| PFFFT: a pretty fast FFT. |
| |
| TL;DR |
| -- |
| |
| PFFFT does 1D Fast Fourier Transforms, of single precision real and |
| complex vectors. It tries do it fast, it tries to be correct, and it |
| tries to be small. Computations do take advantage of SSE1 instructions |
| on x86 cpus, Altivec on powerpc cpus, and NEON on ARM cpus. The |
| license is BSD-like. |
| |
| |
| Why does it exist: |
| -- |
| |
| I was in search of a good performing FFT library , preferably very |
| small and with a very liberal license. |
| |
| When one says "fft library", FFTW ("Fastest Fourier Transform in the |
| West") is probably the first name that comes to mind -- I guess that |
| 99% of open-source projects that need a FFT do use FFTW, and are happy |
| with it. However, it is quite a large library , which does everything |
| fft related (2d transforms, 3d transforms, other transformations such |
| as discrete cosine , or fast hartley). And it is licensed under the |
| GNU GPL , which means that it cannot be used in non open-source |
| products. |
| |
| An alternative to FFTW that is really small, is the venerable FFTPACK |
| v4, which is available on NETLIB. A more recent version (v5) exists, |
| but it is larger as it deals with multi-dimensional transforms. This |
| is a library that is written in FORTRAN 77, a language that is now |
| considered as a bit antiquated by many. FFTPACKv4 was written in 1985, |
| by Dr Paul Swarztrauber of NCAR, more than 25 years ago ! And despite |
| its age, benchmarks show it that it still a very good performing FFT |
| library, see for example the 1d single precision benchmarks here: |
| http://www.fftw.org/speed/opteron-2.2GHz-32bit/ . It is however not |
| competitive with the fastest ones, such as FFTW, Intel MKL, AMD ACML, |
| Apple vDSP. The reason for that is that those libraries do take |
| advantage of the SSE SIMD instructions available on Intel CPUs, |
| available since the days of the Pentium III. These instructions deal |
| with small vectors of 4 floats at a time, instead of a single float |
| for a traditionnal FPU, so when using these instructions one may expect |
| a 4-fold performance improvement. |
| |
| The idea was to take this fortran fftpack v4 code, translate to C, |
| modify it to deal with those SSE instructions, and check that the |
| final performance is not completely ridiculous when compared to other |
| SIMD FFT libraries. Translation to C was performed with f2c ( |
| http://www.netlib.org/f2c/ ). The resulting file was a bit edited in |
| order to remove the thousands of gotos that were introduced by |
| f2c. You will find the fftpack.h and fftpack.c sources in the |
| repository, this a complete translation of |
| http://www.netlib.org/fftpack/ , with the discrete cosine transform |
| and the test program. There is no license information in the netlib |
