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go/src/math/asinh_s390x.s

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math: use SIMD to accelerate additional scalar math functions on s390x 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>
2017-03-24 14:43:02 -06:00
// Copyright 2017 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
#include "textflag.h"
// Minimax polynomial coefficients and other constants
DATA ·asinhrodataL18<> + 0(SB)/8, $0.749999999977387502E-01
DATA ·asinhrodataL18<> + 8(SB)/8, $-.166666666666657082E+00
DATA ·asinhrodataL18<> + 16(SB)/8, $0.303819368237360639E-01
DATA ·asinhrodataL18<> + 24(SB)/8, $-.446428569571752982E-01
DATA ·asinhrodataL18<> + 32(SB)/8, $0.173500047922695924E-01
DATA ·asinhrodataL18<> + 40(SB)/8, $-.223719767210027185E-01
DATA ·asinhrodataL18<> + 48(SB)/8, $0.113655037946822130E-01
DATA ·asinhrodataL18<> + 56(SB)/8, $0.579747490622448943E-02
DATA ·asinhrodataL18<> + 64(SB)/8, $-.139372433914359122E-01
DATA ·asinhrodataL18<> + 72(SB)/8, $-.218674325255800840E-02
DATA ·asinhrodataL18<> + 80(SB)/8, $-.891074277756961157E-02
DATA ·asinhrodataL18<> + 88(SB)/8, $.41375273347623353626
DATA ·asinhrodataL18<> + 96(SB)/8, $.51487302528619766235E+04
DATA ·asinhrodataL18<> + 104(SB)/8, $-1.67526912689208984375
DATA ·asinhrodataL18<> + 112(SB)/8, $0.181818181818181826E+00
DATA ·asinhrodataL18<> + 120(SB)/8, $-.165289256198351540E-01
DATA ·asinhrodataL18<> + 128(SB)/8, $0.200350613573012186E-02
DATA ·asinhrodataL18<> + 136(SB)/8, $-.273205381970859341E-03
DATA ·asinhrodataL18<> + 144(SB)/8, $0.397389654305194527E-04
DATA ·asinhrodataL18<> + 152(SB)/8, $0.938370938292558173E-06
DATA ·asinhrodataL18<> + 160(SB)/8, $0.212881813645679599E-07
DATA ·asinhrodataL18<> + 168(SB)/8, $-.602107458843052029E-05
DATA ·asinhrodataL18<> + 176(SB)/8, $-.148682720127920854E-06
DATA ·asinhrodataL18<> + 184(SB)/8, $-5.5
DATA ·asinhrodataL18<> + 192(SB)/8, $1.0
DATA ·asinhrodataL18<> + 200(SB)/8, $1.0E-20
GLOBL ·asinhrodataL18<> + 0(SB), RODATA, $208
// Table of log correction terms
DATA ·asinhtab2080<> + 0(SB)/8, $0.585235384085551248E-01
DATA ·asinhtab2080<> + 8(SB)/8, $0.412206153771168640E-01
DATA ·asinhtab2080<> + 16(SB)/8, $0.273839003221648339E-01
DATA ·asinhtab2080<> + 24(SB)/8, $0.166383778368856480E-01
DATA ·asinhtab2080<> + 32(SB)/8, $0.866678223433169637E-02
DATA ·asinhtab2080<> + 40(SB)/8, $0.319831684989627514E-02
DATA ·asinhtab2080<> + 48(SB)/8, $0.0
DATA ·asinhtab2080<> + 56(SB)/8, $-.113006378583725549E-02
DATA ·asinhtab2080<> + 64(SB)/8, $-.367979419636602491E-03
DATA ·asinhtab2080<> + 72(SB)/8, $0.213172484510484979E-02
DATA ·asinhtab2080<> + 80(SB)/8, $0.623271047682013536E-02
DATA ·asinhtab2080<> + 88(SB)/8, $0.118140812789696885E-01
DATA ·asinhtab2080<> + 96(SB)/8, $0.187681358930914206E-01
DATA ·asinhtab2080<> + 104(SB)/8, $0.269985148668178992E-01
DATA ·asinhtab2080<> + 112(SB)/8, $0.364186619761331328E-01
DATA ·asinhtab2080<> + 120(SB)/8, $0.469505379381388441E-01
GLOBL ·asinhtab2080<> + 0(SB), RODATA, $128
// Asinh returns the inverse hyperbolic sine of the argument.
