mirror of
https://github.com/golang/go
synced 2024-11-13 20:10:32 -07:00
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>
300 lines
8.7 KiB
ArmAsm
300 lines
8.7 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 ·erfrodataL13<> + 0(SB)/8, $0.243673229298474689E+01
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DATA ·erfrodataL13<> + 8(SB)/8, $-.654905018503145600E+00
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DATA ·erfrodataL13<> + 16(SB)/8, $0.404669310217538718E+01
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DATA ·erfrodataL13<> + 24(SB)/8, $-.564189219162765367E+00
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DATA ·erfrodataL13<> + 32(SB)/8, $-.200104300906596851E+01
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DATA ·erfrodataL13<> + 40(SB)/8, $0.5
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DATA ·erfrodataL13<> + 48(SB)/8, $0.144070097650207154E+00
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DATA ·erfrodataL13<> + 56(SB)/8, $-.116697735205906191E+00
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DATA ·erfrodataL13<> + 64(SB)/8, $0.256847684882319665E-01
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DATA ·erfrodataL13<> + 72(SB)/8, $-.510805169106229148E-02
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DATA ·erfrodataL13<> + 80(SB)/8, $0.885258164825590267E-03
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DATA ·erfrodataL13<> + 88(SB)/8, $-.133861989591931411E-03
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DATA ·erfrodataL13<> + 96(SB)/8, $0.178294867340272534E-04
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DATA ·erfrodataL13<> + 104(SB)/8, $-.211436095674019218E-05
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DATA ·erfrodataL13<> + 112(SB)/8, $0.225503753499344434E-06
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DATA ·erfrodataL13<> + 120(SB)/8, $-.218247939190783624E-07
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DATA ·erfrodataL13<> + 128(SB)/8, $0.193179206264594029E-08
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DATA ·erfrodataL13<> + 136(SB)/8, $-.157440643541715319E-09
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DATA ·erfrodataL13<> + 144(SB)/8, $0.118878583237342616E-10
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DATA ·erfrodataL13<> + 152(SB)/8, $0.554289288424588473E-13
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DATA ·erfrodataL13<> + 160(SB)/8, $-.277649758489502214E-14
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DATA ·erfrodataL13<> + 168(SB)/8, $-.839318416990049443E-12
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DATA ·erfrodataL13<> + 176(SB)/8, $-2.25
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DATA ·erfrodataL13<> + 184(SB)/8, $.12837916709551258632
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DATA ·erfrodataL13<> + 192(SB)/8, $1.0
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DATA ·erfrodataL13<> + 200(SB)/8, $0.500000000000004237e+00
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DATA ·erfrodataL13<> + 208(SB)/8, $1.0
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DATA ·erfrodataL13<> + 216(SB)/8, $0.416666664838056960e-01
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DATA ·erfrodataL13<> + 224(SB)/8, $0.166666666630345592e+00
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DATA ·erfrodataL13<> + 232(SB)/8, $0.138926439368309441e-02
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DATA ·erfrodataL13<> + 240(SB)/8, $0.833349307718286047e-02
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DATA ·erfrodataL13<> + 248(SB)/8, $-.693147180559945286e+00
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DATA ·erfrodataL13<> + 256(SB)/8, $-.144269504088896339e+01
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DATA ·erfrodataL13<> + 264(SB)/8, $281475245147134.9375
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DATA ·erfrodataL13<> + 272(SB)/8, $0.358256136398192529E+01
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DATA ·erfrodataL13<> + 280(SB)/8, $-.554084396500738270E+00
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DATA ·erfrodataL13<> + 288(SB)/8, $0.203630123025312046E+02
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DATA ·erfrodataL13<> + 296(SB)/8, $-.735750304705934424E+01
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DATA ·erfrodataL13<> + 304(SB)/8, $0.250491598091071797E+02
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DATA ·erfrodataL13<> + 312(SB)/8, $-.118955882760959931E+02
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DATA ·erfrodataL13<> + 320(SB)/8, $0.942903335085524187E+01
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DATA ·erfrodataL13<> + 328(SB)/8, $-.564189522219085689E+00
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DATA ·erfrodataL13<> + 336(SB)/8, $-.503767199403555540E+01
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DATA ·erfrodataL13<> + 344(SB)/8, $0xbbc79ca10c924223
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DATA ·erfrodataL13<> + 352(SB)/8, $0.004099975562609307E+01
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DATA ·erfrodataL13<> + 360(SB)/8, $-.324434353381296556E+00
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DATA ·erfrodataL13<> + 368(SB)/8, $0.945204812084476250E-01
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DATA ·erfrodataL13<> + 376(SB)/8, $-.221407443830058214E-01
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DATA ·erfrodataL13<> + 384(SB)/8, $0.426072376238804349E-02
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DATA ·erfrodataL13<> + 392(SB)/8, $-.692229229127016977E-03
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DATA ·erfrodataL13<> + 400(SB)/8, $0.971111253652087188E-04
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DATA ·erfrodataL13<> + 408(SB)/8, $-.119752226272050504E-04
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DATA ·erfrodataL13<> + 416(SB)/8, $0.131662993588532278E-05
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DATA ·erfrodataL13<> + 424(SB)/8, $0.115776482315851236E-07
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DATA ·erfrodataL13<> + 432(SB)/8, $-.780118522218151687E-09
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DATA ·erfrodataL13<> + 440(SB)/8, $-.130465975877241088E-06
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DATA ·erfrodataL13<> + 448(SB)/8, $-0.25
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GLOBL ·erfrodataL13<> + 0(SB), RODATA, $456
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// Table of log correction terms
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DATA ·erftab2066<> + 0(SB)/8, $0.442737824274138381e-01
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DATA ·erftab2066<> + 8(SB)/8, $0.263602189790660309e-01
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DATA ·erftab2066<> + 16(SB)/8, $0.122565642281703586e-01
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DATA ·erftab2066<> + 24(SB)/8, $0.143757052860721398e-02
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DATA ·erftab2066<> + 32(SB)/8, $-.651375034121276075e-02
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DATA ·erftab2066<> + 40(SB)/8, $-.119317678849450159e-01
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DATA ·erftab2066<> + 48(SB)/8, $-.150868749549871069e-01
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DATA ·erftab2066<> + 56(SB)/8, $-.161992609578469234e-01