| repository, but it was confirmed to me by the fftpack v5 curators that |
| the same terms do apply to fftpack v4: |
| http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html . This is a |
| "BSD-like" license, it is compatible with proprietary projects. |
| |
| Adapting fftpack to deal with the SIMD 4-element vectors instead of |
| scalar single precision numbers was more complex than I originally |
| thought, especially with the real transforms, and I ended up writing |
| more code than I planned.. |
| |
| |
| The code: |
| -- |
| |
| Only two files, in good old C, pffft.c and pffft.h . The API is very |
| very simple, just make sure that you read the comments in pffft.h. |
| |
| |
| Comparison with other FFTs: |
| -- |
| |
| The idea was not to break speed records, but to get a decently fast |
| fft that is at least 50% as fast as the fastest FFT -- especially on |
| slowest computers . I'm more focused on getting the best performance |
| on slow cpus (Atom, Intel Core 1, old Athlons, ARM Cortex-A9...), than |
| on getting top performance on today fastest cpus. |
| |
| It can be used in a real-time context as the fft functions do not |
| perform any memory allocation -- that is why they accept a 'work' |
| array in their arguments. |
| |
| It is also a bit focused on performing 1D convolutions, that is why it |
| provides "unordered" FFTs , and a fourier domain convolution |
| operation. |
| |
| |
| Benchmark results (cpu tested: core i7 2600, core 2 quad, core 1 duo, atom N270, cortex-A9) |
| -- |
| |
| The benchmark shows the performance of various fft implementations measured in |
| MFlops, with the number of floating point operations being defined as 5Nlog2(N) |
| for a length N complex fft, and 2.5*Nlog2(N) for a real fft. |
| See http://www.fftw.org/speed/method.html for an explanation of these formulas. |
| |
| MacOS Lion, gcc 4.2, 64-bit, fftw 3.3 on a 3.4 GHz core i7 2600 |
| |
| Built with: |
| |
| gcc-4.2 -o test_pffft -arch x86_64 -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -DHAVE_VECLIB -framework veclib -DHAVE_FFTW -lfftw3f |
| |
| | input len |real FFTPack| real vDSP | real FFTW | real PFFFT | |cplx FFTPack| cplx vDSP | cplx FFTW | cplx PFFFT | |
| |-----------+------------+------------+------------+------------| |------------+------------+------------+------------| |
| | 64 | 2816 | 8596 | 7329 | 8187 | | 2887 | 14898 | 14668 | 11108 | |
| | 96 | 3298 | n/a | 8378 | 7727 | | 3953 | n/a | 15680 | 10878 | |
| | 128 | 3507 | 11575 | 9266 | 10108 | | 4233 | 17598 | 16427 | 12000 | |
| | 160 | 3391 | n/a | 9838 | 10711 | | 4220 | n/a | 16653 | 11187 | |
| | 192 | 3919 | n/a | 9868 | 10956 | | 4297 | n/a | 15770 | 12540 | |
| | 256 | 4283 | 13179 | 10694 | 13128 | | 4545 | 19550 | 16350 | 13822 | |
| | 384 | 3136 | n/a | 10810 | 12061 | | 3600 | n/a | 16103 | 13240 | |