//
// Special cases are:
// Asinh(±0) = ±0
// Asinh(±Inf) = ±Inf
// Asinh(NaN) = NaN
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·asinhAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·asinhrodataL18<>+0(SB), R9
WORD $0xB3CD00C0 //lgdr %r12, %f0
WORD $0xC0293FDF //iilf %r2,1071644671
BYTE $0xFF
BYTE $0xFF
SRAD $32, R12
WORD $0xB917001C //llgtr %r1,%r12
MOVW R1, R6
MOVW R2, R7
CMPBLE R6, R7, L2
WORD $0xC0295FEF //iilf %r2,1609564159
BYTE $0xFF
BYTE $0xFF
MOVW R2, R7
CMPBLE R6, R7, L14
L3:
WORD $0xC0297FEF //iilf %r2,2146435071
BYTE $0xFF
BYTE $0xFF
CMPW R1, R2
BGT L1
WORD $0xB3120000 //ltdbr %f0,%f0
FMOVD F0, F10
BLTU L15
L9:
FMOVD $0, F0
WFADB V0, V10, V0
WORD $0xC0398006 //iilf %r3,2147909631
BYTE $0x7F
BYTE $0xFF
WORD $0xB3CD0050 //lgdr %r5, %f0
SRAD $32, R5
MOVH $0x0, R2
SUBW R5, R3
FMOVD $0, F8
WORD $0xEC4320AF //risbg %r4,%r3,32,128+47,0
BYTE $0x00
BYTE $0x55
BYTE $0x18 //lr %r1,%r4
BYTE $0x14
WORD $0xEC24001F //risbgn %r2,%r4,64-64+0,64-64+0+32-1,64-0-32
BYTE $0x20
BYTE $0x59
SUBW $0x100000, R1
SRAW $8, R1, R1
ORW $0x45000000, R1
BR L6
L2:
MOVD $0x30000000, R2
CMPW R1, R2
BGT L16
FMOVD 200(R9), F2
FMADD F2, F0, F0
L1:
FMOVD F0, ret+8(FP)
RET
L14:
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L17
FMOVD F0, F10
L4:
FMOVD 192(R9), F2
WFMADB V0, V0, V2, V0
WORD $0xB3120000 //ltdbr %f0,%f0
FSQRT F0, F8
L5:
WFADB V8, V10, V0
WORD $0xC0398006 //iilf %r3,2147909631
BYTE $0x7F
BYTE $0xFF
WORD $0xB3CD0050 //lgdr %r5, %f0
SRAD $32, R5
MOVH $0x0, R2
SUBW R5, R3
WORD $0xEC4320AF //risbg %r4,%r3,32,128+47,0
BYTE $0x00
BYTE $0x55
SRAW $8, R4, R1
WORD $0xEC24001F //risbgn %r2,%r4,64-64+0,64-64+0+32-1,64-0-32
BYTE $0x20
BYTE $0x59
ORW $0x45000000, R1
L6:
WORD $0xB3C10022 //ldgr %f2,%r2
FMOVD 184(R9), F0
WFMADB V8, V2, V0, V8
FMOVD 176(R9), F4
WFMADB V10, V2, V8, V2
FMOVD 168(R9), F0
FMOVD 160(R9), F6
FMOVD 152(R9), F1
WFMADB V2, V6, V4, V6
WFMADB V2, V1, V0, V1
WFMDB V2, V2, V4
FMOVD 144(R9), F0
WFMADB V6, V4, V1, V6
FMOVD 136(R9), F1
WORD $0xEC3339BC //risbg %r3,%r3,57,128+60,64-13
BYTE $0x33
BYTE $0x55
WFMADB V2, V0, V1, V0
FMOVD 128(R9), F1
WFMADB V4, V6, V0, V6
FMOVD 120(R9), F0
WFMADB V2, V1, V0, V1
VLVGF $0, R1, V0
WFMADB V4, V6, V1, V4
LDEBR F0, F0
FMOVD 112(R9), F6
WFMADB V2, V4, V6, V4
MOVD $·asinhtab2080<>+0(SB), R1
FMOVD 104(R9), F1
WORD $0x68331000 //ld %f3,0(%r3,%r1)
FMOVD 96(R9), F6
WFMADB V2, V4, V3, V2
WFMADB V0, V1, V6, V0
FMOVD 88(R9), F4
WFMADB V0, V4, V2, V0
MOVD R12, R6
CMPBGT R6, $0, L1
WORD $0xB3130000 //lcdbr %f0,%f0
FMOVD F0, ret+8(FP)
RET
L16:
WFMDB V0, V0, V1
FMOVD 80(R9), F6
WFMDB V1, V1, V4
FMOVD 72(R9), F2
WFMADB V4, V2, V6, V2
FMOVD 64(R9), F3
FMOVD 56(R9), F6
WFMADB V4, V2, V3, V2
FMOVD 48(R9), F3
WFMADB V4, V6, V3, V6
FMOVD 40(R9), F5
FMOVD 32(R9), F3
WFMADB V4, V2, V5, V2
WFMADB V4, V6, V3, V6
FMOVD 24(R9), F5
FMOVD 16(R9), F3
WFMADB V4, V2, V5, V2
WFMADB V4, V6, V3, V6
FMOVD 8(R9), F5
FMOVD 0(R9), F3
WFMADB V4, V2, V5, V2
WFMADB V4, V6, V3, V4
WFMDB V0, V1, V6
WFMADB V1, V4, V2, V4
FMADD F4, F6, F0
FMOVD F0, ret+8(FP)
RET
L17:
WORD $0xB31300A0 //lcdbr %f10,%f0
BR L4
L15:
WORD $0xB31300A0 //lcdbr %f10,%f0
BR L9