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.
4 years ago
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;******************************************************************************
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;* Copyright (c) Lynne
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;*
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;* This file is part of FFmpeg.
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;*
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;* FFmpeg is free software; you can redistribute it and/or
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;* modify it under the terms of the GNU Lesser General Public
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;* License as published by the Free Software Foundation; either
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;* version 2.1 of the License, or (at your option) any later version.
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;*
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;* FFmpeg is distributed in the hope that it will be useful,
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;* but WITHOUT ANY WARRANTY; without even the implied warranty of
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;* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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;* Lesser General Public License for more details.
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;*
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;* You should have received a copy of the GNU Lesser General Public
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;* License along with FFmpeg; if not, write to the Free Software
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;* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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;******************************************************************************
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; Open `doc/transforms.md` to see the code upon which the transforms here were
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; based upon and compare.
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; TODO:
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; carry over registers from smaller transforms to save on ~8 loads/stores
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; check if vinsertf could be faster than verpm2f128 for duplication
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; even faster FFT8 (current one is very #instructions optimized)
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; replace some xors with blends + addsubs?
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; replace some shuffles with vblends?
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; avx512 split-radix
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%include "libavutil/x86/x86util.asm"
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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.
4 years ago
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%define private_prefix ff_tx
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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.
4 years ago
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%if ARCH_X86_64
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%define ptr resq
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%else
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%define ptr resd
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%endif
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%assign i 16
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%rep 14
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cextern tab_ %+ i %+ _float ; ff_tab_i_float...
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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.
4 years ago
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%assign i (i << 1)
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%endrep
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struc AVTXContext
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.len: resd 1 ; Length
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.inv resd 1 ; Inverse flag
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.map: ptr 1 ; Lookup table(s)
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.exp: ptr 1 ; Exponentiation factors
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.tmp: ptr 1 ; Temporary data
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.sub: ptr 1 ; Subcontexts
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.fn: ptr 4 ; Subcontext functions
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.nb_sub: resd 1 ; Subcontext count
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; Everything else is inaccessible
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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.
4 years ago
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endstruc
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SECTION_RODATA 32
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%define POS 0x00000000
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%define NEG 0x80000000
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%define M_SQRT1_2 0.707106781186547524401
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%define COS16_1 0.92387950420379638671875
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%define COS16_3 0.3826834261417388916015625
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d8_mult_odd: dd M_SQRT1_2, -M_SQRT1_2, -M_SQRT1_2, M_SQRT1_2, \
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M_SQRT1_2, -M_SQRT1_2, -M_SQRT1_2, M_SQRT1_2
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s8_mult_odd: dd 1.0, 1.0, -1.0, 1.0, -M_SQRT1_2, -M_SQRT1_2, M_SQRT1_2, M_SQRT1_2
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s8_perm_even: dd 1, 3, 0, 2, 1, 3, 2, 0
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s8_perm_odd1: dd 3, 3, 1, 1, 1, 1, 3, 3
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s8_perm_odd2: dd 1, 2, 0, 3, 1, 0, 0, 1
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s16_mult_even: dd 1.0, 1.0, M_SQRT1_2, M_SQRT1_2, 1.0, -1.0, M_SQRT1_2, -M_SQRT1_2
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s16_mult_odd1: dd COS16_1, COS16_1, COS16_3, COS16_3, COS16_1, -COS16_1, COS16_3, -COS16_3
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s16_mult_odd2: dd COS16_3, -COS16_3, COS16_1, -COS16_1, -COS16_3, -COS16_3, -COS16_1, -COS16_1
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s16_perm: dd 0, 1, 2, 3, 1, 0, 3, 2
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mask_mmmmpppm: dd NEG, NEG, NEG, NEG, POS, POS, POS, NEG
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mask_ppmpmmpm: dd POS, POS, NEG, POS, NEG, NEG, POS, NEG
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mask_mppmmpmp: dd NEG, POS, POS, NEG, NEG, POS, NEG, POS
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mask_mpmppmpm: dd NEG, POS, NEG, POS, POS, NEG, POS, NEG
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mask_pmmppmmp: dd POS, NEG, NEG, POS, POS, NEG, NEG, POS
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mask_pmpmpmpm: times 4 dd POS, NEG
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SECTION .text
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; Load complex values (64 bits) via a lookup table
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; %1 - output register
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; %2 - GRP of base input memory address
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; %3 - GPR of LUT (int32_t indices) address
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; %4 - LUT offset
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; %5 - temporary GPR (only used if vgather is not used)
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; %6 - temporary register (for avx only)
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; %7 - temporary register (for avx only, enables vgatherdpd (AVX2) if FMA3 is set)
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%macro LOAD64_LUT 5-7
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%if %0 > 6 && cpuflag(avx2)
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pcmpeqd %6, %6 ; pcmpeqq has a 0.5 throughput on Zen 3, this has 0.25
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movapd xmm%7, [%3 + %4] ; float mov since vgatherdpd is a float instruction
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vgatherdpd %1, [%2 + xmm%7*8], %6 ; must use separate registers for args
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%else
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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.
4 years ago
|
|
|
mov %5d, [%3 + %4 + 0]
|
|
|
|
|
movsd xmm%1, [%2 + %5q*8]
|
|
|
|
|
%if mmsize == 32
|
|
|
|
|
mov %5d, [%3 + %4 + 8]
|
|
|
|
|
movsd xmm%6, [%2 + %5q*8]
|
|
|
|
|
%endif
|
|
|
|
|
mov %5d, [%3 + %4 + 4]
|
|
|
|
|
movhps xmm%1, [%2 + %5q*8]
|
|
|
|
|
%if mmsize == 32
|
|
|
|
|
mov %5d, [%3 + %4 + 12]
|
|
|
|
|
movhps xmm%6, [%2 + %5q*8]
|
|
|
|
|
vinsertf128 %1, %1, xmm%6, 1
|
|
|
|
|
%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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Single 2-point in-place complex FFT (will do 2 transforms at once in AVX mode)
|
|
|
|
|
; %1 - coefficients (r0.reim, r1.reim)
|
|
|
|
|
; %2 - temporary
|
|
|
|
|
%macro FFT2 2
|
|
|
|
|
shufps %2, %1, %1, q3322
|
|
|
|
|
shufps %1, %1, %1, q1100
|
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.
4 years ago
|
|
|
|
|
|
|
|
addsubps %1, %1, %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.
4 years ago
|
|
|
|
|
|
|
|
shufps %1, %1, %1, q2031
|
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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Single 4-point in-place complex FFT (will do 2 transforms at once in [AVX] mode)
|
|
|
|
|
; %1 - even coefficients (r0.reim, r2.reim, r4.reim, r6.reim)
|
|
|
|
|
; %2 - odd coefficients (r1.reim, r3.reim, r5.reim, r7.reim)
|
|
|
|
|
; %3 - temporary
|
|
|
|
|
%macro FFT4 3
|
|
|
|
|
subps %3, %1, %2 ; r1234, [r5678]
|
|
|
|
|
addps %1, %1, %2 ; t1234, [t5678]
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %2, %1, %3, q1010 ; t12, r12
|
|
|
|
|
shufps %1, %1, %3, q2332 ; t34, r43
|
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.
4 years ago
|
|
|
|
|
|
|
|
subps %3, %2, %1 ; a34, b32
|
|
|
|
|
addps %2, %2, %1 ; a12, b14
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %1, %2, %3, q1010 ; a1234 even
|
|
|
|
|
|
|
|
|
|
shufps %2, %2, %3, q2332 ; b1423
|
|
|
|
|
shufps %2, %2, %2, q1320 ; b1234 odd
|
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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Single/Dual 8-point in-place complex FFT (will do 2 transforms in [AVX] mode)
|
|
|
|
|
; %1 - even coefficients (a0.reim, a2.reim, [b0.reim, b2.reim])
|
|
|
|
|
; %2 - even coefficients (a4.reim, a6.reim, [b4.reim, b6.reim])
|
|
|
|
|
; %3 - odd coefficients (a1.reim, a3.reim, [b1.reim, b3.reim])
|
|
|
|
|
; %4 - odd coefficients (a5.reim, a7.reim, [b5.reim, b7.reim])
|
|
|
|
|
; %5 - temporary
|
|
|
|
|
; %6 - temporary
|
|
|
|
|
%macro FFT8 6
|
|
|
|
|
addps %5, %1, %3 ; q1-8
|
|
|
|
|
addps %6, %2, %4 ; k1-8
|
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.
4 years ago
|
|
|
|
|
|
|
|
subps %1, %1, %3 ; r1-8
|
|
|
|
|
subps %2, %2, %4 ; j1-8
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %4, %1, %1, q2323 ; r4343
|
|
|
|
|
shufps %3, %5, %6, q3032 ; q34, k14
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %1, %1, %1, q1010 ; r1212
|
|
|
|
|
shufps %5, %5, %6, q1210 ; q12, k32
|
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.
4 years ago
|
|
|
|
|
|
|
|
xorps %4, %4, [mask_pmmppmmp] ; r4343 * pmmp
|
|
|
|
|
addps %6, %5, %3 ; s12, g12
|
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.
4 years ago
|
|
|
|
|
|
|
|
mulps %2, %2, [d8_mult_odd] ; r8 * d8_mult_odd
|
|
|
|
|
subps %5, %5, %3 ; s34, g43
|
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.
4 years ago
|
|
|
|
|
|
|
|
addps %3, %1, %4 ; z1234
|
|
|
|
|
unpcklpd %1, %6, %5 ; s1234
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %4, %2, %2, q2301 ; j2143
|
|
|
|
|
shufps %6, %6, %5, q2332 ; g1234
|
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.
4 years ago
|
|
|
|
|
|
|
|
addsubps %2, %2, %4 ; l2143
|
|
|
|
|
shufps %5, %2, %2, q0123 ; l3412
|
|
|
|
|
addsubps %5, %5, %2 ; t1234
|
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.
4 years ago
|
|
|
|
|
|
|
|
subps %2, %1, %6 ; h1234 even
|
|
|
|
|
subps %4, %3, %5 ; u1234 odd
|
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.
4 years ago
|
|
|
|
|
|
|
|
addps %1, %1, %6 ; w1234 even
|
|
|
|
|
addps %3, %3, %5 ; o1234 odd
|
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.
4 years ago
|
|
|
%endmacro
|
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|
|
|
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|
|
; Single 8-point in-place complex FFT in 20 instructions
|
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|
; %1 - even coefficients (r0.reim, r2.reim, r4.reim, r6.reim)
|
|
|
|
|
; %2 - odd coefficients (r1.reim, r3.reim, r5.reim, r7.reim)
|
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|
|
|
; %3 - temporary
|
|
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|
; %4 - temporary
|
|
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|
%macro FFT8_AVX 4
|
|
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|
|
subps %3, %1, %2 ; r1234, r5678
|
|
|
|
|
addps %1, %1, %2 ; q1234, q5678
|
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.
4 years ago
|
|
|
|
|
|
|
|
vpermilps %2, %3, [s8_perm_odd1] ; r4422, r6688
|
|
|
|
|
shufps %4, %1, %1, q3322 ; q1122, q5566
|
|
|
|
|
|
|
|
|
|
movsldup %3, %3 ; r1133, r5577
|
|
|
|
|
shufps %1, %1, %1, q1100 ; q3344, q7788
|
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.
4 years ago
|
|
|
|
|
|
|
|
addsubps %3, %3, %2 ; z1234, z5678
|
|
|
|
|
addsubps %1, %1, %4 ; s3142, s7586
|
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.
4 years ago
|
|
|
|
|
|
|
|
mulps %3, %3, [s8_mult_odd] ; z * s8_mult_odd
|
|
|
|
|
vpermilps %1, %1, [s8_perm_even] ; s1234, s5687 !
