lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
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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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#include "libavutil/aarch64/asm.S"
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/* Open `doc/transforms.md` to see the code upon which the transforms here were
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* based upon.
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*
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* File conventions:
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* GPRs: x0-x3 - arguments, untouched
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* x4 - Lookup table base pointer
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* x5-x6 - macro ld1 temps/function scratch
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* x7-x9 - FFT table state
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* x10-x17 - lookup table/macro scratch
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* w19-w20 - current/target length when needed
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* x21-x22 - len*2, len*6
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*
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* Vectors: v0-v7 - coefficients
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* v8-v15 - coefficients when needed, otherwise untouched
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* v16-v30 - used as needed
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* v31 - -1.0, +1.0, -1.0, +1.0. Never touched after loading.
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*
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* Stack: backup for v8-v15 and x19-x22 when needed, and transform lengths
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*/
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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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/* We only ever load this once at the start, and then live with losing an
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* entire register as we need to lug this all the time everywhere.
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* Clearly should be integrated into an fsadd and fmlsa, but "muh RISC!". */
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const subadd, align=4
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.float -1.0, 1.0, -1.0, 1.0
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endconst
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.macro LOAD_SUBADD
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movrel x5, subadd
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ld1 { v31.4s }, [x5]
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.endm
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.macro SETUP_LUT no_lut=0
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.if \no_lut == 0
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ldr x4, [x0, #8]
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.endif
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.endm
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.macro LOAD_INPUT dst1, dst2, dst3, dst4, src, no_lut=0, discont=0
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.if \no_lut == 1
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.if \discont == 1
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ldp q\dst1\(), q\dst2\(), [\src\()]
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ldp q\dst3\(), q\dst4\(), [\src\(), #32]
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add \src\(), \src\(), #64
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.else
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ld1 { v\dst1\().4s, v\dst2\().4s, v\dst3\().4s, v\dst4\().4s }, [\src], #64
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.endif
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.else
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ldp w10, w11, [x4, #0 ]
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ldp w12, w13, [x4, #8 ]
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ldp w14, w15, [x4, #16]
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ldp w16, w17, [x4, #24]
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add x4, x4, #32
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ldr d\dst1, [\src, x10, lsl #3]
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add x11, \src, x11, lsl #3
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ldr d\dst2, [\src, x12, lsl #3]
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add x13, \src, x13, lsl #3
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ldr d\dst3, [\src, x14, lsl #3]
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add x15, \src, x15, lsl #3
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ldr d\dst4, [\src, x16, lsl #3]
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add x17, \src, x17, lsl #3
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ld1 { v\dst1\().d }[1], [x11]
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ld1 { v\dst2\().d }[1], [x13]
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ld1 { v\dst3\().d }[1], [x15]
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ld1 { v\dst4\().d }[1], [x17]
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.endif
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.endm
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.macro FFT4 e0, o0, standalone
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fadd v16.4s, \e0\().4s, \o0\().4s // r1..4
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fsub \e0\().4s, \e0\().4s, \o0\().4s // t1..4
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rev64 v18.4s, \e0\().4s
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zip2 \o0\().2d, v16.2d, \e0\().2d
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zip1 v17.2d, v16.2d, \e0\().2d
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mov \o0\().d[1], v18.d[1]
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fadd \e0\().4s, v17.4s, \o0\().4s // a1,2 b1,4
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fsub v16.4s, v17.4s, \o0\().4s // a3,4 b3,2
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mov \o0\().16b, v16.16b // Swap once again...
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mov \o0\().s[3], \e0\().s[3]
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mov \e0\().s[3], v16.s[3]
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.if \standalone == 0
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uzp2 \o0\().2d, \e0\().2d, \o0\().2d
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uzp1 \e0\().2d, \e0\().2d, v16.2d
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.endif
