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math: use SIMD to accelerate additional scalar math functions on s390x

Browse source 
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>
This commit is contained in:
Bill O'Farrell 2017-03-24 16:43:02 -04:00 committed by Michael Munday
parent 8c49c06b48
commit 88672de7af
34 changed files with 4720 additions and 65 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

144
src/math/acos_s390x.s Normal file
View file

@ -0,0 +1,144 @@
// 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 ·acosrodataL13<> + 0(SB)/8, $0.314159265358979323E+01 //pi
DATA ·acosrodataL13<> + 8(SB)/8, $-0.0
DATA ·acosrodataL13<> + 16(SB)/8, $0x7ff8000000000000 //Nan
DATA ·acosrodataL13<> + 24(SB)/8, $-1.0
DATA ·acosrodataL13<> + 32(SB)/8, $1.0
DATA ·acosrodataL13<> + 40(SB)/8, $0.166666666666651626E+00
DATA ·acosrodataL13<> + 48(SB)/8, $0.750000000042621169E-01
DATA ·acosrodataL13<> + 56(SB)/8, $0.446428567178116477E-01
DATA ·acosrodataL13<> + 64(SB)/8, $0.303819660378071894E-01
DATA ·acosrodataL13<> + 72(SB)/8, $0.223715011892010405E-01
DATA ·acosrodataL13<> + 80(SB)/8, $0.173659424522364952E-01
DATA ·acosrodataL13<> + 88(SB)/8, $0.137810186504372266E-01
DATA ·acosrodataL13<> + 96(SB)/8, $0.134066870961173521E-01
DATA ·acosrodataL13<> + 104(SB)/8, $-.412335502831898721E-02
DATA ·acosrodataL13<> + 112(SB)/8, $0.867383739532082719E-01
DATA ·acosrodataL13<> + 120(SB)/8, $-.328765950607171649E+00
DATA ·acosrodataL13<> + 128(SB)/8, $0.110401073869414626E+01
DATA ·acosrodataL13<> + 136(SB)/8, $-.270694366992537307E+01
DATA ·acosrodataL13<> + 144(SB)/8, $0.500196500770928669E+01
DATA ·acosrodataL13<> + 152(SB)/8, $-.665866959108585165E+01
DATA ·acosrodataL13<> + 160(SB)/8, $-.344895269334086578E+01
DATA ·acosrodataL13<> + 168(SB)/8, $0.927437952918301659E+00
DATA ·acosrodataL13<> + 176(SB)/8, $0.610487478874645653E+01
DATA ·acosrodataL13<> + 184(SB)/8, $0.157079632679489656e+01
DATA ·acosrodataL13<> + 192(SB)/8, $0.0
GLOBL ·acosrodataL13<> + 0(SB), RODATA, $200
// Acos returns the arccosine, in radians, of the argument.
//
// Special case is:
// Acos(x) = NaN if x < -1 or x > 1
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·acosAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·acosrodataL13<>+0(SB), R9
WORD $0xB3CD00C0 //lgdr %r12, %f0
FMOVD F0, F10
SRAD $32, R12
WORD $0xC0293FE6 //iilf %r2,1072079005
BYTE $0xA0
BYTE $0x9D
WORD $0xB917001C //llgtr %r1,%r12
CMPW R1,R2
BGT L2
FMOVD 192(R9), F8
FMADD F0, F0, F8
FMOVD 184(R9), F1
L3:
WFMDB V8, V8, V2
FMOVD 176(R9), F6
FMOVD 168(R9), F0
FMOVD 160(R9), F4
WFMADB V2, V0, V6, V0
FMOVD 152(R9), F6
WFMADB V2, V4, V6, V4
FMOVD 144(R9), F6
WFMADB V2, V0, V6, V0
FMOVD 136(R9), F6
WFMADB V2, V4, V6, V4
FMOVD 128(R9), F6
WFMADB V2, V0, V6, V0
FMOVD 120(R9), F6
WFMADB V2, V4, V6, V4
FMOVD 112(R9), F6
WFMADB V2, V0, V6, V0
FMOVD 104(R9), F6
WFMADB V2, V4, V6, V4
FMOVD 96(R9), F6
WFMADB V2, V0, V6, V0
FMOVD 88(R9), F6
WFMADB V2, V4, V6, V4
FMOVD 80(R9), F6
WFMADB V2, V0, V6, V0
FMOVD 72(R9), F6
WFMADB V2, V4, V6, V4
FMOVD 64(R9), F6
WFMADB V2, V0, V6, V0
FMOVD 56(R9), F6
WFMADB V2, V4, V6, V4
FMOVD 48(R9), F6
WFMADB V2, V0, V6, V0
FMOVD 40(R9), F6
WFMADB V2, V4, V6, V2
FMOVD 192(R9), F4
WFMADB V8, V0, V2, V0
WFMADB V10, V8, V4, V8
FMADD F0, F8, F10
WFSDB V10, V1, V10
L1:
FMOVD F10, ret+8(FP)
RET
L2:
WORD $0xC0293FEF //iilf %r2,1072693247
BYTE $0xFF
BYTE $0xFF
CMPW R1, R2
BLE L12
L4:
WORD $0xED009020 //cdb %f0,.L34-.L13(%r9)
BYTE $0x00
BYTE $0x19
BEQ L8
WORD $0xED009018 //cdb %f0,.L35-.L13(%r9)
BYTE $0x00
BYTE $0x19
BEQ L9
WFCEDBS V10, V10, V0
BVS L1
FMOVD 16(R9), F10
BR L1
L12:
FMOVD 24(R9), F0
FMADD F10, F10, F0
WORD $0xB3130080 //lcdbr %f8,%f0
WORD $0xED009008 //cdb %f0,.L37-.L13(%r9)
BYTE $0x00
BYTE $0x19
FSQRT F8, F10
L5:
MOVW R12, R4
CMPBLE R4, $0, L7
WORD $0xB31300AA //lcdbr %f10,%f10
FMOVD $0, F1
BR L3
L9:
FMOVD 0(R9), F10
BR L1
L8:
FMOVD $0, F0
FMOVD F0, ret+8(FP)
RET
L7:
FMOVD 0(R9), F1
BR L3

4
src/math/acosh.go
View file

@ -39,7 +39,9 @@ package math
// Acosh(+Inf) = +Inf
// Acosh(x) = NaN if x < 1
// Acosh(NaN) = NaN
func Acosh(x float64) float64 {
func Acosh(x float64) float64
func acosh(x float64) float64 {
const (
Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
Large = 1 << 28 // 2**28

172
src/math/acosh_s390x.s Normal file
View file

@ -0,0 +1,172 @@
// 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 ·acoshrodataL11<> + 0(SB)/8, $-1.0
DATA ·acoshrodataL11<> + 8(SB)/8, $.41375273347623353626
DATA ·acoshrodataL11<> + 16(SB)/8, $.51487302528619766235E+04
DATA ·acoshrodataL11<> + 24(SB)/8, $-1.67526912689208984375
DATA ·acoshrodataL11<> + 32(SB)/8, $0.181818181818181826E+00
DATA ·acoshrodataL11<> + 40(SB)/8, $-.165289256198351540E-01
DATA ·acoshrodataL11<> + 48(SB)/8, $0.200350613573012186E-02
DATA ·acoshrodataL11<> + 56(SB)/8, $-.273205381970859341E-03
DATA ·acoshrodataL11<> + 64(SB)/8, $0.397389654305194527E-04
DATA ·acoshrodataL11<> + 72(SB)/8, $0.938370938292558173E-06
DATA ·acoshrodataL11<> + 80(SB)/8, $-.602107458843052029E-05
DATA ·acoshrodataL11<> + 88(SB)/8, $0.212881813645679599E-07
DATA ·acoshrodataL11<> + 96(SB)/8, $-.148682720127920854E-06
DATA ·acoshrodataL11<> + 104(SB)/8, $-5.5
DATA ·acoshrodataL11<> + 112(SB)/8, $0x7ff8000000000000 //Nan
GLOBL ·acoshrodataL11<> + 0(SB), RODATA, $120
// Table of log correction terms
DATA ·acoshtab2068<> + 0(SB)/8, $0.585235384085551248E-01
DATA ·acoshtab2068<> + 8(SB)/8, $0.412206153771168640E-01
DATA ·acoshtab2068<> + 16(SB)/8, $0.273839003221648339E-01
DATA ·acoshtab2068<> + 24(SB)/8, $0.166383778368856480E-01
DATA ·acoshtab2068<> + 32(SB)/8, $0.866678223433169637E-02
DATA ·acoshtab2068<> + 40(SB)/8, $0.319831684989627514E-02
DATA ·acoshtab2068<> + 48(SB)/8, $0.0
DATA ·acoshtab2068<> + 56(SB)/8, $-.113006378583725549E-02
DATA ·acoshtab2068<> + 64(SB)/8, $-.367979419636602491E-03
DATA ·acoshtab2068<> + 72(SB)/8, $0.213172484510484979E-02
DATA ·acoshtab2068<> + 80(SB)/8, $0.623271047682013536E-02
DATA ·acoshtab2068<> + 88(SB)/8, $0.118140812789696885E-01
DATA ·acoshtab2068<> + 96(SB)/8, $0.187681358930914206E-01
DATA ·acoshtab2068<> + 104(SB)/8, $0.269985148668178992E-01
DATA ·acoshtab2068<> + 112(SB)/8, $0.364186619761331328E-01
DATA ·acoshtab2068<> + 120(SB)/8, $0.469505379381388441E-01
GLOBL ·acoshtab2068<> + 0(SB), RODATA, $128
// Acosh returns the inverse hyperbolic cosine of the argument.
//
// Special cases are:
// Acosh(+Inf) = +Inf
// Acosh(x) = NaN if x < 1
// Acosh(NaN) = NaN
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·acoshAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·acoshrodataL11<>+0(SB), R9
WORD $0xB3CD0010 //lgdr %r1, %f0
WORD $0xC0295FEF //iilf %r2,1609564159
BYTE $0xFF
BYTE $0xFF
SRAD $32, R1
CMPW R1, R2
BGT L2
WORD $0xC0293FEF //iilf %r2,1072693247
BYTE $0xFF
BYTE $0xFF
CMPW R1, R2
BGT L10
L3:
WFCEDBS V0, V0, V2
BVS L1
FMOVD 112(R9), F0
L1:
FMOVD F0, ret+8(FP)
RET
L2:
WORD $0xC0297FEF //iilf %r2,2146435071
BYTE $0xFF
BYTE $0xFF
MOVW R1, R6
MOVW R2, R7
CMPBGT R6, R7, L1
FMOVD F0, F8
FMOVD $0, F0
WFADB V0, V8, V0
WORD $0xC0398006 //iilf %r3,2147909631
BYTE $0x7F
BYTE $0xFF
WORD $0xB3CD0050 //lgdr %r5, %f0
SRAD $32, R5
MOVH $0x0, R1
SUBW R5, R3
FMOVD $0, F10
WORD $0xEC4320AF //risbg %r4,%r3,32,128+47,0
BYTE $0x00
BYTE $0x55
WORD $0xEC3339BC //risbg %r3,%r3,57,128+60,64-13
BYTE $0x33
BYTE $0x55
BYTE $0x18 //lr %r2,%r4
BYTE $0x24
WORD $0xEC14001F //risbgn %r1,%r4,64-64+0,64-64+0+32-1,64-0-32
BYTE $0x20
BYTE $0x59
SUBW $0x100000, R2
SRAW $8, R2, R2
ORW $0x45000000, R2
L5:
WORD $0xB3C10001 //ldgr %f0,%r1
FMOVD 104(R9), F2
FMADD F8, F0, F2
FMOVD 96(R9), F4
WFMADB V10, V0, V2, V0
FMOVD 88(R9), F6
FMOVD 80(R9), F2
WFMADB V0, V6, V4, V6
FMOVD 72(R9), F1
WFMDB V0, V0, V4
WFMADB V0, V1, V2, V1
FMOVD 64(R9), F2
WFMADB V6, V4, V1, V6
FMOVD 56(R9), F1
WORD $0xEC3339BC //risbg %r3,%r3,57,128+60,0
BYTE $0x00
BYTE $0x55
WFMADB V0, V2, V1, V2
FMOVD 48(R9), F1
WFMADB V4, V6, V2, V6
FMOVD 40(R9), F2
WFMADB V0, V1, V2, V1
VLVGF $0, R2, V2
WFMADB V4, V6, V1, V4
LDEBR F2, F2
FMOVD 32(R9), F6
WFMADB V0, V4, V6, V4
FMOVD 24(R9), F1
FMOVD 16(R9), F6
MOVD $·acoshtab2068<>+0(SB), R1
WFMADB V2, V1, V6, V2
FMOVD 0(R3)(R1*1), F3
WFMADB V0, V4, V3, V0
FMOVD 8(R9), F4
FMADD F4, F2, F0
FMOVD F0, ret+8(FP)
RET
L10:
FMOVD F0, F8
FMOVD 0(R9), F0
FMADD F8, F8, F0
WORD $0xB3120000 //ltdbr %f0,%f0
FSQRT F0, F10
L4:
WFADB V10, V8, V0
WORD $0xC0398006 //iilf %r3,2147909631
BYTE $0x7F
BYTE $0xFF
WORD $0xB3CD0050 //lgdr %r5, %f0
SRAD $32, R5
MOVH $0x0, R1
SUBW R5, R3
SRAW $8, R3, R2
WORD $0xEC4320AF //risbg %r4,%r3,32,128+47,0
BYTE $0x00
BYTE $0x55
ANDW $0xFFFFFF00, R2
WORD $0xEC3339BC //risbg %r3,%r3,57,128+60,64-13
BYTE $0x33
BYTE $0x55
ORW $0x45000000, R2
WORD $0xEC14001F //risbgn %r1,%r4,64-64+0,64-64+0+32-1,64-0-32
BYTE $0x20
BYTE $0x59
BR L5

48
src/math/arith_s390x.go
View file

@ -22,6 +22,54 @@ func sinhAsm(x float64) float64
func tanhTrampolineSetup(x float64) float64
func tanhAsm(x float64) float64
func log1pTrampolineSetup(x float64) float64
func log1pAsm(x float64) float64
func atanhTrampolineSetup(x float64) float64
func atanhAsm(x float64) float64
func acosTrampolineSetup(x float64) float64
func acosAsm(x float64) float64
func acoshTrampolineSetup(x float64) float64
func acoshAsm(x float64) float64
func asinTrampolineSetup(x float64) float64
func asinAsm(x float64) float64
func asinhTrampolineSetup(x float64) float64
func asinhAsm(x float64) float64
func erfTrampolineSetup(x float64) float64
func erfAsm(x float64) float64
func erfcTrampolineSetup(x float64) float64
func erfcAsm(x float64) float64
func atanTrampolineSetup(x float64) float64
func atanAsm(x float64) float64
func atan2TrampolineSetup(x, y float64) float64
func atan2Asm(x, y float64) float64
func cbrtTrampolineSetup(x float64) float64
func cbrtAsm(x float64) float64
func logTrampolineSetup(x float64) float64
func logAsm(x float64) float64
func tanTrampolineSetup(x float64) float64
func tanAsm(x float64) float64
func expTrampolineSetup(x float64) float64
func expAsm(x float64) float64
func expm1TrampolineSetup(x float64) float64
func expm1Asm(x float64) float64
func powTrampolineSetup(x, y float64) float64
func powAsm(x, y float64) float64
// hasVectorFacility reports whether the machine has the z/Architecture
// vector facility installed and enabled.
func hasVectorFacility() bool