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DATA ·erftab2066<> + 64(SB)/8, $-.154492360403337917e-01
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DATA ·erftab2066<> + 72(SB)/8, $-.129850717389178721e-01
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DATA ·erftab2066<> + 80(SB)/8, $-.892902649276657891e-02
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DATA ·erftab2066<> + 88(SB)/8, $-.338202636596794887e-02
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DATA ·erftab2066<> + 96(SB)/8, $0.357266307045684762e-02
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DATA ·erftab2066<> + 104(SB)/8, $0.118665304327406698e-01
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DATA ·erftab2066<> + 112(SB)/8, $0.214434994118118914e-01
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DATA ·erftab2066<> + 120(SB)/8, $0.322580645161290314e-01
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GLOBL ·erftab2066<> + 0(SB), RODATA, $128
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// Table of +/- 1.0
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DATA ·erftab12067<> + 0(SB)/8, $1.0
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DATA ·erftab12067<> + 8(SB)/8, $-1.0
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GLOBL ·erftab12067<> + 0(SB), RODATA, $16
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// Erf returns the error function of the argument.
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//
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// Special cases are:
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// Erf(+Inf) = 1
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// Erf(-Inf) = -1
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// Erf(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 ·erfAsm(SB), NOSPLIT, $0-16
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FMOVD x+0(FP), F0
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MOVD $·erfrodataL13<>+0(SB), R5
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WORD $0xB3CD0010 //lgdr %r1, %f0
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FMOVD F0, F6
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SRAD $48, R1
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MOVH $16383, R3
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WORD $0xEC2131BF //risbg %r2,%r1,49,128+63,0
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BYTE $0x00
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BYTE $0x55
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MOVW R2, R6
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MOVW R3, R7
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CMPBGT R6, R7, L2
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MOVH $12287, R1
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MOVW R1, R7
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CMPBLE R6, R7 ,L12
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MOVH $16367, R1
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MOVW R1, R7
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CMPBGT R6, R7, L5
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FMOVD 448(R5), F4
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FMADD F0, F0, F4
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FMOVD 440(R5), F3
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WFMDB V4, V4, V2
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FMOVD 432(R5), F0
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FMOVD 424(R5), F1
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WFMADB V2, V0, V3, V0
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FMOVD 416(R5), F3
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WFMADB V2, V1, V3, V1
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FMOVD 408(R5), F5
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FMOVD 400(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V1, V3, V1
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FMOVD 392(R5), F5
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FMOVD 384(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V1, V3, V1
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FMOVD 376(R5), F5
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FMOVD 368(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V1, V3, V1
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FMOVD 360(R5), F5
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FMOVD 352(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V1, V3, V2
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WFMADB V4, V0, V2, V0
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WFMADB V6, V0, V6, V0
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L1:
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FMOVD F0, ret+8(FP)
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RET
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L2:
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MOVH R1, R1
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MOVH $16407, R3
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SRW $31, R1, R1
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MOVW R2, R6
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MOVW R3, R7
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CMPBLE R6, R7, L6
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MOVW R1, R1
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SLD $3, R1, R1
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MOVD $·erftab12067<>+0(SB), R3
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WORD $0x68013000 //ld %f0,0(%r1,%r3)
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MOVH $32751, R1
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MOVW R1, R7
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CMPBGT R6, R7, L7
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FMOVD 344(R5), F2
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FMADD F2, F0, F0
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L7:
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WFCEDBS V6, V6, V2
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BEQ L1
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FMOVD F6, F0
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FMOVD F0, ret+8(FP)
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RET
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L6:
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MOVW R1, R1
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SLD $3, R1, R1
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MOVD $·erftab12067<>+0(SB), R4
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WFMDB V0, V0, V1
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MOVH $0x0, R3
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WORD $0x68014000 //ld %f0,0(%r1,%r4)
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MOVH $16399, R1
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MOVW R2, R6
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MOVW R1, R7
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CMPBGT R6, R7, L8
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FMOVD 336(R5), F3
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FMOVD 328(R5), F2
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FMOVD F1, F4
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WFMADB V1, V2, V3, V2
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WORD $0xED405140 //adb %f4,.L30-.L13(%r5)