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.endm
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const shuf_4pt_x2, align=4
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.byte 24, 25, 26, 27 // reg2, 3
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.byte 12, 13, 14, 15 // reg1, 4
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.byte 8, 9, 10, 11 // reg1, 3
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.byte 28, 29, 30, 31 // reg2, 4
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endconst
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// Identical to FFT4, but does 2 transforms in parallel, with no deinterleaving
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.macro FFT4_X2 e0, o0, e1, o1, \
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t0=v16, t1=v17, t2=v18, t3=v19, t4=v20, t5=v21, t6=v22
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fadd \t0\().4s, \e0\().4s, \o0\().4s // r1234
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fadd \t2\().4s, \e1\().4s, \o1\().4s // r1234
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fsub \e0\().4s, \e0\().4s, \o0\().4s // t1234
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fsub \e1\().4s, \e1\().4s, \o1\().4s // t1234
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movrel x5, shuf_4pt_x2
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rev64 \t4\().4s, \e0\().4s
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rev64 \t5\().4s, \e1\().4s
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zip2 \o0\().2d, \t0\().2d, \e0\().2d // t3,4 r3,4
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zip2 \o1\().2d, \t2\().2d, \e1\().2d // t3,4 r3,4
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ld1 { \t6\().16b }, [x5]
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mov \o0\().d[1], \t4\().d[1]
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mov \o1\().d[1], \t5\().d[1]
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zip1 \t1\().2d, \t0\().2d, \e0\().2d // t1,2 r1,2
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zip1 \t3\().2d, \t2\().2d, \e1\().2d // t1,2 r1,2
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fsub \t4\().4s, \t1\().4s, \o0\().4s // a34 b32
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fadd \t5\().4s, \t1\().4s, \o0\().4s // a12 b14
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fsub \t2\().4s, \t3\().4s, \o1\().4s // a34 b32
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fadd \t3\().4s, \t3\().4s, \o1\().4s // a12 b14
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// TODO: experiment with movs instead of tables here
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tbl \o0\().16b, { \t4\().16b, \t5\().16b }, \t6\().16b // b1234
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tbl \o1\().16b, { \t2\().16b, \t3\().16b }, \t6\().16b // b1234
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zip1 \e0\().2d, \t5\().2d, \t4\().2d // a1234
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// zip2 \o0\().2d, \t5\().2d, \t4\().2d // b1432
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zip1 \e1\().2d, \t3\().2d, \t2\().2d // a1234
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// zip2 \o1\().2d, \t3\().2d, \t2\().2d // b1432
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// rev64 \o0\().4s, \o0\().4s // b4123
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// rev64 \o1\().4s, \o1\().4s // b4123
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// ext \o0\().16b, \o0\().16b, \o0\().16b, #4 // b1234
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// ext \o1\().16b, \o1\().16b, \o1\().16b, #4 // b1234
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.endm
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const tab_8pt, align=4
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.float M_SQRT1_2, -M_SQRT1_2, -M_SQRT1_2, M_SQRT1_2
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endconst
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.macro FFT8 e0, e1, o0, o1, \
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t0=v16, t1=v17, t2=v18, t3=v19, t4=v20, t5=v21, t6=v22
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movrel x5, tab_8pt
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fsub \t1\().4s, \e1\().4s, \o1\().4s // j1234
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fadd \o1\().4s, \e1\().4s, \o1\().4s // k1234
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fsub \t0\().4s, \e0\().4s, \o0\().4s // r1234
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fadd \o0\().4s, \e0\().4s, \o0\().4s // q1234
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ld1 { \t5\().4s }, [x5]
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ext \t4\().16b, \o1\().16b, \o1\().16b, #12
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rev64 \t4\().4s, \t4\().4s
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ext \t2\().16b, \o0\().16b, \t4\().16b, #8 // o0[0,1], o1[3,2]
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mov \o0\().d[1], \t4\().d[1] // o0[3, 4]; o1[1, 4]
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fsub \e1\().4s, \o0\().4s, \t2\().4s // s34, g43
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fadd \t2\().4s, \o0\().4s, \t2\().4s // s12, g12
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rev64 \t6\().4s, v31.4s // 1, -1, 1, -1
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dup \o0\().2d, \t0\().d[0] // r1212
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dup \o1\().2d, \t0\().d[1] // r3434
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rev64 \t4\().4s, \e1\().4s // xxg34
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rev64 \o1\().4s, \o1\().4s // r4343
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ext \t6\().16b, v31.16b, \t6\().16b, #8 // -1, 1, 1, -1
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zip1 \t3\().2d, \t2\().2d, \e1\().2d // s1234
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zip2 \t2\().2d, \t2\().2d, \t4\().2d // g1234
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fadd \e0\().4s, \t3\().4s, \t2\().4s // out_e1
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fsub \e1\().4s, \t3\().4s, \t2\().4s // out_e2
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fmul \t1\().4s, \t1\().4s, \t5\().4s // j * +--+M_SQRT1_2
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fmls \o0\().4s, \o1\().4s, \t6\().4s // z1234
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rev64 \t4\().4s, \t1\().4s // j2143
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fmla \t1\().4s, \t4\().4s, v31.4s // l2143
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rev64 \t4\().4s, \t1\().4s // l1234
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ext \t4\().16b, \t4\().16b, \t4\().16b, #8 // l3412