298
src/math/arith_s390x_test.go
View file

@ -106,6 +106,37 @@ func TestLargeSinNovec(t *testing.T) {
}
}
func TestLargeTanNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
large := float64(100000 * Pi)
for i := 0; i < len(vf); i++ {
f1 := tanLarge[i]
f2 := TanNovec(vf[i] + large)
if !close(f1, f2) {
t.Errorf("Tan(%g) = %g, want %g", vf[i]+large, f2, f1)
}
}
}
func TestTanNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
if f := TanNovec(vf[i]); !veryclose(tan[i], f) {
t.Errorf("Tan(%g) = %g, want %g", vf[i], f, tan[i])
}
}
// same special cases as Sin
for i := 0; i < len(vfsinSC); i++ {
if f := TanNovec(vfsinSC[i]); !alike(sinSC[i], f) {
t.Errorf("Tan(%g) = %g, want %g", vfsinSC[i], f, sinSC[i])
}
}
}
func TestTanhNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
@ -142,3 +173,270 @@ func TestLog10Novec(t *testing.T) {
}
}
}
func TestLog1pNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := vf[i] / 100
if f := Log1pNovec(a); !veryclose(log1p[i], f) {
t.Errorf("Log1p(%g) = %g, want %g", a, f, log1p[i])
}
}
a := 9.0
if f := Log1pNovec(a); f != Ln10 {
t.Errorf("Log1p(%g) = %g, want %g", a, f, Ln10)
}
for i := 0; i < len(vflogSC); i++ {
if f := Log1pNovec(vflog1pSC[i]); !alike(log1pSC[i], f) {
t.Errorf("Log1p(%g) = %g, want %g", vflog1pSC[i], f, log1pSC[i])
}
}
}
func TestAtanhNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := vf[i] / 10
if f := AtanhNovec(a); !veryclose(atanh[i], f) {
t.Errorf("Atanh(%g) = %g, want %g", a, f, atanh[i])
}
}
for i := 0; i < len(vfatanhSC); i++ {
if f := AtanhNovec(vfatanhSC[i]); !alike(atanhSC[i], f) {
t.Errorf("Atanh(%g) = %g, want %g", vfatanhSC[i], f, atanhSC[i])
}
}
}
func TestAcosNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := vf[i] / 10
if f := AcosNovec(a); !close(acos[i], f) {
t.Errorf("Acos(%g) = %g, want %g", a, f, acos[i])
}
}
for i := 0; i < len(vfacosSC); i++ {
if f := AcosNovec(vfacosSC[i]); !alike(acosSC[i], f) {
t.Errorf("Acos(%g) = %g, want %g", vfacosSC[i], f, acosSC[i])
}
}
}
func TestAsinNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := vf[i] / 10
if f := AsinNovec(a); !veryclose(asin[i], f) {
t.Errorf("Asin(%g) = %g, want %g", a, f, asin[i])
}
}
for i := 0; i < len(vfasinSC); i++ {
if f := AsinNovec(vfasinSC[i]); !alike(asinSC[i], f) {
t.Errorf("Asin(%g) = %g, want %g", vfasinSC[i], f, asinSC[i])
}
}
}
func TestAcoshNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := 1 + Abs(vf[i])
if f := AcoshNovec(a); !veryclose(acosh[i], f) {
t.Errorf("Acosh(%g) = %g, want %g", a, f, acosh[i])
}
}
for i := 0; i < len(vfacoshSC); i++ {
if f := AcoshNovec(vfacoshSC[i]); !alike(acoshSC[i], f) {
t.Errorf("Acosh(%g) = %g, want %g", vfacoshSC[i], f, acoshSC[i])
}
}
}
func TestAsinhNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
if f := AsinhNovec(vf[i]); !veryclose(asinh[i], f) {
t.Errorf("Asinh(%g) = %g, want %g", vf[i], f, asinh[i])
}
}
for i := 0; i < len(vfasinhSC); i++ {
if f := AsinhNovec(vfasinhSC[i]); !alike(asinhSC[i], f) {
t.Errorf("Asinh(%g) = %g, want %g", vfasinhSC[i], f, asinhSC[i])
}
}
}
func TestErfNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := vf[i] / 10
if f := ErfNovec(a); !veryclose(erf[i], f) {
t.Errorf("Erf(%g) = %g, want %g", a, f, erf[i])
}
}
for i := 0; i < len(vferfSC); i++ {
if f := ErfNovec(vferfSC[i]); !alike(erfSC[i], f) {
t.Errorf("Erf(%g) = %g, want %g", vferfSC[i], f, erfSC[i])
}
}
}
func TestErfcNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := vf[i] / 10
if f := ErfcNovec(a); !veryclose(erfc[i], f) {
t.Errorf("Erfc(%g) = %g, want %g", a, f, erfc[i])
}
}
for i := 0; i < len(vferfcSC); i++ {
if f := ErfcNovec(vferfcSC[i]); !alike(erfcSC[i], f) {
t.Errorf("Erfc(%g) = %g, want %g", vferfcSC[i], f, erfcSC[i])
}
}
}
func TestAtanNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
if f := AtanNovec(vf[i]); !veryclose(atan[i], f) {
t.Errorf("Atan(%g) = %g, want %g", vf[i], f, atan[i])
}
}
for i := 0; i < len(vfatanSC); i++ {
if f := AtanNovec(vfatanSC[i]); !alike(atanSC[i], f) {
t.Errorf("Atan(%g) = %g, want %g", vfatanSC[i], f, atanSC[i])
}
}
}
func TestAtan2Novec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
if f := Atan2Novec(10, vf[i]); !veryclose(atan2[i], f) {
t.Errorf("Atan2(10, %g) = %g, want %g", vf[i], f, atan2[i])
}
}
for i := 0; i < len(vfatan2SC); i++ {
if f := Atan2Novec(vfatan2SC[i][0], vfatan2SC[i][1]); !alike(atan2SC[i], f) {
t.Errorf("Atan2(%g, %g) = %g, want %g", vfatan2SC[i][0], vfatan2SC[i][1], f, atan2SC[i])
}
}
}
func TestCbrtNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
if f := CbrtNovec(vf[i]); !veryclose(cbrt[i], f) {
t.Errorf("Cbrt(%g) = %g, want %g", vf[i], f, cbrt[i])
}
}
for i := 0; i < len(vfcbrtSC); i++ {
if f := CbrtNovec(vfcbrtSC[i]); !alike(cbrtSC[i], f) {
t.Errorf("Cbrt(%g) = %g, want %g", vfcbrtSC[i], f, cbrtSC[i])
}
}
}
func TestLogNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := Abs(vf[i])
if f := LogNovec(a); log[i] != f {
t.Errorf("Log(%g) = %g, want %g", a, f, log[i])
}
}
if f := LogNovec(10); f != Ln10 {
t.Errorf("Log(%g) = %g, want %g", 10.0, f, Ln10)
}
for i := 0; i < len(vflogSC); i++ {
if f := LogNovec(vflogSC[i]); !alike(logSC[i], f) {
t.Errorf("Log(%g) = %g, want %g", vflogSC[i], f, logSC[i])
}
}
}
func TestExpNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
testExpNovec(t, Exp, "Exp")
testExpNovec(t, ExpGo, "ExpGo")
}
func testExpNovec(t *testing.T, Exp func(float64) float64, name string) {
for i := 0; i < len(vf); i++ {
if f := ExpNovec(vf[i]); !veryclose(exp[i], f) {
t.Errorf("%s(%g) = %g, want %g", name, vf[i], f, exp[i])
}
}
for i := 0; i < len(vfexpSC); i++ {
if f := ExpNovec(vfexpSC[i]); !alike(expSC[i], f) {
t.Errorf("%s(%g) = %g, want %g", name, vfexpSC[i], f, expSC[i])
}
}
}
func TestExpm1Novec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
a := vf[i] / 100
if f := Expm1Novec(a); !veryclose(expm1[i], f) {
t.Errorf("Expm1(%g) = %g, want %g", a, f, expm1[i])
}
}
for i := 0; i < len(vf); i++ {
a := vf[i] * 10
if f := Expm1Novec(a); !close(expm1Large[i], f) {
t.Errorf("Expm1(%g) = %g, want %g", a, f, expm1Large[i])
}
}
for i := 0; i < len(vfexpm1SC); i++ {
if f := Expm1Novec(vfexpm1SC[i]); !alike(expm1SC[i], f) {
t.Errorf("Expm1(%g) = %g, want %g", vfexpm1SC[i], f, expm1SC[i])
}
}
}
func TestPowNovec(t *testing.T) {
if !HasVX {
t.Skipf("no vector support")
}
for i := 0; i < len(vf); i++ {
if f := PowNovec(10, vf[i]); !close(pow[i], f) {
t.Errorf("Pow(10, %g) = %g, want %g", vf[i], f, pow[i])
}
}
for i := 0; i < len(vfpowSC); i++ {
if f := PowNovec(vfpowSC[i][0], vfpowSC[i][1]); !alike(powSC[i], f) {
t.Errorf("Pow(%g, %g) = %g, want %g", vfpowSC[i][0], vfpowSC[i][1], f, powSC[i])
}
}
}

162
src/math/asin_s390x.s Normal file
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@ -0,0 +1,162 @@
// 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 ·asinrodataL15<> + 0(SB)/8, $-1.309611320495605469
DATA ·asinrodataL15<> + 8(SB)/8, $0x3ff921fb54442d18
DATA ·asinrodataL15<> + 16(SB)/8, $0xbff921fb54442d18
DATA ·asinrodataL15<> + 24(SB)/8, $1.309611320495605469
DATA ·asinrodataL15<> + 32(SB)/8, $-0.0
DATA ·asinrodataL15<> + 40(SB)/8, $1.199437040755305217
DATA ·asinrodataL15<> + 48(SB)/8, $0.166666666666651626E+00
DATA ·asinrodataL15<> + 56(SB)/8, $0.750000000042621169E-01
DATA ·asinrodataL15<> + 64(SB)/8, $0.446428567178116477E-01
DATA ·asinrodataL15<> + 72(SB)/8, $0.303819660378071894E-01
DATA ·asinrodataL15<> + 80(SB)/8, $0.223715011892010405E-01
DATA ·asinrodataL15<> + 88(SB)/8, $0.173659424522364952E-01
DATA ·asinrodataL15<> + 96(SB)/8, $0.137810186504372266E-01
DATA ·asinrodataL15<> + 104(SB)/8, $0.134066870961173521E-01
DATA ·asinrodataL15<> + 112(SB)/8, $-.412335502831898721E-02
DATA ·asinrodataL15<> + 120(SB)/8, $0.867383739532082719E-01
DATA ·asinrodataL15<> + 128(SB)/8, $-.328765950607171649E+00
DATA ·asinrodataL15<> + 136(SB)/8, $0.110401073869414626E+01
DATA ·asinrodataL15<> + 144(SB)/8, $-.270694366992537307E+01
DATA ·asinrodataL15<> + 152(SB)/8, $0.500196500770928669E+01
DATA ·asinrodataL15<> + 160(SB)/8, $-.665866959108585165E+01
DATA ·asinrodataL15<> + 168(SB)/8, $-.344895269334086578E+01
DATA ·asinrodataL15<> + 176(SB)/8, $0.927437952918301659E+00
DATA ·asinrodataL15<> + 184(SB)/8, $0.610487478874645653E+01
DATA ·asinrodataL15<> + 192(SB)/8, $0x7ff8000000000000 //+Inf
DATA ·asinrodataL15<> + 200(SB)/8, $-1.0
DATA ·asinrodataL15<> + 208(SB)/8, $1.0
DATA ·asinrodataL15<> + 216(SB)/8, $1.00000000000000000e-20
GLOBL ·asinrodataL15<> + 0(SB), RODATA, $224
// Asin returns the arcsine, in radians, of the argument.
//
// Special cases are:
// Asin(±0) = ±0=
// Asin(x) = NaN if x < -1 or x > 1
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·asinAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·asinrodataL15<>+0(SB), R9
WORD $0xB3CD0070 //lgdr %r7, %f0
FMOVD F0, F8
SRAD $32, R7
WORD $0xC0193FE6 //iilf %r1,1072079005
BYTE $0xA0
BYTE $0x9D
WORD $0xB91700C7 //llgtr %r12,%r7
MOVW R12, R8
MOVW R1, R6
CMPBGT R8, R6, L2
WORD $0xC0193BFF //iilf %r1,1006632959
BYTE $0xFF
BYTE $0xFF
MOVW R1, R6
CMPBGT R8, R6, L13
L3:
FMOVD 216(R9), F0
FMADD F0, F8, F8
L1:
FMOVD F8, ret+8(FP)
RET
L2:
WORD $0xC0193FEF //iilf %r1,1072693247
BYTE $0xFF
BYTE $0xFF
CMPW R12, R1
BLE L14
L5:
WORD $0xED0090D0 //cdb %f0,.L17-.L15(%r9)
BYTE $0x00
BYTE $0x19
BEQ L9
WORD $0xED0090C8 //cdb %f0,.L18-.L15(%r9)
BYTE $0x00
BYTE $0x19
BEQ L10
WFCEDBS V8, V8, V0
BVS L1
FMOVD 192(R9), F8
BR L1
L13:
WFMDB V0, V0, V10
L4:
WFMDB V10, V10, V0
FMOVD 184(R9), F6
FMOVD 176(R9), F2
FMOVD 168(R9), F4
WFMADB V0, V2, V6, V2
FMOVD 160(R9), F6
WFMADB V0, V4, V6, V4
FMOVD 152(R9), F6
WFMADB V0, V2, V6, V2
FMOVD 144(R9), F6
WFMADB V0, V4, V6, V4
FMOVD 136(R9), F6
WFMADB V0, V2, V6, V2
WORD $0xC0193FE6 //iilf %r1,1072079005
BYTE $0xA0
BYTE $0x9D
FMOVD 128(R9), F6
WFMADB V0, V4, V6, V4
FMOVD 120(R9), F6
WFMADB V0, V2, V6, V2
FMOVD 112(R9), F6
WFMADB V0, V4, V6, V4
FMOVD 104(R9), F6
WFMADB V0, V2, V6, V2
FMOVD 96(R9), F6
WFMADB V0, V4, V6, V4
FMOVD 88(R9), F6
WFMADB V0, V2, V6, V2
FMOVD 80(R9), F6
WFMADB V0, V4, V6, V4
FMOVD 72(R9), F6
WFMADB V0, V2, V6, V2
FMOVD 64(R9), F6
WFMADB V0, V4, V6, V4
FMOVD 56(R9), F6
WFMADB V0, V2, V6, V2
FMOVD 48(R9), F6
WFMADB V0, V4, V6, V0
WFMDB V8, V10, V4
FMADD F2, F10, F0
FMADD F0, F4, F8
CMPW R12, R1
BLE L1
FMOVD 40(R9), F0
FMADD F0, F1, F8
FMOVD F8, ret+8(FP)
RET
L14:
FMOVD 200(R9), F0
FMADD F8, F8, F0
WORD $0xB31300A0 //lcdbr %f10,%f0
WORD $0xED009020 //cdb %f0,.L39-.L15(%r9)
BYTE $0x00
BYTE $0x19
FSQRT F10, F8
L6:
MOVW R7, R6
CMPBLE R6, $0, L8
WORD $0xB3130088 //lcdbr %f8,%f8
FMOVD 24(R9), F1
BR L4
L10:
FMOVD 16(R9), F8
BR L1
L9:
FMOVD 8(R9), F8
FMOVD F8, ret+8(FP)
RET
L8:
FMOVD 0(R9), F1
BR L4

4
src/math/asinh.go
View file

@ -36,7 +36,9 @@ package math
// Asinh(±0) = ±0
// Asinh(±Inf) = ±Inf
// Asinh(NaN) = NaN
func Asinh(x float64) float64 {
func Asinh(x float64) float64
func asinh(x float64) float64 {
const (
Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
NearZero = 1.0 / (1 << 28) // 2**-28

223
src/math/asinh_s390x.s Normal file
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@ -0,0 +1,223 @@
// 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

17
src/math/asinh_stub.s Normal file
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@ -0,0 +1,17 @@
// 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.
// +build 386 amd64 amd64p32 arm
#include "textflag.h"
TEXT ·Acosh(SB),NOSPLIT,$0
JMP ·acosh(SB)
TEXT ·Asinh(SB),NOSPLIT,$0
JMP ·asinh(SB)
TEXT ·Atanh(SB),NOSPLIT,$0
JMP ·atanh(SB)

302
src/math/atan2_s390x.s Normal file
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@ -0,0 +1,302 @@
// 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"
#define PosInf 0x7FF0000000000000
#define NegInf 0xFFF0000000000000
#define NegZero 0x8000000000000000
#define Pi 0x400921FB54442D18
#define NegPi 0xC00921FB54442D18
#define Pi3Div4 0x4002D97C7F3321D2 // 3Pi/4
#define NegPi3Div4 0xC002D97C7F3321D2 // -3Pi/4
#define PiDiv4 0x3FE921FB54442D18 // Pi/4
#define NegPiDiv4 0xBFE921FB54442D18 // -Pi/4
// Minimax polynomial coefficients and other constants
DATA ·atan2rodataL25<> + 0(SB)/8, $0.199999999999554423E+00
DATA ·atan2rodataL25<> + 8(SB)/8, $-.333333333333330928E+00
DATA ·atan2rodataL25<> + 16(SB)/8, $0.111111110136634272E+00
DATA ·atan2rodataL25<> + 24(SB)/8, $-.142857142828026806E+00
DATA ·atan2rodataL25<> + 32(SB)/8, $0.769228118888682505E-01
DATA ·atan2rodataL25<> + 40(SB)/8, $0.588059263575587687E-01
DATA ·atan2rodataL25<> + 48(SB)/8, $-.909090711945939878E-01
DATA ·atan2rodataL25<> + 56(SB)/8, $-.666641501287528609E-01
DATA ·atan2rodataL25<> + 64(SB)/8, $0.472329433805024762E-01
DATA ·atan2rodataL25<> + 72(SB)/8, $-.525380587584426406E-01
DATA ·atan2rodataL25<> + 80(SB)/8, $-.422172007412067035E-01
DATA ·atan2rodataL25<> + 88(SB)/8, $0.366935664549587481E-01
DATA ·atan2rodataL25<> + 96(SB)/8, $0.220852012160300086E-01
DATA ·atan2rodataL25<> + 104(SB)/8, $-.299856214685512712E-01
DATA ·atan2rodataL25<> + 112(SB)/8, $0.726338160757602439E-02
DATA ·atan2rodataL25<> + 120(SB)/8, $0.134893651284712515E-04
DATA ·atan2rodataL25<> + 128(SB)/8, $-.291935324869629616E-02
DATA ·atan2rodataL25<> + 136(SB)/8, $-.154797890856877418E-03
DATA ·atan2rodataL25<> + 144(SB)/8, $0.843488472994227321E-03
DATA ·atan2rodataL25<> + 152(SB)/8, $-.139950258898989925E-01
GLOBL ·atan2rodataL25<> + 0(SB), RODATA, $160
DATA ·atan2xpi2h<> + 0(SB)/8, $0x3ff330e4e4fa7b1b
DATA ·atan2xpi2h<> + 8(SB)/8, $0xbff330e4e4fa7b1b
DATA ·atan2xpi2h<> + 16(SB)/8, $0x400330e4e4fa7b1b
DATA ·atan2xpi2h<> + 24(SB)/8, $0xc00330e4e4fa7b1b
GLOBL ·atan2xpi2h<> + 0(SB), RODATA, $32
DATA ·atan2xpim<> + 0(SB)/8, $0x3ff4f42b00000000
GLOBL ·atan2xpim<> + 0(SB), RODATA, $8
// Atan2 returns the arc tangent of y/x, using
// the signs of the two to determine the quadrant
// of the return value.
//
// Special cases are (in order):
// Atan2(y, NaN) = NaN
// Atan2(NaN, x) = NaN
// Atan2(+0, x>=0) = +0
// Atan2(-0, x>=0) = -0
// Atan2(+0, x<=-0) = +Pi
// Atan2(-0, x<=-0) = -Pi
// Atan2(y>0, 0) = +Pi/2
// Atan2(y<0, 0) = -Pi/2
// Atan2(+Inf, +Inf) = +Pi/4
// Atan2(-Inf, +Inf) = -Pi/4
// Atan2(+Inf, -Inf) = 3Pi/4
// Atan2(-Inf, -Inf) = -3Pi/4
// Atan2(y, +Inf) = 0
// Atan2(y>0, -Inf) = +Pi
// Atan2(y<0, -Inf) = -Pi
// Atan2(+Inf, x) = +Pi/2
// Atan2(-Inf, x) = -Pi/2
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·atan2Asm(SB), NOSPLIT, $0-24
// special case
MOVD x+0(FP), R1
MOVD y+8(FP), R2
// special case Atan2(NaN, y) = NaN
MOVD $~(1<<63), R5
AND R1, R5 // x = |x|
MOVD $PosInf, R3
CMPUBLT R3, R5, returnX
// special case Atan2(x, NaN) = NaN
MOVD $~(1<<63), R5
AND R2, R5
CMPUBLT R3, R5, returnY
MOVD $NegZero, R3
CMPUBEQ R3, R1, xIsNegZero
MOVD $0, R3
CMPUBEQ R3, R1, xIsPosZero
MOVD $PosInf, R4
CMPUBEQ R4, R2, yIsPosInf
MOVD $NegInf, R4
CMPUBEQ R4, R2, yIsNegInf
BR Normal
xIsNegZero:
// special case Atan(-0, y>=0) = -0
MOVD $0, R4
CMPBLE R4, R2, returnX
//special case Atan2(-0, y<=-0) = -Pi
MOVD $NegZero, R4
CMPBGE R4, R2, returnNegPi
BR Normal
xIsPosZero:
//special case Atan2(0, 0) = 0
MOVD $0, R4
CMPUBEQ R4, R2, returnX
//special case Atan2(0, y<=-0) = Pi
MOVD $NegZero, R4
CMPBGE R4, R2, returnPi
BR Normal
yIsNegInf:
//special case Atan2(+Inf, -Inf) = 3Pi/4
MOVD $PosInf, R3
CMPUBEQ R3, R1, posInfNegInf
//special case Atan2(-Inf, -Inf) = -3Pi/4
MOVD $NegInf, R3
CMPUBEQ R3, R1, negInfNegInf
BR Normal
yIsPosInf:
//special case Atan2(+Inf, +Inf) = Pi/4
MOVD $PosInf, R3
CMPUBEQ R3, R1, posInfPosInf
//special case Atan2(-Inf, +Inf) = -Pi/4
MOVD $NegInf, R3
CMPUBEQ R3, R1, negInfPosInf
//special case Atan2(-Pi, +Inf) = Pi
MOVD $NegPi, R3
CMPUBEQ R3, R1, negPiPosInf
Normal:
FMOVD x+0(FP), F0
FMOVD y+8(FP), F2
MOVD $·atan2rodataL25<>+0(SB), R9
WORD $0xB3CD0020 //lgdr %r2,%f0
WORD $0xB3CD0012 //lgdr %r1,%f2
WORD $0xEC2220BF //risbgn %r2,%r2,64-32,128+63,64+0+32
BYTE $0x60
BYTE $0x59
WORD $0xEC1120BF //risbgn %r1,%r1,64-32,128+63,64+0+32
BYTE $0x60
BYTE $0x59
WORD $0xB9170032 //llgtr %r3,%r2
WORD $0xEC523FBF //risbg %r5,%r2,64-1,128+63,64+32+1
BYTE $0x61
BYTE $0x55
WORD $0xB9170041 //llgtr %r4,%r1
WFLCDB V0, V20
MOVW R4, R6
MOVW R3, R7
CMPUBLT R6, R7, L17
WFDDB V2, V0, V3
ADDW $2, R5, R2
MOVW R4, R6
MOVW R3, R7
CMPUBLE R6, R7, L20
L3:
WFMDB V3, V3, V4
VLEG $0, 152(R9), V18
VLEG $0, 144(R9), V16
FMOVD 136(R9), F1
FMOVD 128(R9), F5
FMOVD 120(R9), F6
WFMADB V4, V16, V5, V16
WFMADB V4, V6, V1, V6
FMOVD 112(R9), F7
WFMDB V4, V4, V1
WFMADB V4, V7, V18, V7
VLEG $0, 104(R9), V18
WFMADB V1, V6, V16, V6
CMPWU R4, R3
FMOVD 96(R9), F5
VLEG $0, 88(R9), V16
WFMADB V4, V5, V18, V5
VLEG $0, 80(R9), V18
VLEG $0, 72(R9), V22
WFMADB V4, V16, V18, V16
VLEG $0, 64(R9), V18
WFMADB V1, V7, V5, V7
WFMADB V4, V18, V22, V18
WFMDB V1, V1, V5
WFMADB V1, V16, V18, V16
VLEG $0, 56(R9), V18
WFMADB V5, V6, V7, V6
VLEG $0, 48(R9), V22
FMOVD 40(R9), F7
WFMADB V4, V7, V18, V7
VLEG $0, 32(R9), V18
WFMADB V5, V6, V16, V6
WFMADB V4, V18, V22, V18
VLEG $0, 24(R9), V16
WFMADB V1, V7, V18, V7
VLEG $0, 16(R9), V18
VLEG $0, 8(R9), V22
WFMADB V4, V18, V16, V18
VLEG $0, 0(R9), V16
WFMADB V5, V6, V7, V6
WFMADB V4, V16, V22, V16
FMUL F3, F4
WFMADB V1, V18, V16, V1
FMADD F6, F5, F1
WFMADB V4, V1, V3, V4
BLT L18
BGT L7
WORD $0xB3120022 //ltdbr %f2,%f2
BLTU L21
L8:
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L22
L9:
WFCHDBS V2, V0, V0
BNE L18
L7:
MOVW R1, R6
CMPBGE R6, $0, L1
L18:
WORD $0xEC223ABC //risbg %r2,%r2,58,128+60,3
BYTE $0x03
BYTE $0x55
MOVD $·atan2xpi2h<>+0(SB), R1
MOVD ·atan2xpim<>+0(SB), R3
WORD $0xB3C10003 //ldgr %f0,%r3
WORD $0xED021000 //madb %f4,%f0,0(%r2,%r1)
BYTE $0x40
BYTE $0x1E
L1:
FMOVD F4, ret+16(FP)
RET
L20:
WORD $0xB3120022 //ltdbr %f2,%f2
BLTU L23
FMOVD F2, F6
L4:
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L24
FMOVD F0, F4
L5:
WFCHDBS V6, V4, V4
BEQ L3
L17:
WFDDB V0, V2, V4
BYTE $0x18 //lr %r2,%r5
BYTE $0x25
WORD $0xB3130034 //lcdbr %f3,%f4
BR L3
L23:
WORD $0xB3130062 //lcdbr %f6,%f2
BR L4
L22:
VLR V20, V0
BR L9
L21:
WORD $0xB3130022 //lcdbr %f2,%f2
BR L8
L24:
VLR V20, V4
BR L5
returnX: //the result is same as the first argument
MOVD R1, ret+16(FP)
RET
returnY: //the result is same as the second argument
MOVD R2, ret+16(FP)
RET
returnPi:
MOVD $Pi, R1
MOVD R1, ret+16(FP)
RET
returnNegPi:
MOVD $NegPi, R1
MOVD R1, ret+16(FP)
RET
posInfNegInf:
MOVD $Pi3Div4, R1
MOVD R1, ret+16(FP)
RET
negInfNegInf:
MOVD $NegPi3Div4, R1
MOVD R1, ret+16(FP)
RET
posInfPosInf:
MOVD $PiDiv4, R1
MOVD R1, ret+16(FP)
RET
negInfPosInf:
MOVD $NegPiDiv4, R1
MOVD R1, ret+16(FP)
RET
negPiPosInf:
MOVD $NegZero, R1
MOVD R1, ret+16(FP)
RET