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %2, %3, %3, q2332 ; junk, z7887
|
|
|
|
|
xorps %4, %1, [mask_mmmmpppm] ; e1234, e5687 !
|
|
|
|
|
|
|
|
|
|
vpermilps %3, %3, [s8_perm_odd2] ; z2314, z6556
|
|
|
|
|
vperm2f128 %1, %1, %4, 0x03 ; e5687, s1234
|
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.
4 years ago
|
|
|
|
|
|
|
|
addsubps %2, %2, %3 ; junk, t5678
|
|
|
|
|
subps %1, %1, %4 ; w1234, w5678 even
|
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.
4 years ago
|
|
|
|
|
|
|
|
vperm2f128 %2, %2, %2, 0x11 ; t5678, t5678
|
|
|
|
|
vperm2f128 %3, %3, %3, 0x00 ; z2314, z2314
|
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.
4 years ago
|
|
|
|
|
|
|
|
xorps %2, %2, [mask_ppmpmmpm] ; t * ppmpmmpm
|
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.
4 years ago
|
|
|
addps %2, %3, %2 ; u1234, u5678 odd
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Single 16-point in-place complex FFT
|
|
|
|
|
; %1 - even coefficients (r0.reim, r2.reim, r4.reim, r6.reim)
|
|
|
|
|
; %2 - even coefficients (r8.reim, r10.reim, r12.reim, r14.reim)
|
|
|
|
|
; %3 - odd coefficients (r1.reim, r3.reim, r5.reim, r7.reim)
|
|
|
|
|
; %4 - odd coefficients (r9.reim, r11.reim, r13.reim, r15.reim)
|
|
|
|
|
; %5, %6 - temporary
|
|
|
|
|
; %7, %8 - temporary (optional)
|
|
|
|
|
%macro FFT16 6-8
|
|
|
|
|
FFT4 %3, %4, %5
|
|
|
|
|
%if %0 > 7
|
|
|
|
|
FFT8_AVX %1, %2, %6, %7
|
|
|
|
|
movaps %8, [mask_mpmppmpm]
|
|
|
|
|
movaps %7, [s16_perm]
|
|
|
|
|
%define mask %8
|
|
|
|
|
%define perm %7
|
|
|
|
|
%elif %0 > 6
|
|
|
|
|
FFT8_AVX %1, %2, %6, %7
|
|
|
|
|
movaps %7, [s16_perm]
|
|
|
|
|
%define mask [mask_mpmppmpm]
|
|
|
|
|
%define perm %7
|
|
|
|
|
%else
|
|
|
|
|
FFT8_AVX %1, %2, %6, %5
|
|
|
|
|
%define mask [mask_mpmppmpm]
|
|
|
|
|
%define perm [s16_perm]
|
|
|
|
|
%endif
|
|
|
|
|
xorps %5, %5, %5 ; 0
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %6, %4, %4, q2301 ; z12.imre, z13.imre...
|
|
|
|
|
shufps %5, %5, %3, q2301 ; 0, 0, z8.imre...
|
|
|
|
|
|
|
|
|
|
mulps %4, %4, [s16_mult_odd1] ; z.reim * costab
|
|
|
|
|
xorps %5, %5, [mask_mppmmpmp]
|
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.
4 years ago
|
|
|
%if cpuflag(fma3)
|
|
|
|
|
fmaddps %6, %6, [s16_mult_odd2], %4 ; s[8..15]
|
|
|
|
|
addps %5, %3, %5 ; s[0...7]
|
|
|
|
|
%else
|
|
|
|
|
mulps %6, %6, [s16_mult_odd2] ; z.imre * costab
|
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.
4 years ago
|
|
|
|
|
|
|
|
addps %5, %3, %5 ; s[0...7]
|
|
|
|
|
addps %6, %4, %6 ; s[8..15]
|
|
|
|
|
%endif
|
|
|
|
|
mulps %5, %5, [s16_mult_even] ; s[0...7]*costab
|
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.
4 years ago
|
|
|
|
|
|
|
|
xorps %4, %6, mask ; s[8..15]*mpmppmpm
|
|
|
|
|
xorps %3, %5, mask ; s[0...7]*mpmppmpm
|
|
|
|
|
|
|
|
|
|
vperm2f128 %4, %4, %4, 0x01 ; s[12..15, 8..11]
|
|
|
|
|
vperm2f128 %3, %3, %3, 0x01 ; s[4..7, 0..3]
|
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.
4 years ago
|
|
|
|
|
|
|
|
addps %6, %6, %4 ; y56, u56, y34, u34
|
|
|
|
|
addps %5, %5, %3 ; w56, x56, w34, x34
|
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.
4 years ago
|
|
|
|
|
|
|
|
vpermilps %6, %6, perm ; y56, u56, y43, u43
|
|
|
|
|
vpermilps %5, %5, perm ; w56, x56, w43, x43
|
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.
4 years ago
|
|
|
|
|
|
|
|
subps %4, %2, %6 ; odd part 2
|
|
|
|
|
addps %3, %2, %6 ; odd part 1
|
|
|
|
|
|
|
|
|
|
subps %2, %1, %5 ; even part 2
|
|
|
|
|
addps %1, %1, %5 ; even part 1
|
|
|
|
|
%undef mask
|
|
|
|
|
%undef perm
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Cobmines m0...m8 (tx1[even, even, odd, odd], tx2,3[even], tx2,3[odd]) coeffs
|
|
|
|
|
; Uses all 16 of registers.
|
|
|
|
|
; Output is slightly permuted such that tx2,3's coefficients are interleaved
|
|
|
|
|
; on a 2-point basis (look at `doc/transforms.md`)
|
|
|
|
|
%macro SPLIT_RADIX_COMBINE 17
|
|
|
|
|
%if %1 && mmsize == 32
|
|
|
|
|
vperm2f128 %14, %6, %7, 0x20 ; m2[0], m2[1], m3[0], m3[1] even
|
|
|
|
|
vperm2f128 %16, %9, %8, 0x20 ; m2[0], m2[1], m3[0], m3[1] odd
|
|
|
|
|
vperm2f128 %15, %6, %7, 0x31 ; m2[2], m2[3], m3[2], m3[3] even
|
|
|
|
|
vperm2f128 %17, %9, %8, 0x31 ; m2[2], m2[3], m3[2], m3[3] odd
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
shufps %12, %10, %10, q2200 ; cos00224466
|
|
|
|
|
shufps %13, %11, %11, q1133 ; wim77553311
|
|
|
|
|
movshdup %10, %10 ; cos11335577
|
|
|
|
|
shufps %11, %11, %11, q0022 ; wim66442200
|
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.
4 years ago
|
|
|
|
|
|
|
|
%if %1 && mmsize == 32
|
|
|
|
|
shufps %6, %14, %14, q2301 ; m2[0].imre, m2[1].imre, m2[2].imre, m2[3].imre even
|
|
|
|
|
shufps %8, %16, %16, q2301 ; m2[0].imre, m2[1].imre, m2[2].imre, m2[3].imre odd
|
|
|
|
|
shufps %7, %15, %15, q2301 ; m3[0].imre, m3[1].imre, m3[2].imre, m3[3].imre even
|
|
|
|
|
shufps %9, %17, %17, q2301 ; m3[0].imre, m3[1].imre, m3[2].imre, m3[3].imre odd
|
|
|
|
|
|
|
|
|
|
mulps %14, %14, %13 ; m2[0123]reim * wim7531 even
|
|
|
|
|
mulps %16, %16, %11 ; m2[0123]reim * wim7531 odd
|
|
|
|
|
mulps %15, %15, %13 ; m3[0123]reim * wim7531 even
|
|
|
|
|
mulps %17, %17, %11 ; m3[0123]reim * wim7531 odd
|
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.
4 years ago
|
|
|
%else
|
|
|
|
|
mulps %14, %6, %13 ; m2,3[01]reim * wim7531 even
|
|
|
|
|
mulps %16, %8, %11 ; m2,3[01]reim * wim7531 odd
|
|
|
|
|
mulps %15, %7, %13 ; m2,3[23]reim * wim7531 even
|
|
|
|
|
mulps %17, %9, %11 ; m2,3[23]reim * wim7531 odd
|
|
|
|
|
; reorder the multiplies to save movs reg, reg in the %if above
|
|
|
|
|
shufps %6, %6, %6, q2301 ; m2[0].imre, m2[1].imre, m3[0].imre, m3[1].imre even
|
|
|
|
|
shufps %8, %8, %8, q2301 ; m2[0].imre, m2[1].imre, m3[0].imre, m3[1].imre odd
|
|
|
|
|
shufps %7, %7, %7, q2301 ; m2[2].imre, m2[3].imre, m3[2].imre, m3[3].imre even
|
|
|
|
|
shufps %9, %9, %9, q2301 ; m2[2].imre, m2[3].imre, m3[2].imre, m3[3].imre odd
|
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.
4 years ago
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
%if cpuflag(fma3) ; 11 - 5 = 6 instructions saved through FMA!
|
|
|
|
|
fmaddsubps %6, %6, %12, %14 ; w[0..8] even
|
|
|
|
|
fmaddsubps %8, %8, %10, %16 ; w[0..8] odd
|
|
|
|
|
fmsubaddps %7, %7, %12, %15 ; j[0..8] even
|
|
|
|
|
fmsubaddps %9, %9, %10, %17 ; j[0..8] odd
|
|
|
|
|
movaps %13, [mask_pmpmpmpm] ; "subaddps? pfft, who needs that!"
|
|
|
|
|
%else
|
|
|
|
|
mulps %6, %6, %12 ; m2,3[01]imre * cos0246
|
|
|
|
|
mulps %8, %8, %10 ; m2,3[01]imre * cos0246
|
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.
4 years ago
|
|
|
movaps %13, [mask_pmpmpmpm] ; "subaddps? pfft, who needs that!"
|
|
|
|
|
mulps %7, %7, %12 ; m2,3[23]reim * cos0246
|
|
|
|
|
mulps %9, %9, %10 ; m2,3[23]reim * cos0246
|
|
|
|
|
addsubps %6, %6, %14 ; w[0..8]
|
|
|
|
|
addsubps %8, %8, %16 ; w[0..8]
|
|
|
|
|
xorps %15, %15, %13 ; +-m2,3[23]imre * wim7531
|
|
|
|
|
xorps %17, %17, %13 ; +-m2,3[23]imre * wim7531
|
|
|
|
|
addps %7, %7, %15 ; j[0..8]
|
|
|
|
|
addps %9, %9, %17 ; j[0..8]
|
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.
4 years ago
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
addps %14, %6, %7 ; t10235476 even
|
|
|
|
|
addps %16, %8, %9 ; t10235476 odd
|
|
|
|
|
subps %15, %6, %7 ; +-r[0..7] even
|
|
|
|
|
subps %17, %8, %9 ; +-r[0..7] odd
|
|
|
|
|
|
|
|
|
|
shufps %14, %14, %14, q2301 ; t[0..7] even
|
|
|
|
|
shufps %16, %16, %16, q2301 ; t[0..7] odd
|
|
|
|
|
xorps %15, %15, %13 ; r[0..7] even
|
|
|
|
|
xorps %17, %17, %13 ; r[0..7] odd
|
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.