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fmla \t4\().4s, \t1\().4s, v31.4s // t1234
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fadd \o1\().4s, \o0\().4s, \t4\().4s // out_o2
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fsub \o0\().4s, \o0\().4s, \t4\().4s // out_o1
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.endm
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// Identical as FFT8, but does 2 transforms in parallel
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.macro FFT8_X2 e0, e1, o0, o1, e2, e3, o2, o3
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movrel x5, tab_8pt
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fadd v19.4s, \e3\().4s, \o3\().4s // k1234
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fadd v17.4s, \e1\().4s, \o1\().4s // k1234
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fadd v18.4s, \e2\().4s, \o2\().4s // q1234
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fadd v16.4s, \e0\().4s, \o0\().4s // q1234
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ld1 { v23.4s }, [x5]
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ext v22.16b, v19.16b, v19.16b, #12
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ext v21.16b, v17.16b, v17.16b, #12
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rev64 v22.4s, v22.4s
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rev64 v21.4s, v21.4s
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ext v19.16b, v18.16b, v22.16b, #8
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ext v17.16b, v16.16b, v21.16b, #8
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mov v18.d[1], v22.d[1]
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mov v21.d[0], v16.d[0]
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fadd v22.4s, v18.4s, v19.4s // s12, g12
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fsub v19.4s, v18.4s, v19.4s // s34, g43
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fsub v18.4s, v21.4s, v17.4s // s34, g43
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fadd v16.4s, v21.4s, v17.4s // s12, g12
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fsub \e0\().4s, \e0\().4s, \o0\().4s // r1234
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fsub v20.4s, \e1\().4s, \o1\().4s // j1234
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fsub \e2\().4s, \e2\().4s, \o2\().4s // r1234
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fsub v21.4s, \e3\().4s, \o3\().4s // j1234
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rev64 v24.4s, v31.4s // 1, -1, 1, -1
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zip1 v17.2d, v16.2d, v18.2d // s1234
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zip1 \e1\().2d, v22.2d, v19.2d // s1234
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|
|
|
rev64 v18.4s, v18.4s // xxg34
|
|
|
|
rev64 v19.4s, v19.4s // xxg34
|
|
|
|
|
|
|
|
zip2 v16.2d, v16.2d, v18.2d // g1234
|
|
|
|
zip2 \e3\().2d, v22.2d, v19.2d // g1234
|
|
|
|
|
|
|
|
dup \o0\().2d, \e0\().d[0] // r1212
|
|
|
|
dup \o1\().2d, \e0\().d[1] // r3434
|
|
|
|
dup \o2\().2d, \e2\().d[0] // r1212
|
|
|
|
dup \o3\().2d, \e2\().d[1] // r3434
|
|
|
|
|
|
|
|
fadd \e2\().4s, \e1\().4s, \e3\().4s // out_e1
|
|
|
|
fsub \e3\().4s, \e1\().4s, \e3\().4s // out_e2
|
|
|
|
fadd \e0\().4s, v17.4s, v16.4s // out_e1
|
|
|
|
fsub \e1\().4s, v17.4s, v16.4s // out_e2
|
|
|
|
|
|
|
|
ext v24.16b, v31.16b, v24.16b, #8 // -1, 1, 1, -1
|
|
|
|
rev64 \o1\().4s, \o1\().4s // r4343
|
|
|
|
rev64 \o3\().4s, \o3\().4s // r4343
|
|
|
|
|
|
|
|
fmul v19.4s, v20.4s, v23.4s // j * +--+M_SQRT1_2
|
|
|
|
fmul v21.4s, v21.4s, v23.4s // j * +--+M_SQRT1_2
|
|
|
|
|
|
|
|
rev64 v20.4s, v19.4s // j2143
|
|
|
|
rev64 v18.4s, v21.4s // j2143
|
|
|
|
|
|
|
|
fmls \o0\().4s, \o1\().4s, v24.4s // z1234
|
|
|
|
fmls \o2\().4s, \o3\().4s, v24.4s // z1234
|
|
|
|
|
|
|
|
fmla v19.4s, v20.4s, v31.4s // l2143
|
|
|
|
fmla v21.4s, v18.4s, v31.4s // l2143
|
|
|
|
|
|
|
|
rev64 v20.4s, v19.4s // l1234
|
|
|
|
rev64 v18.4s, v21.4s // l1234
|
|
|
|
ext v20.16b, v20.16b, v20.16b, #8 // l3412
|
|
|
|
ext v18.16b, v18.16b, v18.16b, #8 // l3412
|
|
|
|
|
|
|
|
fmla v20.4s, v19.4s, v31.4s // t1234
|
|
|
|
fmla v18.4s, v21.4s, v31.4s // t1234
|
|
|
|
|
|
|
|
fadd \o1\().4s, \o0\().4s, v20.4s // out_o2
|
|
|
|
fadd \o3\().4s, \o2\().4s, v18.4s // out_o2
|
|
|
|
fsub \o0\().4s, \o0\().4s, v20.4s // out_o1
|
|
|
|
fsub \o2\().4s, \o2\().4s, v18.4s // out_o1
|
|
|
|
.endm
|
|
|
|
|
|
|
|
const tab_16pt, align=4
|
|
|
|
.float -COS16_1, COS16_1, -COS16_3, COS16_3 // Could be +-+- too
|
|
|
|
.float COS16_3, COS16_3, COS16_1, COS16_1
|
|
|
|
.float 1.0, 1.0, M_SQRT1_2, M_SQRT1_2
|
|
|
|
endconst
|
|
|
|
|
|
|
|
// 16-point FFT
|
|
|
|
// t3, t4, t5, t6 must be sequential
|
|
|
|
.macro FFT16 e0, e1, e2, e3, o0, o1, o2, o3, \
|
|
|
|
t0=v16, t1=v17, t2=v18, t3=v19, t4=v20, t5=v21, t6=v22
|
|
|
|
|
|
|
|
FFT8 \e0, \e1, \e2, \e3, \t0, \t1, \t2, \t3, \t4, \t5, \t6
|
|
|
|
FFT4_X2 \o0, \o1, \o2, \o3, \t0, \t1, \t2, \t3, \t4, \t5, \t6
|
|
|
|
|
|
|
|
movrel x5, tab_16pt
|
|
|
|
|
|
|
|
rev64 \t0\().4s, \o0\().4s // z[ 8, 9].imre
|
|
|
|
rev64 \t1\().4s, \o2\().4s // z[10,11].imre
|
|
|
|
|
|
|
|
ins \t0\().d[0], xzr
|
|
|
|
ins \t1\().d[0], xzr
|
|
|
|
|
|
|
|
ld1 { \t4\().4s, \t5\().4s, \t6\().4s }, [x5]
|
|
|
|
// TODO: We could derive \t4\() or \t5\() from either, but it seems cheaper to load
|
|
|
|
|
|
|
|
fmla \o2\().4s, \t1\().4s, v31.4s // s[4567]
|
|
|
|
fmls \o0\().4s, \t0\().4s, v31.4s // s[0123]
|
|
|
|
|
|
|
|
fmul \t2\().4s, \o1\().4s, \t4\().4s
|
|
|
|
fmul \t3\().4s, \o3\().4s, \t4\().4s
|
|
|
|
|
|
|
|
rev64 \o3\().4s, \o3\().4s
|
|
|
|
rev64 \o1\().4s, \o1\().4s
|
|
|
|
|
|
|
|
fmla \t3\().4s, \o3\().4s, \t5\().4s // s[12, 13, 14, 15]
|
|
|
|
fmls \t2\().4s, \o1\().4s, \t5\().4s // s[ 8, 9, 10, 11]
|
|
|
|
|
|
|
|
fmul \t1\().4s, \o2\().4s, \t6\().4s // s[4567] * mult
|
|
|
|
fmul \t0\().4s, \o0\().4s, \t6\().4s // s[0123] * mult
|
|
|
|
|
|
|
|
mov \o1\().16b, \t3\().16b
|
|
|
|
mov \o2\().16b, \t1\().16b
|
|
|
|
|
|
|
|
fsub \t3\().4s, \t3\().4s, \t2\().4s // y34, u34
|
|
|
|
fsub \t1\().4s, \t1\().4s, \t0\().4s // w34, x34
|
|
|
|
|
|
|
|
fadd \t2\().4s, \t2\().4s, \o1\().4s // y56, u56
|
|
|
|
rev64 \t3\().4s, \t3\().4s
|
|
|
|
fadd \t0\().4s, \t0\().4s, \o2\().4s // w56, x56
|
|
|
|
rev64 \t1\().4s, \t1\().4s
|
|
|
|
|
|
|
|
fmul \t2\().4s, \t2\().4s, v31.4s
|
|
|
|
fmul \t1\().4s, \t1\().4s, v31.4s
|
|
|
|
|
|
|
|
fadd \o3\().4s, \e3\().4s, \t3\().4s
|
|
|
|
fsub \o2\().4s, \e3\().4s, \t3\().4s
|
|
|
|
fsub \o1\().4s, \e2\().4s, \t2\().4s
|
|
|
|
fadd \o0\().4s, \e2\().4s, \t2\().4s
|
|
|
|
|
|
|
|
fsub \e2\().4s, \e0\().4s, \t0\().4s
|
|
|
|
fadd \e0\().4s, \e0\().4s, \t0\().4s
|
|
|
|
fsub \e3\().4s, \e1\().4s, \t1\().4s
|
|
|
|
fadd \e1\().4s, \e1\().4s, \t1\().4s
|
|
|
|
.endm
|
|
|
|
|
|
|
|
function ff_tx_fft2_float_neon, export=1
|
|
|
|