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@ -0,0 +1,132 @@
// 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 ·atanrodataL8<> + 0(SB)/8, $0.199999999999554423E+00
DATA ·atanrodataL8<> + 8(SB)/8, $0.111111110136634272E+00
DATA ·atanrodataL8<> + 16(SB)/8, $-.142857142828026806E+00
DATA ·atanrodataL8<> + 24(SB)/8, $-.333333333333330928E+00
DATA ·atanrodataL8<> + 32(SB)/8, $0.769228118888682505E-01
DATA ·atanrodataL8<> + 40(SB)/8, $0.588059263575587687E-01
DATA ·atanrodataL8<> + 48(SB)/8, $-.666641501287528609E-01
DATA ·atanrodataL8<> + 56(SB)/8, $-.909090711945939878E-01
DATA ·atanrodataL8<> + 64(SB)/8, $0.472329433805024762E-01
DATA ·atanrodataL8<> + 72(SB)/8, $0.366935664549587481E-01
DATA ·atanrodataL8<> + 80(SB)/8, $-.422172007412067035E-01
DATA ·atanrodataL8<> + 88(SB)/8, $-.299856214685512712E-01
DATA ·atanrodataL8<> + 96(SB)/8, $0.220852012160300086E-01
DATA ·atanrodataL8<> + 104(SB)/8, $0.726338160757602439E-02
DATA ·atanrodataL8<> + 112(SB)/8, $0.843488472994227321E-03
DATA ·atanrodataL8<> + 120(SB)/8, $0.134893651284712515E-04
DATA ·atanrodataL8<> + 128(SB)/8, $-.525380587584426406E-01
DATA ·atanrodataL8<> + 136(SB)/8, $-.139950258898989925E-01
DATA ·atanrodataL8<> + 144(SB)/8, $-.291935324869629616E-02
DATA ·atanrodataL8<> + 152(SB)/8, $-.154797890856877418E-03
GLOBL ·atanrodataL8<> + 0(SB), RODATA, $160
DATA ·atanxpi2h<> + 0(SB)/8, $0x3ff330e4e4fa7b1b
DATA ·atanxpi2h<> + 8(SB)/8, $0xbff330e4e4fa7b1b
DATA ·atanxpi2h<> + 16(SB)/8, $0x400330e4e4fa7b1b
DATA ·atanxpi2h<> + 24(SB)/4, $0xc00330e4e4fa7b1b
GLOBL ·atanxpi2h<> + 0(SB), RODATA, $32
DATA ·atanxpim<> + 0(SB)/8, $0x3ff4f42b00000000
GLOBL ·atanxpim<> + 0(SB), RODATA, $8
DATA ·atanxmone<> + 0(SB)/8, $-1.0
GLOBL ·atanxmone<> + 0(SB), RODATA, $8
// Atan returns the arctangent, in radians, of the argument.
//
// Special cases are:
// Atan(±0) = ±0
// Atan(±Inf) = ±Pi/2Pi
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·atanAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
//special case Atan(±0) = ±0
FMOVD $(0.0), F1
FCMPU F0, F1
BEQ atanIsZero
MOVD $·atanrodataL8<>+0(SB), R5
MOVH $0x3FE0, R3
WORD $0xB3CD0010 //lgdr %r1,%f0
WORD $0xEC1120BF //risbgn %r1,%r1,64-32,128+63,64+0+32
BYTE $0x60
BYTE $0x59
RLL $16, R1, R2
ANDW $0x7FF0, R2
MOVW R2, R6
MOVW R3, R7
CMPUBLE R6, R7, L6
MOVD $·atanxmone<>+0(SB), R3
FMOVD 0(R3), F2
WFDDB V0, V2, V0
WORD $0xEC113FBF //risbg %r1,%r1,64-1,128+63,64+32+1
BYTE $0x61
BYTE $0x55
MOVD $·atanxpi2h<>+0(SB), R3
MOVWZ R1, R1
SLD $3, R1, R1
WORD $0x68813000 //ld %f8,0(%r1,%r3)
L6:
WFMDB V0, V0, V2
FMOVD 152(R5), F6
FMOVD 144(R5), F1
FMOVD 136(R5), F7
VLEG $0, 128(R5), V16
FMOVD 120(R5), F4
FMOVD 112(R5), F5
WFMADB V2, V4, V6, V4
WFMADB V2, V5, V1, V5
WFMDB V2, V2, V6
FMOVD 104(R5), F3
FMOVD 96(R5), F1
WFMADB V2, V3, V7, V3
MOVH $0x3FE0, R1
FMOVD 88(R5), F7
WFMADB V2, V1, V7, V1
FMOVD 80(R5), F7
WFMADB V6, V3, V1, V3
WFMADB V6, V4, V5, V4
WFMDB V6, V6, V1
FMOVD 72(R5), F5
WFMADB V2, V5, V7, V5
FMOVD 64(R5), F7
WFMADB V2, V7, V16, V7
VLEG $0, 56(R5), V16
WFMADB V6, V5, V7, V5
WFMADB V1, V4, V3, V4
FMOVD 48(R5), F7
FMOVD 40(R5), F3
WFMADB V2, V3, V7, V3
FMOVD 32(R5), F7
WFMADB V2, V7, V16, V7
VLEG $0, 24(R5), V16
WFMADB V1, V4, V5, V4
FMOVD 16(R5), F5
WFMADB V6, V3, V7, V3
FMOVD 8(R5), F7
WFMADB V2, V7, V5, V7
FMOVD 0(R5), F5
WFMADB V2, V5, V16, V5
WFMADB V1, V4, V3, V4
WFMADB V6, V7, V5, V6
FMUL F0, F2
FMADD F4, F1, F6
FMADD F6, F2, F0
MOVW R2, R6
MOVW R1, R7
CMPUBLE R6, R7, L1
MOVD $·atanxpim<>+0(SB), R1
WORD $0xED801000 //madb %f0,%f8,0(%r1)
BYTE $0x00
BYTE $0x1E
L1:
atanIsZero:
FMOVD F0, ret+8(FP)
RET

4
src/math/atanh.go
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@ -44,7 +44,9 @@ package math
// Atanh(-1) = -Inf
// Atanh(x) = NaN if x < -1 or x > 1
// Atanh(NaN) = NaN
func Atanh(x float64) float64 {
func Atanh(x float64) float64
func atanh(x float64) float64 {
const NearZero = 1.0 / (1 << 28) // 2**-28
// special cases
switch {

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@ -0,0 +1,178 @@
// 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 ·atanhrodataL10<> + 0(SB)/8, $.41375273347623353626
DATA ·atanhrodataL10<> + 8(SB)/8, $.51487302528619766235E+04
DATA ·atanhrodataL10<> + 16(SB)/8, $-1.67526912689208984375
DATA ·atanhrodataL10<> + 24(SB)/8, $0.181818181818181826E+00
DATA ·atanhrodataL10<> + 32(SB)/8, $-.165289256198351540E-01
DATA ·atanhrodataL10<> + 40(SB)/8, $0.200350613573012186E-02
DATA ·atanhrodataL10<> + 48(SB)/8, $0.397389654305194527E-04
DATA ·atanhrodataL10<> + 56(SB)/8, $-.273205381970859341E-03
DATA ·atanhrodataL10<> + 64(SB)/8, $0.938370938292558173E-06
DATA ·atanhrodataL10<> + 72(SB)/8, $-.148682720127920854E-06
DATA ·atanhrodataL10<> + 80(SB)/8, $ 0.212881813645679599E-07
DATA ·atanhrodataL10<> + 88(SB)/8, $-.602107458843052029E-05
DATA ·atanhrodataL10<> + 96(SB)/8, $-5.5
DATA ·atanhrodataL10<> + 104(SB)/8, $-0.5
DATA ·atanhrodataL10<> + 112(SB)/8, $0.0
DATA ·atanhrodataL10<> + 120(SB)/8, $0x7ff8000000000000 //Nan
DATA ·atanhrodataL10<> + 128(SB)/8, $-1.0
DATA ·atanhrodataL10<> + 136(SB)/8, $1.0
DATA ·atanhrodataL10<> + 144(SB)/8, $1.0E-20
GLOBL ·atanhrodataL10<> + 0(SB), RODATA, $152
// Table of log correction terms
DATA ·atanhtab2076<> + 0(SB)/8, $0.585235384085551248E-01
DATA ·atanhtab2076<> + 8(SB)/8, $0.412206153771168640E-01
DATA ·atanhtab2076<> + 16(SB)/8, $0.273839003221648339E-01
DATA ·atanhtab2076<> + 24(SB)/8, $0.166383778368856480E-01
DATA ·atanhtab2076<> + 32(SB)/8, $0.866678223433169637E-02
DATA ·atanhtab2076<> + 40(SB)/8, $0.319831684989627514E-02
DATA ·atanhtab2076<> + 48(SB)/8, $0.000000000000000000E+00
DATA ·atanhtab2076<> + 56(SB)/8, $-.113006378583725549E-02
DATA ·atanhtab2076<> + 64(SB)/8, $-.367979419636602491E-03
DATA ·atanhtab2076<> + 72(SB)/8, $0.213172484510484979E-02
DATA ·atanhtab2076<> + 80(SB)/8, $0.623271047682013536E-02
DATA ·atanhtab2076<> + 88(SB)/8, $0.118140812789696885E-01
DATA ·atanhtab2076<> + 96(SB)/8, $0.187681358930914206E-01
DATA ·atanhtab2076<> + 104(SB)/8, $0.269985148668178992E-01
DATA ·atanhtab2076<> + 112(SB)/8, $0.364186619761331328E-01
DATA ·atanhtab2076<> + 120(SB)/8, $0.469505379381388441E-01
GLOBL ·atanhtab2076<> + 0(SB), RODATA, $128
// Table of +/- .5
DATA ·atanhtabh2075<> + 0(SB)/8, $0.5
DATA ·atanhtabh2075<> + 8(SB)/8, $-.5
GLOBL ·atanhtabh2075<> + 0(SB), RODATA, $16
// Atanh returns the inverse hyperbolic tangent of the argument.
//
// Special cases are:
// Atanh(1) = +Inf
// Atanh(±0) = ±0
// Atanh(-1) = -Inf
// Atanh(x) = NaN if x < -1 or x > 1
// Atanh(NaN) = NaN
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·atanhAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·atanhrodataL10<>+0(SB), R5
WORD $0xB3CD0010 //lgdr %r1, %f0
WORD $0xC0393FEF //iilf %r3,1072693247
BYTE $0xFF
BYTE $0xFF
SRAD $32, R1
WORD $0xB9170021 //llgtr %r2,%r1
MOVW R2, R6
MOVW R3, R7
CMPBGT R6, R7, L2
WORD $0xC0392FFF //iilf %r3,805306367
BYTE $0xFF
BYTE $0xFF
MOVW R2, R6
MOVW R3, R7
CMPBGT R6, R7, L9
L3:
FMOVD 144(R5), F2
FMADD F2, F0, F0
L1:
FMOVD F0, ret+8(FP)
RET
L2:
WORD $0xED005088 //cdb %f0,.L12-.L10(%r5)
BYTE $0x00
BYTE $0x19
BEQ L5
WORD $0xED005080 //cdb %f0,.L13-.L10(%r5)
BYTE $0x00
BYTE $0x19
BEQ L5
WFCEDBS V0, V0, V2
BVS L1
FMOVD 120(R5), F0
BR L1
L5:
WORD $0xED005070 //ddb %f0,.L15-.L10(%r5)
BYTE $0x00
BYTE $0x1D
FMOVD F0, ret+8(FP)
RET
L9:
FMOVD F0, F2
MOVD $·atanhtabh2075<>+0(SB), R2
SRW $31, R1, R1
FMOVD 104(R5), F4
MOVW R1, R1
SLD $3, R1, R1
WORD $0x68012000 //ld %f0,0(%r1,%r2)
WFMADB V2, V4, V0, V4
VLEG $0, 96(R5), V16
FDIV F4, F2
WORD $0xC0298006 //iilf %r2,2147909631
BYTE $0x7F
BYTE $0xFF
FMOVD 88(R5), F6
FMOVD 80(R5), F1
FMOVD 72(R5), F7
FMOVD 64(R5), F5
FMOVD F2, F4
WORD $0xED405088 //adb %f4,.L12-.L10(%r5)
BYTE $0x00
BYTE $0x1A
WORD $0xB3CD0044 //lgdr %r4, %f4
SRAD $32, R4
FMOVD F4, F3
WORD $0xED305088 //sdb %f3,.L12-.L10(%r5)
BYTE $0x00
BYTE $0x1B
SUBW R4, R2
WFSDB V3, V2, V3
WORD $0xEC1220AF //risbg %r1,%r2,32,128+47,0
BYTE $0x00
BYTE $0x55
SLD $32, R1, R1
WORD $0xB3C10021 //ldgr %f2,%r1
WFMADB V4, V2, V16, V4
SRAW $8, R2, R1
WFMADB V4, V5, V6, V5
WFMDB V4, V4, V6
WFMADB V4, V1, V7, V1
WFMADB V2, V3, V4, V2
WFMADB V1, V6, V5, V1
FMOVD 56(R5), F3
FMOVD 48(R5), F5
WFMADB V4, V5, V3, V4
FMOVD 40(R5), F3
FMADD F1, F6, F4
FMOVD 32(R5), F1
FMADD F3, F2, F1
ANDW $0xFFFFFF00, R1
WFMADB V6, V4, V1, V6
FMOVD 24(R5), F3
ORW $0x45000000, R1
WFMADB V2, V6, V3, V6
VLVGF $0, R1, V4
LDEBR F4, F4
WORD $0xEC2239BC //risbg %r2,%r2,57,128+60,64-13
BYTE $0x33
BYTE $0x55
MOVD $·atanhtab2076<>+0(SB), R1
FMOVD 16(R5), F3
WORD $0x68521000 //ld %f5,0(%r2,%r1)
FMOVD 8(R5), F1
WFMADB V2, V6, V5, V2
WFMADB V4, V3, V1, V4
FMOVD 0(R5), F6
FMADD F6, F4, F2
FMUL F2, F0
FMOVD F0, ret+8(FP)
RET

4
src/math/cbrt.go
View file

@ -22,7 +22,9 @@ package math
// Cbrt(±0) = ±0
// Cbrt(±Inf) = ±Inf
// Cbrt(NaN) = NaN
func Cbrt(x float64) float64 {
func Cbrt(x float64) float64
func cbrt(x float64) float64 {
const (
B1 = 715094163 // (682-0.03306235651)*2**20
B2 = 696219795 // (664-0.03306235651)*2**20