4 years ago
|
|
|
|
|
|
|
|
subps %6, %2, %14 ; m2,3[01] even
|
|
|
|
|
subps %8, %4, %16 ; m2,3[01] odd
|
|
|
|
|
subps %7, %3, %15 ; m2,3[23] even
|
|
|
|
|
subps %9, %5, %17 ; m2,3[23] odd
|
|
|
|
|
|
|
|
|
|
addps %2, %2, %14 ; m0 even
|
|
|
|
|
addps %4, %4, %16 ; m0 odd
|
|
|
|
|
addps %3, %3, %15 ; m1 even
|
|
|
|
|
addps %5, %5, %17 ; m1 odd
|
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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Same as above, only does one parity at a time, takes 3 temporary registers,
|
|
|
|
|
; however, if the twiddles aren't needed after this, the registers they use
|
|
|
|
|
; can be used as any of the temporary registers.
|
|
|
|
|
%macro SPLIT_RADIX_COMBINE_HALF 10
|
|
|
|
|
%if %1
|
|
|
|
|
shufps %8, %6, %6, q2200 ; cos00224466
|
|
|
|
|
shufps %9, %7, %7, q1133 ; wim77553311
|
|
|
|
|
%else
|
|
|
|
|
shufps %8, %6, %6, q3311 ; cos11335577
|
|
|
|
|
shufps %9, %7, %7, q0022 ; wim66442200
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
mulps %10, %4, %9 ; m2,3[01]reim * wim7531 even
|
|
|
|
|
mulps %9, %9, %5 ; m2,3[23]reim * wim7531 even
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %4, %4, %4, q2301 ; m2[0].imre, m2[1].imre, m3[0].imre, m3[1].imre even
|
|
|
|
|
shufps %5, %5, %5, q2301 ; m2[2].imre, m2[3].imre, m3[2].imre, m3[3].imre even
|
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.
4 years ago
|
|
|
|
|
|
|
|
%if cpuflag(fma3)
|
|
|
|
|
fmaddsubps %4, %4, %8, %10 ; w[0..8] even
|
|
|
|
|
fmsubaddps %5, %5, %8, %9 ; j[0..8] even
|
|
|
|
|
movaps %10, [mask_pmpmpmpm]
|
|
|
|
|
%else
|
|
|
|
|
mulps %4, %4, %8 ; m2,3[01]imre * cos0246
|
|
|
|
|
mulps %5, %5, %8 ; m2,3[23]reim * cos0246
|
|
|
|
|
addsubps %4, %4, %10 ; w[0..8]
|
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.
4 years ago
|
|
|
movaps %10, [mask_pmpmpmpm]
|
|
|
|
|
xorps %9, %9, %10 ; +-m2,3[23]imre * wim7531
|
|
|
|
|
addps %5, %5, %9 ; j[0..8]
|
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.
4 years ago
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
addps %8, %4, %5 ; t10235476
|
|
|
|
|
subps %9, %4, %5 ; +-r[0..7]
|
|
|
|
|
|
|
|
|
|
shufps %8, %8, %8, q2301 ; t[0..7]
|
|
|
|
|
xorps %9, %9, %10 ; r[0..7]
|
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.
4 years ago
|
|
|
|
|
|
|
|
subps %4, %2, %8 ; %3,3[01]
|
|
|
|
|
subps %5, %3, %9 ; %3,3[23]
|
|
|
|
|
|
|
|
|
|
addps %2, %2, %8 ; m0
|
|
|
|
|
addps %3, %3, %9 ; m1
|
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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Same as above, tries REALLY hard to use 2 temporary registers.
|
|
|
|
|
%macro SPLIT_RADIX_COMBINE_LITE 9
|
|
|
|
|
%if %1
|
|
|
|
|
shufps %8, %6, %6, q2200 ; cos00224466
|
|
|
|
|
shufps %9, %7, %7, q1133 ; wim77553311
|
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.
4 years ago
|
|
|
%else
|
|
|
|
|
shufps %8, %6, %6, q3311 ; cos11335577
|
|
|
|
|
shufps %9, %7, %7, q0022 ; wim66442200
|
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.
4 years ago
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
mulps %9, %9, %4 ; m2,3[01]reim * wim7531 even
|
|
|
|
|
shufps %4, %4, %4, q2301 ; m2[0].imre, m2[1].imre, m3[0].imre, m3[1].imre even
|
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.
4 years ago
|
|
|
|
|
|
|
|
%if cpuflag(fma3)
|
|
|
|
|
fmaddsubps %4, %4, %8, %9 ; w[0..8] even
|
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.
4 years ago
|
|
|
%else
|
|
|
|
|
mulps %4, %4, %8 ; m2,3[01]imre * cos0246
|
|
|
|
|
addsubps %4, %4, %9 ; w[0..8]
|
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.
4 years ago
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
%if %1
|
|
|
|
|
shufps %9, %7, %7, q1133 ; wim77553311
|
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.
4 years ago
|
|
|
%else
|
|
|
|
|
shufps %9, %7, %7, q0022 ; wim66442200
|
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.
4 years ago
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
mulps %9, %9, %5 ; m2,3[23]reim * wim7531 even
|
|
|
|
|
shufps %5, %5, %5, q2301 ; m2[2].imre, m2[3].imre, m3[2].imre, m3[3].imre even
|
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.
4 years ago
|
|
|
%if cpuflag (fma3)
|
|
|
|
|
fmsubaddps %5, %5, %8, %9 ; j[0..8] even
|
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.
4 years ago
|
|
|
%else
|
|
|
|
|
mulps %5, %5, %8 ; m2,3[23]reim * cos0246
|
|
|
|
|
xorps %9, %9, [mask_pmpmpmpm] ; +-m2,3[23]imre * wim7531
|
|
|
|
|
addps %5, %5, %9 ; j[0..8]
|
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.
4 years ago
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
addps %8, %4, %5 ; t10235476
|
|
|
|
|
subps %9, %4, %5 ; +-r[0..7]
|
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.
4 years ago
|
|
|
|
|
|
|
|
shufps %8, %8, %8, q2301 ; t[0..7]
|
|
|
|
|
xorps %9, %9, [mask_pmpmpmpm] ; r[0..7]
|
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.
4 years ago
|
|
|
|
|
|
|
|
subps %4, %2, %8 ; %3,3[01]
|
|
|
|
|
subps %5, %3, %9 ; %3,3[23]
|
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.
4 years ago
|
|
|
|
|
|
|
|
addps %2, %2, %8 ; m0
|
|
|
|
|
addps %3, %3, %9 ; m1
|
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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
%macro SPLIT_RADIX_COMBINE_64 0
|
|
|
|
|
SPLIT_RADIX_COMBINE_LITE 1, m0, m1, tx1_e0, tx2_e0, tw_e, tw_o, tmp1, tmp2
|
|
|
|
|
|
|
|
|
|
movaps [outq + 0*mmsize], m0
|
|
|
|
|
movaps [outq + 4*mmsize], m1
|
|
|
|
|
movaps [outq + 8*mmsize], tx1_e0
|
|
|
|
|
movaps [outq + 12*mmsize], tx2_e0
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE_HALF 0, m2, m3, tx1_o0, tx2_o0, tw_e, tw_o, tmp1, tmp2, m0
|
|
|
|
|
|
|
|
|
|
movaps [outq + 2*mmsize], m2
|
|
|
|
|
movaps [outq + 6*mmsize], m3
|
|
|
|
|
movaps [outq + 10*mmsize], tx1_o0
|
|
|
|
|
movaps [outq + 14*mmsize], tx2_o0
|
|
|
|
|
|
|
|
|
|
movaps tw_e, [tab_64_float + mmsize]
|
|
|
|
|
vperm2f128 tw_o, tw_o, [tab_64_float + 64 - 4*7 - mmsize], 0x23
|
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.
4 years ago
|
|
|
|
|
|
|
|
movaps m0, [outq + 1*mmsize]
|
|
|
|
|
movaps m1, [outq + 3*mmsize]
|
|
|
|
|
movaps m2, [outq + 5*mmsize]
|
|
|
|
|
movaps m3, [outq + 7*mmsize]
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE 0, m0, m2, m1, m3, tx1_e1, tx2_e1, tx1_o1, tx2_o1, tw_e, tw_o, \
|
|
|
|
|
tmp1, tmp2, tx2_o0, tx1_o0, tx2_e0, tx1_e0 ; temporary registers
|
|
|
|
|
|
|
|
|
|
movaps [outq + 1*mmsize], m0
|
|
|
|
|
movaps [outq + 3*mmsize], m1
|
|
|
|
|
movaps [outq + 5*mmsize], m2
|
|
|
|
|
movaps [outq + 7*mmsize], m3
|
|
|
|
|
|
|
|
|
|
movaps [outq + 9*mmsize], tx1_e1
|
|
|
|
|
movaps [outq + 11*mmsize], tx1_o1
|
|
|
|
|
movaps [outq + 13*mmsize], tx2_e1
|
|
|
|
|
movaps [outq + 15*mmsize], tx2_o1
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Perform a single even/odd split radix combination with loads and stores
|
|
|
|
|
; The _4 indicates this is a quarter of the iterations required to complete a full
|
|
|
|
|
; combine loop
|
|
|
|
|
; %1 must contain len*2, %2 must contain len*4, %3 must contain len*6
|
|
|
|
|
%macro SPLIT_RADIX_LOAD_COMBINE_4 8
|
|
|
|
|
movaps m8, [rtabq + (%5)*mmsize + %7]
|
|
|
|
|
vperm2f128 m9, m9, [itabq - (%5)*mmsize + %8], 0x23
|
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.
4 years ago
|
|
|
|
|
|
|
|
movaps m0, [outq + (0 + %4)*mmsize + %6]
|
|
|
|
|
movaps m2, [outq + (2 + %4)*mmsize + %6]
|
|
|
|
|
movaps m1, [outq + %1 + (0 + %4)*mmsize + %6]
|
|
|
|
|
movaps m3, [outq + %1 + (2 + %4)*mmsize + %6]
|
|
|
|
|
|
|
|
|
|
movaps m4, [outq + %2 + (0 + %4)*mmsize + %6]
|
|
|
|
|
movaps m6, [outq + %2 + (2 + %4)*mmsize + %6]
|
|
|
|
|
movaps m5, [outq + %3 + (0 + %4)*mmsize + %6]
|
|
|
|
|
movaps m7, [outq + %3 + (2 + %4)*mmsize + %6]
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE 0, m0, m1, m2, m3, \
|
|
|
|
|
m4, m5, m6, m7, \
|
|
|
|
|
m8, m9, \
|
|
|
|
|
m10, m11, m12, m13, m14, m15
|
|
|
|
|
|
|
|
|
|
movaps [outq + (0 + %4)*mmsize + %6], m0
|
|
|
|
|
movaps [outq + (2 + %4)*mmsize + %6], m2
|
|
|
|
|
movaps [outq + %1 + (0 + %4)*mmsize + %6], m1
|
|
|
|
|
movaps [outq + %1 + (2 + %4)*mmsize + %6], m3
|
|
|
|
|
|
|
|
|
|
movaps [outq + %2 + (0 + %4)*mmsize + %6], m4
|
|
|
|
|
movaps [outq + %2 + (2 + %4)*mmsize + %6], m6
|
|
|
|
|
movaps [outq + %3 + (0 + %4)*mmsize + %6], m5
|
|
|
|
|
movaps [outq + %3 + (2 + %4)*mmsize + %6], m7
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
%macro SPLIT_RADIX_LOAD_COMBINE_FULL 2-5
|
|
|
|
|
%if %0 > 2
|
|
|
|
|
%define offset_c %3
|
|
|
|
|
%else
|
|
|
|
|
%define offset_c 0
|
|
|
|
|
%endif
|
|
|
|
|
%if %0 > 3
|
|
|
|
|
%define offset_r %4
|
|
|
|
|
%else
|
|
|
|
|
%define offset_r 0
|
|
|
|
|
%endif
|
|
|
|
|
%if %0 > 4
|
|
|
|
|
%define offset_i %5
|
|
|
|
|
%else
|
|
|
|
|
%define offset_i 0
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_4 %1, 2*%1, %2, 0, 0, offset_c, offset_r, offset_i
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_4 %1, 2*%1, %2, 1, 1, offset_c, offset_r, offset_i
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_4 %1, 2*%1, %2, 4, 2, offset_c, offset_r, offset_i
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_4 %1, 2*%1, %2, 5, 3, offset_c, offset_r, offset_i
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
; Perform a single even/odd split radix combination with loads, deinterleaves and
|
|
|
|
|
; stores. The _2 indicates this is a half of the iterations required to complete
|
|
|
|
|
; a full combine+deinterleave loop
|
|
|
|
|
; %3 must contain len*2, %4 must contain len*4, %5 must contain len*6
|
|
|
|
|
%macro SPLIT_RADIX_COMBINE_DEINTERLEAVE_2 6
|
|
|
|
|
movaps m8, [rtabq + (0 + %2)*mmsize]
|
|
|
|
|
vperm2f128 m9, m9, [itabq - (0 + %2)*mmsize], 0x23
|
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.