ld2r { v0.2d, v1.2d }, [x2]
|
|
|
|
|
|
|
|
fneg v2.2s, v1.2s
|
|
|
|
mov v2.d[1], v1.d[0]
|
|
|
|
|
|
|
|
fsub v2.4s, v0.4s, v2.4s
|
|
|
|
|
|
|
|
st1 { v2.4s }, [x1]
|
|
|
|
ret
|
|
|
|
endfunc
|
|
|
|
|
|
|
|
.macro FFT4_FN name, inv
|
|
|
|
function ff_tx_fft4_\name\()_float_neon, export=1
|
|
|
|
ld1 {v0.4s, v1.4s}, [x2]
|
|
|
|
|
|
|
|
.if \inv == 1
|
|
|
|
mov v2.d[0], v0.d[1]
|
|
|
|
mov v0.d[1], v1.d[1]
|
|
|
|
mov v1.d[1], v2.d[0]
|
|
|
|
.endif
|
|
|
|
|
|
|
|
FFT4 v0, v1, 1
|
|
|
|
|
|
|
|
st1 { v0.4s, v1.4s }, [x1]
|
|
|
|
ret
|
|
|
|
endfunc
|
|
|
|
.endm
|
|
|
|
|
|
|
|
FFT4_FN fwd, 0
|
|
|
|
FFT4_FN inv, 1
|
|
|
|
|
|
|
|
.macro FFT8_FN name, no_perm
|
|
|
|
function ff_tx_fft8_\name\()_neon, export=1
|
|
|
|
SETUP_LUT \no_perm
|
|
|
|
LOAD_INPUT 0, 1, 2, 3, x2, \no_perm
|
|
|
|
|
|
|
|
LOAD_SUBADD
|
|
|
|
FFT8 v0, v1, v2, v3
|
|
|
|
|
|
|
|
zip1 v16.2d, v0.2d, v2.2d
|
|
|
|
zip2 v17.2d, v0.2d, v2.2d
|
|
|
|
zip1 v18.2d, v1.2d, v3.2d
|
|
|
|
zip2 v19.2d, v1.2d, v3.2d
|
|
|
|
st1 { v16.4s, v17.4s, v18.4s, v19.4s }, [x1]
|
|
|
|
|
|
|
|
ret
|
|
|
|
endfunc
|
|
|
|
.endm
|
|
|
|
|
|
|
|
FFT8_FN float, 0
|
|
|
|
FFT8_FN ns_float, 1
|
|
|
|
|
|
|
|
.macro FFT16_FN name, no_perm
|
|
|
|
function ff_tx_fft16_\name\()_neon, export=1
|
|
|
|
SETUP_LUT \no_perm
|
|
|
|
LOAD_INPUT 0, 1, 2, 3, x2, \no_perm
|
|
|
|
LOAD_INPUT 4, 5, 6, 7, x2, \no_perm
|
|
|
|
|
|
|
|
LOAD_SUBADD
|
|
|
|
FFT16 v0, v1, v2, v3, v4, v5, v6, v7
|
|
|
|
|
|
|
|
zip1 v20.2d, v0.2d, v4.2d
|
|
|
|
zip2 v21.2d, v0.2d, v4.2d
|
|
|
|
zip1 v22.2d, v1.2d, v6.2d
|
|
|
|
zip2 v23.2d, v1.2d, v6.2d
|
|
|
|
st1 { v20.4s, v21.4s, v22.4s, v23.4s }, [x1], #64
|
|
|
|
|
|
|
|
zip1 v24.2d, v2.2d, v5.2d
|
|
|
|
zip2 v25.2d, v2.2d, v5.2d
|
|
|
|
zip1 v26.2d, v3.2d, v7.2d
|
|
|
|
zip2 v27.2d, v3.2d, v7.2d
|
|
|
|
st1 { v24.4s, v25.4s, v26.4s, v27.4s }, [x1]
|
|
|
|
|
|
|
|
ret
|
|
|
|
endfunc
|
|
|
|
.endm
|
|
|
|
|
|
|
|
FFT16_FN float, 0
|
|
|
|
FFT16_FN ns_float, 1
|
|
|
|
|
|
|
|
.macro SETUP_SR_RECOMB len, re, im, dec
|
|
|
|
ldr w5, =(\len - 4*7)
|
|
|
|
movrel \re, X(ff_tx_tab_\len\()_float)
|
|
|
|
add \im, \re, x5
|
|
|
|
mov \dec, #-32
|
|
|
|
|
|
|
|
.if \len > 32
|
|
|
|
mov x21, #2*\len
|
|
|
|
add x22, x21, x21, lsl #1
|
|
|
|
.endif
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro SR_COMBINE e0, e1, e2, e3, e4, e5, e6, e7, \
|
|
|
|
o0, o1, o2, o3, o4, o5, o6, o7, \
|
|
|
|
re, im, dec, swap_im, \
|
|
|
|
t0=v16, t1=v17, t2=v18, t3=v19, t4=v20, t5=v21, \
|
|
|
|
t6=v22, t7=v23, t8=v24, t9=v25, ta=v26, tb=v27
|
|
|
|
|
|
|
|
ld1 { \t8\().4s, \t9\().4s }, [\im], \dec
|
|
|
|
ld1 { \t0\().4s, \t1\().4s }, [\re], #32
|
|
|
|
|
|
|
|
.if \swap_im == 1
|
|
|
|
ext \t2\().16b, \t9\().16b, \t9\().16b, #8
|
|
|
|
ext \t3\().16b, \t8\().16b, \t8\().16b, #8
|
|
|
|
.else
|
|
|
|
ext \t2\().16b, \t8\().16b, \t8\().16b, #8
|
|
|
|
ext \t3\().16b, \t9\().16b, \t9\().16b, #8
|
|
|
|
.endif
|
|
|
|
|
|
|
|
trn1 \t4\().4s, \t0\().4s, \t0\().4s // cos0022
|
|
|
|
trn2 \t0\().4s, \t0\().4s, \t0\().4s // cos4466
|
|
|
|
trn1 \t5\().4s, \t1\().4s, \t1\().4s // cos1133
|
|
|
|
trn2 \t1\().4s, \t1\().4s, \t1\().4s // cos5577
|
|
|
|
|
|
|
|
rev64 \t6\().4s, \o0\().4s // E m2[0,1].imre
|
|
|
|
rev64 \t7\().4s, \o2\().4s // O m2[0,1].imre
|
|
|
|
rev64 \t8\().4s, \o4\().4s // E m2[2,3].imre
|
|
|
|
rev64 \t9\().4s, \o6\().4s // O m2[2,3].imre
|
|
|
|
|
|
|
|
fmul \t6\().4s, \t6\().4s, \t4\().4s // E m2[0,1].imre*t1[0,2]
|
|
|
|
fmul \t7\().4s, \t7\().4s, \t0\().4s // O m2[0,1].imre*t1[0,2]
|
|
|
|
fmul \t8\().4s, \t8\().4s, \t4\().4s // E m2[2,3].imre*t1[0,2]
|
|
|
|
fmul \t9\().4s, \t9\().4s, \t0\().4s // O m2[2,3].imre*t1[0,2]
|
|
|
|
|
|
|
|
rev64 \ta\().4s, \o1\().4s // E m3[0,1].imre
|
|
|
|
rev64 \tb\().4s, \o3\().4s // O m3[0,1].imre
|
|
|
|
rev64 \t4\().4s, \o5\().4s // E m3[2,3].imre
|
|
|
|
rev64 \t0\().4s, \o7\().4s // O m3[2,3].imre
|
|
|
|
|
|
|
|
fmul \ta\().4s, \ta\().4s, \t5\().4s // E m3[0,1].imre*t1[4,6]
|
|
|
|
fmul \tb\().4s, \tb\().4s, \t1\().4s // O m3[0,1].imre*t1[4,6]
|
|
|
|
fmul \t4\().4s, \t4\().4s, \t5\().4s // E m3[2,3].imre*t1[4,6]
|
|
|
|
fmul \t0\().4s, \t0\().4s, \t1\().4s // O m3[2,3].imre*t1[4,6]
|
|
|
|
|
|
|
|
trn1 \t5\().4s, \t3\().4s, \t3\().4s // wim2200
|
|
|
|
trn2 \t3\().4s, \t3\().4s, \t3\().4s // wim3311
|
|
|
|
trn1 \t1\().4s, \t2\().4s, \t2\().4s // wim6644
|
|
|
|
trn2 \t2\().4s, \t2\().4s, \t2\().4s // wim7755
|
|
|
|
|
|
|
|
fmul \t5\().4s, \t5\().4s, v31.4s
|
|
|
|
fmul \t3\().4s, \t3\().4s, v31.4s
|
|
|
|
fmul \t1\().4s, \t1\().4s, v31.4s
|
|
|
|
fmul \t2\().4s, \t2\().4s, v31.4s
|
|
|
|
|
|
|
|
fmla \t7\().4s, \o2\().4s, \t5\().4s // O w0123
|
|
|
|
fmls \t9\().4s, \o6\().4s, \t5\().4s // O j0123
|
|
|
|
fmla \t6\().4s, \o0\().4s, \t3\().4s // E w0123
|
|
|
|
fmls \t8\().4s, \o4\().4s, \t3\().4s // E j0123
|
|
|
|
|
|
|
|
fmla \ta\().4s, \o1\().4s, \t2\().4s // E w4567
|
|
|
|
fmla \tb\().4s, \o3\().4s, \t1\().4s // O w4567
|
|
|
|
fmls \t4\().4s, \o5\().4s, \t2\().4s // E j4567
|
|
|
|
fmls \t0\().4s, \o7\().4s, \t1\().4s // O j4567
|
|
|
|
|
|
|
|
fsub \t2\().4s, \t7\().4s, \t9\().4s
|
|
|
|
fsub \t1\().4s, \t8\().4s, \t6\().4s
|
|
|
|
fsub \t3\().4s, \t4\().4s, \ta\().4s
|
|
|
|
fsub \t5\().4s, \t0\().4s, \tb\().4s
|
|
|
|
|
|
|
|
fadd \t6\().4s, \t8\().4s, \t6\().4s
|
|
|
|
fadd \t7\().4s, \t9\().4s, \t7\().4s
|
|
|
|
fadd \t8\().4s, \t4\().4s, \ta\().4s
|
|
|
|
fadd \t9\().4s, \t0\().4s, \tb\().4s
|
|
|
|
|
|
|
|
fmul \t1\().4s, \t1\().4s, v31.4s
|
|
|
|
fmul \t2\().4s, \t2\().4s, v31.4s
|
|
|
|
fmul \t3\().4s, \t3\().4s, v31.4s
|
|
|
|
fmul \t5\().4s, \t5\().4s, v31.4s
|
|
|
|
|
|
|
|
rev64 \t6\().4s, \t6\().4s
|
|
|
|
rev64 \t8\().4s, \t8\().4s
|
|
|
|
rev64 \t7\().4s, \t7\().4s
|
|
|
|
rev64 \t9\().4s, \t9\().4s
|
|
|
|
|
|
|
|
fsub \o0\().4s, \e0\().4s, \t6\().4s
|
|
|
|
fsub \o1\().4s, \e1\().4s, \t8\().4s
|
|
|
|
fsub \o2\().4s, \e2\().4s, \t1\().4s
|
|
|
|
fsub \o3\().4s, \e3\().4s, \t3\().4s
|
|
|
|
|
|
|
|
fsub \o4\().4s, \e4\().4s, \t7\().4s
|
|
|
|
fsub \o5\().4s, \e6\().4s, \t9\().4s
|
|
|
|
fadd \o6\().4s, \e5\().4s, \t2\().4s
|
|
|
|
fsub \o7\().4s, \e7\().4s, \t5\().4s
|
|
|
|
|
|
|
|
fadd \e0\().4s, \e0\().4s, \t6\().4s
|
|
|
|
fadd \e1\().4s, \e1\().4s, \t8\().4s
|
|
|
|
fadd \e2\().4s, \e2\().4s, \t1\().4s
|
|
|
|
fadd \e3\().4s, \e3\().4s, \t3\().4s
|
|
|
|
|
|
|
|
fadd \e4\().4s, \e4\().4s, \t7\().4s
|
|
|
|
fsub \e5\().4s, \e5\().4s, \t2\().4s // swapped
|
|
|
|
fadd \e6\().4s, \e6\().4s, \t9\().4s // swapped
|
|
|
|
fadd \e7\().4s, \e7\().4s, \t5\().4s
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro SR_COMBINE_HALF e0, e1, e2, e3, \
|
|
|
|
o0, o1, o2, o3, \
|
|
|
|
c0, c1, c2, c3, \
|
|
|
|
t0, t1, t2, t3, t4, t5, part
|
|
|
|
|
|
|
|
.if \part == 0
|
|
|
|
trn1 \t4\().4s, \c0\().4s, \c0\().4s // cos0022
|
|
|
|
trn1 \c1\().4s, \c1\().4s, \c1\().4s // cos1133
|
|
|
|
.else
|
|
|
|
trn2 \t4\().4s, \c0\().4s, \c0\().4s // cos0022
