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threads - fft

This folder provides a multi-threading solution for calculating the Fast Fourier Transform. This solution is mostly intended for benchmarking.

Print Logtalk, Prolog backend, and kernel versions (if running as a notebook):

%versions

Start by loading the example and the required library files:

logtalk_load(fft(loader)).

NOTE: some example queries below use a proprietary predicate time/1 in order to get accurate goal times. This predicate is found on several Prolog systems. For other Prolog compilers, replace the time/1 call by any appropriate timing calls (e.g., cputime/0).

Start by testing the results for the various multi-threading versions to check the results using a random number generator to create an initial list:

N=8, cgenerator::list(N,L), fft(1)::fft(N,L,F1), fft(2)::fft(N,L,F2), fft(4)::fft(N,L,F4).

<!-- N = 8, L = [c(0.562342, 0.37745), c(0.448983, 0.0468073), c(0.482978, 0.81187), c(0.229581, 0.879153), c(0.39853, 0.909), c(0.248164, 0.314326), c(0.744353, 0.0665809), c(0.381964, 0.993583)], F1 = [c(3.4969, 4.39877), c(-0.0616465, -0.866927), c(1.24514, 0.493602), c(0.929429, -0.127675), c(0.879511, -0.0689684), c(-1.10131, -0.718926), c(-1.77806, 0.322397), c(0.888774, -0.412674)], F2 = [c(3.4969, 4.39877), c(-0.0616465, -0.866927), c(1.24514, 0.493602), c(0.929429, -0.127675), c(0.879511, -0.0689684), c(-1.10131, -0.718926), c(-1.77806, 0.322397), c(0.888774, -0.412674)], F4 = [c(3.4969, 4.39877), c(-0.0616465, -0.866927), c(1.24514, 0.493602), c(0.929429, -0.127675), c(0.879511, -0.0689684), c(-1.10131, -0.718926), c(-1.77806, 0.322397), c(0.888774, -0.412674)]

true. -->

Now we check using known results - in this case against Matlab... too lazy to do my own calcs:

N=8, L=[c(1,0),c(2,0),c(3,0),c(4,0),c(5,0),c(6,0),c(7,0),c(8,0)], fft(4)::fft(N,L,F4), fft(8)::fft(N,L,F8).

<!-- N = 8, L = [c(1, 0), c(2, 0), c(3, 0), c(4, 0), c(5, 0), c(6, 0), c(7, 0), c(8, 0)], F4 = [c(36.0, 0.0), c(-4.0, -9.65686), c(-4.0, -4.0), c(-4.0, -1.65686), c(-4.0, 0.0), c(-4.0, 1.65686), c(-4.0, 4.0), c(-4.0, 9.65686)], F8 = [c(36.0, 0.0), c(-4.0, -9.65686), c(-4.0, -4.0), c(-4.0, -1.65686), c(-4.0, 0.0), c(-4.0, 1.65686), c(-4.0, 4.0), c(-4.0, 9.65686)]

true. -->

From Matlab - we can see that the results are ok for 4 and 8 threads... within rounding errors...

EDUÂ» x = [1 ,2,3,4,5,6,7,8] EDUÂ» fft(x,8) ans = 36.00000000000000 -4.00000000000000 + 9.65685424949238i -4.00000000000000 + 4.00000000000000i -4.00000000000000 + 1.65685424949238i -4.00000000000000 -4.00000000000000 - 1.65685424949238i -4.00000000000000 - 4.00000000000000i -4.00000000000000 - 9.65685424949238i

Now a longer test with N=16384...

N=16384, cgenerator::list(N, L), time(fft(1)::fft(N,L,F1)), time(fft(2)::fft(N,L,F2)), time(fft(4)::fft(N,L,F3)).

<!-- % 1,540,128 inferences, 1.18 CPU in 1.27 seconds (93% CPU, 1305193 Lips) % 16,496 inferences, 1.23 CPU in 0.77 seconds (159% CPU, 13411 Lips) % 16,495 inferences, 1.34 CPU in 0.54 seconds (249% CPU, 12310 Lips)