162
src/math/cbrt_s390x.s Normal file
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@ -0,0 +1,162 @@
// 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 ·cbrtrodataL9<> + 0(SB)/8, $-.00016272731015974436E+00
DATA ·cbrtrodataL9<> + 8(SB)/8, $0.66639548758285293179E+00
DATA ·cbrtrodataL9<> + 16(SB)/8, $0.55519402697349815993E+00
DATA ·cbrtrodataL9<> + 24(SB)/8, $0.49338566048766782004E+00
DATA ·cbrtrodataL9<> + 32(SB)/8, $0.45208160036325611486E+00
DATA ·cbrtrodataL9<> + 40(SB)/8, $0.43099892837778637816E+00
DATA ·cbrtrodataL9<> + 48(SB)/8, $1.000244140625
DATA ·cbrtrodataL9<> + 56(SB)/8, $0.33333333333333333333E+00
DATA ·cbrtrodataL9<> + 64(SB)/8, $79228162514264337593543950336.
GLOBL ·cbrtrodataL9<> + 0(SB), RODATA, $72
// Index tables
DATA ·cbrttab32069<> + 0(SB)/8, $0x404030303020202
DATA ·cbrttab32069<> + 8(SB)/8, $0x101010101000000
DATA ·cbrttab32069<> + 16(SB)/8, $0x808070706060605
DATA ·cbrttab32069<> + 24(SB)/8, $0x505040404040303
DATA ·cbrttab32069<> + 32(SB)/8, $0xe0d0c0c0b0b0b0a
DATA ·cbrttab32069<> + 40(SB)/8, $0xa09090908080808
DATA ·cbrttab32069<> + 48(SB)/8, $0x11111010100f0f0f
DATA ·cbrttab32069<> + 56(SB)/8, $0xe0e0e0e0e0d0d0d
DATA ·cbrttab32069<> + 64(SB)/8, $0x1515141413131312
DATA ·cbrttab32069<> + 72(SB)/8, $0x1212111111111010
GLOBL ·cbrttab32069<> + 0(SB), RODATA, $80
DATA ·cbrttab22068<> + 0(SB)/8, $0x151015001420141
DATA ·cbrttab22068<> + 8(SB)/8, $0x140013201310130
DATA ·cbrttab22068<> + 16(SB)/8, $0x122012101200112
DATA ·cbrttab22068<> + 24(SB)/8, $0x111011001020101
DATA ·cbrttab22068<> + 32(SB)/8, $0x10000f200f100f0
DATA ·cbrttab22068<> + 40(SB)/8, $0xe200e100e000d2
DATA ·cbrttab22068<> + 48(SB)/8, $0xd100d000c200c1
DATA ·cbrttab22068<> + 56(SB)/8, $0xc000b200b100b0
DATA ·cbrttab22068<> + 64(SB)/8, $0xa200a100a00092
DATA ·cbrttab22068<> + 72(SB)/8, $0x91009000820081
DATA ·cbrttab22068<> + 80(SB)/8, $0x80007200710070
DATA ·cbrttab22068<> + 88(SB)/8, $0x62006100600052
DATA ·cbrttab22068<> + 96(SB)/8, $0x51005000420041
DATA ·cbrttab22068<> + 104(SB)/8, $0x40003200310030
DATA ·cbrttab22068<> + 112(SB)/8, $0x22002100200012
DATA ·cbrttab22068<> + 120(SB)/8, $0x11001000020001
GLOBL ·cbrttab22068<> + 0(SB), RODATA, $128
DATA ·cbrttab12067<> + 0(SB)/8, $0x53e1529051324fe1
DATA ·cbrttab12067<> + 8(SB)/8, $0x4e904d324be14a90
DATA ·cbrttab12067<> + 16(SB)/8, $0x493247e146904532
DATA ·cbrttab12067<> + 24(SB)/8, $0x43e1429041323fe1
DATA ·cbrttab12067<> + 32(SB)/8, $0x3e903d323be13a90
DATA ·cbrttab12067<> + 40(SB)/8, $0x393237e136903532
DATA ·cbrttab12067<> + 48(SB)/8, $0x33e1329031322fe1
DATA ·cbrttab12067<> + 56(SB)/8, $0x2e902d322be12a90
DATA ·cbrttab12067<> + 64(SB)/8, $0xd3e1d290d132cfe1
DATA ·cbrttab12067<> + 72(SB)/8, $0xce90cd32cbe1ca90
DATA ·cbrttab12067<> + 80(SB)/8, $0xc932c7e1c690c532
DATA ·cbrttab12067<> + 88(SB)/8, $0xc3e1c290c132bfe1
DATA ·cbrttab12067<> + 96(SB)/8, $0xbe90bd32bbe1ba90
DATA ·cbrttab12067<> + 104(SB)/8, $0xb932b7e1b690b532
DATA ·cbrttab12067<> + 112(SB)/8, $0xb3e1b290b132afe1
DATA ·cbrttab12067<> + 120(SB)/8, $0xae90ad32abe1aa90
GLOBL ·cbrttab12067<> + 0(SB), RODATA, $128
// Cbrt returns the cube root of the argument.
//
// Special cases are:
// Cbrt(±0) = ±0
// Cbrt(±Inf) = ±Inf
// Cbrt(NaN) = NaN
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·cbrtAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·cbrtrodataL9<>+0(SB), R9
WORD $0xB3CD0020 //lgdr %r2, %f0
WORD $0xC039000F //iilf %r3,1048575
BYTE $0xFF
BYTE $0xFF
SRAD $32, R2
WORD $0xB9170012 //llgtr %r1,%r2
MOVW R1, R6
MOVW R3, R7
CMPBLE R6, R7, L2
WORD $0xC0397FEF //iilf %r3,2146435071
BYTE $0xFF
BYTE $0xFF
MOVW R3, R7
CMPBLE R6, R7, L8
L1:
FMOVD F0, ret+8(FP)
RET
L3:
L2:
WORD $0xB3120000 //ltdbr %f0,%f0
BEQ L1
FMOVD F0, F2
WORD $0xED209040 //mdb %f2,.L10-.L9(%r9)
BYTE $0x00
BYTE $0x1C
MOVH $0x200, R4
WORD $0xB3CD0022 //lgdr %r2, %f2
SRAD $32, R2
L4:
WORD $0xEC3239BE //risbg %r3,%r2,57,128+62,64-25
BYTE $0x27
BYTE $0x55
MOVD $·cbrttab12067<>+0(SB), R1
WORD $0x48131000 //lh %r1,0(%r3,%r1)
WORD $0xEC3239BE //risbg %r3,%r2,57,128+62,64-19
BYTE $0x2D
BYTE $0x55
MOVD $·cbrttab22068<>+0(SB), R5
WORD $0xEC223CBF //risbgn %r2,%r2,64-4,128+63,64+44+4
BYTE $0x70
BYTE $0x59
WORD $0x4A135000 //ah %r1,0(%r3,%r5)
BYTE $0x18 //lr %r3,%r1
BYTE $0x31
MOVD $·cbrttab32069<>+0(SB), R1
FMOVD 56(R9), F1
FMOVD 48(R9), F5
WORD $0xEC23393B //rosbg %r2,%r3,57,59,4
BYTE $0x04
BYTE $0x56
WORD $0xE3121000 //llc %r1,0(%r2,%r1)
BYTE $0x00
BYTE $0x94
ADDW R3, R1
ADDW R4, R1
SLW $16, R1, R1
SLD $32, R1, R1
WORD $0xB3C10021 //ldgr %f2,%r1
WFMDB V2, V2, V4
WFMDB V4, V0, V6
WFMSDB V4, V6, V2, V4
FMOVD 40(R9), F6
FMSUB F1, F4, F2
FMOVD 32(R9), F4
WFMDB V2, V2, V3
FMOVD 24(R9), F1
FMUL F3, F0
FMOVD 16(R9), F3
WFMADB V2, V0, V5, V2
FMOVD 8(R9), F5
FMADD F6, F2, F4
WFMADB V2, V1, V3, V1
WFMDB V2, V2, V6
FMOVD 0(R9), F3
WFMADB V4, V6, V1, V4
WFMADB V2, V5, V3, V2
FMADD F4, F6, F2
FMADD F2, F0, F0
FMOVD F0, ret+8(FP)
RET
L8:
MOVH $0x0, R4
BR L4

11
src/math/cbrt_stub.s Normal file
View file

@ -0,0 +1,11 @@
// 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.
// +build 386 amd64 amd64p32 arm
#include "textflag.h"
TEXT ·Cbrt(SB),NOSPLIT,$0
JMP ·cbrt(SB)

8
src/math/erf.go
View file

@ -185,7 +185,9 @@ const (
// Erf(+Inf) = 1
// Erf(-Inf) = -1
// Erf(NaN) = NaN
func Erf(x float64) float64 {
func Erf(x float64) float64
func erf(x float64) float64 {
const (
VeryTiny = 2.848094538889218e-306 // 0x0080000000000000
Small = 1.0 / (1 << 28) // 2**-28
@ -262,7 +264,9 @@ func Erf(x float64) float64 {
// Erfc(+Inf) = 0
// Erfc(-Inf) = 2
// Erfc(NaN) = NaN
func Erfc(x float64) float64 {
func Erfc(x float64) float64
func erfc(x float64) float64 {
const Tiny = 1.0 / (1 << 56) // 2**-56
// special cases
switch {

299
src/math/erf_s390x.s Normal file
View file

@ -0,0 +1,299 @@
// 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 ·erfrodataL13<> + 0(SB)/8, $0.243673229298474689E+01
DATA ·erfrodataL13<> + 8(SB)/8, $-.654905018503145600E+00
DATA ·erfrodataL13<> + 16(SB)/8, $0.404669310217538718E+01
DATA ·erfrodataL13<> + 24(SB)/8, $-.564189219162765367E+00
DATA ·erfrodataL13<> + 32(SB)/8, $-.200104300906596851E+01
DATA ·erfrodataL13<> + 40(SB)/8, $0.5
DATA ·erfrodataL13<> + 48(SB)/8, $0.144070097650207154E+00
DATA ·erfrodataL13<> + 56(SB)/8, $-.116697735205906191E+00
DATA ·erfrodataL13<> + 64(SB)/8, $0.256847684882319665E-01
DATA ·erfrodataL13<> + 72(SB)/8, $-.510805169106229148E-02
DATA ·erfrodataL13<> + 80(SB)/8, $0.885258164825590267E-03
DATA ·erfrodataL13<> + 88(SB)/8, $-.133861989591931411E-03
DATA ·erfrodataL13<> + 96(SB)/8, $0.178294867340272534E-04
DATA ·erfrodataL13<> + 104(SB)/8, $-.211436095674019218E-05
DATA ·erfrodataL13<> + 112(SB)/8, $0.225503753499344434E-06
DATA ·erfrodataL13<> + 120(SB)/8, $-.218247939190783624E-07
DATA ·erfrodataL13<> + 128(SB)/8, $0.193179206264594029E-08
DATA ·erfrodataL13<> + 136(SB)/8, $-.157440643541715319E-09
DATA ·erfrodataL13<> + 144(SB)/8, $0.118878583237342616E-10
DATA ·erfrodataL13<> + 152(SB)/8, $0.554289288424588473E-13
DATA ·erfrodataL13<> + 160(SB)/8, $-.277649758489502214E-14
DATA ·erfrodataL13<> + 168(SB)/8, $-.839318416990049443E-12
DATA ·erfrodataL13<> + 176(SB)/8, $-2.25
DATA ·erfrodataL13<> + 184(SB)/8, $.12837916709551258632
DATA ·erfrodataL13<> + 192(SB)/8, $1.0
DATA ·erfrodataL13<> + 200(SB)/8, $0.500000000000004237e+00
DATA ·erfrodataL13<> + 208(SB)/8, $1.0
DATA ·erfrodataL13<> + 216(SB)/8, $0.416666664838056960e-01
DATA ·erfrodataL13<> + 224(SB)/8, $0.166666666630345592e+00
DATA ·erfrodataL13<> + 232(SB)/8, $0.138926439368309441e-02
DATA ·erfrodataL13<> + 240(SB)/8, $0.833349307718286047e-02
DATA ·erfrodataL13<> + 248(SB)/8, $-.693147180559945286e+00
DATA ·erfrodataL13<> + 256(SB)/8, $-.144269504088896339e+01
DATA ·erfrodataL13<> + 264(SB)/8, $281475245147134.9375
DATA ·erfrodataL13<> + 272(SB)/8, $0.358256136398192529E+01
DATA ·erfrodataL13<> + 280(SB)/8, $-.554084396500738270E+00
DATA ·erfrodataL13<> + 288(SB)/8, $0.203630123025312046E+02
DATA ·erfrodataL13<> + 296(SB)/8, $-.735750304705934424E+01
DATA ·erfrodataL13<> + 304(SB)/8, $0.250491598091071797E+02
DATA ·erfrodataL13<> + 312(SB)/8, $-.118955882760959931E+02
DATA ·erfrodataL13<> + 320(SB)/8, $0.942903335085524187E+01
DATA ·erfrodataL13<> + 328(SB)/8, $-.564189522219085689E+00
DATA ·erfrodataL13<> + 336(SB)/8, $-.503767199403555540E+01
DATA ·erfrodataL13<> + 344(SB)/8, $0xbbc79ca10c924223
DATA ·erfrodataL13<> + 352(SB)/8, $0.004099975562609307E+01
DATA ·erfrodataL13<> + 360(SB)/8, $-.324434353381296556E+00
DATA ·erfrodataL13<> + 368(SB)/8, $0.945204812084476250E-01
DATA ·erfrodataL13<> + 376(SB)/8, $-.221407443830058214E-01
DATA ·erfrodataL13<> + 384(SB)/8, $0.426072376238804349E-02
DATA ·erfrodataL13<> + 392(SB)/8, $-.692229229127016977E-03
DATA ·erfrodataL13<> + 400(SB)/8, $0.971111253652087188E-04
DATA ·erfrodataL13<> + 408(SB)/8, $-.119752226272050504E-04
DATA ·erfrodataL13<> + 416(SB)/8, $0.131662993588532278E-05
DATA ·erfrodataL13<> + 424(SB)/8, $0.115776482315851236E-07
DATA ·erfrodataL13<> + 432(SB)/8, $-.780118522218151687E-09
DATA ·erfrodataL13<> + 440(SB)/8, $-.130465975877241088E-06
DATA ·erfrodataL13<> + 448(SB)/8, $-0.25
GLOBL ·erfrodataL13<> + 0(SB), RODATA, $456
// Table of log correction terms
DATA ·erftab2066<> + 0(SB)/8, $0.442737824274138381e-01
DATA ·erftab2066<> + 8(SB)/8, $0.263602189790660309e-01
DATA ·erftab2066<> + 16(SB)/8, $0.122565642281703586e-01
DATA ·erftab2066<> + 24(SB)/8, $0.143757052860721398e-02
DATA ·erftab2066<> + 32(SB)/8, $-.651375034121276075e-02
DATA ·erftab2066<> + 40(SB)/8, $-.119317678849450159e-01
DATA ·erftab2066<> + 48(SB)/8, $-.150868749549871069e-01
DATA ·erftab2066<> + 56(SB)/8, $-.161992609578469234e-01
DATA ·erftab2066<> + 64(SB)/8, $-.154492360403337917e-01
DATA ·erftab2066<> + 72(SB)/8, $-.129850717389178721e-01
DATA ·erftab2066<> + 80(SB)/8, $-.892902649276657891e-02
DATA ·erftab2066<> + 88(SB)/8, $-.338202636596794887e-02
DATA ·erftab2066<> + 96(SB)/8, $0.357266307045684762e-02
DATA ·erftab2066<> + 104(SB)/8, $0.118665304327406698e-01
DATA ·erftab2066<> + 112(SB)/8, $0.214434994118118914e-01
DATA ·erftab2066<> + 120(SB)/8, $0.322580645161290314e-01
GLOBL ·erftab2066<> + 0(SB), RODATA, $128
// Table of +/- 1.0
DATA ·erftab12067<> + 0(SB)/8, $1.0
DATA ·erftab12067<> + 8(SB)/8, $-1.0
GLOBL ·erftab12067<> + 0(SB), RODATA, $16
// Erf returns the error function of the argument.
//
// Special cases are:
// Erf(+Inf) = 1
// Erf(-Inf) = -1
// Erf(NaN) = NaN
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·erfAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·erfrodataL13<>+0(SB), R5
WORD $0xB3CD0010 //lgdr %r1, %f0
FMOVD F0, F6
SRAD $48, R1
MOVH $16383, R3
WORD $0xEC2131BF //risbg %r2,%r1,49,128+63,0
BYTE $0x00
BYTE $0x55
MOVW R2, R6
MOVW R3, R7
CMPBGT R6, R7, L2
MOVH $12287, R1
MOVW R1, R7
CMPBLE R6, R7 ,L12
MOVH $16367, R1
MOVW R1, R7
CMPBGT R6, R7, L5
FMOVD 448(R5), F4
FMADD F0, F0, F4
FMOVD 440(R5), F3
WFMDB V4, V4, V2
FMOVD 432(R5), F0
FMOVD 424(R5), F1
WFMADB V2, V0, V3, V0
FMOVD 416(R5), F3
WFMADB V2, V1, V3, V1
FMOVD 408(R5), F5
FMOVD 400(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V1, V3, V1
FMOVD 392(R5), F5
FMOVD 384(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V1, V3, V1
FMOVD 376(R5), F5
FMOVD 368(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V1, V3, V1
FMOVD 360(R5), F5
FMOVD 352(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V1, V3, V2
WFMADB V4, V0, V2, V0
WFMADB V6, V0, V6, V0
L1:
FMOVD F0, ret+8(FP)
RET
L2:
MOVH R1, R1
MOVH $16407, R3
SRW $31, R1, R1
MOVW R2, R6
MOVW R3, R7
CMPBLE R6, R7, L6
MOVW R1, R1
SLD $3, R1, R1
MOVD $·erftab12067<>+0(SB), R3
WORD $0x68013000 //ld %f0,0(%r1,%r3)
MOVH $32751, R1
MOVW R1, R7
CMPBGT R6, R7, L7
FMOVD 344(R5), F2
FMADD F2, F0, F0
L7:
WFCEDBS V6, V6, V2
BEQ L1
FMOVD F6, F0
FMOVD F0, ret+8(FP)
RET
L6:
MOVW R1, R1
SLD $3, R1, R1
MOVD $·erftab12067<>+0(SB), R4
WFMDB V0, V0, V1
MOVH $0x0, R3
WORD $0x68014000 //ld %f0,0(%r1,%r4)
MOVH $16399, R1
MOVW R2, R6
MOVW R1, R7
CMPBGT R6, R7, L8
FMOVD 336(R5), F3
FMOVD 328(R5), F2
FMOVD F1, F4
WFMADB V1, V2, V3, V2
WORD $0xED405140 //adb %f4,.L30-.L13(%r5)
BYTE $0x00
BYTE $0x1A
FMOVD 312(R5), F3
WFMADB V1, V2, V3, V2
FMOVD 304(R5), F3
WFMADB V1, V4, V3, V4
FMOVD 296(R5), F3
WFMADB V1, V2, V3, V2
FMOVD 288(R5), F3
WFMADB V1, V4, V3, V4
FMOVD 280(R5), F3
WFMADB V1, V2, V3, V2
FMOVD 272(R5), F3
WFMADB V1, V4, V3, V4
L9:
FMOVD 264(R5), F3
FMUL F4, F6
FMOVD 256(R5), F4
WFMADB V1, V4, V3, V4
FDIV F6, F2
WORD $0xB3CD0014 //lgdr %r1, %f4
FSUB F3, F4
FMOVD 248(R5), F6
WFMSDB V4, V6, V1, V4
FMOVD 240(R5), F1
FMOVD 232(R5), F6
WFMADB V4, V6, V1, V6
FMOVD 224(R5), F1
FMOVD 216(R5), F3
WFMADB V4, V3, V1, V3
WFMDB V4, V4, V1
FMOVD 208(R5), F5
WFMADB V6, V1, V3, V6
FMOVD 200(R5), F3
MOVH R1,R1
WFMADB V4, V3, V5, V3
WORD $0xEC2139BC //risbg %r2,%r1,57,128+60,3
BYTE $0x03
BYTE $0x55
WFMADB V1, V6, V3, V6
WORD $0xEC31000F //risbgn %r3,%r1,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
MOVD $·erftab2066<>+0(SB), R1
FMOVD 192(R5), F1
WORD $0xB3C10033 //ldgr %f3,%r3
WORD $0xED221000 //madb %f2,%f2,0(%r2,%r1)
BYTE $0x20
BYTE $0x1E
WFMADB V4, V6, V1, V4
FMUL F3, F2
FMADD F4, F2, F0
FMOVD F0, ret+8(FP)
RET
L12:
FMOVD 184(R5), F0
WFMADB V6, V0, V6, V0
FMOVD F0, ret+8(FP)
RET
L5:
FMOVD 176(R5), F1
FMADD F0, F0, F1
FMOVD 168(R5), F3
WFMDB V1, V1, V2
FMOVD 160(R5), F0
FMOVD 152(R5), F4
WFMADB V2, V0, V3, V0
FMOVD 144(R5), F3
WFMADB V2, V4, V3, V4
FMOVD 136(R5), F5
FMOVD 128(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V4, V3, V4
FMOVD 120(R5), F5
FMOVD 112(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V4, V3, V4
FMOVD 104(R5), F5
FMOVD 96(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V4, V3, V4
FMOVD 88(R5), F5
FMOVD 80(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V4, V3, V4
FMOVD 72(R5), F5
FMOVD 64(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V4, V3, V4
FMOVD 56(R5), F5
FMOVD 48(R5), F3
WFMADB V2, V0, V5, V0
WFMADB V2, V4, V3, V2
FMOVD 40(R5), F4
WFMADB V1, V0, V2, V0
FMUL F6, F0
FMADD F4, F6, F0
FMOVD F0, ret+8(FP)
RET
L8:
FMOVD 32(R5), F3
FMOVD 24(R5), F2
FMOVD F1, F4
WFMADB V1, V2, V3, V2
WORD $0xED405010 //adb %f4,.L68-.L13(%r5)
BYTE $0x00
BYTE $0x1A
FMOVD 8(R5), F3
WFMADB V1, V2, V3, V2
FMOVD ·erfrodataL13<>+0(SB), F3
WFMADB V1, V4, V3, V4
BR L9