|
|
|
|
trn2 \c1\().4s, \c1\().4s, \c1\().4s // cos1133
|
|
|
|
.endif
|
|
|
|
.if \part == 0
|
|
|
|
trn2 \t5\().4s, \c2\().4s, \c2\().4s // wim7755
|
|
|
|
trn2 \c3\().4s, \c3\().4s, \c3\().4s // wim3311
|
|
|
|
.else
|
|
|
|
trn1 \t5\().4s, \c2\().4s, \c2\().4s // wim7755
|
|
|
|
trn1 \c3\().4s, \c3\().4s, \c3\().4s // wim3311
|
|
|
|
.endif
|
|
|
|
|
|
|
|
fmul \t5\().4s, \t5\().4s, v31.4s
|
|
|
|
fmul \c3\().4s, \c3\().4s, v31.4s
|
|
|
|
|
|
|
|
rev64 \t0\().4s, \o0\().4s // E m2[0,1].imre
|
|
|
|
rev64 \t1\().4s, \o2\().4s // E m2[2,3].imre
|
|
|
|
rev64 \t2\().4s, \o1\().4s // E m3[0,1].imre
|
|
|
|
rev64 \t3\().4s, \o3\().4s // E m3[2,3].imre
|
|
|
|
|
|
|
|
fmul \o0\().4s, \o0\().4s, \c3\().4s // E m2[0,1].imre*t1[0,2]
|
|
|
|
fmul \o1\().4s, \o1\().4s, \t5\().4s // E m3[0,1].imre*t1[4,6]
|
|
|
|
fmla \o0\().4s, \t0\().4s, \t4\().4s // E w0123
|
|
|
|
fmla \o1\().4s, \t2\().4s, \c1\().4s // E w4567
|
|
|
|
|
|
|
|
fmul \t1\().4s, \t1\().4s, \t4\().4s // E m2[2,3].imre*t1[0,2]
|
|
|
|
fmul \t3\().4s, \t3\().4s, \c1\().4s // E m3[2,3].imre*t1[4,6]
|
|
|
|
fmls \t1\().4s, \o2\().4s, \c3\().4s // E j0123
|
|
|
|
fmls \t3\().4s, \o3\().4s, \t5\().4s // E j4567
|
|
|
|
|
|
|
|
fsub \t0\().4s, \t1\().4s, \o0\().4s
|
|
|
|
fadd \t1\().4s, \t1\().4s, \o0\().4s
|
|
|
|
fadd \t2\().4s, \t3\().4s, \o1\().4s
|
|
|
|
fsub \t3\().4s, \t3\().4s, \o1\().4s
|
|
|
|
|
|
|
|
fmul \t0\().4s, \t0\().4s, v31.4s
|
|
|
|
fmul \t3\().4s, \t3\().4s, v31.4s
|
|
|
|
|
|
|
|
rev64 \t1\().4s, \t1\().4s
|
|
|
|
rev64 \t2\().4s, \t2\().4s
|
|
|
|
|
|
|
|
.if \part == 0
|
|
|
|
fsub \o0\().4s, \e0\().4s, \t1\().4s
|
|
|
|
fsub \o1\().4s, \e1\().4s, \t2\().4s
|
|
|
|
fsub \o2\().4s, \e2\().4s, \t0\().4s
|
|
|
|
fsub \o3\().4s, \e3\().4s, \t3\().4s
|
|
|
|
.else
|
|
|
|
fsub \o0\().4s, \e0\().4s, \t1\().4s
|
|
|
|
fadd \o2\().4s, \e1\().4s, \t2\().4s
|
|
|
|
fsub \o1\().4s, \e2\().4s, \t0\().4s
|
|
|
|
fadd \o3\().4s, \e3\().4s, \t3\().4s
|
|
|
|
.endif
|
|
|
|
|
|
|
|
.if \part == 0
|
|
|
|
fadd \e0\().4s, \e0\().4s, \t1\().4s
|
|
|
|
fadd \e1\().4s, \e1\().4s, \t2\().4s
|
|
|
|
fadd \e2\().4s, \e2\().4s, \t0\().4s
|
|
|
|
fadd \e3\().4s, \e3\().4s, \t3\().4s
|
|
|
|
.else
|
|
|
|
fadd \e0\().4s, \e0\().4s, \t1\().4s
|
|
|
|
fsub \e1\().4s, \e1\().4s, \t2\().4s // swapped
|
|
|
|
fadd \e2\().4s, \e2\().4s, \t0\().4s // swapped
|
|
|
|
fsub \e3\().4s, \e3\().4s, \t3\().4s
|
|
|
|
.endif
|
|
|
|
.endm
|
|
|
|
|
|
|
|
/* Same as SR_COMBINE_HALF, but heroically tries to use 3 temporary registers
|
|
|
|
* without touching the tables. */
|
|
|
|
.macro SR_COMBINE_LITE e0, e1, e2, e3, \
|
|
|
|
o0, o1, o2, o3, \
|
|
|
|
c0, c1, c2, c3, \
|
|
|
|
t0, t1, t2, part
|
|
|
|
|
|
|
|
rev64 \t0\().4s, \o0\().4s // E m2[0,1].imre
|
|
|
|
rev64 \t1\().4s, \o2\().4s // E m2[2,3].imre
|
|
|
|
.if \part == 0
|
|
|
|
trn2 \t2\().4s, \c3\().4s, \c3\().4s // wim3311
|
|
|
|
.else
|
|
|
|
trn1 \t2\().4s, \c3\().4s, \c3\().4s // wim3311
|
|
|
|
.endif
|
|
|
|
fmul \t2\().4s, \t2\().4s, v31.4s
|
|
|
|
fmul \o2\().4s, \o2\().4s, \t2\().4s
|
|
|
|
fmul \o0\().4s, \o0\().4s, \t2\().4s // E m2[0,1].imre*t1[0,2]
|
|
|
|
.if \part == 0
|
|
|
|
trn1 \t2\().4s, \c0\().4s, \c0\().4s // cos0022
|
|
|
|
.else
|
|
|
|
trn2 \t2\().4s, \c0\().4s, \c0\().4s // cos0022
|
|
|
|
.endif
|
|
|
|
fmul \t1\().4s, \t1\().4s, \t2\().4s // E m2[2,3].imre*t1[0,2]
|
|
|
|
fmla \o0\().4s, \t0\().4s, \t2\().4s // E w0123
|
|
|
|
fsub \t1\().4s, \t1\().4s, \o2\().4s // E j0123
|
|
|
|
|
|
|
|
rev64 \t2\().4s, \o1\().4s // E m3[0,1].imre
|
|
|
|
rev64 \o2\().4s, \o3\().4s // E m3[2,3].imre
|
|
|
|
|
|
|
|
.if \part == 0
|
|
|
|
trn2 \t0\().4s, \c2\().4s, \c2\().4s // wim7755
|
|
|
|
.else
|
|
|
|
trn1 \t0\().4s, \c2\().4s, \c2\().4s // wim7755
|
|
|
|
.endif
|
|
|
|
fmul \t0\().4s, \t0\().4s, v31.4s
|
|
|
|
|
|
|
|
fmul \o1\().4s, \o1\().4s, \t0\().4s // E m3[0,1].imre*t1[4,6]
|
|
|
|
fmul \o3\().4s, \o3\().4s, \t0\().4s
|
|
|
|
|
|
|
|
.if \part == 0
|
|
|
|
trn1 \t0\().4s, \c1\().4s, \c1\().4s // cos1133
|
|
|
|
.else
|
|
|
|
trn2 \t0\().4s, \c1\().4s, \c1\().4s // cos1133
|
|
|
|
.endif
|
|
|
|
fmul \o2\().4s, \o2\().4s, \t0\().4s // E m3[2,3].imre*t1[4,6]
|
|
|
|
fmla \o1\().4s, \t2\().4s, \t0\().4s // E w4567
|
|
|
|
fsub \o2\().4s, \o2\().4s, \o3\().4s // E j4567
|
|
|
|
|
|
|
|
fsub \t0\().4s, \t1\().4s, \o0\().4s
|
|
|
|
fadd \o0\().4s, \t1\().4s, \o0\().4s
|
|
|
|
fadd \t2\().4s, \o2\().4s, \o1\().4s
|
|
|
|
fsub \t1\().4s, \o2\().4s, \o1\().4s
|
|
|
|
|
|
|
|
fmul \t0\().4s, \t0\().4s, v31.4s
|
|
|
|
fmul \t1\().4s, \t1\().4s, v31.4s
|
|
|
|
|
|
|
|
rev64 \t2\().4s, \t2\().4s
|
|
|
|
rev64 \o0\().4s, \o0\().4s
|
|
|
|
|
|
|
|
.if \part == 0
|
|
|
|
fsub \o1\().4s, \e1\().4s, \t2\().4s
|
|
|
|
fsub \o2\().4s, \e2\().4s, \t0\().4s
|
|
|
|
fsub \o3\().4s, \e3\().4s, \t1\().4s
|
|
|
|
.else
|
|
|
|
fadd \o2\().4s, \e1\().4s, \t0\().4s
|
|
|
|
fsub \o1\().4s, \e2\().4s, \t2\().4s
|
|
|
|
fadd \o3\().4s, \e3\().4s, \t1\().4s
|
|
|
|
.endif
|
|
|
|
|
|
|
|
.if \part == 0
|
|
|
|
fadd \e1\().4s, \e1\().4s, \t2\().4s
|
|
|
|
fadd \e2\().4s, \e2\().4s, \t0\().4s
|
|
|
|
fadd \e3\().4s, \e3\().4s, \t1\().4s
|
|
|
|
.else
|
|
|
|
fsub \e1\().4s, \e1\().4s, \t0\().4s // swapped
|
|
|
|
fadd \e2\().4s, \e2\().4s, \t2\().4s // swapped
|
|
|
|
fsub \e3\().4s, \e3\().4s, \t1\().4s
|
|
|
|
.endif
|
|
|
|
|
|
|
|
mov \t1\().16b, \o0\().16b
|
|
|
|
|
|
|
|
fsub \o0\().4s, \e0\().4s, \t1\().4s
|
|
|
|
fadd \e0\().4s, \e0\().4s, \t1\().4s
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro SR_COMBINE_4 len, part, off
|
2023-10-17 12:47:27 +02:00
|
|
|
add x10, x1, x21
|
|
|
|
add x11, x1, x21, lsl #1
|
|
|
|
add x12, x1, x22
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q0, q1, [x1, #((0 + \part)*32 + \off)]
|
|
|
|
ldp q4, q5, [x1, #((2 + \part)*32 + \off)]
|
|
|
|
ldp q2, q3, [x10, #((0 + \part)*32 + \off)]
|
|
|
|
ldp q6, q7, [x10, #((2 + \part)*32 + \off)]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q8, q9, [x11, #((0 + \part)*32 + \off)]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
ldp q10, q11, [x11, #((2 + \part)*32 + \off)]
|
|
|
|
ldp q12, q13, [x12, #((0 + \part)*32 + \off)]
|
|
|
|
ldp q14, q15, [x12, #((2 + \part)*32 + \off)]
|
|
|
|
|
|
|
|
SR_COMBINE v0, v1, v2, v3, v4, v6, v5, v7, \
|
|
|
|
v8, v9, v10, v11, v12, v13, v14, v15, \
|
|
|
|
x7, x8, x9, 0
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
stp q0, q1, [x1, #((0 + \part)*32 + \off)]
|
|
|
|
stp q4, q5, [x1, #((2 + \part)*32 + \off)]
|
|
|
|
stp q2, q3, [x10, #((0 + \part)*32 + \off)]
|
|
|
|
stp q6, q7, [x10, #((2 + \part)*32 + \off)]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
stp q8, q9, [x11, #((0 + \part)*32 + \off)]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
stp q12, q13, [x11, #((2 + \part)*32 + \off)]
|
|
|
|
stp q10, q11, [x12, #((0 + \part)*32 + \off)]
|
|
|
|
stp q14, q15, [x12, #((2 + \part)*32 + \off)]
