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lavu/x86: add FFT assembly 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.
2021-04-10 01:54:22 +00:00
/*
* This file is part of FFmpeg.
*
* FFmpeg is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* FFmpeg is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with FFmpeg; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#define TX_FLOAT
#include "libavutil/tx_priv.h"
#include "libavutil/attributes.h"
#include "libavutil/x86/cpu.h"
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
#include "config.h"
lavu/x86: add FFT assembly 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.
2021-04-10 01:54:22 +00:00
lavu/tx: refactor assembly codelet definition This commit does some refactoring to make defining assembly codelets smaller, and fixes compiler redefinition warnings. It also allows for other assembly versions to reuse the same boilerplate code as x86. Finally, it also adds the out_of_place flag to all assembly codelets. This changes nothing, as out-of-place operation was assumed to be available anyway, but this makes it more explicit.
2022-02-07 02:30:27 +00:00
TX_DECL_FN(fft2, sse3)
TX_DECL_FN(fft4_fwd, sse2)
TX_DECL_FN(fft4_inv, sse2)
TX_DECL_FN(fft8, sse3)
TX_DECL_FN(fft8_ns, sse3)
TX_DECL_FN(fft8, avx)
TX_DECL_FN(fft8_ns, avx)
TX_DECL_FN(fft16, avx)
TX_DECL_FN(fft16_ns, avx)
TX_DECL_FN(fft16, fma3)
TX_DECL_FN(fft16_ns, fma3)
TX_DECL_FN(fft32, avx)
TX_DECL_FN(fft32_ns, avx)
TX_DECL_FN(fft32, fma3)
TX_DECL_FN(fft32_ns, fma3)
TX_DECL_FN(fft_sr, avx)
TX_DECL_FN(fft_sr_ns, avx)
TX_DECL_FN(fft_sr, avx2)
TX_DECL_FN(fft_sr_ns, avx2)
x86/tx_float: add permute-free FFT versions These are used in the PFA transforms and MDCTs.
2022-01-25 21:39:09 +00:00
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
#define DECL_INIT_FN(basis, interleave) \
lavu/tx: refactor assembly codelet definition This commit does some refactoring to make defining assembly codelets smaller, and fixes compiler redefinition warnings. It also allows for other assembly versions to reuse the same boilerplate code as x86. Finally, it also adds the out_of_place flag to all assembly codelets. This changes nothing, as out-of-place operation was assumed to be available anyway, but this makes it more explicit.
2022-02-07 02:30:27 +00:00
static av_cold int b ##basis## _i ##interleave(AVTXContext *s, \
const FFTXCodelet *cd, \
uint64_t flags, \
FFTXCodeletOptions *opts, \
int len, int inv, \
const void *scale) \
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
{ \
const int inv_lookup = opts ? opts->invert_lookup : 1; \
ff_tx_init_tabs_float(len); \
x86/tx_float: add permute-free FFT versions These are used in the PFA transforms and MDCTs.
2022-01-25 21:39:09 +00:00
if (cd->max_len == 2) \
return ff_tx_gen_ptwo_revtab(s, inv_lookup); \
else \
return ff_tx_gen_split_radix_parity_revtab(s, inv_lookup, \
basis, interleave); \
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
}
lavu/x86: add FFT assembly 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.
2021-04-10 01:54:22 +00:00
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
DECL_INIT_FN(8, 0)
DECL_INIT_FN(8, 2)
lavu/x86: add FFT assembly 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.
2021-04-10 01:54:22 +00:00
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
const FFTXCodelet * const ff_tx_codelet_list_float_x86[] = {
lavu/tx: refactor assembly codelet definition This commit does some refactoring to make defining assembly codelets smaller, and fixes compiler redefinition warnings. It also allows for other assembly versions to reuse the same boilerplate code as x86. Finally, it also adds the out_of_place flag to all assembly codelets. This changes nothing, as out-of-place operation was assumed to be available anyway, but this makes it more explicit.