4 years ago
|
|
|
|
|
|
|
|
movaps m0, [outq + (0 + 0 + %1)*mmsize + %6]
|
|
|
|
|
movaps m2, [outq + (2 + 0 + %1)*mmsize + %6]
|
|
|
|
|
movaps m1, [outq + %3 + (0 + 0 + %1)*mmsize + %6]
|
|
|
|
|
movaps m3, [outq + %3 + (2 + 0 + %1)*mmsize + %6]
|
|
|
|
|
|
|
|
|
|
movaps m4, [outq + %4 + (0 + 0 + %1)*mmsize + %6]
|
|
|
|
|
movaps m6, [outq + %4 + (2 + 0 + %1)*mmsize + %6]
|
|
|
|
|
movaps m5, [outq + %5 + (0 + 0 + %1)*mmsize + %6]
|
|
|
|
|
movaps m7, [outq + %5 + (2 + 0 + %1)*mmsize + %6]
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE 0, m0, m1, m2, m3, \
|
|
|
|
|
m4, m5, m6, m7, \
|
|
|
|
|
m8, m9, \
|
|
|
|
|
m10, m11, m12, m13, m14, m15
|
|
|
|
|
|
|
|
|
|
unpckhpd m10, m0, m2
|
|
|
|
|
unpckhpd m11, m1, m3
|
|
|
|
|
unpckhpd m12, m4, m6
|
|
|
|
|
unpckhpd m13, m5, m7
|
|
|
|
|
unpcklpd m0, m0, m2
|
|
|
|
|
unpcklpd m1, m1, m3
|
|
|
|
|
unpcklpd m4, m4, m6
|
|
|
|
|
unpcklpd m5, m5, m7
|
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.
4 years ago
|
|
|
|
|
|
|
|
vextractf128 [outq + (0 + 0 + %1)*mmsize + %6 + 0], m0, 0
|
|
|
|
|
vextractf128 [outq + (0 + 0 + %1)*mmsize + %6 + 16], m10, 0
|
|
|
|
|
vextractf128 [outq + %3 + (0 + 0 + %1)*mmsize + %6 + 0], m1, 0
|
|
|
|
|
vextractf128 [outq + %3 + (0 + 0 + %1)*mmsize + %6 + 16], m11, 0
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + %4 + (0 + 0 + %1)*mmsize + %6 + 0], m4, 0
|
|
|
|
|
vextractf128 [outq + %4 + (0 + 0 + %1)*mmsize + %6 + 16], m12, 0
|
|
|
|
|
vextractf128 [outq + %5 + (0 + 0 + %1)*mmsize + %6 + 0], m5, 0
|
|
|
|
|
vextractf128 [outq + %5 + (0 + 0 + %1)*mmsize + %6 + 16], m13, 0
|
|
|
|
|
|
|
|
|
|
vperm2f128 m10, m10, m0, 0x13
|
|
|
|
|
vperm2f128 m11, m11, m1, 0x13
|
|
|
|
|
vperm2f128 m12, m12, m4, 0x13
|
|
|
|
|
vperm2f128 m13, m13, m5, 0x13
|
|
|
|
|
|
|
|
|
|
movaps m8, [rtabq + (1 + %2)*mmsize]
|
|
|
|
|
vperm2f128 m9, m9, [itabq - (1 + %2)*mmsize], 0x23
|
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.
4 years ago
|
|
|
|
|
|
|
|
movaps m0, [outq + (0 + 1 + %1)*mmsize + %6]
|
|
|
|
|
movaps m2, [outq + (2 + 1 + %1)*mmsize + %6]
|
|
|
|
|
movaps m1, [outq + %3 + (0 + 1 + %1)*mmsize + %6]
|
|
|
|
|
movaps m3, [outq + %3 + (2 + 1 + %1)*mmsize + %6]
|
|
|
|
|
|
|
|
|
|
movaps [outq + (0 + 1 + %1)*mmsize + %6], m10 ; m0 conflict
|
|
|
|
|
movaps [outq + %3 + (0 + 1 + %1)*mmsize + %6], m11 ; m1 conflict
|
|
|
|
|
|
|
|
|
|
movaps m4, [outq + %4 + (0 + 1 + %1)*mmsize + %6]
|
|
|
|
|
movaps m6, [outq + %4 + (2 + 1 + %1)*mmsize + %6]
|
|
|
|
|
movaps m5, [outq + %5 + (0 + 1 + %1)*mmsize + %6]
|
|
|
|
|
movaps m7, [outq + %5 + (2 + 1 + %1)*mmsize + %6]
|
|
|
|
|
|
|
|
|
|
movaps [outq + %4 + (0 + 1 + %1)*mmsize + %6], m12 ; m4 conflict
|
|
|
|
|
movaps [outq + %5 + (0 + 1 + %1)*mmsize + %6], m13 ; m5 conflict
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE 0, m0, m1, m2, m3, \
|
|
|
|
|
m4, m5, m6, m7, \
|
|
|
|
|
m8, m9, \
|
|
|
|
|
m10, m11, m12, m13, m14, m15 ; temporary registers
|
|
|
|
|
|
|
|
|
|
unpcklpd m8, m0, m2
|
|
|
|
|
unpcklpd m9, m1, m3
|
|
|
|
|
unpcklpd m10, m4, m6
|
|
|
|
|
unpcklpd m11, m5, m7
|
|
|
|
|
unpckhpd m0, m0, m2
|
|
|
|
|
unpckhpd m1, m1, m3
|
|
|
|
|
unpckhpd m4, m4, m6
|
|
|
|
|
unpckhpd m5, m5, m7
|
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.
4 years ago
|
|
|
|
|
|
|
|
vextractf128 [outq + (2 + 0 + %1)*mmsize + %6 + 0], m8, 0
|
|
|
|
|
vextractf128 [outq + (2 + 0 + %1)*mmsize + %6 + 16], m0, 0
|
|
|
|
|
vextractf128 [outq + (2 + 1 + %1)*mmsize + %6 + 0], m8, 1
|
|
|
|
|
vextractf128 [outq + (2 + 1 + %1)*mmsize + %6 + 16], m0, 1
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + %3 + (2 + 0 + %1)*mmsize + %6 + 0], m9, 0
|
|
|
|
|
vextractf128 [outq + %3 + (2 + 0 + %1)*mmsize + %6 + 16], m1, 0
|
|
|
|
|
vextractf128 [outq + %3 + (2 + 1 + %1)*mmsize + %6 + 0], m9, 1
|
|
|
|
|
vextractf128 [outq + %3 + (2 + 1 + %1)*mmsize + %6 + 16], m1, 1
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + %4 + (2 + 0 + %1)*mmsize + %6 + 0], m10, 0
|
|
|
|
|
vextractf128 [outq + %4 + (2 + 0 + %1)*mmsize + %6 + 16], m4, 0
|
|
|
|
|
vextractf128 [outq + %4 + (2 + 1 + %1)*mmsize + %6 + 0], m10, 1
|
|
|
|
|
vextractf128 [outq + %4 + (2 + 1 + %1)*mmsize + %6 + 16], m4, 1
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + %5 + (2 + 0 + %1)*mmsize + %6 + 0], m11, 0
|
|
|
|
|
vextractf128 [outq + %5 + (2 + 0 + %1)*mmsize + %6 + 16], m5, 0
|
|
|
|
|
vextractf128 [outq + %5 + (2 + 1 + %1)*mmsize + %6 + 0], m11, 1
|
|
|
|
|
vextractf128 [outq + %5 + (2 + 1 + %1)*mmsize + %6 + 16], m5, 1
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
%macro SPLIT_RADIX_COMBINE_DEINTERLEAVE_FULL 2-3
|
|
|
|
|
%if %0 > 2
|
|
|
|
|
%define offset %3
|
|
|
|
|
%else
|
|
|
|
|
%define offset 0
|
|
|
|
|
%endif
|
|
|
|
|
SPLIT_RADIX_COMBINE_DEINTERLEAVE_2 0, 0, %1, %1*2, %2, offset
|
|
|
|
|
SPLIT_RADIX_COMBINE_DEINTERLEAVE_2 4, 2, %1, %1*2, %2, offset
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
INIT_XMM sse3
|
|
|
|
|
cglobal fft2_float, 4, 4, 2, ctx, out, in, stride
|
|
|
|
|
movaps m0, [inq]
|
|
|
|
|
FFT2 m0, m1
|
|
|
|
|
movaps [outq], m0
|
|
|
|
|
RET
|
|
|
|
|
|
|
|
|
|
%macro FFT4 2
|
|
|
|
|
INIT_XMM sse2
|
|
|
|
|
cglobal fft4_ %+ %1 %+ _float, 4, 4, 3, ctx, out, in, stride
|
|
|
|
|
movaps m0, [inq + 0*mmsize]
|
|
|
|
|
movaps m1, [inq + 1*mmsize]
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
shufps m2, m1, m0, q3210
|
|
|
|
|
shufps m0, m0, m1, q3210
|
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.
4 years ago
|
|
|
movaps m1, m2
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
FFT4 m0, m1, m2
|
|
|
|
|
|
|
|
|
|
unpcklpd m2, m0, m1
|
|
|
|
|
unpckhpd m0, m0, m1
|
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.
4 years ago
|
|
|
|
|
|
|
|
movaps [outq + 0*mmsize], m2
|
|
|
|
|
movaps [outq + 1*mmsize], m0
|
|
|
|
|
|
|
|
|
|
RET
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
FFT4 fwd, 0
|
|
|
|
|
FFT4 inv, 1
|
|
|
|
|
|
|
|
|
|
%macro FFT8_SSE_FN 1
|
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.
4 years ago
|
|
|
INIT_XMM sse3
|
|
|
|
|
%if %1
|
|
|
|
|
cglobal fft8_asm_float, 0, 0, 0, ctx, out, in, tmp
|
|
|
|
|
movaps m0, [inq + 0*mmsize]
|
|
|
|
|
movaps m1, [inq + 1*mmsize]
|
|
|
|
|
movaps m2, [inq + 2*mmsize]
|
|
|
|
|
movaps m3, [inq + 3*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
cglobal fft8_float, 4, 4, 6, ctx, out, in, tmp
|
|
|
|
|
mov ctxq, [ctxq + AVTXContext.map]
|
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.
4 years ago
|
|
|
LOAD64_LUT m0, inq, ctxq, (mmsize/2)*0, tmpq
|
|
|
|
|
LOAD64_LUT m1, inq, ctxq, (mmsize/2)*1, tmpq
|
|
|
|
|
LOAD64_LUT m2, inq, ctxq, (mmsize/2)*2, tmpq
|
|
|
|
|
LOAD64_LUT m3, inq, ctxq, (mmsize/2)*3, tmpq
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
FFT8 m0, m1, m2, m3, m4, m5
|
|
|
|
|
|
|
|
|
|
unpcklpd m4, m0, m3
|
|
|
|
|
unpcklpd m5, m1, m2
|
|
|
|
|
unpckhpd m0, m0, m3
|
|
|
|
|
unpckhpd m1, m1, m2
|
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.
4 years ago
|
|
|
|
|
|
|
|
movups [outq + 0*mmsize], m4
|
|
|
|
|
movups [outq + 1*mmsize], m0
|
|
|
|
|
movups [outq + 2*mmsize], m5
|
|
|
|
|
movups [outq + 3*mmsize], m1
|
|
|
|
|
|
|
|
|
|
%if %1
|
|
|
|
|
ret
|
|
|
|
|
%else
|
|
|
|
|
RET
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
%if %1
|
|
|
|
|
cglobal fft8_ns_float, 4, 4, 6, ctx, out, in, tmp
|
|
|
|
|
call mangle(ff_tx_fft8_asm_float_sse3)
|
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.