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro SR_COMBINE_FULL len, off=0
|
2023-10-17 12:47:27 +02:00
|
|
|
add x10, x1, x21
|
|
|
|
add x11, x1, x21, lsl #1
|
|
|
|
add x12, x1, x22
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
|
|
|
SR_COMBINE_4 \len, 0, \off
|
|
|
|
SR_COMBINE_4 \len, 1, \off
|
|
|
|
SR_COMBINE_4 \len, 4, \off
|
|
|
|
SR_COMBINE_4 \len, 5, \off
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro SR_COMBINE_D2 part, off
|
|
|
|
add x10, x1, #((\part)*32 + \off)
|
|
|
|
add x11, x14, #((\part)*32 + \off)
|
|
|
|
add x12, x15, #((\part)*32 + \off)
|
|
|
|
add x13, x16, #((\part)*32 + \off)
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q0, q1, [x10]
|
|
|
|
ldp q4, q5, [x10, #(2*32)]
|
|
|
|
ldp q2, q3, [x11]
|
|
|
|
ldp q6, q7, [x11, #(2*32)]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q8, q9, [x12]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
ldp q10, q11, [x12, #(2*32)]
|
|
|
|
ldp q12, q13, [x13]
|
|
|
|
ldp q14, q15, [x13, #(2*32)]
|
|
|
|
|
|
|
|
SR_COMBINE v0, v1, v2, v3, v4, v6, v5, v7, \
|
|
|
|
v8, v9, v10, v11, v12, v13, v14, v15, \
|
|
|
|
x7, x8, x9, 0, \
|
|
|
|
v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27
|
|
|
|
|
|
|
|
zip1 v16.2d, v0.2d, v4.2d
|
|
|
|
zip2 v17.2d, v0.2d, v4.2d
|
|
|
|
zip1 v18.2d, v1.2d, v5.2d
|
|
|
|
zip2 v19.2d, v1.2d, v5.2d
|
|
|
|
|
|
|
|
zip1 v20.2d, v2.2d, v6.2d
|
|
|
|
zip2 v21.2d, v2.2d, v6.2d
|
|
|
|
zip1 v22.2d, v3.2d, v7.2d
|
|
|
|
zip2 v23.2d, v3.2d, v7.2d
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q0, q1, [x10, #(1*32)]
|
|
|
|
ldp q4, q5, [x10, #(3*32)]
|
|
|
|
ldp q2, q3, [x11, #(1*32)]
|
|
|
|
ldp q6, q7, [x11, #(3*32)]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
|
|
|
st1 { v16.4s, v17.4s, v18.4s, v19.4s }, [x10], #64
|
|
|
|
st1 { v20.4s, v21.4s, v22.4s, v23.4s }, [x11], #64
|
|
|
|
|
|
|
|
zip1 v20.2d, v8.2d, v12.2d
|
|
|
|
zip2 v21.2d, v8.2d, v12.2d
|
|
|
|
zip1 v22.2d, v9.2d, v13.2d
|
|
|
|
zip2 v23.2d, v9.2d, v13.2d
|
|
|
|
zip1 v24.2d, v10.2d, v14.2d
|
|
|
|
zip2 v25.2d, v10.2d, v14.2d
|
|
|
|
zip1 v26.2d, v11.2d, v15.2d
|
|
|
|
zip2 v27.2d, v11.2d, v15.2d
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q8, q9, [x12, #(1*32)]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
ldp q10, q11, [x12, #(3*32)]
|
|
|
|
ldp q12, q13, [x13, #(1*32)]
|
|
|
|
ldp q14, q15, [x13, #(3*32)]
|
|
|
|
|
|
|
|
st1 { v20.4s, v21.4s, v22.4s, v23.4s }, [x12], #64
|
|
|
|
st1 { v24.4s, v25.4s, v26.4s, v27.4s }, [x13], #64
|
|
|
|
|
|
|
|
SR_COMBINE v0, v1, v2, v3, v4, v6, v5, v7, \
|
|
|
|
v8, v9, v10, v11, v12, v13, v14, v15, \
|
|
|
|
x7, x8, x9, 0, \
|
|
|
|
v16, v17, v18, v19, v20, v21, v22, v23, v24, v25, v26, v27
|
|
|
|
|
|
|
|
zip1 v16.2d, v0.2d, v4.2d
|
|
|
|
zip2 v17.2d, v0.2d, v4.2d
|
|
|
|
zip1 v18.2d, v1.2d, v5.2d
|
|
|
|
zip2 v19.2d, v1.2d, v5.2d
|
|
|
|
st1 { v16.4s, v17.4s, v18.4s, v19.4s }, [x10]
|
|
|
|
|
|
|
|
zip1 v16.2d, v2.2d, v6.2d
|
|
|
|
zip2 v17.2d, v2.2d, v6.2d
|
|
|
|
zip1 v18.2d, v3.2d, v7.2d
|
|
|
|
zip2 v19.2d, v3.2d, v7.2d
|
|
|
|
st1 { v16.4s, v17.4s, v18.4s, v19.4s }, [x11]
|
|
|
|
|
|
|
|
zip1 v20.2d, v8.2d, v12.2d
|
|
|
|
zip2 v21.2d, v8.2d, v12.2d
|
|
|
|
zip1 v22.2d, v9.2d, v13.2d
|
|
|
|
zip2 v23.2d, v9.2d, v13.2d
|
|
|
|
st1 { v20.4s, v21.4s, v22.4s, v23.4s }, [x12]
|
|
|
|
|
|
|
|
zip1 v24.2d, v10.2d, v14.2d
|
|
|
|
zip2 v25.2d, v10.2d, v14.2d
|
|
|
|
zip1 v26.2d, v11.2d, v15.2d
|
|
|
|
zip2 v27.2d, v11.2d, v15.2d
|
|
|
|
st1 { v24.4s, v25.4s, v26.4s, v27.4s }, [x13]
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro SR_COMBINE_DINT off=0
|
|
|
|
add x14, x1, x21
|
|
|
|
add x15, x1, x21, lsl #1
|
|
|
|
add x16, x1, x22
|
|
|
|
|
|
|
|
SR_COMBINE_D2 0, \off
|
|
|
|
SR_COMBINE_D2 4, \off
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro FFT32_FN name, no_perm
|
|
|
|
function ff_tx_fft32_\name\()_neon, export=1
|
2022-10-09 21:17:47 +02:00
|
|
|
stp d14, d15, [sp, #-16*4]!
|
|
|
|
stp d8, d9, [sp, #16*3]
|
|
|
|
stp d10, d11, [sp, #16*2]
|
|
|
|
stp d12, d13, [sp, #16]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
|
|
|
LOAD_SUBADD
|
|
|
|
SETUP_SR_RECOMB 32, x7, x8, x9
|
|
|
|
|
|
|
|
SETUP_LUT \no_perm
|
2023-10-17 13:04:41 +02:00
|
|
|
LOAD_INPUT 0, 1, 2, 3, x2, \no_perm
|
|
|
|
LOAD_INPUT 4, 5, 6, 7, x2, \no_perm
|
|
|
|
LOAD_INPUT 8, 9, 10, 11, x2, \no_perm
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
LOAD_INPUT 12, 13, 14, 15, x2, \no_perm
|
|
|
|
|
|
|
|
FFT8_X2 v8, v9, v10, v11, v12, v13, v14, v15
|
|
|
|
FFT16 v0, v1, v2, v3, v4, v5, v6, v7
|
|
|
|
|
|
|
|
SR_COMBINE v0, v1, v2, v3, v4, v5, v6, v7, \
|
|
|
|
v8, v9, v10, v11, v12, v13, v14, v15, \
|
|
|
|
x7, x8, x9, 0
|
|
|
|
|
|
|
|
zip1 v16.2d, v0.2d, v4.2d
|
|
|
|
zip2 v17.2d, v0.2d, v4.2d
|
|
|
|
zip1 v18.2d, v1.2d, v6.2d
|
|
|
|
zip2 v19.2d, v1.2d, v6.2d
|
|
|
|
st1 { v16.4s, v17.4s, v18.4s, v19.4s }, [x1], #64
|
|
|
|
|
|
|
|
zip1 v20.2d, v2.2d, v5.2d
|
|
|
|
zip2 v21.2d, v2.2d, v5.2d
|
|
|
|
zip1 v22.2d, v3.2d, v7.2d
|
|
|
|
zip2 v23.2d, v3.2d, v7.2d
|
|
|
|
st1 { v20.4s, v21.4s, v22.4s, v23.4s }, [x1], #64
|
|
|
|
|
|
|
|
zip1 v24.2d, v8.2d, v12.2d
|
|
|
|
zip2 v25.2d, v8.2d, v12.2d
|
|
|
|
zip1 v26.2d, v9.2d, v13.2d
|
|
|
|
zip2 v27.2d, v9.2d, v13.2d
|
|
|
|
st1 { v24.4s, v25.4s, v26.4s, v27.4s }, [x1], #64
|
|
|
|
|
|
|
|
zip1 v28.2d, v10.2d, v14.2d
|
|
|
|
zip2 v29.2d, v10.2d, v14.2d
|
|
|
|
zip1 v30.2d, v11.2d, v15.2d
|
|
|
|
zip2 v31.2d, v11.2d, v15.2d
|
|
|
|
st1 { v28.4s, v29.4s, v30.4s, v31.4s }, [x1]
|
|
|
|
|
2022-10-09 21:17:47 +02:00
|
|
|
ldp d12, d13, [sp, #16]
|
|
|
|
ldp d10, d11, [sp, #16*2]
|
|
|
|
ldp d8, d9, [sp, #16*3]
|
|
|
|
ldp d14, d15, [sp], #16*4
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
|
|
|
ret
|
|
|
|
endfunc
|
|
|
|
.endm
|
|
|
|
|
|
|
|
FFT32_FN float, 0
|
|
|
|
FFT32_FN ns_float, 1
|
|
|
|
|
|
|
|
.macro cmp_imm reg, imm
|
|
|
|
.if \imm >= 4096
|
|
|
|
cmp \reg, #((\imm)/4096), lsl #12
|
|
|
|
.else
|
|
|
|
cmp \reg, #(\imm)
|
|
|
|
.endif
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro SR_TRANSFORM_DEF len, next=0
|
|
|
|
\len:
|
|
|
|
stp x20, x30, [sp, #-16]!
|
|
|
|
mov w20, #(\len/4)
|
|
|
|
mov x5, #((\len*4) - (\len/1))
|
|
|
|
add x1, x1, x5
|
|
|
|
bl 32b
|
|
|
|
mov x5, #((\len*2) - (\len/2))
|
|
|
|
add x1, x1, x5
|
|
|
|
bl 32b
|
|
|
|
ldp x20, x30, [sp], #16
|
|
|
|
ldr w5, =(\len*6 + \len/2)
|
|
|
|
sub x1, x1, x5
|
|
|
|
|
|
|
|
SETUP_SR_RECOMB \len, x7, x8, x9
|
|
|
|
|
|
|
|
.if \next\() != 0
|
|
|
|
cmp_imm w19, \len
|
|
|
|
b.eq 0f
|
|
|
|
|
|
|
|
mov w5, #(\len/128)
|
|
|
|
\len\()5:
|
|
|
|
SR_COMBINE_FULL \len
|
|
|
|
add x1, x1, 8*32
|
|
|
|
subs w5, w5, 1
|
|
|
|
b.gt \len\()5b
|
|
|
|
|
|
|
|
cmp_imm w20, \len
|
|
|
|
b.gt \next\()f
|
|
|
|
ret
|
|
|
|
.endif
|
|
|
|
.endm
|
|
|
|
|
|
|
|
.macro FFT_SPLIT_RADIX_FN name, no_perm
|
|
|
|
function ff_tx_fft_sr_\name\()_neon, export=1
|
2022-10-09 21:17:47 +02:00
|
|
|
stp x21, x22, [sp, #-16*6]!