2022-02-07 02:30:27 +00:00
TX_DEF(fft2, FFT, 2, 2, 2, 0, 128, NULL, sse3, SSE3, AV_TX_INPLACE, 0),
TX_DEF(fft2, FFT, 2, 2, 2, 0, 192, b8_i0, sse3, SSE3, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
TX_DEF(fft4_fwd, FFT, 4, 4, 2, 0, 128, NULL, sse2, SSE2, AV_TX_INPLACE | FF_TX_FORWARD_ONLY, 0),
TX_DEF(fft4_fwd, FFT, 4, 4, 2, 0, 192, b8_i0, sse2, SSE2, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
TX_DEF(fft4_inv, FFT, 4, 4, 2, 0, 128, NULL, sse2, SSE2, AV_TX_INPLACE | FF_TX_INVERSE_ONLY, 0),
TX_DEF(fft8, FFT, 8, 8, 2, 0, 128, b8_i0, sse3, SSE3, AV_TX_INPLACE, 0),
TX_DEF(fft8_ns, FFT, 8, 8, 2, 0, 192, b8_i0, sse3, SSE3, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
TX_DEF(fft8, FFT, 8, 8, 2, 0, 256, b8_i0, avx, AVX, AV_TX_INPLACE, 0),
TX_DEF(fft8_ns, FFT, 8, 8, 2, 0, 320, b8_i0, avx, AVX, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
TX_DEF(fft16, FFT, 16, 16, 2, 0, 256, b8_i2, avx, AVX, AV_TX_INPLACE, 0),
TX_DEF(fft16_ns, FFT, 16, 16, 2, 0, 320, b8_i2, avx, AVX, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
TX_DEF(fft16, FFT, 16, 16, 2, 0, 288, b8_i2, fma3, FMA3, AV_TX_INPLACE, 0),
TX_DEF(fft16_ns, FFT, 16, 16, 2, 0, 352, b8_i2, fma3, FMA3, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
lavu/x86/tx_float: fix FMA3 implying AVX2 is available It's the other way around - AVX2 implies FMA3 is available.
2021-04-24 16:45:02 +00:00
#if ARCH_X86_64
lavu/tx: refactor assembly codelet definition This commit does some refactoring to make defining assembly codelets smaller, and fixes compiler redefinition warnings. It also allows for other assembly versions to reuse the same boilerplate code as x86. Finally, it also adds the out_of_place flag to all assembly codelets. This changes nothing, as out-of-place operation was assumed to be available anyway, but this makes it more explicit.
2022-02-07 02:30:27 +00:00
TX_DEF(fft32, FFT, 32, 32, 2, 0, 256, b8_i2, avx, AVX, AV_TX_INPLACE, 0),
TX_DEF(fft32_ns, FFT, 32, 32, 2, 0, 320, b8_i2, avx, AVX, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
TX_DEF(fft32, FFT, 32, 32, 2, 0, 288, b8_i2, fma3, FMA3, AV_TX_INPLACE, 0),
TX_DEF(fft32_ns, FFT, 32, 32, 2, 0, 352, b8_i2, fma3, FMA3, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
#if HAVE_AVX2_EXTERNAL
lavu/tx: refactor assembly codelet definition This commit does some refactoring to make defining assembly codelets smaller, and fixes compiler redefinition warnings. It also allows for other assembly versions to reuse the same boilerplate code as x86. Finally, it also adds the out_of_place flag to all assembly codelets. This changes nothing, as out-of-place operation was assumed to be available anyway, but this makes it more explicit.
2022-02-07 02:30:27 +00:00
TX_DEF(fft_sr, FFT, 64, 131072, 2, 0, 256, b8_i2, avx, AVX, 0, 0),
TX_DEF(fft_sr_ns, FFT, 64, 131072, 2, 0, 320, b8_i2, avx, AVX, AV_TX_INPLACE | FF_TX_PRESHUFFLE, 0),
TX_DEF(fft_sr, FFT, 64, 131072, 2, 0, 288, b8_i2, avx2, AVX2, 0, AV_CPU_FLAG_AVXSLOW),
TX_DEF(fft_sr_ns, FFT, 64, 131072, 2, 0, 352, b8_i2, avx2, AVX2, AV_TX_INPLACE | FF_TX_PRESHUFFLE,
AV_CPU_FLAG_AVXSLOW),
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
#endif
#endif
lavu/x86: add FFT assembly 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.
2021-04-10 01:54:22 +00:00
lavu/tx: rewrite internal code as a tree-based codelet constructor This commit rewrites the internal transform code into a constructor that stitches transforms (codelets). This allows for transforms to reuse arbitrary parts of other transforms, and allows transforms to be stacked onto one another (such as a full iMDCT using a half-iMDCT which in turn uses an FFT). It also permits for each step to be individually replaced by assembly or a custom implementation (such as an ASIC).
2022-01-20 06:14:46 +00:00
NULL,
};