14
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// 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.
// +build 386 amd64 amd64p32 arm
#include "textflag.h"
TEXT ·Erf(SB),NOSPLIT,$0
JMP ·erf(SB)
TEXT ·Erfc(SB),NOSPLIT,$0
JMP ·erfc(SB)

530
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// 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"
#define NegInf 0xFFF0000000000000
// Minimax polynomial coefficients and other constants
DATA ·erfcrodataL38<> + 0(SB)/8, $.234875460637085087E-01
DATA ·erfcrodataL38<> + 8(SB)/8, $.234469449299256284E-01
DATA ·erfcrodataL38<> + 16(SB)/8, $-.606918710392844955E-04
DATA ·erfcrodataL38<> + 24(SB)/8, $-.198827088077636213E-04
DATA ·erfcrodataL38<> + 32(SB)/8, $.257805645845475331E-06
DATA ·erfcrodataL38<> + 40(SB)/8, $-.184427218110620284E-09
DATA ·erfcrodataL38<> + 48(SB)/8, $.122408098288933181E-10
DATA ·erfcrodataL38<> + 56(SB)/8, $.484691106751495392E-07
DATA ·erfcrodataL38<> + 64(SB)/8, $-.150147637632890281E-08
DATA ·erfcrodataL38<> + 72(SB)/8, $23.999999999973521625
DATA ·erfcrodataL38<> + 80(SB)/8, $27.226017111108365754
DATA ·erfcrodataL38<> + 88(SB)/8, $-2.0
DATA ·erfcrodataL38<> + 96(SB)/8, $0.100108802034478228E+00
DATA ·erfcrodataL38<> + 104(SB)/8, $0.244588413746558125E+00
DATA ·erfcrodataL38<> + 112(SB)/8, $-.669188879646637174E-01
DATA ·erfcrodataL38<> + 120(SB)/8, $0.151311447000953551E-01
DATA ·erfcrodataL38<> + 128(SB)/8, $-.284720833493302061E-02
DATA ·erfcrodataL38<> + 136(SB)/8, $0.455491239358743212E-03
DATA ·erfcrodataL38<> + 144(SB)/8, $-.631850539280720949E-04
DATA ·erfcrodataL38<> + 152(SB)/8, $0.772532660726086679E-05
DATA ·erfcrodataL38<> + 160(SB)/8, $-.843706007150936940E-06
DATA ·erfcrodataL38<> + 168(SB)/8, $-.735330214904227472E-08
DATA ·erfcrodataL38<> + 176(SB)/8, $0.753002008837084967E-09
DATA ·erfcrodataL38<> + 184(SB)/8, $0.832482036660624637E-07
DATA ·erfcrodataL38<> + 192(SB)/8, $-0.75
DATA ·erfcrodataL38<> + 200(SB)/8, $.927765678007128609E-01
DATA ·erfcrodataL38<> + 208(SB)/8, $.903621209344751506E-01
DATA ·erfcrodataL38<> + 216(SB)/8, $-.344203375025257265E-02
DATA ·erfcrodataL38<> + 224(SB)/8, $-.869243428221791329E-03
DATA ·erfcrodataL38<> + 232(SB)/8, $.174699813107105603E-03
DATA ·erfcrodataL38<> + 240(SB)/8, $.649481036316130000E-05
DATA ·erfcrodataL38<> + 248(SB)/8, $-.895265844897118382E-05
DATA ·erfcrodataL38<> + 256(SB)/8, $.135970046909529513E-05
DATA ·erfcrodataL38<> + 264(SB)/8, $.277617717014748015E-06
DATA ·erfcrodataL38<> + 272(SB)/8, $.810628018408232910E-08
DATA ·erfcrodataL38<> + 280(SB)/8, $.210430084693497985E-07
DATA ·erfcrodataL38<> + 288(SB)/8, $-.342138077525615091E-08
DATA ·erfcrodataL38<> + 296(SB)/8, $-.165467946798610800E-06
DATA ·erfcrodataL38<> + 304(SB)/8, $5.999999999988412824
DATA ·erfcrodataL38<> + 312(SB)/8, $.468542210149072159E-01
DATA ·erfcrodataL38<> + 320(SB)/8, $.465343528567604256E-01
DATA ·erfcrodataL38<> + 328(SB)/8, $-.473338083650201733E-03
DATA ·erfcrodataL38<> + 336(SB)/8, $-.147220659069079156E-03
DATA ·erfcrodataL38<> + 344(SB)/8, $.755284723554388339E-05
DATA ·erfcrodataL38<> + 352(SB)/8, $.116158570631428789E-05
DATA ·erfcrodataL38<> + 360(SB)/8, $-.155445501551602389E-06
DATA ·erfcrodataL38<> + 368(SB)/8, $-.616940119847805046E-10
DATA ·erfcrodataL38<> + 376(SB)/8, $-.728705590727563158E-10
DATA ·erfcrodataL38<> + 384(SB)/8, $-.983452460354586779E-08
DATA ·erfcrodataL38<> + 392(SB)/8, $.365156164194346316E-08
DATA ·erfcrodataL38<> + 400(SB)/8, $11.999999999996530775
DATA ·erfcrodataL38<> + 408(SB)/8, $0.467773498104726584E-02
DATA ·erfcrodataL38<> + 416(SB)/8, $0.206669853540920535E-01
DATA ·erfcrodataL38<> + 424(SB)/8, $0.413339707081841473E-01
DATA ·erfcrodataL38<> + 432(SB)/8, $0.482229658262131320E-01
DATA ·erfcrodataL38<> + 440(SB)/8, $0.344449755901841897E-01
DATA ·erfcrodataL38<> + 448(SB)/8, $0.130890907240765465E-01
DATA ·erfcrodataL38<> + 456(SB)/8, $-.459266344100642687E-03
DATA ·erfcrodataL38<> + 464(SB)/8, $-.337888800856913728E-02
DATA ·erfcrodataL38<> + 472(SB)/8, $-.159103061687062373E-02
DATA ·erfcrodataL38<> + 480(SB)/8, $-.501128905515922644E-04
DATA ·erfcrodataL38<> + 488(SB)/8, $0.262775855852903132E-03
DATA ·erfcrodataL38<> + 496(SB)/8, $0.103860982197462436E-03
DATA ·erfcrodataL38<> + 504(SB)/8, $-.548835785414200775E-05
DATA ·erfcrodataL38<> + 512(SB)/8, $-.157075054646618214E-04
DATA ·erfcrodataL38<> + 520(SB)/8, $-.480056366276045110E-05
DATA ·erfcrodataL38<> + 528(SB)/8, $0.198263013759701555E-05
DATA ·erfcrodataL38<> + 536(SB)/8, $-.224394262958888780E-06
DATA ·erfcrodataL38<> + 544(SB)/8, $-.321853693146683428E-06
DATA ·erfcrodataL38<> + 552(SB)/8, $0.445073894984683537E-07
DATA ·erfcrodataL38<> + 560(SB)/8, $0.660425940000555729E-06
DATA ·erfcrodataL38<> + 568(SB)/8, $2.0
DATA ·erfcrodataL38<> + 576(SB)/8, $8.63616855509444462538e-78
DATA ·erfcrodataL38<> + 584(SB)/8, $1.00000000000000222044
DATA ·erfcrodataL38<> + 592(SB)/8, $0.500000000000004237e+00
DATA ·erfcrodataL38<> + 600(SB)/8, $0.416666664838056960e-01
DATA ·erfcrodataL38<> + 608(SB)/8, $0.166666666630345592e+00
DATA ·erfcrodataL38<> + 616(SB)/8, $0.138926439368309441e-02
DATA ·erfcrodataL38<> + 624(SB)/8, $0.833349307718286047e-02
DATA ·erfcrodataL38<> + 632(SB)/8, $-.693147180558298714e+00
DATA ·erfcrodataL38<> + 640(SB)/8, $-.164659495826017651e-11
DATA ·erfcrodataL38<> + 648(SB)/8, $.179001151181866548E+00
DATA ·erfcrodataL38<> + 656(SB)/8, $-.144269504088896339e+01
DATA ·erfcrodataL38<> + 664(SB)/8, $+281475245147134.9375
DATA ·erfcrodataL38<> + 672(SB)/8, $.163116780021877404E+00
DATA ·erfcrodataL38<> + 680(SB)/8, $-.201574395828120710E-01
DATA ·erfcrodataL38<> + 688(SB)/8, $-.185726336009394125E-02
DATA ·erfcrodataL38<> + 696(SB)/8, $.199349204957273749E-02
DATA ·erfcrodataL38<> + 704(SB)/8, $-.554902415532606242E-03
DATA ·erfcrodataL38<> + 712(SB)/8, $-.638914789660242846E-05
DATA ·erfcrodataL38<> + 720(SB)/8, $-.424441522653742898E-04
DATA ·erfcrodataL38<> + 728(SB)/8, $.827967511921486190E-04
DATA ·erfcrodataL38<> + 736(SB)/8, $.913965446284062654E-05
DATA ·erfcrodataL38<> + 744(SB)/8, $.277344791076320853E-05
DATA ·erfcrodataL38<> + 752(SB)/8, $-.467239678927239526E-06
DATA ·erfcrodataL38<> + 760(SB)/8, $.344814065920419986E-07
DATA ·erfcrodataL38<> + 768(SB)/8, $-.366013491552527132E-05
DATA ·erfcrodataL38<> + 776(SB)/8, $.181242810023783439E-05
DATA ·erfcrodataL38<> + 784(SB)/8, $2.999999999991234567
DATA ·erfcrodataL38<> + 792(SB)/8, $1.0
GLOBL ·erfcrodataL38<> + 0(SB), RODATA, $800
// Table of log correction terms
DATA ·erfctab2069<> + 0(SB)/8, $0.442737824274138381e-01
DATA ·erfctab2069<> + 8(SB)/8, $0.263602189790660309e-01
DATA ·erfctab2069<> + 16(SB)/8, $0.122565642281703586e-01
DATA ·erfctab2069<> + 24(SB)/8, $0.143757052860721398e-02
DATA ·erfctab2069<> + 32(SB)/8, $-.651375034121276075e-02
DATA ·erfctab2069<> + 40(SB)/8, $-.119317678849450159e-01
DATA ·erfctab2069<> + 48(SB)/8, $-.150868749549871069e-01
DATA ·erfctab2069<> + 56(SB)/8, $-.161992609578469234e-01
DATA ·erfctab2069<> + 64(SB)/8, $-.154492360403337917e-01
DATA ·erfctab2069<> + 72(SB)/8, $-.129850717389178721e-01
DATA ·erfctab2069<> + 80(SB)/8, $-.892902649276657891e-02
DATA ·erfctab2069<> + 88(SB)/8, $-.338202636596794887e-02
DATA ·erfctab2069<> + 96(SB)/8, $0.357266307045684762e-02
DATA ·erfctab2069<> + 104(SB)/8, $0.118665304327406698e-01
DATA ·erfctab2069<> + 112(SB)/8, $0.214434994118118914e-01
DATA ·erfctab2069<> + 120(SB)/8, $0.322580645161290314e-01
GLOBL ·erfctab2069<> + 0(SB), RODATA, $128
// Erfc returns the complementary error function of the argument.
//
// Special cases are:
// Erfc(+Inf) = 0
// Erfc(-Inf) = 2
// Erfc(NaN) = NaN
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·erfcAsm(SB), NOSPLIT, $0-16
//special case Erfc(+Inf) = 0
MOVD x+0(FP), R1
MOVD $NegInf, R2
CMPUBEQ R1, R2, erfcIsPosInf
FMOVD x+0(FP), F0
MOVD $·erfcrodataL38<>+0(SB), R9
WORD $0xB3CD0010 //lgdr %r1, %f0
FMOVD F0, F2
SRAD $48, R1
MOVH $0x3FFF, R3
MOVH R1, R2
ANDW $0x7FFF, R1
MOVW R1, R6
MOVW R3, R7
CMPBGT R6, R7, L2
MOVH $0x3FEF, R3
MOVW R3, R7
CMPBGT R6, R7, L3
MOVH $0x2FFF, R2
MOVW R2, R7
CMPBGT R6, R7, L4
FMOVD 792(R9), F0
WFSDB V2, V0, V2
FMOVD F2, ret+8(FP)
RET
L2:
WORD $0xB3120000 //ltdbr %f0,%f0
MOVH $0x0, R4
BLTU L3
FMOVD F0, F1
L9:
MOVH $0x400F, R3
MOVW R1, R6
MOVW R3, R7
CMPBGT R6, R7, L10
FMOVD 784(R9), F3
FSUB F1, F3
VLEG $0, 776(R9), V20
WFDDB V1, V3, V6
VLEG $0, 768(R9), V18
FMOVD 760(R9), F7
FMOVD 752(R9), F5
VLEG $0, 744(R9), V16
FMOVD 736(R9), F3
FMOVD 728(R9), F2
FMOVD 720(R9), F4
WFMDB V6, V6, V1
FMUL F0, F0
MOVH $0x0, R3
WFMADB V1, V7, V20, V7
WFMADB V1, V5, V18, V5
WFMADB V1, V7, V16, V7
WFMADB V1, V5, V3, V5
WFMADB V1, V7, V4, V7
WFMADB V1, V5, V2, V5
FMOVD 712(R9), F2
WFMADB V1, V7, V2, V7
FMOVD 704(R9), F2
WFMADB V1, V5, V2, V5
FMOVD 696(R9), F2
WFMADB V1, V7, V2, V7
FMOVD 688(R9), F2
MOVH $0x0, R1
WFMADB V1, V5, V2, V5
FMOVD 680(R9), F2
WFMADB V1, V7, V2, V7
FMOVD 672(R9), F2
WFMADB V1, V5, V2, V1
FMOVD 664(R9), F3
WFMADB V6, V7, V1, V7
FMOVD 656(R9), F5
FMOVD 648(R9), F2
WFMADB V0, V5, V3, V5
WFMADB V6, V7, V2, V7
L11:
WORD $0xB3CD0065 //lgdr %r6, %f5
WFSDB V0, V0, V2
WORD $0xED509298 //sdb %f5,.L55-.L38(%r9)
BYTE $0x00
BYTE $0x1B
FMOVD 640(R9), F6
FMOVD 632(R9), F4
WFMSDB V5, V6, V2, V6
WFMSDB V5, V4, V0, V4
FMOVD 624(R9), F2
FADD F6, F4
FMOVD 616(R9), F0
FMOVD 608(R9), F6
WFMADB V4, V0, V2, V0
FMOVD 600(R9), F3
WFMDB V4, V4, V2
MOVH R6,R6
ADD R6, R3
WFMADB V4, V3, V6, V3
FMOVD 592(R9), F6
WFMADB V0, V2, V3, V0
FMOVD 584(R9), F3
WFMADB V4, V6, V3, V6
WORD $0xECC339BC //risbg %r12,%r3,57,128+60,3
BYTE $0x03
BYTE $0x55
WFMADB V2, V0, V6, V0
MOVD $·erfctab2069<>+0(SB), R5
WORD $0x682C5000 //ld %f2,0(%r12,%r5)
FMADD F2, F4, F4
WORD $0xEC43000F //risbgn %r4,%r3,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WFMADB V4, V0, V2, V4
WORD $0xB3C10024 //ldgr %f2,%r4
FMADD F4, F2, F2
MOVW R2, R6
CMPBLE R6, $0, L20
MOVW R1, R6
CMPBEQ R6, $0, L21
WORD $0xED709240 //mdb %f7,.L66-.L38(%r9)
BYTE $0x00
BYTE $0x1C
L21:
FMUL F7, F2
L1:
FMOVD F2, ret+8(FP)
RET
L3:
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L30
FMOVD 568(R9), F2
WFSDB V0, V2, V0
L8:
WFMDB V0, V0, V4
FMOVD 560(R9), F2
FMOVD 552(R9), F6
FMOVD 544(R9), F1
WFMADB V4, V6, V2, V6
FMOVD 536(R9), F2
WFMADB V4, V1, V2, V1
FMOVD 528(R9), F3
FMOVD 520(R9), F2
WFMADB V4, V6, V3, V6
WFMADB V4, V1, V2, V1
FMOVD 512(R9), F3
FMOVD 504(R9), F2
WFMADB V4, V6, V3, V6
WFMADB V4, V1, V2, V1
FMOVD 496(R9), F3
FMOVD 488(R9), F2
WFMADB V4, V6, V3, V6
WFMADB V4, V1, V2, V1
FMOVD 480(R9), F3
FMOVD 472(R9), F2
WFMADB V4, V6, V3, V6
WFMADB V4, V1, V2, V1
FMOVD 464(R9), F3
FMOVD 456(R9), F2
WFMADB V4, V6, V3, V6
WFMADB V4, V1, V2, V1
FMOVD 448(R9), F3
FMOVD 440(R9), F2
WFMADB V4, V6, V3, V6
WFMADB V4, V1, V2, V1
FMOVD 432(R9), F3
FMOVD 424(R9), F2
WFMADB V4, V6, V3, V6
WFMADB V4, V1, V2, V1
FMOVD 416(R9), F3
FMOVD 408(R9), F2
WFMADB V4, V6, V3, V6
FMADD F1, F4, F2
FMADD F6, F0, F2
MOVW R2, R6
CMPBGE R6, $0, L1
FMOVD 568(R9), F0
WFSDB V2, V0, V2
BR L1
L10:
MOVH $0x401F, R3
MOVW R1, R6
MOVW R3, R7
CMPBLE R6, R7, L36
MOVH $0x402F, R3
MOVW R3, R7
CMPBGT R6, R7, L13
FMOVD 400(R9), F3
FSUB F1, F3
VLEG $0, 392(R9), V20
WFDDB V1, V3, V6
VLEG $0, 384(R9), V18
FMOVD 376(R9), F2
FMOVD 368(R9), F4
VLEG $0, 360(R9), V16
FMOVD 352(R9), F7
FMOVD 344(R9), F3
FMUL F0, F0
WFMDB V6, V6, V1
FMOVD 656(R9), F5
MOVH $0x0, R3
WFMADB V1, V2, V20, V2
WFMADB V1, V4, V18, V4
WFMADB V1, V2, V16, V2
WFMADB V1, V4, V7, V4
WFMADB V1, V2, V3, V2
FMOVD 336(R9), F3
WFMADB V1, V4, V3, V4
FMOVD 328(R9), F3
WFMADB V1, V2, V3, V2
FMOVD 320(R9), F3
WFMADB V1, V4, V3, V1
FMOVD 312(R9), F7
WFMADB V6, V2, V1, V2
MOVH $0x0, R1
FMOVD 664(R9), F3
FMADD F2, F6, F7
WFMADB V0, V5, V3, V5
BR L11
L35:
WORD $0xB3130010 //lcdbr %f1,%f0
BR L9
L36:
FMOVD 304(R9), F3
FSUB F1, F3
VLEG $0, 296(R9), V20
WFDDB V1, V3, V6
FMOVD 288(R9), F5
FMOVD 280(R9), F1
FMOVD 272(R9), F2
VLEG $0, 264(R9), V18
VLEG $0, 256(R9), V16
FMOVD 248(R9), F3
FMOVD 240(R9), F4
WFMDB V6, V6, V7
FMUL F0, F0
MOVH $0x0, R3
FMADD F5, F7, F1
WFMADB V7, V2, V20, V2
WFMADB V7, V1, V18, V1
WFMADB V7, V2, V16, V2
WFMADB V7, V1, V3, V1
WFMADB V7, V2, V4, V2
FMOVD 232(R9), F4
WFMADB V7, V1, V4, V1
FMOVD 224(R9), F4
WFMADB V7, V2, V4, V2
FMOVD 216(R9), F4
WFMADB V7, V1, V4, V1
FMOVD 208(R9), F4
MOVH $0x0, R1
WFMADB V7, V2, V4, V7
FMOVD 656(R9), F5
WFMADB V6, V1, V7, V1
FMOVD 664(R9), F3
FMOVD 200(R9), F7
WFMADB V0, V5, V3, V5
FMADD F1, F6, F7
BR L11
L4:
FMOVD 192(R9), F1
FMADD F0, F0, F1
FMOVD 184(R9), F3
WFMDB V1, V1, V0
FMOVD 176(R9), F4
FMOVD 168(R9), F6
WFMADB V0, V4, V3, V4
FMOVD 160(R9), F3
WFMADB V0, V6, V3, V6
FMOVD 152(R9), F5
FMOVD 144(R9), F3
WFMADB V0, V4, V5, V4
WFMADB V0, V6, V3, V6
FMOVD 136(R9), F5
FMOVD 128(R9), F3
WFMADB V0, V4, V5, V4
WFMADB V0, V6, V3, V6
FMOVD 120(R9), F5
FMOVD 112(R9), F3
WFMADB V0, V4, V5, V4
WFMADB V0, V6, V3, V6
FMOVD 104(R9), F5
FMOVD 96(R9), F3
WFMADB V0, V4, V5, V4
WFMADB V0, V6, V3, V0
FMOVD F2, F6
FMADD F4, F1, F0
WORD $0xED609318 //sdb %f6,.L39-.L38(%r9)
BYTE $0x00
BYTE $0x1B
WFMSDB V2, V0, V6, V2
FMOVD F2, ret+8(FP)
RET
L30:
WORD $0xED009238 //adb %f0,.L67-.L38(%r9)
BYTE $0x00
BYTE $0x1A
BR L8
L20:
FMOVD 88(R9), F0
WFMADB V7, V2, V0, V2
WORD $0xB3130022 //lcdbr %f2,%f2
FMOVD F2, ret+8(FP)
RET
L13:
MOVH $0x403A, R3
MOVW R1, R6
MOVW R3, R7
CMPBLE R6, R7, L4
WORD $0xED109050 //cdb %f1,.L128-.L38(%r9)
BYTE $0x00
BYTE $0x19
BGE L37
BVS L37
FMOVD 72(R9), F6
FSUB F1, F6
MOVH $0x1000, R3
FDIV F1, F6
MOVH $0x1000, R1
L17:
WFMDB V6, V6, V1
FMOVD 64(R9), F2
FMOVD 56(R9), F4
FMOVD 48(R9), F3
WFMADB V1, V3, V2, V3
FMOVD 40(R9), F2
WFMADB V1, V2, V4, V2
FMOVD 32(R9), F4
WFMADB V1, V3, V4, V3
FMOVD 24(R9), F4
WFMADB V1, V2, V4, V2
FMOVD 16(R9), F4
WFMADB V1, V3, V4, V3
FMOVD 8(R9), F4
WFMADB V1, V2, V4, V1
FMUL F0, F0
WFMADB V3, V6, V1, V3
FMOVD 656(R9), F5
FMOVD 664(R9), F4
FMOVD 0(R9), F7
WFMADB V0, V5, V4, V5
FMADD F6, F3, F7
BR L11
L14:
FMOVD 72(R9), F6
FSUB F1, F6
MOVH $0x403A, R3
FDIV F1, F6
MOVW R1, R6
MOVW R3, R7
CMPBEQ R6, R7, L23
MOVH $0x0, R3
MOVH $0x0, R1
BR L17
L37:
WFCEDBS V0, V0, V0
BVS L1
MOVW R2, R6
CMPBLE R6, $0, L18
MOVH $0x7FEF, R2
MOVW R1, R6
MOVW R2, R7
CMPBGT R6, R7, L24
WORD $0xA5400010 //iihh %r4,16
WORD $0xB3C10024 //ldgr %f2,%r4
FMUL F2, F2
BR L1
L23:
MOVH $0x1000, R3
MOVH $0x1000, R1
BR L17
L24:
FMOVD $0, F2
BR L1
L18:
MOVH $0x7FEF, R2
MOVW R1, R6
MOVW R2, R7
CMPBGT R6, R7, L25
WORD $0xA5408010 //iihh %r4,32784
FMOVD 568(R9), F2
WORD $0xB3C10004 //ldgr %f0,%r4
FMADD F2, F0, F2
BR L1
L25:
FMOVD 568(R9), F2
BR L1
erfcIsPosInf:
FMOVD $(2.0), F1
FMOVD F1, ret+8(FP)
RET