| | 480 | 3477 | n/a | 10632 | 12074 | | 3536 | n/a | 11630 | 12522 | |
| | 512 | 3783 | 15141 | 11267 | 13838 | | 3649 | 20002 | 16560 | 13580 | |
| | 640 | 3639 | n/a | 11164 | 13946 | | 3695 | n/a | 15416 | 13890 | |
| | 768 | 3800 | n/a | 11245 | 13495 | | 3590 | n/a | 15802 | 14552 | |
| | 800 | 3440 | n/a | 10499 | 13301 | | 3659 | n/a | 12056 | 13268 | |
| | 1024 | 3924 | 15605 | 11450 | 15339 | | 3769 | 20963 | 13941 | 15467 | |
| | 2048 | 4518 | 16195 | 11551 | 15532 | | 4258 | 20413 | 13723 | 15042 | |
| | 2400 | 4294 | n/a | 10685 | 13078 | | 4093 | n/a | 12777 | 13119 | |
| | 4096 | 4750 | 16596 | 11672 | 15817 | | 4157 | 19662 | 14316 | 14336 | |
| | 8192 | 3820 | 16227 | 11084 | 12555 | | 3691 | 18132 | 12102 | 13813 | |
| | 9216 | 3864 | n/a | 10254 | 12870 | | 3586 | n/a | 12119 | 13994 | |
| | 16384 | 3822 | 15123 | 10454 | 12822 | | 3613 | 16874 | 12370 | 13881 | |
| | 32768 | 4175 | 14512 | 10662 | 11095 | | 3881 | 14702 | 11619 | 11524 | |
| | 262144 | 3317 | 11429 | 6269 | 9517 | | 2810 | 11729 | 7757 | 10179 | |
| | 1048576 | 2913 | 10551 | 4730 | 5867 | | 2661 | 7881 | 3520 | 5350 | |
| |-----------+------------+------------+------------+------------| |------------+------------+------------+------------| |
| |
| |
| Debian 6, gcc 4.4.5, 64-bit, fftw 3.3.1 on a 3.4 GHz core i7 2600 |
| |
| Built with: |
| gcc -o test_pffft -DHAVE_FFTW -msse2 -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L$HOME/local/lib -I$HOME/local/include/ -lfftw3f -lm |
| |
| | N (input length) | real FFTPack | real FFTW | real PFFFT | | cplx FFTPack | cplx FFTW | cplx PFFFT | |
| |------------------+--------------+--------------+--------------| |--------------+--------------+--------------| |
| | 64 | 3840 | 7680 | 8777 | | 4389 | 20480 | 11171 | |
| | 96 | 4214 | 9633 | 8429 | | 4816 | 22477 | 11238 | |
| | 128 | 3584 | 10240 | 10240 | | 5120 | 23893 | 11947 | |
| | 192 | 4854 | 11095 | 12945 | | 4854 | 22191 | 14121 | |
| | 256 | 4096 | 11703 | 16384 | | 5120 | 23406 | 13653 | |
| | 384 | 4395 | 14651 | 12558 | | 4884 | 19535 | 14651 | |
| | 512 | 5760 | 13166 | 15360 | | 4608 | 23040 | 15360 | |
| | 768 | 4907 | 14020 | 16357 | | 4461 | 19628 | 14020 | |
| | 1024 | 5120 | 14629 | 14629 | | 5120 | 20480 | 15754 | |
| | 2048 | 5632 | 14080 | 18773 | | 4693 | 12516 | 16091 | |
| | 4096 | 5120 | 13653 | 17554 | | 4726 | 7680 | 14456 | |
| | 8192 | 4160 | 7396 | 13312 | | 4437 | 14791 | 13312 | |
| | 9216 | 4210 | 6124 | 13473 | | 4491 | 7282 | 14970 | |
| | 16384 | 3976 | 11010 | 14313 | | 4210 | 11450 | 13631 | |
| | 32768 | 4260 | 10224 | 10954 | | 4260 | 6816 | 11797 | |
| | 262144 | 3736 | 6896 | 9961 | | 2359 | 8965 | 9437 | |
| | 1048576 | 2796 | 4534 | 6453 | | 1864 | 3078 | 5592 | |
| |------------------+--------------+--------------+--------------| |--------------+--------------+--------------| |
| |
| |
| |