4 years ago
|
|
|
RET
|
|
|
|
|
%endif
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
FFT8_SSE_FN 0
|
|
|
|
|
FFT8_SSE_FN 1
|
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.
4 years ago
|
|
|
|
|
|
|
|
%macro FFT8_AVX_FN 1
|
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.
4 years ago
|
|
|
INIT_YMM avx
|
|
|
|
|
%if %1
|
|
|
|
|
cglobal fft8_asm_float, 0, 0, 0, ctx, out, in, tmp
|
|
|
|
|
movaps m0, [inq + 0*mmsize]
|
|
|
|
|
movaps m1, [inq + 1*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
cglobal fft8_float, 4, 4, 4, ctx, out, in, tmp
|
|
|
|
|
mov ctxq, [ctxq + AVTXContext.map]
|
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.
4 years ago
|
|
|
LOAD64_LUT m0, inq, ctxq, (mmsize/2)*0, tmpq, m2
|
|
|
|
|
LOAD64_LUT m1, inq, ctxq, (mmsize/2)*1, tmpq, m3
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
FFT8_AVX m0, m1, m2, m3
|
|
|
|
|
|
|
|
|
|
unpcklpd m2, m0, m1
|
|
|
|
|
unpckhpd m0, m0, m1
|
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.
4 years ago
|
|
|
|
|
|
|
|
; Around 2% faster than 2x vperm2f128 + 2x movapd
|
|
|
|
|
vextractf128 [outq + 16*0], m2, 0
|
|
|
|
|
vextractf128 [outq + 16*1], m0, 0
|
|
|
|
|
vextractf128 [outq + 16*2], m2, 1
|
|
|
|
|
vextractf128 [outq + 16*3], m0, 1
|
|
|
|
|
|
|
|
|
|
%if %1
|
|
|
|
|
ret
|
|
|
|
|
%else
|
|
|
|
|
RET
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
%if %1
|
|
|
|
|
cglobal fft8_ns_float, 4, 4, 4, ctx, out, in, tmp
|
|
|
|
|
call mangle(ff_tx_fft8_asm_float_avx)
|
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.
4 years ago
|
|
|
RET
|
|
|
|
|
%endif
|
|
|
|
|
%endmacro
|
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.
4 years ago
|
|
|
|
|
|
|
|
FFT8_AVX_FN 0
|
|
|
|
|
FFT8_AVX_FN 1
|
|
|
|
|
|
|
|
|
|
%macro FFT16_FN 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.
4 years ago
|
|
|
INIT_YMM %1
|
|
|
|
|
%if %2
|
|
|
|
|
cglobal fft16_asm_float, 0, 0, 0, ctx, out, in, tmp
|
|
|
|
|
movaps m0, [inq + 0*mmsize]
|
|
|
|
|
movaps m1, [inq + 1*mmsize]
|
|
|
|
|
movaps m2, [inq + 2*mmsize]
|
|
|
|
|
movaps m3, [inq + 3*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
cglobal fft16_float, 4, 4, 8, ctx, out, in, tmp
|
|
|
|
|
mov ctxq, [ctxq + AVTXContext.map]
|
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.
4 years ago
|
|
|
LOAD64_LUT m0, inq, ctxq, (mmsize/2)*0, tmpq, m4
|
|
|
|
|
LOAD64_LUT m1, inq, ctxq, (mmsize/2)*1, tmpq, m5
|
|
|
|
|
LOAD64_LUT m2, inq, ctxq, (mmsize/2)*2, tmpq, m6
|
|
|
|
|
LOAD64_LUT m3, inq, ctxq, (mmsize/2)*3, tmpq, m7
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
FFT16 m0, m1, m2, m3, m4, m5, m6, m7
|
|
|
|
|
|
|
|
|
|
unpcklpd m5, m1, m3
|
|
|
|
|
unpcklpd m4, m0, m2
|
|
|
|
|
unpckhpd m1, m1, m3
|
|
|
|
|
unpckhpd m0, m0, m2
|
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.
4 years ago
|
|
|
|
|
|
|
|
vextractf128 [outq + 16*0], m4, 0
|
|
|
|
|
vextractf128 [outq + 16*1], m0, 0
|
|
|
|
|
vextractf128 [outq + 16*2], m4, 1
|
|
|
|
|
vextractf128 [outq + 16*3], m0, 1
|
|
|
|
|
vextractf128 [outq + 16*4], m5, 0
|
|
|
|
|
vextractf128 [outq + 16*5], m1, 0
|
|
|
|
|
vextractf128 [outq + 16*6], m5, 1
|
|
|
|
|
vextractf128 [outq + 16*7], m1, 1
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
ret
|
|
|
|
|
%else
|
|
|
|
|
RET
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
cglobal fft16_ns_float, 4, 4, 8, ctx, out, in, tmp
|
|
|
|
|
call mangle(ff_tx_fft16_asm_float_ %+ %1)
|
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.
4 years ago
|
|
|
RET
|
|
|
|
|
%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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
FFT16_FN avx, 0
|
|
|
|
|
FFT16_FN avx, 1
|
|
|
|
|
FFT16_FN fma3, 0
|
|
|
|
|
FFT16_FN fma3, 1
|
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.
4 years ago
|
|
|
|
|
|
|
|
%macro FFT32_FN 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.
4 years ago
|
|
|
INIT_YMM %1
|
|
|
|
|
%if %2
|
|
|
|
|
cglobal fft32_asm_float, 0, 0, 0, ctx, out, in, tmp
|
|
|
|
|
movaps m4, [inq + 4*mmsize]
|
|
|
|
|
movaps m5, [inq + 5*mmsize]
|
|
|
|
|
movaps m6, [inq + 6*mmsize]
|
|
|
|
|
movaps m7, [inq + 7*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
cglobal fft32_float, 4, 4, 16, ctx, out, in, tmp
|
|
|
|
|
mov ctxq, [ctxq + AVTXContext.map]
|
|
|
|
|
LOAD64_LUT m4, inq, ctxq, (mmsize/2)*4, tmpq, m8, m12
|
|
|
|
|
LOAD64_LUT m5, inq, ctxq, (mmsize/2)*5, tmpq, m9, m13
|
|
|
|
|
LOAD64_LUT m6, inq, ctxq, (mmsize/2)*6, tmpq, m10, m14
|
|
|
|
|
LOAD64_LUT m7, inq, ctxq, (mmsize/2)*7, tmpq, m11, m15
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
FFT8 m4, m5, m6, m7, m8, m9
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
movaps m0, [inq + 0*mmsize]
|
|
|
|
|
movaps m1, [inq + 1*mmsize]
|
|
|
|
|
movaps m2, [inq + 2*mmsize]
|
|
|
|
|
movaps m3, [inq + 3*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
LOAD64_LUT m0, inq, ctxq, (mmsize/2)*0, tmpq, m8, m12
|
|
|
|
|
LOAD64_LUT m1, inq, ctxq, (mmsize/2)*1, tmpq, m9, m13
|
|
|
|
|
LOAD64_LUT m2, inq, ctxq, (mmsize/2)*2, tmpq, m10, m14
|
|
|
|
|
LOAD64_LUT m3, inq, ctxq, (mmsize/2)*3, tmpq, m11, m15
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
movaps m8, [tab_32_float]
|
|
|
|
|
vperm2f128 m9, m9, [tab_32_float + 4*8 - 4*7], 0x23
|
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.
4 years ago
|
|
|
|
|
|
|
|
FFT16 m0, m1, m2, m3, m10, m11, m12, m13
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE 1, m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, \
|
|
|
|
|
m10, m11, m12, m13, m14, m15 ; temporary registers
|
|
|
|
|
|
|
|
|
|
unpcklpd m9, m1, m3
|
|
|
|
|
unpcklpd m10, m5, m7
|
|
|
|
|
unpcklpd m8, m0, m2
|
|
|
|
|
unpcklpd m11, m4, m6
|
|
|
|
|
unpckhpd m1, m1, m3
|
|
|
|
|
unpckhpd m5, m5, m7
|
|
|
|
|
unpckhpd m0, m0, m2
|
|
|
|
|
unpckhpd m4, m4, m6
|
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.
4 years ago
|
|
|
|
|
|
|
|
vextractf128 [outq + 16* 0], m8, 0
|
|
|
|
|
vextractf128 [outq + 16* 1], m0, 0
|
|
|
|
|
vextractf128 [outq + 16* 2], m8, 1
|
|
|
|
|
vextractf128 [outq + 16* 3], m0, 1
|
|
|
|
|
vextractf128 [outq + 16* 4], m9, 0
|
|
|
|
|
vextractf128 [outq + 16* 5], m1, 0
|
|
|
|
|
vextractf128 [outq + 16* 6], m9, 1
|
|
|
|
|
vextractf128 [outq + 16* 7], m1, 1
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + 16* 8], m11, 0
|
|
|
|
|
vextractf128 [outq + 16* 9], m4, 0
|
|
|
|
|
vextractf128 [outq + 16*10], m11, 1
|
|
|
|
|
vextractf128 [outq + 16*11], m4, 1
|
|
|
|
|
vextractf128 [outq + 16*12], m10, 0
|
|
|
|
|
vextractf128 [outq + 16*13], m5, 0
|
|
|
|
|
vextractf128 [outq + 16*14], m10, 1
|
|
|
|
|
vextractf128 [outq + 16*15], m5, 1
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
ret
|
|
|
|
|
%else
|
|
|
|
|
RET
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
cglobal fft32_ns_float, 4, 4, 16, ctx, out, in, tmp
|
|
|
|
|
call mangle(ff_tx_fft32_asm_float_ %+ %1)
|
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.
4 years ago
|
|
|
RET
|
|
|
|
|
%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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
%if ARCH_X86_64
|
|
|
|
|
FFT32_FN avx, 0
|
|
|
|
|
FFT32_FN avx, 1
|
|
|
|
|
FFT32_FN fma3, 0
|
|
|
|
|
FFT32_FN fma3, 1
|
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.
4 years ago
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
%macro FFT_SPLIT_RADIX_DEF 1-2
|
|
|
|
|
ALIGN 16
|
|
|
|
|
.%1 %+ pt:
|
|
|
|
|
PUSH lenq
|
|
|
|
|
mov lenq, (%1/4)
|
|
|
|
|
|
|
|
|
|
add outq, (%1*4) - (%1/1)
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
add outq, (%1*2) - (%1/2) ; the synth loops also increment outq
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
POP lenq
|
|
|
|
|
sub outq, (%1*4) + (%1*2) + (%1/2)
|
|
|
|
|
|
|
|
|
|
lea rtabq, [tab_ %+ %1 %+ _float]
|
|
|
|
|
lea itabq, [tab_ %+ %1 %+ _float + %1 - 4*7]
|
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.
4 years ago
|
|
|
|
|
|
|
|
%if %0 > 1
|
|
|
|
|
cmp tgtq, %1
|
|
|
|
|
je .deinterleave
|
|
|
|
|
|
|
|
|
|
mov tmpq, %1
|
|
|
|
|
|
|
|
|
|
.synth_ %+ %1:
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_FULL 2*%1, 6*%1, 0, 0, 0
|
|
|
|
|
add outq, 8*mmsize
|
|
|
|
|
add rtabq, 4*mmsize
|
|
|
|
|
sub itabq, 4*mmsize
|
|
|
|
|
sub tmpq, 4*mmsize
|
|
|
|
|
jg .synth_ %+ %1
|
|
|
|
|
|
|
|
|
|
cmp lenq, %1
|
|
|
|
|
jg %2 ; can't do math here, nasm doesn't get it
|
|
|
|
|
ret
|
|
|
|
|
%endif
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
%macro FFT_SPLIT_RADIX_FN 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.