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src/math/exp_s390x.s Normal file
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// 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 approximation and other constants
DATA ·exprodataL22<> + 0(SB)/8, $800.0E+00
DATA ·exprodataL22<> + 8(SB)/8, $1.0000000000000022e+00
DATA ·exprodataL22<> + 16(SB)/8, $0.500000000000004237e+00
DATA ·exprodataL22<> + 24(SB)/8, $0.166666666630345592e+00
DATA ·exprodataL22<> + 32(SB)/8, $0.138926439368309441e-02
DATA ·exprodataL22<> + 40(SB)/8, $0.833349307718286047e-02
DATA ·exprodataL22<> + 48(SB)/8, $0.416666664838056960e-01
DATA ·exprodataL22<> + 56(SB)/8, $-.231904681384629956E-16
DATA ·exprodataL22<> + 64(SB)/8, $-.693147180559945286E+00
DATA ·exprodataL22<> + 72(SB)/8, $0.144269504088896339E+01
DATA ·exprodataL22<> + 80(SB)/8, $704.0E+00
GLOBL ·exprodataL22<> + 0(SB), RODATA, $88
DATA ·expxinf<> + 0(SB)/8, $0x7ff0000000000000
GLOBL ·expxinf<> + 0(SB), RODATA, $8
DATA ·expx4ff<> + 0(SB)/8, $0x4ff0000000000000
GLOBL ·expx4ff<> + 0(SB), RODATA, $8
DATA ·expx2ff<> + 0(SB)/8, $0x2ff0000000000000
GLOBL ·expx2ff<> + 0(SB), RODATA, $8
DATA ·expxaddexp<> + 0(SB)/8, $0xc2f0000100003fef
GLOBL ·expxaddexp<> + 0(SB), RODATA, $8
// Log multipliers table
DATA ·exptexp<> + 0(SB)/8, $0.442737824274138381E-01
DATA ·exptexp<> + 8(SB)/8, $0.263602189790660309E-01
DATA ·exptexp<> + 16(SB)/8, $0.122565642281703586E-01
DATA ·exptexp<> + 24(SB)/8, $0.143757052860721398E-02
DATA ·exptexp<> + 32(SB)/8, $-.651375034121276075E-02
DATA ·exptexp<> + 40(SB)/8, $-.119317678849450159E-01
DATA ·exptexp<> + 48(SB)/8, $-.150868749549871069E-01
DATA ·exptexp<> + 56(SB)/8, $-.161992609578469234E-01
DATA ·exptexp<> + 64(SB)/8, $-.154492360403337917E-01
DATA ·exptexp<> + 72(SB)/8, $-.129850717389178721E-01
DATA ·exptexp<> + 80(SB)/8, $-.892902649276657891E-02
DATA ·exptexp<> + 88(SB)/8, $-.338202636596794887E-02
DATA ·exptexp<> + 96(SB)/8, $0.357266307045684762E-02
DATA ·exptexp<> + 104(SB)/8, $0.118665304327406698E-01
DATA ·exptexp<> + 112(SB)/8, $0.214434994118118914E-01
DATA ·exptexp<> + 120(SB)/8, $0.322580645161290314E-01
GLOBL ·exptexp<> + 0(SB), RODATA, $128
// Exp returns e**x, the base-e exponential of x.
//
// Special cases are:
// Exp(+Inf) = +Inf
// Exp(NaN) = NaN
// Very large values overflow to 0 or +Inf.
// Very small values underflow to 1.
// The algorithm used is minimax polynomial approximation using a table of
// polynomial coefficients determined with a Remez exchange algorithm.
TEXT ·expAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·exprodataL22<>+0(SB), R5
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L20
FMOVD F0, F2
L2:
WORD $0xED205050 //cdb %f2,.L23-.L22(%r5)
BYTE $0x00
BYTE $0x19
BGE L16
BVS L16
WFCEDBS V2, V2, V2
BVS LEXITTAGexp
MOVD $·expxaddexp<>+0(SB), R1
FMOVD 72(R5), F6
FMOVD 0(R1), F2
WFMSDB V0, V6, V2, V6
FMOVD 64(R5), F4
FADD F6, F2
FMOVD 56(R5), F1
FMADD F4, F2, F0
FMOVD 48(R5), F3
WFMADB V2, V1, V0, V2
FMOVD 40(R5), F1
FMOVD 32(R5), F4
FMUL F0, F0
WFMADB V2, V4, V1, V4
WORD $0xB3CD0016 //lgdr %r1,%f6
FMOVD 24(R5), F1
WFMADB V2, V3, V1, V3
FMOVD 16(R5), F1
WFMADB V0, V4, V3, V4
FMOVD 8(R5), F3
WFMADB V2, V1, V3, V1
WORD $0xEC3139BC //risbg %r3,%r1,57,128+60,3
BYTE $0x03
BYTE $0x55
WFMADB V0, V4, V1, V0
MOVD $·exptexp<>+0(SB), R2
WORD $0x68432000 //ld %f4,0(%r3,%r2)
FMADD F4, F2, F2
SLD $48, R1, R2
WFMADB V2, V0, V4, V2
WORD $0xB3C10002 //ldgr %f0,%r2
FMADD F0, F2, F0
FMOVD F0, ret+8(FP)
RET
L16:
WFCEDBS V2, V2, V4
BVS LEXITTAGexp
WORD $0xED205000 //cdb %f2,.L33-.L22(%r5)
BYTE $0x00
BYTE $0x19
BLT L6
WFCEDBS V2, V0, V0
BVS L13
MOVD $·expxinf<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
L20:
WORD $0xB3130020 //lcdbr %f2,%f0
BR L2
L6:
MOVD $·expxaddexp<>+0(SB), R1
FMOVD 72(R5), F3
FMOVD 0(R1), F4
WFMSDB V0, V3, V4, V3
FMOVD 64(R5), F6
FADD F3, F4
FMOVD 56(R5), F5
WFMADB V4, V6, V0, V6
FMOVD 32(R5), F1
WFMADB V4, V5, V6, V4
FMOVD 40(R5), F5
FMUL F6, F6
WFMADB V4, V1, V5, V1
FMOVD 48(R5), F7
WORD $0xB3CD0013 //lgdr %r1,%f3
FMOVD 24(R5), F5
WFMADB V4, V7, V5, V7
FMOVD 16(R5), F5
WFMADB V6, V1, V7, V1
FMOVD 8(R5), F7
WFMADB V4, V5, V7, V5
WORD $0xEC3139BC //risbg %r3,%r1,57,128+60,3
BYTE $0x03
BYTE $0x55
WFMADB V6, V1, V5, V6
MOVD $·exptexp<>+0(SB), R2
WFCHDBS V2, V0, V0
WORD $0x68132000 //ld %f1,0(%r3,%r2)
FMADD F1, F4, F4
MOVD $0x4086000000000000, R2
WFMADB V4, V6, V1, V4
BEQ L21
ADDW $0xF000, R1
WORD $0xEC21000F //risbgn %r2,%r1,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WORD $0xB3C10002 //ldgr %f0,%r2
FMADD F0, F4, F0
MOVD $·expx4ff<>+0(SB), R3
FMOVD 0(R3), F2
FMUL F2, F0
FMOVD F0, ret+8(FP)
RET
L13:
FMOVD $0, F0
FMOVD F0, ret+8(FP)
RET
L21:
ADDW $0x1000, R1
WORD $0xEC21000F //risbgn %r2,%r1,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WORD $0xB3C10002 //ldgr %f0,%r2
FMADD F0, F4, F0
MOVD $·expx2ff<>+0(SB), R3
FMOVD 0(R3), F2
FMUL F2, F0
FMOVD F0, ret+8(FP)
RET
LEXITTAGexp:
FMOVD F0, ret+8(FP)
RET

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// 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 approximation and other constants
DATA ·expm1rodataL22<> + 0(SB)/8, $-1.0
DATA ·expm1rodataL22<> + 8(SB)/8, $800.0E+00
DATA ·expm1rodataL22<> + 16(SB)/8, $1.0
DATA ·expm1rodataL22<> + 24(SB)/8, $-.231904681384629956E-16
DATA ·expm1rodataL22<> + 32(SB)/8, $0.50000000000000029671E+00
DATA ·expm1rodataL22<> + 40(SB)/8, $0.16666666666666676570E+00
DATA ·expm1rodataL22<> + 48(SB)/8, $0.83333333323590973444E-02
DATA ·expm1rodataL22<> + 56(SB)/8, $0.13889096526400683566E-02
DATA ·expm1rodataL22<> + 64(SB)/8, $0.41666666661701152924E-01
DATA ·expm1rodataL22<> + 72(SB)/8, $0.19841562053987360264E-03
DATA ·expm1rodataL22<> + 80(SB)/8, $-.693147180559945286E+00
DATA ·expm1rodataL22<> + 88(SB)/8, $0.144269504088896339E+01
DATA ·expm1rodataL22<> + 96(SB)/8, $704.0E+00
GLOBL ·expm1rodataL22<> + 0(SB), RODATA, $104
DATA ·expm1xmone<> + 0(SB)/8, $0xbff0000000000000
GLOBL ·expm1xmone<> + 0(SB), RODATA, $8
DATA ·expm1xinf<> + 0(SB)/8, $0x7ff0000000000000
GLOBL ·expm1xinf<> + 0(SB), RODATA, $8
DATA ·expm1x4ff<> + 0(SB)/8, $0x4ff0000000000000
GLOBL ·expm1x4ff<> + 0(SB), RODATA, $8
DATA ·expm1x2ff<> + 0(SB)/8, $0x2ff0000000000000
GLOBL ·expm1x2ff<> + 0(SB), RODATA, $8
DATA ·expm1xaddexp<> + 0(SB)/8, $0xc2f0000100003ff0
GLOBL ·expm1xaddexp<> + 0(SB), RODATA, $8
// Log multipliers table
DATA ·expm1tab<> + 0(SB)/8, $0.0
DATA ·expm1tab<> + 8(SB)/8, $-.171540871271399150E-01
DATA ·expm1tab<> + 16(SB)/8, $-.306597931864376363E-01
DATA ·expm1tab<> + 24(SB)/8, $-.410200970469965021E-01
DATA ·expm1tab<> + 32(SB)/8, $-.486343079978231466E-01
DATA ·expm1tab<> + 40(SB)/8, $-.538226193725835820E-01
DATA ·expm1tab<> + 48(SB)/8, $-.568439602538111520E-01
DATA ·expm1tab<> + 56(SB)/8, $-.579091847395528847E-01
DATA ·expm1tab<> + 64(SB)/8, $-.571909584179366341E-01
DATA ·expm1tab<> + 72(SB)/8, $-.548312665987204407E-01
DATA ·expm1tab<> + 80(SB)/8, $-.509471843643441085E-01
DATA ·expm1tab<> + 88(SB)/8, $-.456353588448863359E-01
DATA ·expm1tab<> + 96(SB)/8, $-.389755254243262365E-01
DATA ·expm1tab<> + 104(SB)/8, $-.310332908285244231E-01
DATA ·expm1tab<> + 112(SB)/8, $-.218623539150173528E-01
DATA ·expm1tab<> + 120(SB)/8, $-.115062908917949451E-01
GLOBL ·expm1tab<> + 0(SB), RODATA, $128
// Expm1 returns e**x - 1, the base-e exponential of x minus 1.
// It is more accurate than Exp(x) - 1 when x is near zero.
//
// Special cases are:
// Expm1(+Inf) = +Inf
// Expm1(-Inf) = -1
// Expm1(NaN) = NaN
// Very large values overflow to -1 or +Inf.
// The algorithm used is minimax polynomial approximation using a table of
// polynomial coefficients determined with a Remez exchange algorithm.
TEXT ·expm1Asm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·expm1rodataL22<>+0(SB), R5
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L20
FMOVD F0, F2
L2:
WORD $0xED205060 //cdb %f2,.L23-.L22(%r5)
BYTE $0x00
BYTE $0x19
BGE L16
BVS L16
WFCEDBS V2, V2, V2
BVS LEXITTAGexpm1
MOVD $·expm1xaddexp<>+0(SB), R1
FMOVD 88(R5), F1
FMOVD 0(R1), F2
WFMSDB V0, V1, V2, V1
FMOVD 80(R5), F6
WFADB V1, V2, V4
FMOVD 72(R5), F2
FMADD F6, F4, F0
FMOVD 64(R5), F3
FMOVD 56(R5), F6
FMOVD 48(R5), F5
FMADD F2, F0, F6
WFMADB V0, V5, V3, V5
WFMDB V0, V0, V2
WORD $0xB3CD0011 //lgdr %r1,%f1
WFMADB V6, V2, V5, V6
FMOVD 40(R5), F3
FMOVD 32(R5), F5
WFMADB V0, V3, V5, V3
FMOVD 24(R5), F5
WFMADB V2, V6, V3, V2
FMADD F5, F4, F0
FMOVD 16(R5), F6
WFMADB V0, V2, V6, V2
WORD $0xEC3139BC //risbg %r3,%r1,57,128+60,3
BYTE $0x03
BYTE $0x55
WORD $0xB3130022 //lcdbr %f2,%f2
MOVD $·expm1tab<>+0(SB), R2
WORD $0x68432000 //ld %f4,0(%r3,%r2)
FMADD F4, F0, F0
SLD $48, R1, R2
WFMSDB V2, V0, V4, V0
WORD $0xB3C10042 //ldgr %f4,%r2
WORD $0xB3130000 //lcdbr %f0,%f0
FSUB F4, F6
WFMSDB V0, V4, V6, V0
FMOVD F0, ret+8(FP)
RET
L16:
WFCEDBS V2, V2, V4
BVS LEXITTAGexpm1
WORD $0xED205008 //cdb %f2,.L34-.L22(%r5)
BYTE $0x00
BYTE $0x19
BLT L6
WFCEDBS V2, V0, V0
BVS L7
MOVD $·expm1xinf<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
L20:
WORD $0xB3130020 //lcdbr %f2,%f0
BR L2
L6:
MOVD $·expm1xaddexp<>+0(SB), R1
FMOVD 88(R5), F5
FMOVD 0(R1), F4
WFMSDB V0, V5, V4, V5
FMOVD 80(R5), F3
WFADB V5, V4, V1
VLEG $0, 48(R5), V16
WFMADB V1, V3, V0, V3
FMOVD 56(R5), F4
FMOVD 64(R5), F7
FMOVD 72(R5), F6
WFMADB V3, V16, V7, V16
WFMADB V3, V6, V4, V6
WFMDB V3, V3, V4
MOVD $·expm1tab<>+0(SB), R2
WFMADB V6, V4, V16, V6
VLEG $0, 32(R5), V16
FMOVD 40(R5), F7
WFMADB V3, V7, V16, V7
VLEG $0, 24(R5), V16
WFMADB V4, V6, V7, V4
WFMADB V1, V16, V3, V1
FMOVD 16(R5), F6
FMADD F4, F1, F6
WORD $0xB3CD0015 //lgdr %r1,%f5
WORD $0xB3130066 //lcdbr %f6,%f6
WORD $0xEC3139BC //risbg %r3,%r1,57,128+60,3
BYTE $0x03
BYTE $0x55
WORD $0x68432000 //ld %f4,0(%r3,%r2)
FMADD F4, F1, F1
MOVD $0x4086000000000000, R2
FMSUB F1, F6, F4
WORD $0xB3130044 //lcdbr %f4,%f4
WFCHDBS V2, V0, V0
BEQ L21
ADDW $0xF000, R1
WORD $0xEC21000F //risbgn %r2,%r1,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WORD $0xB3C10002 //ldgr %f0,%r2
FMADD F0, F4, F0
MOVD $·expm1x4ff<>+0(SB), R3
FMOVD 0(R5), F4
FMOVD 0(R3), F2
WFMADB V2, V0, V4, V0
FMOVD F0, ret+8(FP)
RET
L7:
MOVD $·expm1xmone<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
L21:
ADDW $0x1000, R1
WORD $0xEC21000F //risbgn %r2,%r1,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WORD $0xB3C10002 //ldgr %f0,%r2
FMADD F0, F4, F0
MOVD $·expm1x2ff<>+0(SB), R3
FMOVD 0(R5), F4
FMOVD 0(R3), F2
WFMADB V2, V0, V4, V0
FMOVD F0, ret+8(FP)
RET
LEXITTAGexpm1:
FMOVD F0, ret+8(FP)
RET