| MacOS Snow Leopard, gcc 4.0, 32-bit, fftw 3.3 on a 1.83 GHz core 1 duo |
| |
| Built with: |
| |
| gcc -o test_pffft -DHAVE_FFTW -DHAVE_VECLIB -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -lfftw3f -framework veclib |
| |
| | input len |real FFTPack| real vDSP | real FFTW | real PFFFT | |cplx FFTPack| cplx vDSP | cplx FFTW | cplx PFFFT | |
| |-----------+------------+------------+------------+------------| |------------+------------+------------+------------| |
| | 64 | 745 | 2145 | 1706 | 2028 | | 961 | 3356 | 3313 | 2300 | |
| | 96 | 877 | n/a | 1976 | 1978 | | 1059 | n/a | 3333 | 2233 | |
| | 128 | 951 | 2808 | 2213 | 2279 | | 1202 | 3803 | 3739 | 2494 | |
| | 192 | 1002 | n/a | 2456 | 2429 | | 1186 | n/a | 3701 | 2508 | |
| | 256 | 1065 | 3205 | 2641 | 2793 | | 1302 | 4013 | 3912 | 2663 | |
| | 384 | 845 | n/a | 2759 | 2499 | | 948 | n/a | 3729 | 2504 | |
| | 512 | 900 | 3476 | 2956 | 2759 | | 974 | 4057 | 3954 | 2645 | |
| | 768 | 910 | n/a | 2912 | 2737 | | 975 | n/a | 3837 | 2614 | |
| | 1024 | 936 | 3583 | 3107 | 3009 | | 1006 | 4124 | 3821 | 2697 | |
| | 2048 | 1057 | 3585 | 3091 | 2837 | | 1089 | 3889 | 3701 | 2513 | |
| | 4096 | 1083 | 3524 | 3092 | 2733 | | 1039 | 3617 | 3462 | 2364 | |
| | 8192 | 874 | 3252 | 2967 | 2363 | | 911 | 3106 | 2789 | 2302 | |
| | 9216 | 898 | n/a | 2420 | 2290 | | 865 | n/a | 2676 | 2204 | |
| | 16384 | 903 | 2892 | 2506 | 2421 | | 899 | 3026 | 2797 | 2289 | |
| | 32768 | 965 | 2837 | 2550 | 2358 | | 920 | 2922 | 2763 | 2240 | |
| | 262144 | 738 | 2422 | 1589 | 1708 | | 610 | 2038 | 1436 | 1091 | |
| | 1048576 | 528 | 1207 | 845 | 880 | | 606 | 1020 | 669 | 1036 | |
| |-----------+------------+------------+------------+------------| |------------+------------+------------+------------| |
| |
| |
| |
| Ubuntu 11.04, gcc 4.5, 32-bit, fftw 3.2 on a 2.66 core 2 quad |
| |
| Built with: |
| gcc -o test_pffft -DHAVE_FFTW -msse -mfpmath=sse -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -lfftw3f -lm |
| |
| | input len |real FFTPack| real FFTW | real PFFFT | |cplx FFTPack| cplx FFTW | cplx PFFFT | |
| |-----------+------------+------------+------------| |------------+------------+------------| |
| | 64 | 1920 | 3614 | 5120 | | 2194 | 7680 | 6467 | |
| | 96 | 1873 | 3549 | 5187 | | 2107 | 8429 | 5863 | |
| | 128 | 2240 | 3773 | 5514 | | 2560 | 7964 | 6827 | |
| | 192 | 1765 | 4569 | 7767 | | 2284 | 9137 | 7061 | |
| | 256 | 2048 | 5461 | 7447 | | 2731 | 9638 | 7802 | |
| | 384 | 1998 | 5861 | 6762 | | 2313 | 9253 | 7644 | |
| | 512 | 2095 | 6144 | 7680 | | 2194 | 10240 | 7089 | |
| | 768 | 2230 | 5773 | 7549 | | 2045 | 10331 | 7010 | |
| | 1024 | 2133 | 6400 | 8533 | | 2133 | 10779 | 7877 | |
| | 2048 | 2011 | 7040 | 8665 | | 1942 | 10240 | 7768 | |
| | 4096 | 2194 | 6827 | 8777 | | 1755 | 9452 | 6827 | |
| | 8192 | 1849 | 6656 | 6656 | | 1752 | 7831 | 6827 | |