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BYTE $0x00
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BYTE $0x1A
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FMOVD 312(R5), F3
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WFMADB V1, V2, V3, V2
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FMOVD 304(R5), F3
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WFMADB V1, V4, V3, V4
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FMOVD 296(R5), F3
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WFMADB V1, V2, V3, V2
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FMOVD 288(R5), F3
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WFMADB V1, V4, V3, V4
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FMOVD 280(R5), F3
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WFMADB V1, V2, V3, V2
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FMOVD 272(R5), F3
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WFMADB V1, V4, V3, V4
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L9:
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FMOVD 264(R5), F3
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FMUL F4, F6
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FMOVD 256(R5), F4
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WFMADB V1, V4, V3, V4
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FDIV F6, F2
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WORD $0xB3CD0014 //lgdr %r1, %f4
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FSUB F3, F4
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FMOVD 248(R5), F6
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WFMSDB V4, V6, V1, V4
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FMOVD 240(R5), F1
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FMOVD 232(R5), F6
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WFMADB V4, V6, V1, V6
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FMOVD 224(R5), F1
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FMOVD 216(R5), F3
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WFMADB V4, V3, V1, V3
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WFMDB V4, V4, V1
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FMOVD 208(R5), F5
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WFMADB V6, V1, V3, V6
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FMOVD 200(R5), F3
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MOVH R1,R1
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WFMADB V4, V3, V5, V3
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WORD $0xEC2139BC //risbg %r2,%r1,57,128+60,3
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BYTE $0x03
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BYTE $0x55
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WFMADB V1, V6, V3, V6
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WORD $0xEC31000F //risbgn %r3,%r1,64-64+0,64-64+0+16-1,64-0-16
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BYTE $0x30
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BYTE $0x59
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MOVD $·erftab2066<>+0(SB), R1
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FMOVD 192(R5), F1
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WORD $0xB3C10033 //ldgr %f3,%r3
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WORD $0xED221000 //madb %f2,%f2,0(%r2,%r1)
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BYTE $0x20
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BYTE $0x1E
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WFMADB V4, V6, V1, V4
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FMUL F3, F2
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FMADD F4, F2, F0
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FMOVD F0, ret+8(FP)
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RET
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L12:
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FMOVD 184(R5), F0
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WFMADB V6, V0, V6, V0
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FMOVD F0, ret+8(FP)
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RET
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L5:
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FMOVD 176(R5), F1
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FMADD F0, F0, F1
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FMOVD 168(R5), F3
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WFMDB V1, V1, V2
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FMOVD 160(R5), F0
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FMOVD 152(R5), F4
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WFMADB V2, V0, V3, V0
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FMOVD 144(R5), F3
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WFMADB V2, V4, V3, V4
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FMOVD 136(R5), F5
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FMOVD 128(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V4, V3, V4
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FMOVD 120(R5), F5
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FMOVD 112(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V4, V3, V4
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FMOVD 104(R5), F5
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FMOVD 96(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V4, V3, V4
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FMOVD 88(R5), F5
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FMOVD 80(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V4, V3, V4
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FMOVD 72(R5), F5
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FMOVD 64(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V4, V3, V4
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FMOVD 56(R5), F5
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FMOVD 48(R5), F3
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WFMADB V2, V0, V5, V0
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WFMADB V2, V4, V3, V2
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FMOVD 40(R5), F4
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WFMADB V1, V0, V2, V0
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FMUL F6, F0
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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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L8:
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FMOVD 32(R5), F3
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FMOVD 24(R5), F2
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FMOVD F1, F4
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WFMADB V1, V2, V3, V2
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WORD $0xED405010 //adb %f4,.L68-.L13(%r5)
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BYTE $0x00
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BYTE $0x1A
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FMOVD 8(R5), F3
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WFMADB V1, V2, V3, V2
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FMOVD ·erfrodataL13<>+0(SB), F3
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WFMADB V1, V4, V3, V4
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BR L9
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