17
src/math/export_s390x_test.go
View file

@ -11,4 +11,21 @@ var CoshNoVec = cosh
var SinNoVec = sin
var SinhNoVec = sinh
var TanhNoVec = tanh
var Log1pNovec = log1p
var AtanhNovec = atanh
var AcosNovec = acos
var AcoshNovec = acosh
var AsinNovec = asin
var AsinhNovec = asinh
var ErfNovec = erf
var ErfcNovec = erfc
var AtanNovec = atan
var Atan2Novec = atan2
var CbrtNovec = cbrt
var LogNovec = log
var TanNovec = tan
var ExpNovec = exp
var Expm1Novec = expm1
var PowNovec = pow
var HypotNovec = hypot
var HasVX = hasVX

186
src/math/log1p_s390x.s Normal file
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@ -0,0 +1,186 @@
// 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"
// Constants
DATA ·log1pxlim<> + 0(SB)/4, $0xfff00000
GLOBL ·log1pxlim<> + 0(SB), RODATA, $4
DATA ·log1pxzero<> + 0(SB)/8, $0.0
GLOBL ·log1pxzero<> + 0(SB), RODATA, $8
DATA ·log1pxminf<> + 0(SB)/8, $0xfff0000000000000
GLOBL ·log1pxminf<> + 0(SB), RODATA, $8
DATA ·log1pxnan<> + 0(SB)/8, $0x7ff8000000000000
GLOBL ·log1pxnan<> + 0(SB), RODATA, $8
DATA ·log1pyout<> + 0(SB)/8, $0x40fce621e71da000
GLOBL ·log1pyout<> + 0(SB), RODATA, $8
DATA ·log1pxout<> + 0(SB)/8, $0x40f1000000000000
GLOBL ·log1pxout<> + 0(SB), RODATA, $8
DATA ·log1pxl2<> + 0(SB)/8, $0xbfda7aecbeba4e46
GLOBL ·log1pxl2<> + 0(SB), RODATA, $8
DATA ·log1pxl1<> + 0(SB)/8, $0x3ffacde700000000
GLOBL ·log1pxl1<> + 0(SB), RODATA, $8
DATA ·log1pxa<> + 0(SB)/8, $5.5
GLOBL ·log1pxa<> + 0(SB), RODATA, $8
DATA ·log1pxmone<> + 0(SB)/8, $-1.0
GLOBL ·log1pxmone<> + 0(SB), RODATA, $8
// Minimax polynomial approximations
DATA ·log1pc8<> + 0(SB)/8, $0.212881813645679599E-07
GLOBL ·log1pc8<> + 0(SB), RODATA, $8
DATA ·log1pc7<> + 0(SB)/8, $-.148682720127920854E-06
GLOBL ·log1pc7<> + 0(SB), RODATA, $8
DATA ·log1pc6<> + 0(SB)/8, $0.938370938292558173E-06
GLOBL ·log1pc6<> + 0(SB), RODATA, $8
DATA ·log1pc5<> + 0(SB)/8, $-.602107458843052029E-05
GLOBL ·log1pc5<> + 0(SB), RODATA, $8
DATA ·log1pc4<> + 0(SB)/8, $0.397389654305194527E-04
GLOBL ·log1pc4<> + 0(SB), RODATA, $8
DATA ·log1pc3<> + 0(SB)/8, $-.273205381970859341E-03
GLOBL ·log1pc3<> + 0(SB), RODATA, $8
DATA ·log1pc2<> + 0(SB)/8, $0.200350613573012186E-02
GLOBL ·log1pc2<> + 0(SB), RODATA, $8
DATA ·log1pc1<> + 0(SB)/8, $-.165289256198351540E-01
GLOBL ·log1pc1<> + 0(SB), RODATA, $8
DATA ·log1pc0<> + 0(SB)/8, $0.181818181818181826E+00
GLOBL ·log1pc0<> + 0(SB), RODATA, $8
// Table of log10 correction terms
DATA ·log1ptab<> + 0(SB)/8, $0.585235384085551248E-01
DATA ·log1ptab<> + 8(SB)/8, $0.412206153771168640E-01
DATA ·log1ptab<> + 16(SB)/8, $0.273839003221648339E-01
DATA ·log1ptab<> + 24(SB)/8, $0.166383778368856480E-01
DATA ·log1ptab<> + 32(SB)/8, $0.866678223433169637E-02
DATA ·log1ptab<> + 40(SB)/8, $0.319831684989627514E-02
DATA ·log1ptab<> + 48(SB)/8, $-.000000000000000000E+00
DATA ·log1ptab<> + 56(SB)/8, $-.113006378583725549E-02
DATA ·log1ptab<> + 64(SB)/8, $-.367979419636602491E-03
DATA ·log1ptab<> + 72(SB)/8, $0.213172484510484979E-02
DATA ·log1ptab<> + 80(SB)/8, $0.623271047682013536E-02
DATA ·log1ptab<> + 88(SB)/8, $0.118140812789696885E-01
DATA ·log1ptab<> + 96(SB)/8, $0.187681358930914206E-01
DATA ·log1ptab<> + 104(SB)/8, $0.269985148668178992E-01
DATA ·log1ptab<> + 112(SB)/8, $0.364186619761331328E-01
DATA ·log1ptab<> + 120(SB)/8, $0.469505379381388441E-01
GLOBL ·log1ptab<> + 0(SB), RODATA, $128
// Log1p returns the natural logarithm of 1 plus its argument x.
// It is more accurate than Log(1 + x) when x is near zero.
//
// Special cases are:
// Log1p(+Inf) = +Inf
// Log1p(±0) = ±0
// Log1p(-1) = -Inf
// Log1p(x < -1) = NaN
// Log1p(NaN) = NaN
// The algorithm used is minimax polynomial approximation
// with coefficients determined with a Remez exchange algorithm.
TEXT ·log1pAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·log1pxmone<>+0(SB), R1
MOVD ·log1pxout<>+0(SB), R2
FMOVD 0(R1), F3
MOVD $·log1pxa<>+0(SB), R1
MOVWZ ·log1pxlim<>+0(SB), R0
FMOVD 0(R1), F1
MOVD $·log1pc8<>+0(SB), R1
FMOVD 0(R1), F5
MOVD $·log1pc7<>+0(SB), R1
VLEG $0, 0(R1), V20
MOVD $·log1pc6<>+0(SB), R1
WFSDB V0, V3, V4
VLEG $0, 0(R1), V18
MOVD $·log1pc5<>+0(SB), R1
VLEG $0, 0(R1), V16
MOVD R2, R5
WORD $0xB3CD0034 //lgdr %r3,%f4
WORD $0xC0190006 //iilf %r1,425983
BYTE $0x7F
BYTE $0xFF
SRAD $32, R3, R3
SUBW R3, R1
SRW $16, R1, R1
BYTE $0x18 //lr %r4,%r1
BYTE $0x41
WORD $0xEC24000F //risbgn %r2,%r4,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WORD $0xEC54101F //risbgn %r5,%r4,64-64+16,64-64+16+16-1,64-16-16
BYTE $0x20
BYTE $0x59
MOVW R0, R6
MOVW R3, R7
CMPBGT R6, R7, L8
WFCEDBS V4, V4, V6
MOVD $·log1pxzero<>+0(SB), R1
FMOVD 0(R1), F2
BVS LEXITTAGlog1p
WORD $0xB3130044
WFCEDBS V2, V4, V6
BEQ L9
WFCHDBS V4, V2, V2
BEQ LEXITTAGlog1p
MOVD $·log1pxnan<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
L8:
WORD $0xB3C10022 //ldgr %f2,%r2
FSUB F4, F3
FMADD F2, F4, F1
MOVD $·log1pc4<>+0(SB), R2
WORD $0xB3130041
FMOVD 0(R2), F7
FSUB F3, F0
MOVD $·log1pc3<>+0(SB), R2
FMOVD 0(R2), F3
MOVD $·log1pc2<>+0(SB), R2
WFMDB V1, V1, V6
FMADD F7, F4, F3
WFMSDB V0, V2, V1, V0
FMOVD 0(R2), F7
WFMADB V4, V5, V20, V5
MOVD $·log1pc1<>+0(SB), R2
FMOVD 0(R2), F2
FMADD F7, F4, F2
WFMADB V4, V18, V16, V4
FMADD F3, F6, F2
WFMADB V5, V6, V4, V5
FMUL F6, F6
MOVD $·log1pc0<>+0(SB), R2
WFMADB V6, V5, V2, V6
FMOVD 0(R2), F4
WFMADB V0, V6, V4, V6
WORD $0xEC1139BC //risbg %r1,%r1,57,128+60,3
BYTE $0x03
BYTE $0x55
MOVD $·log1ptab<>+0(SB), R2
MOVD $·log1pxl1<>+0(SB), R3
WORD $0x68112000 //ld %f1,0(%r1,%r2)
FMOVD 0(R3), F2
WFMADB V0, V6, V1, V0
MOVD $·log1pyout<>+0(SB), R1
WORD $0xB3C10065 //ldgr %f6,%r5
FMOVD 0(R1), F4
WFMSDB V2, V6, V4, V2
MOVD $·log1pxl2<>+0(SB), R1
FMOVD 0(R1), F4
FMADD F4, F2, F0
FMOVD F0, ret+8(FP)
RET
L9:
MOVD $·log1pxminf<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
LEXITTAGlog1p:
FMOVD F0, ret+8(FP)
RET

180
src/math/log_s390x.s Normal file
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@ -0,0 +1,180 @@
// 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 approximations
DATA ·logrodataL21<> + 0(SB)/8, $-.499999999999999778E+00
DATA ·logrodataL21<> + 8(SB)/8, $0.333333333333343751E+00
DATA ·logrodataL21<> + 16(SB)/8, $-.250000000001606881E+00
DATA ·logrodataL21<> + 24(SB)/8, $0.199999999971603032E+00
DATA ·logrodataL21<> + 32(SB)/8, $-.166666663114122038E+00
DATA ·logrodataL21<> + 40(SB)/8, $-.125002923782692399E+00
DATA ·logrodataL21<> + 48(SB)/8, $0.111142014580396256E+00
DATA ·logrodataL21<> + 56(SB)/8, $0.759438932618934220E-01
DATA ·logrodataL21<> + 64(SB)/8, $0.142857144267212549E+00
DATA ·logrodataL21<> + 72(SB)/8, $-.993038938793590759E-01
DATA ·logrodataL21<> + 80(SB)/8, $-1.0
GLOBL ·logrodataL21<> + 0(SB), RODATA, $88
// Constants
DATA ·logxminf<> + 0(SB)/8, $0xfff0000000000000
GLOBL ·logxminf<> + 0(SB), RODATA, $8
DATA ·logxnan<> + 0(SB)/8, $0x7ff8000000000000
GLOBL ·logxnan<> + 0(SB), RODATA, $8
DATA ·logx43f<> + 0(SB)/8, $0x43f0000000000000
GLOBL ·logx43f<> + 0(SB), RODATA, $8
DATA ·logxl2<> + 0(SB)/8, $0x3fda7aecbeba4e46
GLOBL ·logxl2<> + 0(SB), RODATA, $8
DATA ·logxl1<> + 0(SB)/8, $0x3ffacde700000000
GLOBL ·logxl1<> + 0(SB), RODATA, $8
/* Input transform scale and add constants */
DATA ·logxm<> + 0(SB)/8, $0x3fc77604e63c84b1
DATA ·logxm<> + 8(SB)/8, $0x40fb39456ab53250
DATA ·logxm<> + 16(SB)/8, $0x3fc9ee358b945f3f
DATA ·logxm<> + 24(SB)/8, $0x40fb39418bf3b137
DATA ·logxm<> + 32(SB)/8, $0x3fccfb2e1304f4b6
DATA ·logxm<> + 40(SB)/8, $0x40fb393d3eda3022
DATA ·logxm<> + 48(SB)/8, $0x3fd0000000000000
DATA ·logxm<> + 56(SB)/8, $0x40fb393969e70000
DATA ·logxm<> + 64(SB)/8, $0x3fd11117aafbfe04
DATA ·logxm<> + 72(SB)/8, $0x40fb3936eaefafcf
DATA ·logxm<> + 80(SB)/8, $0x3fd2492af5e658b2
DATA ·logxm<> + 88(SB)/8, $0x40fb39343ff01715
DATA ·logxm<> + 96(SB)/8, $0x3fd3b50c622a43dd
DATA ·logxm<> + 104(SB)/8, $0x40fb39315adae2f3
DATA ·logxm<> + 112(SB)/8, $0x3fd56bbeea918777
DATA ·logxm<> + 120(SB)/8, $0x40fb392e21698552
GLOBL ·logxm<> + 0(SB), RODATA, $128
// Log returns the natural logarithm of the argument.
//
// Special cases are:
// Log(+Inf) = +Inf
// Log(0) = -Inf
// Log(x < 0) = NaN
// Log(NaN) = NaN
// The algorithm used is minimax polynomial approximation using a table of
// polynomial coefficients determined with a Remez exchange algorithm.
TEXT ·logAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·logrodataL21<>+0(SB), R9
MOVH $0x8006, R4
WORD $0xB3CD0010 //lgdr %r1,%f0
MOVD $0x3FF0000000000000, R6
SRAD $48, R1, R1
MOVD $0x40F03E8000000000, R8
SUBW R1, R4
WORD $0xEC2420BB //risbg %r2,%r4,32,128+59,0
BYTE $0x00
BYTE $0x55
WORD $0xEC62000F //risbgn %r6,%r2,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WORD $0xEC82101F //risbgn %r8,%r2,64-64+16,64-64+16+16-1,64-16-16
BYTE $0x20
BYTE $0x59
MOVW R1, R7
CMPBGT R7, $22, L17
WORD $0xB3120000 //ltdbr %f0,%f0
MOVD $·logx43f<>+0(SB), R1
FMOVD 0(R1), F2
BLEU L3
MOVH $0x8005, R12
MOVH $0x8405, R0
BR L15
L7:
WORD $0xB3120000 //ltdbr %f0,%f0
BLEU L3
L15:
FMUL F2, F0
WORD $0xB3CD0010 //lgdr %r1,%f0
SRAD $48, R1, R1
SUBW R1, R0, R2
SUBW R1, R12, R3
BYTE $0x18 //lr %r4,%r2
BYTE $0x42
ANDW $0xFFFFFFF0, R3
ANDW $0xFFFFFFF0, R2
BYTE $0x18 //lr %r5,%r1
BYTE $0x51
MOVW R1, R7
CMPBLE R7, $22, L7
WORD $0xEC63000F //risbgn %r6,%r3,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WORD $0xEC82101F //risbgn %r8,%r2,64-64+16,64-64+16+16-1,64-16-16
BYTE $0x20
BYTE $0x59
L2:
MOVH R5, R5
MOVH $0x7FEF, R1
CMPW R5, R1
BGT L1
WORD $0xB3C10026 //ldgr %f2,%r6
FMUL F2, F0
WORD $0xEC4439BB //risbg %r4,%r4,57,128+59,3
BYTE $0x03
BYTE $0x55
FMOVD 80(R9), F2
MOVD $·logxm<>+0(SB), R7
ADD R7, R4
FMOVD 72(R9), F4
WORD $0xED004000 //madb %f2,%f0,0(%r4)
BYTE $0x20
BYTE $0x1E
FMOVD 64(R9), F1
FMOVD F2, F0
FMOVD 56(R9), F2
WFMADB V0, V2, V4, V2
WFMDB V0, V0, V6
FMOVD 48(R9), F4
WFMADB V0, V2, V4, V2
FMOVD 40(R9), F4
WFMADB V2, V6, V1, V2
FMOVD 32(R9), F1
WFMADB V6, V4, V1, V4
FMOVD 24(R9), F1
WFMADB V6, V2, V1, V2
FMOVD 16(R9), F1
WFMADB V6, V4, V1, V4
MOVD $·logxl1<>+0(SB), R1
FMOVD 8(R9), F1
WFMADB V6, V2, V1, V2
FMOVD 0(R9), F1
WFMADB V6, V4, V1, V4
FMOVD 8(R4), F1
WFMADB V0, V2, V4, V2
WORD $0xB3C10048 //ldgr %f4,%r8
WFMADB V6, V2, V0, V2
WORD $0xED401000 //msdb %f1,%f4,0(%r1)
BYTE $0x10
BYTE $0x1F
MOVD ·logxl2<>+0(SB), R1
WORD $0xB3130001 //lcdbr %f0,%f1
WORD $0xB3C10041 //ldgr %f4,%r1
WFMADB V0, V4, V2, V0
L1:
FMOVD F0, ret+8(FP)
RET
L3:
WORD $0xB3120000 //ltdbr %f0,%f0
BEQ L20
BGE L1
BVS L1
MOVD $·logxnan<>+0(SB), R1
FMOVD 0(R1), F0
BR L1
L20:
MOVD $·logxminf<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
L17:
BYTE $0x18 //lr %r5,%r1
BYTE $0x51
BR L2