| | 9216 | 1871 | 5858 | 6416 | | 1643 | 6909 | 6266 | |
| | 16384 | 1883 | 6223 | 6506 | | 1664 | 7340 | 6982 | |
| | 32768 | 1826 | 6390 | 6667 | | 1631 | 7481 | 6971 | |
| | 262144 | 1546 | 4075 | 5977 | | 1299 | 3415 | 3551 | |
| | 1048576 | 1104 | 2071 | 1730 | | 1104 | 1149 | 1834 | |
| |-----------+------------+------------+------------| |------------+------------+------------| |
| |
| |
| |
| Ubuntu 11.04, gcc 4.5, 32-bit, fftw 3.3 on a 1.6 GHz Atom N270 |
| |
| Built with: |
| gcc -o test_pffft -DHAVE_FFTW -msse -mfpmath=sse -O3 -Wall -W pffft.c test_pffft.c fftpack.c -L/usr/local/lib -I/usr/local/include/ -lfftw3f -lm |
| |
| | N (input length) | real FFTPack | real FFTW | real PFFFT | | cplx FFTPack | cplx FFTW | cplx PFFFT | |
| |------------------+--------------+--------------+--------------| |--------------+--------------+--------------| |
| | 64 | 452 | 1041 | 1336 | | 549 | 2318 | 1781 | |
| | 96 | 444 | 1297 | 1297 | | 503 | 2408 | 1686 | |
| | 128 | 527 | 1525 | 1707 | | 543 | 2655 | 1886 | |
| | 192 | 498 | 1653 | 1849 | | 539 | 2678 | 1942 | |
| | 256 | 585 | 1862 | 2156 | | 594 | 2777 | 2244 | |
| | 384 | 499 | 1870 | 1998 | | 511 | 2586 | 1890 | |
| | 512 | 562 | 2095 | 2194 | | 542 | 2973 | 2194 | |
| | 768 | 545 | 2045 | 2133 | | 545 | 2365 | 2133 | |
| | 1024 | 595 | 2133 | 2438 | | 569 | 2695 | 2179 | |
| | 2048 | 587 | 2125 | 2347 | | 521 | 2230 | 1707 | |
| | 4096 | 495 | 1890 | 1834 | | 492 | 1876 | 1672 | |
| | 8192 | 469 | 1548 | 1729 | | 438 | 1740 | 1664 | |
| | 9216 | 468 | 1663 | 1663 | | 446 | 1585 | 1531 | |
| | 16384 | 453 | 1608 | 1767 | | 398 | 1476 | 1664 | |
| | 32768 | 456 | 1420 | 1503 | | 387 | 1388 | 1345 | |
| | 262144 | 309 | 385 | 726 | | 262 | 415 | 840 | |
| | 1048576 | 280 | 351 | 739 | | 261 | 313 | 797 | |
| |------------------+--------------+--------------+--------------| |--------------+--------------+--------------| |
| |
| |
| |
| Windows 7, visual c++ 2010 on a 1.6 GHz Atom N270 |
| |
| Built with: |
| cl /Ox -D_USE_MATH_DEFINES /arch:SSE test_pffft.c pffft.c fftpack.c |
| |
| (visual c++ is definitively not very good with SSE intrinsics...) |
| |
| | N (input length) | real FFTPack | real PFFFT | | cplx FFTPack | cplx PFFFT | |
| |------------------+--------------+--------------| |--------------+--------------| |
| | 64 | 173 | 1009 | | 174 | 1159 | |
| | 96 | 169 | 1029 | | 188 | 1201 | |
| | 128 | 195 | 1242 | | 191 | 1275 | |
| | 192 | 178 | 1312 | | 184 | 1276 | |
| | 256 | 196 | 1591 | | 186 | 1281 | |
| | 384 | 172 | 1409 | | 181 | 1281 | |
| | 512 | 187 | 1640 | | 181 | 1313 | |
| | 768 | 171 | 1614 | | 176 | 1258 | |
| | 1024 | 186 | 1812 | | 178 | 1223 | |
| | 2048 | 190 | 1707 | | 186 | 1099 | |
| | 4096 | 182 | 1446 | | 177 | 975 | |
| | 8192 | 175 | 1345 | | 169 | 1034 | |
| | 9216 | 165 | 1271 | | 168 | 1023 | |
| | 16384 | 166 | 1396 | | 165 | 949 | |
