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https://github.com/golang/go
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88672de7af
As necessary, math functions were structured to use stubs, so that they can
be accelerated with assembly on any platform.
Technique used was minimax polynomial approximation using tables of
polynomial coefficients, with argument range reduction.
Benchmark New Old Speedup
BenchmarkAcos 12.2 47.5 3.89
BenchmarkAcosh 18.5 56.2 3.04
BenchmarkAsin 13.1 40.6 3.10
BenchmarkAsinh 19.4 62.8 3.24
BenchmarkAtan 10.1 23 2.28
BenchmarkAtanh 19.1 53.2 2.79
BenchmarkAtan2 16.5 33.9 2.05
BenchmarkCbrt 14.8 58 3.92
BenchmarkErf 10.8 20.1 1.86
BenchmarkErfc 11.2 23.5 2.10
BenchmarkExp 8.77 53.8 6.13
BenchmarkExpm1 10.1 38.3 3.79
BenchmarkLog 13.1 40.1 3.06
BenchmarkLog1p 12.7 38.3 3.02
BenchmarkPowInt 31.7 40.5 1.28
BenchmarkPowFrac 33.1 141 4.26
BenchmarkTan 11.5 30 2.61
Accuracy was tested against a high precision
reference function to determine maximum error.
Note: ulperr is error in "units in the last place"
max
ulperr
Acos 1.15
Acosh 1.07
Asin 2.22
Asinh 1.72
Atan 1.41
Atanh 3.00
Atan2 1.45
Cbrt 1.18
Erf 1.29
Erfc 4.82
Exp 1.00
Expm1 2.26
Log 0.94
Log1p 2.39
Tan 3.14
Pow will have 99.99% correctly rounded results with reasonable inputs
producing numeric (non Inf or NaN) results
Change-Id: I850e8cf7b70426e8b54ec49d74acd4cddc8c6cb2
Reviewed-on: https://go-review.googlesource.com/38585
Reviewed-by: Michael Munday <munday@ca.ibm.com>
Run-TryBot: Michael Munday <munday@ca.ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
224 lines
6.1 KiB
ArmAsm
224 lines
6.1 KiB
ArmAsm
// Copyright 2017 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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#include "textflag.h"
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// Minimax polynomial coefficients and other constants
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DATA ·asinhrodataL18<> + 0(SB)/8, $0.749999999977387502E-01
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DATA ·asinhrodataL18<> + 8(SB)/8, $-.166666666666657082E+00
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DATA ·asinhrodataL18<> + 16(SB)/8, $0.303819368237360639E-01
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DATA ·asinhrodataL18<> + 24(SB)/8, $-.446428569571752982E-01
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DATA ·asinhrodataL18<> + 32(SB)/8, $0.173500047922695924E-01
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DATA ·asinhrodataL18<> + 40(SB)/8, $-.223719767210027185E-01
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DATA ·asinhrodataL18<> + 48(SB)/8, $0.113655037946822130E-01
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DATA ·asinhrodataL18<> + 56(SB)/8, $0.579747490622448943E-02
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DATA ·asinhrodataL18<> + 64(SB)/8, $-.139372433914359122E-01
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DATA ·asinhrodataL18<> + 72(SB)/8, $-.218674325255800840E-02
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DATA ·asinhrodataL18<> + 80(SB)/8, $-.891074277756961157E-02
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DATA ·asinhrodataL18<> + 88(SB)/8, $.41375273347623353626
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DATA ·asinhrodataL18<> + 96(SB)/8, $.51487302528619766235E+04
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DATA ·asinhrodataL18<> + 104(SB)/8, $-1.67526912689208984375
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DATA ·asinhrodataL18<> + 112(SB)/8, $0.181818181818181826E+00
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DATA ·asinhrodataL18<> + 120(SB)/8, $-.165289256198351540E-01
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DATA ·asinhrodataL18<> + 128(SB)/8, $0.200350613573012186E-02
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DATA ·asinhrodataL18<> + 136(SB)/8, $-.273205381970859341E-03
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DATA ·asinhrodataL18<> + 144(SB)/8, $0.397389654305194527E-04
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DATA ·asinhrodataL18<> + 152(SB)/8, $0.938370938292558173E-06
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DATA ·asinhrodataL18<> + 160(SB)/8, $0.212881813645679599E-07
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DATA ·asinhrodataL18<> + 168(SB)/8, $-.602107458843052029E-05
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DATA ·asinhrodataL18<> + 176(SB)/8, $-.148682720127920854E-06
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DATA ·asinhrodataL18<> + 184(SB)/8, $-5.5
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DATA ·asinhrodataL18<> + 192(SB)/8, $1.0
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DATA ·asinhrodataL18<> + 200(SB)/8, $1.0E-20
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GLOBL ·asinhrodataL18<> + 0(SB), RODATA, $208
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// Table of log correction terms
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DATA ·asinhtab2080<> + 0(SB)/8, $0.585235384085551248E-01
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DATA ·asinhtab2080<> + 8(SB)/8, $0.412206153771168640E-01
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DATA ·asinhtab2080<> + 16(SB)/8, $0.273839003221648339E-01
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DATA ·asinhtab2080<> + 24(SB)/8, $0.166383778368856480E-01
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DATA ·asinhtab2080<> + 32(SB)/8, $0.866678223433169637E-02
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DATA ·asinhtab2080<> + 40(SB)/8, $0.319831684989627514E-02
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DATA ·asinhtab2080<> + 48(SB)/8, $0.0
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DATA ·asinhtab2080<> + 56(SB)/8, $-.113006378583725549E-02
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DATA ·asinhtab2080<> + 64(SB)/8, $-.367979419636602491E-03
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DATA ·asinhtab2080<> + 72(SB)/8, $0.213172484510484979E-02
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DATA ·asinhtab2080<> + 80(SB)/8, $0.623271047682013536E-02
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DATA ·asinhtab2080<> + 88(SB)/8, $0.118140812789696885E-01
