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To compile chkfft in Linux:
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$ gfortran -o chkfft chkfft.f90 four2a.f90 f77_wisdom.f90 gran.c -lfftw3f
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To compile chkfft in Windows (you may need to customize the hard-coded
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path shown here for libfftw3f-3.dll):
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> gfortran -o chkfft chkfft.f90 four2a.f90 f77_wisdom.f90 gran.c \
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/JTSDK-QT/appsupport/runtime/libfftw3f-3.dll
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To see a brief usage message, type chkfft at the command prompt:
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$ chkfft
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Usage: chkfft <nfft | infile> nr nw nc np
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nfft: length of FFT
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nfft=0: do lengths 2^n, n=2^4 to 2^23
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infile: name of file with nfft values, one per line
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nr: 0/1 to not read (or read) wisdom
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nw: 0/1 to not write (or write) wisdom
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nc: 0/1 for real or complex data
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np: 0-4 patience for finding best algorithm
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As an example, to measure the speed of a complex DFT of length 131072:
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#######################################################################
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$ chkfft 131072 0 1 1 2
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nfft: 131072 nr: 0 nw 1 nc: 1 np: 2
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NFFT Time rms MHz MFlops iters tplan
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-------------------------------------------------------------
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131072 0.0021948 0.00000032 59.72 5076.1 231 2.9
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#######################################################################
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Program output shows that on the test machine the average time for one
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forward (or inverse) transform of length N=131072 is about 2.2 ms,
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corresponding to slightly over 5 GFlops computing speed. The planning
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time in FFTW was 2.9 s.
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Running the command again with parameter nr=1 will use the
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"wisdom" already accumulated for complex N=131072 FFTs. The execution
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speed will be essentially the same, but no planning time is required:
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#######################################################################
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$ chkfft 131072 1 1 1 2
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nfft: 131072 nr: 1 nw 1 nc: 1 np: 2
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NFFT Time rms MHz MFlops iters tplan
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-------------------------------------------------------------
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131072 0.0021575 0.00000032 60.75 5164.0 235 0.0
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#######################################################################
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Optimized algorithms can compute DFTs much faster for lengths that are
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the product of small integers. Length N=131072 = 2^17 is a good
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example, and FFTs should be very efficient. For comparison, look at
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the speed for N=131071, a prime number. The average time is now about
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7 times larger:
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#######################################################################
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C:\JTSDK-QT\src\wsjtx\lib>chkfft 131071 1 1 1 2
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nfft: 131071 nr: 1 nw 1 nc: 1 np: 2
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NFFT Time rms MHz MFlops iters tplan
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-------------------------------------------------------------
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131071 0.0153637 0.00000065 8.53 725.2 33 5.6
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#######################################################################
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Here's an example that measures execution times for all integral
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power-of-2 lengths from 2^4 to 2^23:
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#######################################################################
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$ chkfft 0 1 1 1 2
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nfft: 0 nr: 1 nw 1 nc: 1 np: 2
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n N=2^n Time rms MHz MFlops iters tplan
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---------------------------------------------------------------
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4 16 0.0000003 0.00000014 58.61 1172.2 1000000 0.0
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5 32 0.0000004 0.00000016 89.19 2229.6 1000000 0.0
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6 64 0.0000006 0.00000016 109.44 3283.2 866975 0.0
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7 128 0.0000009 0.00000021 135.92 4757.1 538369 0.0
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8 256 0.0000016 0.00000020 158.40 6335.8 313701 0.0
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9 512 0.0000032 0.00000021 162.53 7313.8 160943 0.1
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10 1024 0.0000067 0.00000023 152.53 7626.5 75521 0.1
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11 2048 0.0000136 0.00000025 150.42 8273.3 37239 0.2
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12 4096 0.0000316 0.00000027 129.75 7784.8 16060 0.3
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13 8192 0.0000720 0.00000026 113.75 7393.8 7040 0.5
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14 16384 0.0001620 0.00000028 101.11 7078.0 3129 0.9
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15 32768 0.0003227 0.00000030 101.53 7615.1 1571 1.7
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16 65536 0.0010020 0.00000030 65.41 5232.5 506 4.1
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17 131072 0.0021575 0.00000032 60.75 5164.0 235 0.0
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18 262144 0.0053937 0.00000032 48.60 4374.2 94 3.6
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19 524288 0.0190668 0.00000034 27.50 2612.2 27 6.8
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20 1048576 0.0468001 0.00000035 22.41 2240.5 11 2.4
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21 2097152 0.0936012 0.00000036 22.41 2352.5 6 31.6
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22 4194304 0.1949997 0.00000037 21.51 2366.0 3 9.8
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23 8388608 0.4212036 0.00000038 19.92 2290.3 2 112.9
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#######################################################################
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Test data for all transforms is gaussian random noise of zero mean and
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standard deviation 1. Tabulated values of "rms" are the
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root-mean-square differences between the original data and the
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back-transfmred data.
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File nfft.dat contains all numbers between 2^3 and 2^23 that have
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no factor greater than 7, followed by their factors. These numbers
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are good choices for FFT lengths.
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