N = 16384, L = [c(0.0980332, 0.534537), c(0.783046, 0.0702899), c(0.00399351, 0.458403), c(0.332693, 0.365153), c(0.584027, 0.271888), c(0.0550958, 0.545072), c(0.190854, 0.288811), c(0.0521769, 0.123861), c(..., ...)|...], F1 = [c(8174.33, 8219.08), c(-20.8685, -26.0953), c(25.668, 53.9194), c(-27.0944, 19.5957), c(21.5431, -19.3457), c(29.1652, -14.5477), c(-9.71613, -11.4724), c(-30.8867, -26.4551), c(..., ...)|...], F2 = [c(8174.33, 8219.08), c(-20.8685, -26.0953), c(25.668, 53.9194), c(-27.0944, 19.5957), c(21.5431, -19.3457), c(29.1652, -14.5477), c(-9.71613, -11.4724), c(-30.8867, -26.4551), c(..., ...)|...], F3 = [c(8174.33, 8219.08), c(-20.8685, -26.0953), c(25.668, 53.9194), c(-27.0944, 19.5957), c(21.5431, -19.3457), c(29.1652, -14.5477), c(-9.71613, -11.4724), c(-30.8867, -26.4551), c(..., .

true. -->

A smaller test:

N=8192, cgenerator::list(N, L), time(fft(1)::fft(N,L,F1)), time(fft(2)::fft(N,L,F2)), time(fft(4)::fft(N,L,F3)).

<!-- % 720,928 inferences, 0.55 CPU in 0.58 seconds (94% CPU, 1310778 Lips) % 8,304 inferences, 0.55 CPU in 0.33 seconds (166% CPU, 15098 Lips) % 8,304 inferences, 0.59 CPU in 0.24 seconds (241% CPU, 14075 Lips)

N = 8192, L = [c(0.108653, 0.130382), c(0.299788, 0.366249), c(0.797314, 0.0934765), c(0.618671, 0.557751), c(0.23189, 0.736263), c(0.157462, 0.455775), c(0.398063, 0.128278), c(0.0265977, 0.540345), c(..., ...)|...], F1 = [c(4119.95, 4113.57), c(-11.2542, 19.0867), c(29.8736, 13.7454), c(2.13094, -50.7658), c(-35.5401, 2.62093), c(-19.7409, 38.7919), c(28.3842, 56.9097), c(-11.8783, 8.50143), c(..., ...)|...], F2 = [c(4119.95, 4113.57), c(-11.2542, 19.0867), c(29.8736, 13.7454), c(2.13094, -50.7658), c(-35.5401, 2.62093), c(-19.7409, 38.7919), c(28.3842, 56.9097), c(-11.8783, 8.50143), c(..., ...)|...], F3 = [c(4119.95, 4113.57), c(-11.2542, 19.0867), c(29.8736, 13.7454), c(2.13094, -50.7658), c(-35.5401, 2.62093), c(-19.7409, 38.7919), c(28.3842, 56.9097), c(-11.8783, 8.50143), c(..., ...)|...]

true. -->

A very big test:

N is 65536, cgenerator::list(N, L), time(fft(1)::fft(N,L,F1)), time(fft(2)::fft(N,L,F2)), time(fft(4)::fft(N,L,F3)).

<!-- % 6,946,848 inferences, 5.91 CPU in 6.42 seconds (92% CPU, 1175440 Lips) % 65,648 inferences, 6.03 CPU in 3.80 seconds (159% CPU, 10887 Lips) % 65,648 inferences, 6.31 CPU in 2.54 seconds (249% CPU, 10404 Lips)

N = 65536, L = [c(0.416673, 0.410381), c(0.340778, 0.930646), c(0.373208, 0.0208154), c(0.853131, 0.265193), c(0.661878, 0.674402), c(0.99455, 0.599138), c(0.109308, 0.617546), c(0.187351, 0.0837411), c(..., ...)|...], F1 = [c(32814.3, 32830.9), c(125.184, 70.4444), c(-100.912, 55.0937), c(3.58732, -131.877), c(107.255, 2.85792), c(-128.124, 25.6776), c(56.3197, -29.6811), c(-66.6174, -108.857), c(..., ...)|...], F2 = [c(32814.3, 32830.9), c(125.184, 70.4444), c(-100.912, 55.0937), c(3.58732, -131.877), c(107.255, 2.85792), c(-128.124, 25.6776), c(56.3197, -29.6811), c(-66.6174, -108.857), c(..., ...)|...], F3 = [c(32814.3, 32830.9), c(125.184, 70.4444), c(-100.912, 55.0937), c(3.58732, -131.877), c(107.255, 2.85792), c(-128.124, 25.6776), c(56.3197, -29.6811), c(-66.6174, -108.857), c(..., ...)|...]

true. -->