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DATA ·asinhtab2080<> + 96(SB)/8, $0.187681358930914206E-01
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DATA ·asinhtab2080<> + 104(SB)/8, $0.269985148668178992E-01
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DATA ·asinhtab2080<> + 112(SB)/8, $0.364186619761331328E-01
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DATA ·asinhtab2080<> + 120(SB)/8, $0.469505379381388441E-01
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GLOBL ·asinhtab2080<> + 0(SB), RODATA, $128
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// Asinh returns the inverse hyperbolic sine of the argument.
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//
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// Special cases are:
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// Asinh(±0) = ±0
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// Asinh(±Inf) = ±Inf
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// Asinh(NaN) = NaN
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// The algorithm used is minimax polynomial approximation
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// with coefficients determined with a Remez exchange algorithm.
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TEXT ·asinhAsm(SB), NOSPLIT, $0-16
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FMOVD x+0(FP), F0
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MOVD $·asinhrodataL18<>+0(SB), R9
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WORD $0xB3CD00C0 //lgdr %r12, %f0
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WORD $0xC0293FDF //iilf %r2,1071644671
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BYTE $0xFF
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BYTE $0xFF
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SRAD $32, R12
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WORD $0xB917001C //llgtr %r1,%r12
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MOVW R1, R6
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MOVW R2, R7
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CMPBLE R6, R7, L2
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WORD $0xC0295FEF //iilf %r2,1609564159
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BYTE $0xFF
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BYTE $0xFF
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MOVW R2, R7
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CMPBLE R6, R7, L14
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L3:
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WORD $0xC0297FEF //iilf %r2,2146435071
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BYTE $0xFF
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BYTE $0xFF
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CMPW R1, R2
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BGT L1
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WORD $0xB3120000 //ltdbr %f0,%f0
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FMOVD F0, F10
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BLTU L15
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L9:
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FMOVD $0, F0
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WFADB V0, V10, V0
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WORD $0xC0398006 //iilf %r3,2147909631
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BYTE $0x7F
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BYTE $0xFF
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WORD $0xB3CD0050 //lgdr %r5, %f0
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SRAD $32, R5
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MOVH $0x0, R2
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SUBW R5, R3
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FMOVD $0, F8
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WORD $0xEC4320AF //risbg %r4,%r3,32,128+47,0
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BYTE $0x00
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BYTE $0x55
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BYTE $0x18 //lr %r1,%r4
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BYTE $0x14
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WORD $0xEC24001F //risbgn %r2,%r4,64-64+0,64-64+0+32-1,64-0-32
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BYTE $0x20
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BYTE $0x59
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SUBW $0x100000, R1
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SRAW $8, R1, R1
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ORW $0x45000000, R1
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BR L6
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L2:
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MOVD $0x30000000, R2
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CMPW R1, R2
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BGT L16
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FMOVD 200(R9), F2
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FMADD F2, F0, F0
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L1:
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FMOVD F0, ret+8(FP)
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RET
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L14:
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WORD $0xB3120000 //ltdbr %f0,%f0
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BLTU L17
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FMOVD F0, F10
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L4:
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FMOVD 192(R9), F2
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WFMADB V0, V0, V2, V0
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WORD $0xB3120000 //ltdbr %f0,%f0
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FSQRT F0, F8
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L5:
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WFADB V8, V10, V0
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WORD $0xC0398006 //iilf %r3,2147909631
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BYTE $0x7F
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BYTE $0xFF