4 years ago
|
|
|
INIT_YMM %1
|
|
|
|
|
%if %2
|
|
|
|
|
cglobal fft_sr_asm_float, 0, 0, 0, ctx, out, in, tmp, len, lut, itab, rtab, tgt
|
|
|
|
|
%else
|
|
|
|
|
cglobal fft_sr_float, 4, 9, 16, 272, ctx, out, in, tmp, len, lut, itab, rtab, tgt
|
|
|
|
|
movsxd lenq, dword [ctxq + AVTXContext.len]
|
|
|
|
|
mov lutq, [ctxq + AVTXContext.map]
|
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.
4 years ago
|
|
|
mov tgtq, lenq
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
; Bottom-most/32-point transform ===============================================
|
|
|
|
|
ALIGN 16
|
|
|
|
|
.32pt:
|
|
|
|
|
%if %2
|
|
|
|
|
movaps m4, [inq + 4*mmsize]
|
|
|
|
|
movaps m5, [inq + 5*mmsize]
|
|
|
|
|
movaps m6, [inq + 6*mmsize]
|
|
|
|
|
movaps m7, [inq + 7*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
LOAD64_LUT m4, inq, lutq, (mmsize/2)*4, tmpq, m8, m12
|
|
|
|
|
LOAD64_LUT m5, inq, lutq, (mmsize/2)*5, tmpq, m9, m13
|
|
|
|
|
LOAD64_LUT m6, inq, lutq, (mmsize/2)*6, tmpq, m10, m14
|
|
|
|
|
LOAD64_LUT m7, inq, lutq, (mmsize/2)*7, tmpq, m11, m15
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
FFT8 m4, m5, m6, m7, m8, m9
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
movaps m0, [inq + 0*mmsize]
|
|
|
|
|
movaps m1, [inq + 1*mmsize]
|
|
|
|
|
movaps m2, [inq + 2*mmsize]
|
|
|
|
|
movaps m3, [inq + 3*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
LOAD64_LUT m0, inq, lutq, (mmsize/2)*0, tmpq, m8, m12
|
|
|
|
|
LOAD64_LUT m1, inq, lutq, (mmsize/2)*1, tmpq, m9, m13
|
|
|
|
|
LOAD64_LUT m2, inq, lutq, (mmsize/2)*2, tmpq, m10, m14
|
|
|
|
|
LOAD64_LUT m3, inq, lutq, (mmsize/2)*3, tmpq, m11, m15
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
movaps m8, [tab_32_float]
|
|
|
|
|
vperm2f128 m9, m9, [tab_32_float + 32 - 4*7], 0x23
|
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.
4 years ago
|
|
|
|
|
|
|
|
FFT16 m0, m1, m2, m3, m10, m11, m12, m13
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE 1, m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, \
|
|
|
|
|
m10, m11, m12, m13, m14, m15 ; temporary registers
|
|
|
|
|
|
|
|
|
|
movaps [outq + 1*mmsize], m1
|
|
|
|
|
movaps [outq + 3*mmsize], m3
|
|
|
|
|
movaps [outq + 5*mmsize], m5
|
|
|
|
|
movaps [outq + 7*mmsize], m7
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
add inq, 8*mmsize
|
|
|
|
|
%else
|
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.
4 years ago
|
|
|
add lutq, (mmsize/2)*8
|
|
|
|
|
%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.
4 years ago
|
|
|
cmp lenq, 32
|
|
|
|
|
jg .64pt
|
|
|
|
|
|
|
|
|
|
movaps [outq + 0*mmsize], m0
|
|
|
|
|
movaps [outq + 2*mmsize], m2
|
|
|
|
|
movaps [outq + 4*mmsize], m4
|
|
|
|
|
movaps [outq + 6*mmsize], m6
|
|
|
|
|
|
|
|
|
|
ret
|
|
|
|
|
|
|
|
|
|
; 64-point transform ===========================================================
|
|
|
|
|
ALIGN 16
|
|
|
|
|
.64pt:
|
|
|
|
|
; Helper defines, these make it easier to track what's happening
|
|
|
|
|
%define tx1_e0 m4
|
|
|
|
|
%define tx1_e1 m5
|
|
|
|
|
%define tx1_o0 m6
|
|
|
|
|
%define tx1_o1 m7
|
|
|
|
|
%define tx2_e0 m8
|
|
|
|
|
%define tx2_e1 m9
|
|
|
|
|
%define tx2_o0 m10
|
|
|
|
|
%define tx2_o1 m11
|
|
|
|
|
%define tw_e m12
|
|
|
|
|
%define tw_o m13
|
|
|
|
|
%define tmp1 m14
|
|
|
|
|
%define tmp2 m15
|
|
|
|
|
|
|
|
|
|
SWAP m4, m1
|
|
|
|
|
SWAP m6, m3
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
movaps tx1_e0, [inq + 0*mmsize]
|
|
|
|
|
movaps tx1_e1, [inq + 1*mmsize]
|
|
|
|
|
movaps tx1_o0, [inq + 2*mmsize]
|
|
|
|
|
movaps tx1_o1, [inq + 3*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
LOAD64_LUT tx1_e0, inq, lutq, (mmsize/2)*0, tmpq, tw_e, tmp1
|
|
|
|
|
LOAD64_LUT tx1_e1, inq, lutq, (mmsize/2)*1, tmpq, tw_o, tmp2
|
|
|
|
|
LOAD64_LUT tx1_o0, inq, lutq, (mmsize/2)*2, tmpq, tw_e, tmp1
|
|
|
|
|
LOAD64_LUT tx1_o1, inq, lutq, (mmsize/2)*3, tmpq, tw_o, tmp2
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
FFT16 tx1_e0, tx1_e1, tx1_o0, tx1_o1, tw_e, tw_o, tx2_o0, tx2_o1
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
movaps tx2_e0, [inq + 4*mmsize]
|
|
|
|
|
movaps tx2_e1, [inq + 5*mmsize]
|
|
|
|
|
movaps tx2_o0, [inq + 6*mmsize]
|
|
|
|
|
movaps tx2_o1, [inq + 7*mmsize]
|
|
|
|
|
%else
|
|
|
|
|
LOAD64_LUT tx2_e0, inq, lutq, (mmsize/2)*4, tmpq, tw_e, tmp1
|
|
|
|
|
LOAD64_LUT tx2_e1, inq, lutq, (mmsize/2)*5, tmpq, tw_o, tmp2
|
|
|
|
|
LOAD64_LUT tx2_o0, inq, lutq, (mmsize/2)*6, tmpq, tw_e, tmp1
|
|
|
|
|
LOAD64_LUT tx2_o1, inq, lutq, (mmsize/2)*7, tmpq, tw_o, tmp2
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
FFT16 tx2_e0, tx2_e1, tx2_o0, tx2_o1, tmp1, tmp2, tw_e, tw_o
|
|
|
|
|
|
|
|
|
|
movaps tw_e, [tab_64_float]
|
|
|
|
|
vperm2f128 tw_o, tw_o, [tab_64_float + 64 - 4*7], 0x23
|
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.
4 years ago
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
add inq, 8*mmsize
|
|
|
|
|
%else
|
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.
4 years ago
|
|
|
add lutq, (mmsize/2)*8
|
|
|
|
|
%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.
4 years ago
|
|
|
cmp tgtq, 64
|
|
|
|
|
je .64pt_deint
|
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.
4 years ago
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE_64
|
|
|
|
|
|
|
|
|
|
cmp lenq, 64
|
|
|
|
|
jg .128pt
|
|
|
|
|
ret
|
|
|
|
|
|
|
|
|
|
; 128-point transform ==========================================================
|
|
|
|
|
ALIGN 16
|
|
|
|
|
.128pt:
|
|
|
|
|
PUSH lenq
|
|
|
|
|
mov lenq, 32
|
|
|
|
|
|
|
|
|
|
add outq, 16*mmsize
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
add outq, 8*mmsize
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
POP lenq
|
|
|
|
|
sub outq, 24*mmsize
|
|
|
|
|
|
|
|
|
|
lea rtabq, [tab_128_float]
|
|
|
|
|
lea itabq, [tab_128_float + 128 - 4*7]
|
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.
4 years ago
|
|
|
|
|
|
|
|
cmp tgtq, 128
|
|
|
|
|
je .deinterleave
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_FULL 2*128, 6*128
|
|
|
|
|
|
|
|
|
|
cmp lenq, 128
|
|
|
|
|
jg .256pt
|
|
|
|
|
ret
|
|
|
|
|
|
|
|
|
|
; 256-point transform ==========================================================
|
|
|
|
|
ALIGN 16
|
|
|
|
|
.256pt:
|
|
|
|
|
PUSH lenq
|
|
|
|
|
mov lenq, 64
|
|
|
|
|
|
|
|
|
|
add outq, 32*mmsize
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
add outq, 16*mmsize
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
POP lenq
|
|
|
|
|
sub outq, 48*mmsize
|
|
|
|
|
|
|
|
|
|
lea rtabq, [tab_256_float]
|
|
|
|
|
lea itabq, [tab_256_float + 256 - 4*7]
|
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.
4 years ago
|
|
|
|
|
|
|
|
cmp tgtq, 256
|
|
|
|
|
je .deinterleave
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_FULL 2*256, 6*256
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_FULL 2*256, 6*256, 8*mmsize, 4*mmsize, -4*mmsize
|
|
|
|
|
|
|
|
|
|
cmp lenq, 256
|
|
|
|
|
jg .512pt
|
|
|
|
|
ret
|
|
|
|
|
|
|
|
|
|
; 512-point transform ==========================================================
|
|
|
|
|
ALIGN 16
|
|
|
|
|
.512pt:
|
|
|
|
|
PUSH lenq
|
|
|
|
|
mov lenq, 128
|
|
|
|
|
|
|
|
|
|
add outq, 64*mmsize
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
add outq, 32*mmsize
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
POP lenq
|
|
|
|
|
sub outq, 96*mmsize
|
|
|
|
|
|
|
|
|
|
lea rtabq, [tab_512_float]
|
|
|
|
|
lea itabq, [tab_512_float + 512 - 4*7]
|
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.
4 years ago
|
|
|
|
|
|
|
|
cmp tgtq, 512
|
|
|
|
|
je .deinterleave
|
|
|
|
|
|
|
|
|
|
mov tmpq, 4
|
|
|
|
|
|
|
|
|
|
.synth_512:
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_FULL 2*512, 6*512
|
|
|
|
|
add outq, 8*mmsize
|
|
|
|
|
add rtabq, 4*mmsize
|
|
|
|
|
sub itabq, 4*mmsize
|
|
|
|
|
sub tmpq, 1
|
|
|
|
|
jg .synth_512
|
|
|
|
|
|
|
|
|
|
cmp lenq, 512
|
|
|
|
|
jg .1024pt
|
|
|
|
|
ret
|
|
|
|
|
|
|
|
|
|
; 1024-point transform ==========================================================
|
|
|
|
|
ALIGN 16
|
|
|
|
|
.1024pt:
|
|
|
|
|
PUSH lenq
|
|
|
|
|
mov lenq, 256
|
|
|
|
|
|
|
|
|
|
add outq, 96*mmsize
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
add outq, 64*mmsize
|
|
|
|
|
call .32pt
|
|
|
|
|
|
|
|
|
|
POP lenq
|
|
|
|
|
sub outq, 192*mmsize
|
|
|
|
|
|
|
|
|
|
lea rtabq, [tab_1024_float]
|
|
|
|
|
lea itabq, [tab_1024_float + 1024 - 4*7]
|
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.