|
|
|
|
stp d8, d9, [sp, #16*5]
|
|
|
|
stp d10, d11, [sp, #16*4]
|
|
|
|
stp d12, d13, [sp, #16*3]
|
|
|
|
stp d14, d15, [sp, #16*2]
|
|
|
|
stp x19, x20, [sp, #16]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
|
|
|
ldr w19, [x0, #0] // global target
|
|
|
|
mov w20, w19 // local length
|
|
|
|
|
|
|
|
LOAD_SUBADD
|
|
|
|
SETUP_LUT \no_perm
|
|
|
|
|
|
|
|
32:
|
|
|
|
SETUP_SR_RECOMB 32, x7, x8, x9
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
LOAD_INPUT 0, 1, 2, 3, x2, \no_perm
|
|
|
|
LOAD_INPUT 4, 6, 5, 7, x2, \no_perm, 1
|
|
|
|
LOAD_INPUT 8, 9, 10, 11, x2, \no_perm
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
LOAD_INPUT 12, 13, 14, 15, x2, \no_perm
|
|
|
|
|
|
|
|
FFT8_X2 v8, v9, v10, v11, v12, v13, v14, v15
|
|
|
|
FFT16 v0, v1, v2, v3, v4, v6, v5, v7
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
SR_COMBINE v0, v1, v2, v3, v4, v6, v5, v7, \
|
|
|
|
v8, v9, v10, v11, v12, v13, v14, v15, \
|
|
|
|
x7, x8, x9, 0
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
stp q2, q3, [x1, #32*1]
|
|
|
|
stp q6, q7, [x1, #32*3]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
stp q10, q11, [x1, #32*5]
|
|
|
|
stp q14, q15, [x1, #32*7]
|
|
|
|
|
|
|
|
cmp w20, #32
|
|
|
|
b.gt 64f
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
stp q0, q1, [x1, #32*0]
|
|
|
|
stp q4, q5, [x1, #32*2]
|
|
|
|
stp q8, q9, [x1, #32*4]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
stp q12, q13, [x1, #32*6]
|
|
|
|
|
|
|
|
ret
|
|
|
|
64:
|
|
|
|
SETUP_SR_RECOMB 64, x7, x8, x9
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
LOAD_INPUT 2, 3, 10, 11, x2, \no_perm, 1
|
|
|
|
LOAD_INPUT 6, 14, 7, 15, x2, \no_perm, 1
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
|
|
|
FFT16 v2, v3, v10, v11, v6, v14, v7, v15
|
|
|
|
|
|
|
|
LOAD_INPUT 16, 17, 18, 19, x2, \no_perm
|
|
|
|
LOAD_INPUT 20, 22, 21, 23, x2, \no_perm, 1
|
|
|
|
|
|
|
|
FFT16 v16, v17, v18, v19, v20, v22, v21, v23, \
|
|
|
|
v24, v25, v26, v27, v28, v29, v30
|
|
|
|
|
|
|
|
ld1 { v26.4s, v27.4s }, [x8], x9
|
|
|
|
ldp q24, q25, [x7], #32
|
|
|
|
|
|
|
|
ext v26.16b, v26.16b, v26.16b, #8
|
|
|
|
ext v27.16b, v27.16b, v27.16b, #8
|
|
|
|
|
|
|
|
cmp w19, #64
|
|
|
|
b.eq 2f // custom deinterleave
|
|
|
|
|
|
|
|
// TODO: investigate doing the 2 combines like in deinterleave
|
|
|
|
// TODO: experiment with spilling to gprs and converting to HALF or full
|
2023-10-17 13:04:41 +02:00
|
|
|
SR_COMBINE_LITE v0, v1, v8, v9, \
|
|
|
|
v2, v3, v16, v17, \
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
v24, v25, v26, v27, \
|
|
|
|
v28, v29, v30, 0
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
stp q0, q1, [x1, #32* 0]
|
|
|
|
stp q8, q9, [x1, #32* 4]
|
|
|
|
stp q2, q3, [x1, #32* 8]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
stp q16, q17, [x1, #32*12]
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
SR_COMBINE_HALF v4, v5, v12, v13, \
|
|
|
|
v6, v7, v20, v21, \
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
v24, v25, v26, v27, \
|
|
|
|
v28, v29, v30, v0, v1, v8, 1
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
stp q4, q20, [x1, #32* 2]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
stp q12, q21, [x1, #32* 6]
|
2023-10-17 13:04:41 +02:00
|
|
|
stp q6, q5, [x1, #32*10]
|
|
|
|
stp q7, q13, [x1, #32*14]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q2, q3, [x1, #32*1]
|
|
|
|
ldp q6, q7, [x1, #32*3]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
ldp q12, q13, [x1, #32*5]
|
|
|
|
ldp q16, q17, [x1, #32*7]
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
SR_COMBINE v2, v3, v12, v13, v6, v16, v7, v17, \
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
v10, v11, v14, v15, v18, v19, v22, v23, \
|
2023-10-17 13:04:41 +02:00
|
|
|
x7, x8, x9, 0, \
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
v24, v25, v26, v27, v28, v29, v30, v8, v0, v1, v4, v5
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
stp q2, q3, [x1, #32* 1]
|
|
|
|
stp q6, q7, [x1, #32* 3]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
stp q12, q13, [x1, #32* 5]
|
|
|
|
stp q16, q17, [x1, #32* 7]
|
|
|
|
|
|
|
|
stp q10, q11, [x1, #32* 9]
|
|
|
|
stp q18, q19, [x1, #32*11]
|
|
|
|
stp q14, q15, [x1, #32*13]
|
|
|
|
stp q22, q23, [x1, #32*15]
|
|
|
|
|
|
|
|
cmp w20, #64
|
|
|
|
b.gt 128f
|
|
|
|
ret
|
|
|
|
128:
|
|
|
|
stp x20, x30, [sp, #-16]!
|
|
|
|
mov w20, #32
|
|
|
|
add x1, x1, #16*32
|
|
|
|
bl 32b
|
|
|
|
add x1, x1, #8*32
|
|
|
|
bl 32b
|
|
|
|
ldp x20, x30, [sp], #16
|
|
|
|
sub x1, x1, #24*32
|
|
|
|
|
|
|
|
SETUP_SR_RECOMB 128, x7, x8, x9
|
|
|
|
|
|
|
|
cmp w19, #128
|
|
|
|
b.eq 0f
|
|
|
|
|
|
|
|
SR_COMBINE_FULL 128
|
|
|
|
|
|
|
|
cmp w20, #128
|
|
|
|
b.gt 256f
|
|
|
|
ret
|
|
|
|
256:
|
|
|
|
stp x20, x30, [sp, #-16]!
|
|
|
|
mov w20, #64
|
|
|
|
add x1, x1, #32*32
|
|
|
|
bl 32b
|
|
|
|
add x1, x1, #16*32
|
|
|
|
bl 32b
|
|
|
|
ldp x20, x30, [sp], #16
|
|
|
|
sub x1, x1, #48*32
|
|
|
|
|
|
|
|
SETUP_SR_RECOMB 256, x7, x8, x9
|
|
|
|
|
|
|
|
cmp w19, #256
|
|
|
|
b.eq 0f
|
|
|
|
|
|
|
|
SR_COMBINE_FULL 256
|
|
|
|
SR_COMBINE_FULL 256, 8*32
|
|
|
|
|
|
|
|
cmp w20, #256
|
|
|
|
b.gt 512f
|
|
|
|
ret
|
|
|
|
512:
|
|
|
|
stp x20, x30, [sp, #-16]!
|
|
|
|
mov w20, #128
|
|
|
|
add x1, x1, #64*32
|
|
|
|
bl 32b
|
|
|
|
add x1, x1, #32*32
|
|
|
|
bl 32b
|
|
|
|
ldp x20, x30, [sp], #16
|
|
|
|
sub x1, x1, #96*32
|
|
|
|
|
|
|
|
SETUP_SR_RECOMB 512, x7, x8, x9
|
|
|
|
|
|
|
|
cmp w19, #512
|
|
|
|
b.eq 0f
|
|
|
|
|
|
|
|
mov x5, 4
|
|
|
|
5125:
|
|
|
|
SR_COMBINE_FULL 512
|
|
|
|
add x1, x1, 8*32
|
|
|
|
subs w5, w5, 1
|
|
|
|
b.gt 5125b
|
|
|
|
|
|
|
|
cmp w20, #512
|
|
|
|
b.gt 1024f
|
|
|
|
|
|
|
|
ret
|
|
|
|
1024:
|
|
|
|
stp x20, x30, [sp, #-16]!