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WORD $0xB3CD0050 //lgdr %r5, %f0
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SRAD $32, R5
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MOVH $0x0, R2
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SUBW R5, R3
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WORD $0xEC4320AF //risbg %r4,%r3,32,128+47,0
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BYTE $0x00
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BYTE $0x55
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SRAW $8, R4, R1
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WORD $0xEC24001F //risbgn %r2,%r4,64-64+0,64-64+0+32-1,64-0-32
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BYTE $0x20
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BYTE $0x59
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ORW $0x45000000, R1
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L6:
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WORD $0xB3C10022 //ldgr %f2,%r2
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FMOVD 184(R9), F0
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WFMADB V8, V2, V0, V8
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FMOVD 176(R9), F4
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WFMADB V10, V2, V8, V2
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FMOVD 168(R9), F0
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FMOVD 160(R9), F6
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FMOVD 152(R9), F1
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WFMADB V2, V6, V4, V6
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WFMADB V2, V1, V0, V1
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WFMDB V2, V2, V4
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FMOVD 144(R9), F0
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WFMADB V6, V4, V1, V6
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FMOVD 136(R9), F1
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WORD $0xEC3339BC //risbg %r3,%r3,57,128+60,64-13
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BYTE $0x33
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BYTE $0x55
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WFMADB V2, V0, V1, V0
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FMOVD 128(R9), F1
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WFMADB V4, V6, V0, V6
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FMOVD 120(R9), F0
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WFMADB V2, V1, V0, V1
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VLVGF $0, R1, V0
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WFMADB V4, V6, V1, V4
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LDEBR F0, F0
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FMOVD 112(R9), F6
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WFMADB V2, V4, V6, V4
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MOVD $·asinhtab2080<>+0(SB), R1
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FMOVD 104(R9), F1
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WORD $0x68331000 //ld %f3,0(%r3,%r1)
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FMOVD 96(R9), F6
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WFMADB V2, V4, V3, V2
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WFMADB V0, V1, V6, V0
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FMOVD 88(R9), F4
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WFMADB V0, V4, V2, V0
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MOVD R12, R6
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CMPBGT R6, $0, L1
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WORD $0xB3130000 //lcdbr %f0,%f0
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FMOVD F0, ret+8(FP)
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RET
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L16:
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WFMDB V0, V0, V1
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FMOVD 80(R9), F6
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WFMDB V1, V1, V4
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FMOVD 72(R9), F2
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WFMADB V4, V2, V6, V2
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FMOVD 64(R9), F3
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FMOVD 56(R9), F6
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WFMADB V4, V2, V3, V2
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FMOVD 48(R9), F3
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WFMADB V4, V6, V3, V6
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FMOVD 40(R9), F5
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FMOVD 32(R9), F3
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WFMADB V4, V2, V5, V2
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WFMADB V4, V6, V3, V6
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FMOVD 24(R9), F5
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FMOVD 16(R9), F3
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WFMADB V4, V2, V5, V2
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WFMADB V4, V6, V3, V6
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FMOVD 8(R9), F5
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FMOVD 0(R9), F3
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WFMADB V4, V2, V5, V2
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WFMADB V4, V6, V3, V4
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WFMDB V0, V1, V6
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WFMADB V1, V4, V2, V4
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FMADD F4, F6, F0
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FMOVD F0, ret+8(FP)
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RET
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L17:
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WORD $0xB31300A0 //lcdbr %f10,%f0
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BR L4
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L15:
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WORD $0xB31300A0 //lcdbr %f10,%f0
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BR L9
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