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This commit adds a pure x86 assembly SIMD version of the FFT in libavutil/tx. The design of this pure assembly FFT is pretty unconventional. On the lowest level, instead of splitting the complex numbers into real and imaginary parts, we keep complex numbers together but split them in terms of parity. This saves a number of shuffles in each transform, but more importantly, it splits each transform into two independent paths, which we process using separate registers in parallel. This allows us to keep all units saturated and lets us use all available registers to avoid dependencies. Moreover, it allows us to double the granularity of our per-load permutation, skipping many expensive lookups and allowing us to use just 4 loads per register, rather than 8, or in case FMA3 (and by extension, AVX2), use the vgatherdpd instruction, which is at least as fast as 4 separate loads on old hardware, and quite a bit faster on modern CPUs). Higher up, we go for a bottom-up construction of large transforms, foregoing the traditional per-transform call-return recursion chains. Instead, we always start at the bottom-most basis transform (in this case, a 32-point transform), and continue constructing larger and larger transforms until we return to the top-most transform. This way, we only touch the stack 3 times per a complete target transform: once for the 1/2 length transform and two times for the 1/4 length transform. The combination algorithm we use is a standard Split-Radix algorithm, as used in our C code. Although a version with less operations exists (Steven G. Johnson and Matteo Frigo's "A modified split-radix FFT with fewer arithmetic operations", IEEE Trans. Signal Process. 55 (1), 111–119 (2007), which is the one FFTW uses), it only has 2% less operations and requires at least 4x the binary code (due to it needing 4 different paths to do a single transform). That version also has other issues which prevent it from being implemented with SIMD code as efficiently, which makes it lose the marginal gains it offered, and cannot be performed bottom-up, requiring many recursive call-return chains, whose overhead adds up. We go through a lot of effort to minimize load/stores by keeping as much in registers in between construcring transforms. This saves us around 32 cycles, on paper, but in reality a lot more due to load/store aliasing (a load from a memory location cannot be issued while there's a store pending, and there are only so many (2 for Zen 3) load/store units in a CPU). Also, we interleave coefficients during the last stage to save on a store+load per register. Each of the smallest, basis transforms (4, 8 and 16-point in our case) has been extremely optimized. Our 8-point transform is barely 20 instructions in total, beating our old implementation 8-point transform by 1 instruction. Our 2x8-point transform is 23 instructions, beating our old implementation by 6 instruction and needing 50% less cycles. Our 16-point transform's combination code takes slightly more instructions than our old implementation, but makes up for it by requiring a lot less arithmetic operations. Overall, the transform was optimized for the timings of Zen 3, which at the time of writing has the most IPC from all documented CPUs. Shuffles were preferred over arithmetic operations due to their 1/0.5 latency/throughput. On average, this code is 30% faster than our old libavcodec implementation. It's able to trade blows with the previously-untouchable FFTW on small transforms, and due to its tiny size and better prediction, outdoes FFTW on larger transforms by 11% on the largest currently supported size. |
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| .. | ||
| asm.h | ||
| bswap.h | ||
| cpu.c | ||
| cpu.h | ||
| cpuid.asm | ||
| emms.asm | ||
| emms.h | ||
| fixed_dsp_init.c | ||
| fixed_dsp.asm | ||
| float_dsp_init.c | ||
| float_dsp.asm | ||
| imgutils_init.c | ||
| imgutils.asm | ||
| intmath.h | ||
| intreadwrite.h | ||
| lls_init.c | ||
| lls.asm | ||
| Makefile | ||
| pixelutils_init.c | ||
| pixelutils.asm | ||
| pixelutils.h | ||
| timer.h | ||
| tx_float_init.c | ||
| tx_float.asm | ||
| w64xmmtest.h | ||
| x86inc.asm | ||
| x86util.asm | ||