| | 32768 | 172 | 1311 | | 161 | 881 | |
| | 262144 | 136 | 632 | | 134 | 629 | |
| | 1048576 | 134 | 698 | | 127 | 623 | |
| |------------------+--------------+--------------| |--------------+--------------| |
| |
| |
| |
| Ubuntu 12.04, gcc-4.7.3, 32-bit, with fftw 3.3.3 (built with --enable-neon), on a 1.2GHz ARM Cortex A9 (Tegra 3) |
| |
| Built with: |
| gcc-4.7 -O3 -DHAVE_FFTW -march=armv7-a -mtune=cortex-a9 -mfloat-abi=hard -mfpu=neon -ffast-math test_pffft.c pffft.c -o test_pffft_arm fftpack.c -lm -I/usr/local/include/ -L/usr/local/lib/ -lfftw3f |
| |
| | input len |real FFTPack| real FFTW | real PFFFT | |cplx FFTPack| cplx FFTW | cplx PFFFT | |
| |-----------+------------+------------+------------| |------------+------------+------------| |
| | 64 | 549 | 452 | 731 | | 512 | 602 | 640 | |
| | 96 | 421 | 272 | 702 | | 496 | 571 | 602 | |
| | 128 | 498 | 512 | 815 | | 597 | 618 | 652 | |
| | 160 | 521 | 536 | 815 | | 586 | 669 | 625 | |
| | 192 | 539 | 571 | 883 | | 485 | 597 | 626 | |
| | 256 | 640 | 539 | 975 | | 569 | 611 | 671 | |
| | 384 | 499 | 610 | 879 | | 499 | 602 | 637 | |
| | 480 | 518 | 507 | 877 | | 496 | 661 | 616 | |
| | 512 | 524 | 591 | 1002 | | 549 | 678 | 668 | |
| | 640 | 542 | 612 | 955 | | 568 | 663 | 645 | |
| | 768 | 557 | 613 | 981 | | 491 | 663 | 598 | |
| | 800 | 514 | 353 | 882 | | 514 | 360 | 574 | |
| | 1024 | 640 | 640 | 1067 | | 492 | 683 | 602 | |
| | 2048 | 587 | 640 | 908 | | 486 | 640 | 552 | |
| | 2400 | 479 | 368 | 777 | | 422 | 376 | 518 | |
| | 4096 | 511 | 614 | 853 | | 426 | 640 | 534 | |
| | 8192 | 415 | 584 | 708 | | 386 | 622 | 516 | |
| | 9216 | 419 | 571 | 687 | | 364 | 586 | 506 | |
| | 16384 | 426 | 577 | 716 | | 398 | 606 | 530 | |
| | 32768 | 417 | 572 | 673 | | 399 | 572 | 468 | |
| | 262144 | 219 | 380 | 293 | | 255 | 431 | 343 | |
| | 1048576 | 202 | 274 | 237 | | 265 | 282 | 355 | |
| |-----------+------------+------------+------------| |------------+------------+------------| |
| |
| Same platform as above, but this time pffft and fftpack are built with clang 3.2: |
| |
| clang -O3 -DHAVE_FFTW -march=armv7-a -mtune=cortex-a9 -mfloat-abi=hard -mfpu=neon -ffast-math test_pffft.c pffft.c -o test_pffft_arm fftpack.c -lm -I/usr/local/include/ -L/usr/local/lib/ -lfftw3f |
| |
| | input len |real FFTPack| real FFTW | real PFFFT | |cplx FFTPack| cplx FFTW | cplx PFFFT | |
| |-----------+------------+------------+------------| |------------+------------+------------| |
| | 64 | 427 | 452 | 853 | | 427 | 602 | 1024 | |
| | 96 | 351 | 276 | 843 | | 337 | 571 | 963 | |
| | 128 | 373 | 512 | 996 | | 390 | 618 | 1054 | |
| | 160 | 426 | 536 | 987 | | 375 | 669 | 914 | |
| | 192 | 404 | 571 | 1079 | | 388 | 588 | 1079 | |
| | 256 | 465 | 539 | 1205 | | 445 | 602 | 1170 | |
| | 384 | 366 | 610 | 1099 | | 343 | 594 | 1099 | |
| | 480 | 356 | 507 | 1140 | | 335 | 651 | 931 | |