|
|
|
|
mov w20, #256
|
|
|
|
add x1, x1, #96*32
|
|
|
|
bl 32b
|
|
|
|
add x1, x1, #64*32
|
|
|
|
bl 32b
|
|
|
|
ldp x20, x30, [sp], #16
|
|
|
|
mov x5, #192*32
|
|
|
|
sub x1, x1, x5
|
|
|
|
|
|
|
|
SETUP_SR_RECOMB 1024, x7, x8, x9
|
|
|
|
|
|
|
|
cmp w19, #1024
|
|
|
|
b.eq 0f
|
|
|
|
|
|
|
|
mov w5, 8
|
|
|
|
10245:
|
|
|
|
SR_COMBINE_FULL 1024
|
|
|
|
add x1, x1, 8*32
|
|
|
|
subs w5, w5, 1
|
|
|
|
b.gt 10245b
|
|
|
|
|
|
|
|
cmp w20, #1024
|
|
|
|
b.gt 2048f
|
|
|
|
|
|
|
|
ret
|
|
|
|
|
|
|
|
SR_TRANSFORM_DEF 2048, 4096
|
|
|
|
SR_TRANSFORM_DEF 4096, 8192
|
|
|
|
SR_TRANSFORM_DEF 8192, 16384
|
|
|
|
SR_TRANSFORM_DEF 16384, 32768
|
|
|
|
SR_TRANSFORM_DEF 32768, 65536
|
|
|
|
SR_TRANSFORM_DEF 65536, 131072
|
|
|
|
SR_TRANSFORM_DEF 131072
|
|
|
|
|
|
|
|
0: // general deinterleave loop
|
|
|
|
SR_COMBINE_DINT
|
|
|
|
add x1, x1, #32*8
|
|
|
|
subs w19, w19, #32*4
|
|
|
|
b.gt 0b
|
|
|
|
|
2022-10-09 21:17:47 +02:00
|
|
|
ldp x19, x20, [sp, #16]
|
|
|
|
ldp d14, d15, [sp, #16*2]
|
|
|
|
ldp d12, d13, [sp, #16*3]
|
|
|
|
ldp d10, d11, [sp, #16*4]
|
|
|
|
ldp d8, d9, [sp, #16*5]
|
|
|
|
ldp x21, x22, [sp], #16*6
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
|
|
|
|
ret
|
|
|
|
|
|
|
|
2: // special case for 64 point deinterleave
|
|
|
|
mov x10, v23.d[0]
|
|
|
|
mov x11, v23.d[1]
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
SR_COMBINE_LITE v0, v1, v8, v9, \
|
|
|
|
v2, v3, v16, v17, \
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
v24, v25, v26, v27, \
|
|
|
|
v28, v29, v30, 0
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
SR_COMBINE_HALF v4, v5, v12, v13, \
|
|
|
|
v6, v7, v20, v21, \
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
v24, v25, v26, v27, \
|
|
|
|
v28, v29, v30, v23, v24, v26, 1
|
|
|
|
|
|
|
|
zip1 v23.2d, v0.2d, v4.2d
|
|
|
|
zip2 v24.2d, v0.2d, v4.2d
|
|
|
|
zip1 v25.2d, v1.2d, v20.2d
|
|
|
|
zip2 v26.2d, v1.2d, v20.2d
|
|
|
|
|
|
|
|
zip1 v27.2d, v8.2d, v12.2d
|
|
|
|
zip2 v28.2d, v8.2d, v12.2d
|
|
|
|
zip1 v29.2d, v9.2d, v21.2d
|
|
|
|
zip2 v30.2d, v9.2d, v21.2d
|
|
|
|
|
|
|
|
mov v20.16b, v5.16b
|
|
|
|
mov v21.16b, v7.16b
|
|
|
|
mov x12, x1
|
|
|
|
add x13, x1, #32* 4
|
|
|
|
add x14, x1, #32* 8
|
|
|
|
add x15, x1, #32*12
|
|
|
|
|
|
|
|
zip1 v4.2d, v2.2d, v6.2d
|
|
|
|
zip2 v5.2d, v2.2d, v6.2d
|
|
|
|
zip1 v6.2d, v3.2d, v20.2d
|
|
|
|
zip2 v7.2d, v3.2d, v20.2d
|
|
|
|
|
|
|
|
zip1 v0.2d, v16.2d, v21.2d
|
|
|
|
zip2 v1.2d, v16.2d, v21.2d
|
|
|
|
zip1 v2.2d, v17.2d, v13.2d
|
|
|
|
zip2 v3.2d, v17.2d, v13.2d
|
|
|
|
|
|
|
|
// stp is faster by a little on A53, but this is faster on M1s (theory)
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q8, q9, [x1, #32*1]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
ldp q12, q13, [x1, #32*5]
|
|
|
|
|
|
|
|
st1 { v23.4s, v24.4s, v25.4s, v26.4s }, [x12], #64 // 32* 0...1
|
|
|
|
st1 { v27.4s, v28.4s, v29.4s, v30.4s }, [x13], #64 // 32* 4...5
|
|
|
|
st1 { v4.4s, v5.4s, v6.4s, v7.4s }, [x14], #64 // 32* 8...9
|
|
|
|
st1 { v0.4s, v1.4s, v2.4s, v3.4s }, [x15], #64 // 32*12..13
|
|
|
|
|
|
|
|
mov v23.d[0], x10
|
|
|
|
mov v23.d[1], x11
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
ldp q6, q7, [x1, #32*3]
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
ldp q16, q17, [x1, #32*7]
|
|
|
|
|
2023-10-17 13:04:41 +02:00
|
|
|
SR_COMBINE v8, v9, v12, v13, v6, v16, v7, v17, \
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
v10, v11, v14, v15, v18, v19, v22, v23, \
|
2023-10-17 13:04:41 +02:00
|
|
|
x7, x8, x9, 0, \
|
lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
|
|
|
v24, v25, v26, v27, v28, v29, v30, v4, v0, v1, v5, v20
|
|
|
|
|
|
|
|
zip1 v0.2d, v8.2d, v6.2d
|
|
|
|
zip2 v1.2d, v8.2d, v6.2d
|
|
|
|
zip1 v2.2d, v9.2d, v7.2d
|
|
|
|
zip2 v3.2d, v9.2d, v7.2d
|
|
|
|
st1 { v0.4s, v1.4s, v2.4s, v3.4s }, [x12]
|
|
|
|
|
|
|
|
zip1 v4.2d, v12.2d, v16.2d
|
|
|
|
zip2 v5.2d, v12.2d, v16.2d
|
|
|
|
zip1 v6.2d, v13.2d, v17.2d
|
|
|
|
zip2 v7.2d, v13.2d, v17.2d
|
|
|
|
st1 { v4.4s, v5.4s, v6.4s, v7.4s }, [x13]
|
|
|
|
|
|
|
|
zip1 v0.2d, v10.2d, v18.2d
|
|
|
|
zip2 v1.2d, v10.2d, v18.2d
|
|
|
|
zip1 v2.2d, v11.2d, v19.2d
|
|
|
|
zip2 v3.2d, v11.2d, v19.2d
|
|
|
|
st1 { v0.4s, v1.4s, v2.4s, v3.4s }, [x14]
|
|
|
|
|
|
|
|
zip1 v4.2d, v14.2d, v22.2d
|
|
|
|
zip2 v5.2d, v14.2d, v22.2d
|
|
|
|
zip1 v6.2d, v15.2d, v23.2d
|
|
|
|
zip2 v7.2d, v15.2d, v23.2d
|
|
|
|
st1 { v4.4s, v5.4s, v6.4s, v7.4s }, [x15]
|
|
|
|
|
2022-10-09 21:17:47 +02:00
|
|
|
ldp x19, x20, [sp, #16]
|
|
|
|
ldp d14, d15, [sp, #16*2]
|
|
|
|
ldp d12, d13, [sp, #16*3]
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ldp d10, d11, [sp, #16*4]
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ldp d8, d9, [sp, #16*5]
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ldp x21, x22, [sp], #16*6
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lavu/tx: implement aarch64 NEON SIMD FFT
The fastest fast Fourier transform in not just the west, but the world,
now for the most popular toy ISA.
On a high level, it follows the design of the AVX2 version closely,
with the exception that the input is slightly less permuted as we don't have
to do lane switching with the input on double 4pt and 8pt.
On a low level, the lack of subadd/addsub instructions REALLY penalizes
any attempt at writing an FFT. That single register matters a lot,
and reloading it simply takes unacceptably long.
In x86 land, vendors would've noticed developers need this.
In ARM land, you get a badly designed complex multiplication instruction
we cannot use, that's not present on 95% of devices. Because only
compilers matter, right?
Future optimization options are very few, perhaps better register
management to use more ld1/st1s.
All timings below are in cycles:
A53:
Length | C | New (lavu) | Old (lavc) | FFTW
------ |-------------|-------------|-------------|-----
4 | 842 | 420 | 1210 | 1460
8 | 1538 | 1020 | 1850 | 2520
16 | 3717 | 1900 | 3700 | 3990
32 | 9156 | 4070 | 8289 | 8860
64 | 21160 | 9931 | 18600 | 19625
128 | 49180 | 23278 | 41922 | 41922
256 | 112073 | 53876 | 93202 | 101092
512 | 252864 | 122884 | 205897 | 207868
1024 | 560512 | 278322 | 458071 | 453053
2048 | 1295402 | 775835 | 1038205 | 1020265
4096 | 3281263 | 2021221 | 2409718 | 2577554
8192 | 8577845 | 4780526 | 5673041 | 6802722
Apple M1
New - Total for len 512 reps 2097152 = 1.459141 s
Old - Total for len 512 reps 2097152 = 2.251344 s
FFTW - Total for len 512 reps 2097152 = 1.868429 s
New - Total for len 1024 reps 4194304 = 6.490080 s
Old - Total for len 1024 reps 4194304 = 9.604949 s
FFTW - Total for len 1024 reps 4194304 = 7.889281 s
New - Total for len 16384 reps 262144 = 10.374001 s
Old - Total for len 16384 reps 262144 = 15.266713 s
FFTW - Total for len 16384 reps 262144 = 12.341745 s
New - Total for len 65536 reps 8192 = 1.769812 s
Old - Total for len 65536 reps 8192 = 4.209413 s
FFTW - Total for len 65536 reps 8192 = 3.012365 s
New - Total for len 131072 reps 4096 = 1.942836 s
Old - Segfaults
FFTW - Total for len 131072 reps 4096 = 3.713713 s
Thanks to wbs for some simplifications, assembler fixes and a review
and to jannau for giving it a look.
2022-02-03 13:27:03 +02:00
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ret
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endfunc
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.endm
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FFT_SPLIT_RADIX_FN float, 0
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FFT_SPLIT_RADIX_FN ns_float, 1
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