4 years ago
|
|
|
|
|
|
|
|
cmp tgtq, 1024
|
|
|
|
|
je .deinterleave
|
|
|
|
|
|
|
|
|
|
mov tmpq, 8
|
|
|
|
|
|
|
|
|
|
.synth_1024:
|
|
|
|
|
SPLIT_RADIX_LOAD_COMBINE_FULL 2*1024, 6*1024
|
|
|
|
|
add outq, 8*mmsize
|
|
|
|
|
add rtabq, 4*mmsize
|
|
|
|
|
sub itabq, 4*mmsize
|
|
|
|
|
sub tmpq, 1
|
|
|
|
|
jg .synth_1024
|
|
|
|
|
|
|
|
|
|
cmp lenq, 1024
|
|
|
|
|
jg .2048pt
|
|
|
|
|
ret
|
|
|
|
|
|
|
|
|
|
; 2048 to 131072-point transforms ==============================================
|
|
|
|
|
FFT_SPLIT_RADIX_DEF 2048, .4096pt
|
|
|
|
|
FFT_SPLIT_RADIX_DEF 4096, .8192pt
|
|
|
|
|
FFT_SPLIT_RADIX_DEF 8192, .16384pt
|
|
|
|
|
FFT_SPLIT_RADIX_DEF 16384, .32768pt
|
|
|
|
|
FFT_SPLIT_RADIX_DEF 32768, .65536pt
|
|
|
|
|
FFT_SPLIT_RADIX_DEF 65536, .131072pt
|
|
|
|
|
FFT_SPLIT_RADIX_DEF 131072
|
|
|
|
|
|
|
|
|
|
;===============================================================================
|
|
|
|
|
; Final synthesis + deinterleaving code
|
|
|
|
|
;===============================================================================
|
|
|
|
|
.deinterleave:
|
|
|
|
|
imul tmpq, lenq, 2
|
|
|
|
|
lea lutq, [4*lenq + tmpq]
|
|
|
|
|
|
|
|
|
|
.synth_deinterleave:
|
|
|
|
|
SPLIT_RADIX_COMBINE_DEINTERLEAVE_FULL tmpq, lutq
|
|
|
|
|
add outq, 8*mmsize
|
|
|
|
|
add rtabq, 4*mmsize
|
|
|
|
|
sub itabq, 4*mmsize
|
|
|
|
|
sub lenq, 4*mmsize
|
|
|
|
|
jg .synth_deinterleave
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
ret
|
|
|
|
|
%else
|
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.
4 years ago
|
|
|
RET
|
|
|
|
|
%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.
4 years ago
|
|
|
|
|
|
|
|
; 64-point deinterleave which only has to load 4 registers =====================
|
|
|
|
|
.64pt_deint:
|
|
|
|
|
SPLIT_RADIX_COMBINE_LITE 1, m0, m1, tx1_e0, tx2_e0, tw_e, tw_o, tmp1, tmp2
|
|
|
|
|
SPLIT_RADIX_COMBINE_HALF 0, m2, m3, tx1_o0, tx2_o0, tw_e, tw_o, tmp1, tmp2, tw_e
|
|
|
|
|
|
|
|
|
|
unpcklpd tmp1, m0, m2
|
|
|
|
|
unpcklpd tmp2, m1, m3
|
|
|
|
|
unpcklpd tw_o, tx1_e0, tx1_o0
|
|
|
|
|
unpcklpd tw_e, tx2_e0, tx2_o0
|
|
|
|
|
unpckhpd m0, m0, m2
|
|
|
|
|
unpckhpd m1, m1, m3
|
|
|
|
|
unpckhpd tx1_e0, tx1_e0, tx1_o0
|
|
|
|
|
unpckhpd tx2_e0, tx2_e0, tx2_o0
|
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.
4 years ago
|
|
|
|
|
|
|
|
vextractf128 [outq + 0*mmsize + 0], tmp1, 0
|
|
|
|
|
vextractf128 [outq + 0*mmsize + 16], m0, 0
|
|
|
|
|
vextractf128 [outq + 4*mmsize + 0], tmp2, 0
|
|
|
|
|
vextractf128 [outq + 4*mmsize + 16], m1, 0
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + 8*mmsize + 0], tw_o, 0
|
|
|
|
|
vextractf128 [outq + 8*mmsize + 16], tx1_e0, 0
|
|
|
|
|
vextractf128 [outq + 9*mmsize + 0], tw_o, 1
|
|
|
|
|
vextractf128 [outq + 9*mmsize + 16], tx1_e0, 1
|
|
|
|
|
|
|
|
|
|
vperm2f128 tmp1, tmp1, m0, 0x31
|
|
|
|
|
vperm2f128 tmp2, tmp2, m1, 0x31
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + 12*mmsize + 0], tw_e, 0
|
|
|
|
|
vextractf128 [outq + 12*mmsize + 16], tx2_e0, 0
|
|
|
|
|
vextractf128 [outq + 13*mmsize + 0], tw_e, 1
|
|
|
|
|
vextractf128 [outq + 13*mmsize + 16], tx2_e0, 1
|
|
|
|
|
|
|
|
|
|
movaps tw_e, [tab_64_float + mmsize]
|
|
|
|
|
vperm2f128 tw_o, tw_o, [tab_64_float + 64 - 4*7 - mmsize], 0x23
|
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.
4 years ago
|
|
|
|
|
|
|
|
movaps m0, [outq + 1*mmsize]
|
|
|
|
|
movaps m1, [outq + 3*mmsize]
|
|
|
|
|
movaps m2, [outq + 5*mmsize]
|
|
|
|
|
movaps m3, [outq + 7*mmsize]
|
|
|
|
|
|
|
|
|
|
movaps [outq + 1*mmsize], tmp1
|
|
|
|
|
movaps [outq + 5*mmsize], tmp2
|
|
|
|
|
|
|
|
|
|
SPLIT_RADIX_COMBINE 0, m0, m2, m1, m3, tx1_e1, tx2_e1, tx1_o1, tx2_o1, tw_e, tw_o, \
|
|
|
|
|
tmp1, tmp2, tx2_o0, tx1_o0, tx2_e0, tx1_e0 ; temporary registers
|
|
|
|
|
|
|
|
|
|
unpcklpd tmp1, m0, m1
|
|
|
|
|
unpcklpd tmp2, m2, m3
|
|
|
|
|
unpcklpd tw_e, tx1_e1, tx1_o1
|
|
|
|
|
unpcklpd tw_o, tx2_e1, tx2_o1
|
|
|
|
|
unpckhpd m0, m0, m1
|
|
|
|
|
unpckhpd m2, m2, m3
|
|
|
|
|
unpckhpd tx1_e1, tx1_e1, tx1_o1
|
|
|
|
|
unpckhpd tx2_e1, tx2_e1, tx2_o1
|
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.
4 years ago
|
|
|
|
|
|
|
|
vextractf128 [outq + 2*mmsize + 0], tmp1, 0
|
|
|
|
|
vextractf128 [outq + 2*mmsize + 16], m0, 0
|
|
|
|
|
vextractf128 [outq + 3*mmsize + 0], tmp1, 1
|
|
|
|
|
vextractf128 [outq + 3*mmsize + 16], m0, 1
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + 6*mmsize + 0], tmp2, 0
|
|
|
|
|
vextractf128 [outq + 6*mmsize + 16], m2, 0
|
|
|
|
|
vextractf128 [outq + 7*mmsize + 0], tmp2, 1
|
|
|
|
|
vextractf128 [outq + 7*mmsize + 16], m2, 1
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + 10*mmsize + 0], tw_e, 0
|
|
|
|
|
vextractf128 [outq + 10*mmsize + 16], tx1_e1, 0
|
|
|
|
|
vextractf128 [outq + 11*mmsize + 0], tw_e, 1
|
|
|
|
|
vextractf128 [outq + 11*mmsize + 16], tx1_e1, 1
|
|
|
|
|
|
|
|
|
|
vextractf128 [outq + 14*mmsize + 0], tw_o, 0
|
|
|
|
|
vextractf128 [outq + 14*mmsize + 16], tx2_e1, 0
|
|
|
|
|
vextractf128 [outq + 15*mmsize + 0], tw_o, 1
|
|
|
|
|
vextractf128 [outq + 15*mmsize + 16], tx2_e1, 1
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
ret
|
|
|
|
|
%else
|
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.
4 years ago
|
|
|
RET
|
|
|
|
|
%endif
|
|
|
|
|
|
|
|
|
|
%if %2
|
|
|
|
|
cglobal fft_sr_ns_float, 4, 9, 16, 272, ctx, out, in, tmp, len, lut, itab, rtab, tgt
|
|
|
|
|
movsxd lenq, dword [ctxq + AVTXContext.len]
|
|
|
|
|
mov lutq, [ctxq + AVTXContext.map]
|
|
|
|
|
mov tgtq, lenq
|
|
|
|
|
|
|
|
|
|
call mangle(ff_tx_fft_sr_asm_float_ %+ %1)
|
|
|
|
|
RET
|
|
|
|
|
%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.
4 years ago
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
%if ARCH_X86_64
|
|
|
|
|
FFT_SPLIT_RADIX_FN fma3, 0
|
|
|
|
|
FFT_SPLIT_RADIX_FN fma3, 1
|
|
|
|
|
%if HAVE_AVX2_EXTERNAL
|
|
|
|
|
FFT_SPLIT_RADIX_FN avx2, 0
|
|
|
|
|
FFT_SPLIT_RADIX_FN avx2, 1
|
|
|
|
|
%endif
|
|
|
|
|
%endif
|
x86/tx_float: implement inverse MDCT AVX2 assembly
This commit implements an iMDCT in pure assembly.
This is capable of processing any mod-8 transforms, rather than just
power of two, but since power of two is all we have assembly for
currently, that's what's supported.
It would really benefit if we could somehow use the C code to decide
which function to jump into, but exposing function labels from assebly
into C is anything but easy.
The post-transform loop could probably be improved.
This was somewhat annoying to write, as we must support arbitrary
strides during runtime. There's a fast branch for stride == 4 bytes
and a slower one which uses vgatherdps.