| | 512 | 411 | 591 | 1213 | | 384 | 649 | 1124 | |
| | 640 | 398 | 612 | 1193 | | 373 | 654 | 901 | |
| | 768 | 409 | 613 | 1227 | | 383 | 663 | 1044 | |
| | 800 | 411 | 348 | 1073 | | 353 | 358 | 809 | |
| | 1024 | 427 | 640 | 1280 | | 413 | 692 | 1004 | |
| | 2048 | 414 | 626 | 1126 | | 371 | 640 | 853 | |
| | 2400 | 399 | 373 | 898 | | 319 | 368 | 653 | |
| | 4096 | 404 | 602 | 1059 | | 357 | 633 | 778 | |
| | 8192 | 332 | 584 | 792 | | 308 | 616 | 716 | |
| | 9216 | 322 | 561 | 783 | | 299 | 586 | 687 | |
| | 16384 | 344 | 568 | 778 | | 314 | 617 | 745 | |
| | 32768 | 342 | 564 | 737 | | 314 | 552 | 629 | |
| | 262144 | 201 | 383 | 313 | | 227 | 435 | 413 | |
| | 1048576 | 187 | 262 | 251 | | 228 | 281 | 409 | |
| |-----------+------------+------------+------------| |------------+------------+------------| |
| |
| So it looks like, on ARM, gcc 4.7 is the best at scalar floating point |
| (the fftpack performance numbers are better with gcc), while clang is |
| the best with neon intrinsics (see how pffft perf has improved with |
| clang 3.2). |
| |
| |
| NVIDIA Jetson TK1 board, gcc-4.8.2. The cpu is a 2.3GHz cortex A15 (Tegra K1). |
| |
| Built with: |
| gcc -O3 -march=armv7-a -mtune=native -mfloat-abi=hard -mfpu=neon -ffast-math test_pffft.c pffft.c -o test_pffft_arm fftpack.c -lm |
| |
| | input len |real FFTPack| real PFFFT | |cplx FFTPack| cplx PFFFT | |
| |-----------+------------+------------| |------------+------------| |
| | 64 | 1735 | 3308 | | 1994 | 3744 | |
| | 96 | 1596 | 3448 | | 1987 | 3572 | |
| | 128 | 1807 | 4076 | | 2255 | 3960 | |
| | 160 | 1769 | 4083 | | 2071 | 3845 | |
| | 192 | 1990 | 4233 | | 2017 | 3939 | |
| | 256 | 2191 | 4882 | | 2254 | 4346 | |
| | 384 | 1878 | 4492 | | 2073 | 4012 | |
| | 480 | 1748 | 4398 | | 1923 | 3951 | |
| | 512 | 2030 | 5064 | | 2267 | 4195 | |
| | 640 | 1918 | 4756 | | 2094 | 4184 | |
| | 768 | 2099 | 4907 | | 2048 | 4297 | |
| | 800 | 1822 | 4555 | | 1880 | 4063 | |
| | 1024 | 2232 | 5355 | | 2187 | 4420 | |
| | 2048 | 2176 | 4983 | | 2027 | 3602 | |
| | 2400 | 1741 | 4256 | | 1710 | 3344 | |
| | 4096 | 1816 | 3914 | | 1851 | 3349 | |
| | 8192 | 1716 | 3481 | | 1700 | 3255 | |
| | 9216 | 1735 | 3589 | | 1653 | 3094 | |
| | 16384 | 1567 | 3483 | | 1637 | 3244 | |
| | 32768 | 1624 | 3240 | | 1655 | 3156 | |
| | 262144 | 1012 | 1898 | | 983 | 1503 | |
| | 1048576 | 876 | 1154 | | 868 | 1341 | |
| |-----------+------------+------------| |------------+------------| |
| |
| The performance on the tegra K1 is pretty impressive. I'm not |
| including the FFTW numbers as they as slightly below the scalar |
| fftpack numbers, so something must be wrong (however it seems to be |
| correctly configured and is using neon simd instructions). |
| |
| When using clang 3.4 the pffft version is even a bit faster, reaching |
| 5.7 GFlops for real ffts of size 1024. |