Zen 3 benchmarks for stride == 4 for old (av_imdct_half) vs new (av_tx):
128pt:
2811 decicycles in av_tx (imdct),16775916 runs, 1300 skips
3082 decicycles in av_imdct_half,16776751 runs, 465 skips
256pt:
4920 decicycles in av_tx (imdct),16775820 runs, 1396 skips
5378 decicycles in av_imdct_half,16776411 runs, 805 skips
512pt:
9668 decicycles in av_tx (imdct),16775774 runs, 1442 skips
10626 decicycles in av_imdct_half,16775647 runs, 1569 skips
1024pt:
19812 decicycles in av_tx (imdct),16777144 runs, 72 skips
23036 decicycles in av_imdct_half,16777167 runs, 49 skips
2 years ago
|
|
|
|
|
|
|
|
%macro IMDCT_FN 1
|
|
|
|
|
INIT_YMM %1
|
|
|
|
|
cglobal mdct_sr_inv_float, 4, 12, 16, 288, ctx, out, in, stride, len, lut, exp, t1, t2, t3, t4, t5
|
|
|
|
|
movsxd lenq, dword [ctxq + AVTXContext.len]
|
|
|
|
|
mov expq, [ctxq + AVTXContext.exp]
|
|
|
|
|
|
|
|
|
|
lea t1d, [lend - 1]
|
|
|
|
|
imul t1d, strided
|
|
|
|
|
|
|
|
|
|
PUSH outq ; backup original output
|
|
|
|
|
mov t5q, [ctxq + AVTXContext.fn] ; subtransform's jump point
|
|
|
|
|
PUSH ctxq ; backup original context
|
|
|
|
|
mov ctxq, [ctxq + AVTXContext.sub] ; load subtransform's context
|
|
|
|
|
mov lutq, [ctxq + AVTXContext.map] ; load subtransform's map
|
|
|
|
|
|
|
|
|
|
cmp strideq, 4
|
|
|
|
|
je .stride4
|
|
|
|
|
|
|
|
|
|
shl strideq, 1
|
|
|
|
|
movd xm4, strided
|
|
|
|
|
vpbroadcastd m4, xm4 ; stride splatted
|
|
|
|
|
movd xm5, t1d
|
|
|
|
|
vpbroadcastd m5, xm5 ; offset splatted
|
|
|
|
|
|
|
|
|
|
mov t2q, outq ; don't modify the original output
|
|
|
|
|
pcmpeqd m15, m15 ; set all bits to 1
|
|
|
|
|
|
|
|
|
|
.stridex_pre:
|
|
|
|
|
pmulld m2, m4, [lutq] ; multiply by stride
|
|
|
|
|
movaps m0, m15
|
|
|
|
|
psubd m3, m5, m2 ; subtract from offset
|
|
|
|
|
movaps m1, m15
|
|
|
|
|
vgatherdps m6, [inq + m2], m0 ; im
|
|
|
|
|
vgatherdps m7, [inq + m3], m1 ; re
|
|
|
|
|
|
|
|
|
|
movaps m8, [expq + 0*mmsize] ; tab 1
|
|
|
|
|
movaps m9, [expq + 1*mmsize] ; tab 2
|
|
|
|
|
|
|
|
|
|
unpcklps m0, m7, m6 ; re, im, re, im
|
|
|
|
|
unpckhps m1, m7, m6 ; re, im, re, im
|
|
|
|
|
|
|
|
|
|
vperm2f128 m2, m1, m0, 0x02 ; output order
|
|
|
|
|
vperm2f128 m3, m1, m0, 0x13 ; output order
|
|
|
|
|
|
|
|
|
|
movshdup m10, m8 ; tab 1 imim
|
|
|
|
|
movshdup m11, m9 ; tab 2 imim
|
|
|
|
|
movsldup m12, m8 ; tab 1 rere
|
|
|
|
|
movsldup m13, m9 ; tab 2 rere
|
|
|
|
|
|
|
|
|
|
mulps m10, m2 ; 1 reim * imim
|
|
|
|
|
mulps m11, m3 ; 2 reim * imim
|
|
|
|
|
|
|
|
|
|
shufps m10, m10, m10, q2301
|
|
|
|
|
shufps m11, m11, m11, q2301
|
x86/tx_float: implement inverse MDCT AVX2 assembly
This commit implements an iMDCT in pure assembly.
This is capable of processing any mod-8 transforms, rather than just
power of two, but since power of two is all we have assembly for
currently, that's what's supported.
It would really benefit if we could somehow use the C code to decide
which function to jump into, but exposing function labels from assebly
into C is anything but easy.
The post-transform loop could probably be improved.
This was somewhat annoying to write, as we must support arbitrary
strides during runtime. There's a fast branch for stride == 4 bytes
and a slower one which uses vgatherdps.
Zen 3 benchmarks for stride == 4 for old (av_imdct_half) vs new (av_tx):
128pt:
2811 decicycles in av_tx (imdct),16775916 runs, 1300 skips
3082 decicycles in av_imdct_half,16776751 runs, 465 skips
256pt:
4920 decicycles in av_tx (imdct),16775820 runs, 1396 skips
5378 decicycles in av_imdct_half,16776411 runs, 805 skips
512pt:
9668 decicycles in av_tx (imdct),16775774 runs, 1442 skips
10626 decicycles in av_imdct_half,16775647 runs, 1569 skips
1024pt:
19812 decicycles in av_tx (imdct),16777144 runs, 72 skips
23036 decicycles in av_imdct_half,16777167 runs, 49 skips
2 years ago
|
|
|
|
|
|
|
|
fmaddsubps m10, m12, m2, m10
|
|
|
|
|
fmaddsubps m11, m13, m3, m11
|
|
|
|
|
|
|
|
|
|
mova [t2q + 0*mmsize], m10
|
|
|
|
|
mova [t2q + 1*mmsize], m11
|
|
|
|
|
|
|
|
|
|
add expq, mmsize*2
|
|
|
|
|
add lutq, mmsize
|
|
|
|
|
add t2q, mmsize*2
|
|
|
|
|
sub lenq, mmsize/2
|
|
|
|
|
jg .stridex_pre
|
|
|
|
|
jmp .transform
|
|
|
|
|
|
|
|
|
|
.stride4:
|
|
|
|
|
lea expq, [expq + lenq*4]
|
|
|
|
|
lea lutq, [lutq + lenq*2]
|
|
|
|
|
lea t1q, [inq + t1q]
|
|
|
|
|
lea t1q, [t1q + strideq - mmsize]
|
|
|
|
|
lea t2q, [lenq*2 - mmsize/2]
|
|
|
|
|
|
|
|
|
|
.stride4_pre:
|
|
|
|
|
movaps m4, [inq]
|
|
|
|
|
movaps m3, [t1q]
|
|
|
|
|
|
|
|
|
|
movsldup m1, m4 ; im im, im im
|
|
|
|
|
movshdup m0, m3 ; re re, re re
|
|
|
|
|
movshdup m4, m4 ; re re, re re (2)
|
|
|
|
|
movsldup m3, m3 ; im im, im im (2)
|
|
|
|
|
|
|
|
|
|
movaps m2, [expq] ; tab
|
|
|
|
|
movaps m5, [expq + 2*t2q] ; tab (2)
|
|
|
|
|
|
|
|
|
|
vpermpd m0, m0, q0123 ; flip
|
|
|
|
|
shufps m7, m2, m2, q2301
|
|
|
|
|
vpermpd m4, m4, q0123 ; flip (2)
|
|
|
|
|
shufps m8, m5, m5, q2301
|
|
|
|
|
|
|
|
|
|
mulps m1, m7 ; im im * tab.reim
|
|
|
|
|
mulps m3, m8 ; im im * tab.reim (2)
|
|
|
|
|
|
|
|
|
|
fmaddsubps m0, m0, m2, m1
|
|
|
|
|
fmaddsubps m4, m4, m5, m3
|
|
|
|
|
|
|
|
|
|
vextractf128 xm3, m0, 1
|
|
|
|
|
vextractf128 xm6, m4, 1
|
|
|
|
|
|
|
|
|
|
; scatter
|
|
|
|
|
movsxd strideq, dword [lutq + 0*4]
|
|
|
|
|
movsxd lenq, dword [lutq + 1*4]
|
|
|
|
|
movsxd t3q, dword [lutq + 2*4]
|
|
|
|
|
movsxd t4q, dword [lutq + 3*4]
|
|
|
|
|
|
|
|
|
|
movlps [outq + strideq*8], xm0
|
|
|
|
|
movhps [outq + lenq*8], xm0
|
|
|
|
|
movlps [outq + t3q*8], xm3
|
|
|
|
|
movhps [outq + t4q*8], xm3
|
|
|
|
|
|
|
|
|
|
movsxd strideq, dword [lutq + 0*4 + t2q]
|
|
|
|
|
movsxd lenq, dword [lutq + 1*4 + t2q]
|
|
|
|
|
movsxd t3q, dword [lutq + 2*4 + t2q]
|
|
|
|
|
movsxd t4q, dword [lutq + 3*4 + t2q]
|
|
|
|
|
|
|
|
|
|
movlps [outq + strideq*8], xm4
|
|
|
|
|
movhps [outq + lenq*8], xm4
|
|
|
|
|
movlps [outq + t3q*8], xm6
|
|
|
|
|
movhps [outq + t4q*8], xm6
|
|
|
|
|
|
|
|
|
|
add lutq, mmsize/2
|
|
|
|
|
add expq, mmsize
|
|
|
|
|
add inq, mmsize
|
|
|
|
|
sub t1q, mmsize
|
|
|
|
|
sub t2q, mmsize
|
|
|
|
|
jg .stride4_pre
|
|
|
|
|
|
|
|
|
|
.transform:
|
|
|
|
|
movsxd lenq, dword [ctxq + AVTXContext.len]
|
|
|
|
|
mov t2q, lenq ; target length (for ptwo transforms)
|
|
|
|
|
mov inq, outq ; in-place transform
|
|
|
|
|
call t5q ; call the FFT
|
|
|
|
|
|
|
|
|
|
POP ctxq ; restore original context
|
|
|
|
|
movsxd lenq, dword [ctxq + AVTXContext.len]
|
|
|
|
|
mov expq, [ctxq + AVTXContext.exp]
|
|
|
|
|
lea expq, [expq + lenq*4]
|
|
|
|
|
|
|
|
|
|
lea t1q, [lenq*2] ; high
|
|
|
|
|
lea t2q, [lenq*2 - mmsize] ; low
|
|
|
|
|
|
|
|
|
|
POP outq
|
|
|
|
|
|
|
|
|
|
.post:
|
|
|
|
|
movaps m2, [expq + t1q] ; tab h
|
|
|
|
|
movaps m3, [expq + t2q] ; tab l
|
|
|
|
|
movaps m0, [outq + t1q] ; in h
|
|
|
|
|
movaps m1, [outq + t2q] ; in l
|
|
|
|
|
|
|
|
|
|
movshdup m4, m2 ; tab h imim
|
|
|
|
|
movshdup m5, m3 ; tab l imim
|
|
|
|
|
movsldup m6, m2 ; tab h rere
|
|
|
|
|
movsldup m7, m3 ; tab l rere
|
|
|
|
|
|
|
|
|
|
shufps m2, m0, m0, q2301 ; in h imre
|
|
|
|
|
shufps m3, m1, m1, q2301 ; in l imre
|
|
|
|
|
|
|
|
|
|
mulps m6, m0
|
|
|
|
|
mulps m7, m1
|
|
|
|
|
|
|
|
|
|
fmaddsubps m4, m4, m2, m6
|
|
|
|
|
fmaddsubps m5, m5, m3, m7
|
|
|
|
|
|
|
|
|
|
vpermpd m3, m5, q0123 ; flip
|
|
|
|
|
vpermpd m2, m4, q0123 ; flip
|
|
|
|
|
|
|
|
|
|
blendps m1, m2, m5, 01010101b
|
|
|
|
|
blendps m0, m3, m4, 01010101b
|
|
|
|
|
|
|
|
|
|
movaps [outq + t2q], m1
|
|
|
|
|
movaps [outq + t1q], m0
|
|
|
|
|
|
|
|
|
|
add t1q, mmsize
|
|
|
|
|
sub t2q, mmsize
|
|
|
|
|
jge .post
|
|
|
|
|
|
|
|
|
|
RET
|
|
|
|
|
%endmacro
|
|
|
|
|
|
|
|
|
|
%if ARCH_X86_64 && HAVE_AVX2_EXTERNAL
|
x86/tx_float: implement inverse MDCT AVX2 assembly
This commit implements an iMDCT in pure assembly.
This is capable of processing any mod-8 transforms, rather than just
power of two, but since power of two is all we have assembly for
currently, that's what's supported.
It would really benefit if we could somehow use the C code to decide
which function to jump into, but exposing function labels from assebly
into C is anything but easy.
The post-transform loop could probably be improved.
This was somewhat annoying to write, as we must support arbitrary
strides during runtime. There's a fast branch for stride == 4 bytes
and a slower one which uses vgatherdps.
Zen 3 benchmarks for stride == 4 for old (av_imdct_half) vs new (av_tx):
128pt:
2811 decicycles in av_tx (imdct),16775916 runs, 1300 skips
3082 decicycles in av_imdct_half,16776751 runs, 465 skips
256pt:
4920 decicycles in av_tx (imdct),16775820 runs, 1396 skips
5378 decicycles in av_imdct_half,16776411 runs, 805 skips
512pt:
9668 decicycles in av_tx (imdct),16775774 runs, 1442 skips
10626 decicycles in av_imdct_half,16775647 runs, 1569 skips
1024pt:
19812 decicycles in av_tx (imdct),16777144 runs, 72 skips
23036 decicycles in av_imdct_half,16777167 runs, 49 skips
2 years ago
|
|
|
IMDCT_FN avx2
|
|
|
|
|
%endif
|