4
src/math/pow.go
View file

@ -35,7 +35,9 @@ func isOddInt(x float64) bool {
// Pow(+Inf, y) = +0 for y < 0
// Pow(-Inf, y) = Pow(-0, -y)
// Pow(x, y) = NaN for finite x < 0 and finite non-integer y
func Pow(x, y float64) float64 {
func Pow(x, y float64) float64
func pow(x, y float64) float64 {
switch {
case y == 0 || x == 1:
return 1

666
src/math/pow_s390x.s Normal file
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@ -0,0 +1,666 @@
// 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"
#define PosInf 0x7FF0000000000000
#define NaN 0x7FF8000000000001
#define NegInf 0xFFF0000000000000
#define PosOne 0x3FF0000000000000
#define NegOne 0xBFF0000000000000
#define NegZero 0x8000000000000000
// Minimax polynomial approximation
DATA ·powrodataL51<> + 0(SB)/8, $-1.0
DATA ·powrodataL51<> + 8(SB)/8, $1.0
DATA ·powrodataL51<> + 16(SB)/8, $0.24022650695910110361E+00
DATA ·powrodataL51<> + 24(SB)/8, $0.69314718055994686185E+00
DATA ·powrodataL51<> + 32(SB)/8, $0.96181291057109484809E-02
DATA ·powrodataL51<> + 40(SB)/8, $0.15403814778342868389E-03
DATA ·powrodataL51<> + 48(SB)/8, $0.55504108652095235601E-01
DATA ·powrodataL51<> + 56(SB)/8, $0.13333818813168698658E-02
DATA ·powrodataL51<> + 64(SB)/8, $0.68205322933914439200E-12
DATA ·powrodataL51<> + 72(SB)/8, $-.18466496523378731640E-01
DATA ·powrodataL51<> + 80(SB)/8, $0.19697596291603973706E-02
DATA ·powrodataL51<> + 88(SB)/8, $0.23083120654155209200E+00
DATA ·powrodataL51<> + 96(SB)/8, $0.55324356012093416771E-06
DATA ·powrodataL51<> + 104(SB)/8, $-.40340677224649339048E-05
DATA ·powrodataL51<> + 112(SB)/8, $0.30255507904062541562E-04
DATA ·powrodataL51<> + 120(SB)/8, $-.77453979912413008787E-07
DATA ·powrodataL51<> + 128(SB)/8, $-.23637115549923464737E-03
DATA ·powrodataL51<> + 136(SB)/8, $0.11016119077267717198E-07
DATA ·powrodataL51<> + 144(SB)/8, $0.22608272174486123035E-09
DATA ·powrodataL51<> + 152(SB)/8, $-.15895808101370190382E-08
DATA ·powrodataL51<> + 160(SB)/8, $0x4540190000000000
GLOBL ·powrodataL51<> + 0(SB), RODATA, $168
// Constants
DATA ·pow_x001a<> + 0(SB)/8, $0x1a000000000000
GLOBL ·pow_x001a<> + 0(SB), RODATA, $8
DATA ·pow_xinf<> + 0(SB)/8, $0x7ff0000000000000 //+Inf
GLOBL ·pow_xinf<> + 0(SB), RODATA, $8
DATA ·pow_xnan<> + 0(SB)/8, $0x7ff8000000000000 //NaN
GLOBL ·pow_xnan<> + 0(SB), RODATA, $8
DATA ·pow_x434<> + 0(SB)/8, $0x4340000000000000
GLOBL ·pow_x434<> + 0(SB), RODATA, $8
DATA ·pow_x433<> + 0(SB)/8, $0x4330000000000000
GLOBL ·pow_x433<> + 0(SB), RODATA, $8
DATA ·pow_x43f<> + 0(SB)/8, $0x43f0000000000000
GLOBL ·pow_x43f<> + 0(SB), RODATA, $8
DATA ·pow_xadd<> + 0(SB)/8, $0xc2f0000100003fef
GLOBL ·pow_xadd<> + 0(SB), RODATA, $8
DATA ·pow_xa<> + 0(SB)/8, $0x4019000000000000
GLOBL ·pow_xa<> + 0(SB), RODATA, $8
// Scale correction tables
DATA powiadd<> + 0(SB)/8, $0xf000000000000000
DATA powiadd<> + 8(SB)/8, $0x1000000000000000
GLOBL powiadd<> + 0(SB), RODATA, $16
DATA powxscale<> + 0(SB)/8, $0x4ff0000000000000
DATA powxscale<> + 8(SB)/8, $0x2ff0000000000000
GLOBL powxscale<> + 0(SB), RODATA, $16
// Fractional powers of 2 table
DATA ·powtexp<> + 0(SB)/8, $0.442737824274138381E-01
DATA ·powtexp<> + 8(SB)/8, $0.263602189790660309E-01
DATA ·powtexp<> + 16(SB)/8, $0.122565642281703586E-01
DATA ·powtexp<> + 24(SB)/8, $0.143757052860721398E-02
DATA ·powtexp<> + 32(SB)/8, $-.651375034121276075E-02
DATA ·powtexp<> + 40(SB)/8, $-.119317678849450159E-01
DATA ·powtexp<> + 48(SB)/8, $-.150868749549871069E-01
DATA ·powtexp<> + 56(SB)/8, $-.161992609578469234E-01
DATA ·powtexp<> + 64(SB)/8, $-.154492360403337917E-01
DATA ·powtexp<> + 72(SB)/8, $-.129850717389178721E-01
DATA ·powtexp<> + 80(SB)/8, $-.892902649276657891E-02
DATA ·powtexp<> + 88(SB)/8, $-.338202636596794887E-02
DATA ·powtexp<> + 96(SB)/8, $0.357266307045684762E-02
DATA ·powtexp<> + 104(SB)/8, $0.118665304327406698E-01
DATA ·powtexp<> + 112(SB)/8, $0.214434994118118914E-01
DATA ·powtexp<> + 120(SB)/8, $0.322580645161290314E-01
GLOBL ·powtexp<> + 0(SB), RODATA, $128
// Log multiplier tables
DATA ·powtl<> + 0(SB)/8, $0xbdf9723a80db6a05
DATA ·powtl<> + 8(SB)/8, $0x3e0cfe4a0babe862
DATA ·powtl<> + 16(SB)/8, $0xbe163b42dd33dada
DATA ·powtl<> + 24(SB)/8, $0xbe0cdf9de2a8429c
DATA ·powtl<> + 32(SB)/8, $0xbde9723a80db6a05
DATA ·powtl<> + 40(SB)/8, $0xbdb37fcae081745e
DATA ·powtl<> + 48(SB)/8, $0xbdd8b2f901ac662c
DATA ·powtl<> + 56(SB)/8, $0xbde867dc68c36cc9
DATA ·powtl<> + 64(SB)/8, $0xbdd23e36b47256b7
DATA ·powtl<> + 72(SB)/8, $0xbde4c9b89fcc7933
DATA ·powtl<> + 80(SB)/8, $0xbdd16905cad7cf66
DATA ·powtl<> + 88(SB)/8, $0x3ddb417414aa5529
DATA ·powtl<> + 96(SB)/8, $0xbdce046f2889983c
DATA ·powtl<> + 104(SB)/8, $0x3dc2c3865d072897
DATA ·powtl<> + 112(SB)/8, $0x8000000000000000
DATA ·powtl<> + 120(SB)/8, $0x3dc1ca48817f8afe
DATA ·powtl<> + 128(SB)/8, $0xbdd703518a88bfb7
DATA ·powtl<> + 136(SB)/8, $0x3dc64afcc46942ce
DATA ·powtl<> + 144(SB)/8, $0xbd9d79191389891a
DATA ·powtl<> + 152(SB)/8, $0x3ddd563044da4fa0
DATA ·powtl<> + 160(SB)/8, $0x3e0f42b5e5f8f4b6
DATA ·powtl<> + 168(SB)/8, $0x3e0dfa2c2cbf6ead
DATA ·powtl<> + 176(SB)/8, $0x3e14e25e91661293
DATA ·powtl<> + 184(SB)/8, $0x3e0aac461509e20c
GLOBL ·powtl<> + 0(SB), RODATA, $192
DATA ·powtm<> + 0(SB)/8, $0x3da69e13
DATA ·powtm<> + 8(SB)/8, $0x100003d66fcb6
DATA ·powtm<> + 16(SB)/8, $0x200003d1538df
DATA ·powtm<> + 24(SB)/8, $0x300003cab729e
DATA ·powtm<> + 32(SB)/8, $0x400003c1a784c
DATA ·powtm<> + 40(SB)/8, $0x500003ac9b074
DATA ·powtm<> + 48(SB)/8, $0x60000bb498d22
DATA ·powtm<> + 56(SB)/8, $0x68000bb8b29a2
DATA ·powtm<> + 64(SB)/8, $0x70000bb9a32d4
DATA ·powtm<> + 72(SB)/8, $0x74000bb9946bb
DATA ·powtm<> + 80(SB)/8, $0x78000bb92e34b
DATA ·powtm<> + 88(SB)/8, $0x80000bb6c57dc
DATA ·powtm<> + 96(SB)/8, $0x84000bb4020f7
DATA ·powtm<> + 104(SB)/8, $0x8c000ba93832d
DATA ·powtm<> + 112(SB)/8, $0x9000080000000
DATA ·powtm<> + 120(SB)/8, $0x940003aa66c4c
DATA ·powtm<> + 128(SB)/8, $0x980003b2fb12a
DATA ·powtm<> + 136(SB)/8, $0xa00003bc1def6
DATA ·powtm<> + 144(SB)/8, $0xa80003c1eb0eb
DATA ·powtm<> + 152(SB)/8, $0xb00003c64dcec
DATA ·powtm<> + 160(SB)/8, $0xc00003cc49e4e
DATA ·powtm<> + 168(SB)/8, $0xd00003d12f1de
DATA ·powtm<> + 176(SB)/8, $0xe00003d4a9c6f
DATA ·powtm<> + 184(SB)/8, $0xf00003d846c66
GLOBL ·powtm<> + 0(SB), RODATA, $192
// Table of indeces into multiplier tables
// Adjusted from asm to remove offset and convert
DATA ·powtabi<> + 0(SB)/8, $0x1010101
DATA ·powtabi<> + 8(SB)/8, $0x101020202020203
DATA ·powtabi<> + 16(SB)/8, $0x303030404040405
DATA ·powtabi<> + 24(SB)/8, $0x505050606060708
DATA ·powtabi<> + 32(SB)/8, $0x90a0b0c0d0e0f10
DATA ·powtabi<> + 40(SB)/8, $0x1011111212121313
DATA ·powtabi<> + 48(SB)/8, $0x1314141414151515
DATA ·powtabi<> + 56(SB)/8, $0x1516161617171717
GLOBL ·powtabi<> + 0(SB), RODATA, $64
// Pow returns x**y, the base-x exponential of y.
//
// Special cases are (in order):
// Pow(x, ±0) = 1 for any x
// Pow(1, y) = 1 for any y
// Pow(x, 1) = x for any x
// Pow(NaN, y) = NaN
// Pow(x, NaN) = NaN
// Pow(±0, y) = ±Inf for y an odd integer < 0
// Pow(±0, -Inf) = +Inf
// Pow(±0, +Inf) = +0
// Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
// Pow(±0, y) = ±0 for y an odd integer > 0
// Pow(±0, y) = +0 for finite y > 0 and not an odd integer
// Pow(-1, ±Inf) = 1
// Pow(x, +Inf) = +Inf for |x| > 1
// Pow(x, -Inf) = +0 for |x| > 1
// Pow(x, +Inf) = +0 for |x| < 1
// Pow(x, -Inf) = +Inf for |x| < 1
// Pow(+Inf, y) = +Inf for y > 0
// Pow(+Inf, y) = +0 for y < 0
// Pow(-Inf, y) = Pow(-0, -y)
// Pow(x, y) = NaN for finite x < 0 and finite non-integer y
TEXT ·powAsm(SB), NOSPLIT, $0-24
// special case
MOVD x+0(FP), R1
MOVD y+8(FP), R2
// special case Pow(1, y) = 1 for any y
MOVD $PosOne, R3
CMPUBEQ R1, R3, xIsOne
// special case Pow(x, 1) = x for any x
MOVD $PosOne, R4
CMPUBEQ R2, R4, yIsOne
// special case Pow(x, NaN) = NaN for any x
MOVD $~(1<<63), R5
AND R2, R5 // y = |y|
MOVD $PosInf, R4
CMPUBLT R4, R5, yIsNan
MOVD $NegInf, R3
CMPUBEQ R1, R3, xIsNegInf
MOVD $NegOne, R3
CMPUBEQ R1, R3, xIsNegOne
MOVD $PosInf, R3
CMPUBEQ R1, R3, xIsPosInf
MOVD $NegZero, R3
CMPUBEQ R1, R3, xIsNegZero
MOVD $PosInf, R4
CMPUBEQ R2, R4, yIsPosInf
MOVD $0x0, R3
CMPUBEQ R1, R3, xIsPosZero
CMPBLT R1, R3, xLtZero
BR Normal
xIsPosInf:
// special case Pow(+Inf, y) = +Inf for y > 0
MOVD $0x0, R4
CMPBGT R2, R4, posInfGeZero
BR Normal
xIsNegInf:
//Pow(-Inf, y) = Pow(-0, -y)
FMOVD y+8(FP), F2
FNEG F2, F2 // y = -y
BR negZeroNegY // call Pow(-0, -y)
xIsNegOne:
// special case Pow(-1, ±Inf) = 1
MOVD $PosInf, R4
CMPUBEQ R2, R4, negOnePosInf
MOVD $NegInf, R4
CMPUBEQ R2, R4, negOneNegInf
BR Normal
xIsPosZero:
// special case Pow(+0, -Inf) = +Inf
MOVD $NegInf, R4
CMPUBEQ R2, R4, zeroNegInf
// special case Pow(+0, y < 0) = +Inf
FMOVD y+8(FP), F2
FMOVD $(0.0), F4
FCMPU F2, F4
BLT posZeroLtZero //y < 0.0
BR Normal
xIsNegZero:
// special case Pow(-0, -Inf) = +Inf
MOVD $NegInf, R4
CMPUBEQ R2, R4, zeroNegInf
FMOVD y+8(FP), F2
negZeroNegY:
// special case Pow(x, ±0) = 1 for any x
FMOVD $(0.0), F4
FCMPU F4, F2
BLT negZeroGtZero // y > 0.0
BEQ yIsZero // y = 0.0
FMOVD $(-0.0), F4
FCMPU F4, F2
BLT negZeroGtZero // y > -0.0
BEQ yIsZero // y = -0.0
// special case Pow(-0, y) = -Inf for y an odd integer < 0
// special case Pow(-0, y) = +Inf for finite y < 0 and not an odd integer
FIDBR $5, F2, F4 //F2 translate to integer F4
FCMPU F2, F4
BNE zeroNotOdd // y is not an (odd) integer and y < 0
FMOVD $(2.0), F4
FDIV F4, F2 // F2 = F2 / 2.0
FIDBR $5, F2, F4 //F2 translate to integer F4
FCMPU F2, F4
BNE negZeroOddInt // y is an odd integer and y < 0
BR zeroNotOdd // y is not an (odd) integer and y < 0
negZeroGtZero:
// special case Pow(-0, y) = -0 for y an odd integer > 0
// special case Pow(±0, y) = +0 for finite y > 0 and not an odd integer
FIDBR $5, F2, F4 //F2 translate to integer F4
FCMPU F2, F4
BNE zeroNotOddGtZero // y is not an (odd) integer and y > 0
FMOVD $(2.0), F4
FDIV F4, F2 // F2 = F2 / 2.0
FIDBR $5, F2, F4 //F2 translate to integer F4
FCMPU F2, F4
BNE negZeroOddIntGtZero // y is an odd integer and y > 0
BR zeroNotOddGtZero // y is not an (odd) integer
xLtZero:
// special case Pow(x, y) = NaN for finite x < 0 and finite non-integer y
FMOVD y+8(FP), F2
FIDBR $5, F2, F4
FCMPU F2, F4
BNE ltZeroInt
BR Normal
yIsPosInf:
// special case Pow(x, +Inf) = +Inf for |x| > 1
FMOVD x+0(FP), F1
FMOVD $(1.0), F3
FCMPU F1, F3
BGT gtOnePosInf
FMOVD $(-1.0), F3
FCMPU F1, F3
BLT ltNegOnePosInf
Normal:
FMOVD x+0(FP), F0
FMOVD y+8(FP), F2
MOVD $·powrodataL51<>+0(SB), R9
WORD $0xB3CD0030 //lgdr %r3,%f0
WORD $0xC0298009 //iilf %r2,2148095317
BYTE $0x55
BYTE $0x55
WORD $0xEC1320BF //risbgn %r1,%r3,64-32,128+63,64+0+32
BYTE $0x60
BYTE $0x59
SUBW R1, R2
WORD $0xEC323ABF //risbgn %r3,%r2,64-6,128+63,64+44+6
BYTE $0x72
BYTE $0x59
BYTE $0x18 //lr %r5,%r1
BYTE $0x51
MOVD $·powtabi<>+0(SB), R12
WORD $0xE303C000 //llgc %r0,0(%r3,%r12)
BYTE $0x00
BYTE $0x90
SUBW $0x1A0000, R5
SLD $3, R0, R3
MOVD $·powtm<>+0(SB), R4
MOVH $0x0, R8
ANDW $0x7FF00000, R2
ORW R5, R1
WORD $0x5A234000 //a %r2,0(%r3,%r4)
MOVD $0x3FF0000000000000, R5
WORD $0xEC3228BF //risbg %r3,%r2,64-24,128+63,64+32+24
BYTE $0x78
BYTE $0x55
WORD $0xEC82001F //risbgn %r8,%r2,64-64+0,64-64+0+32-1,64-0-32
BYTE $0x20
BYTE $0x59
ORW $0x45000000, R3
MOVW R1, R6
CMPBLT R6, $0, L42
FMOVD F0, F4
L2:
VLVGF $0, R3, V1
MOVD $·pow_xa<>+0(SB), R2
WORD $0xED3090A0 //lde %f3,.L52-.L51(%r9)
BYTE $0x00
BYTE $0x24
FMOVD 0(R2), F6
FSUBS F1, F3
WORD $0xB3C10018 //ldgr %f1,%r8
WFMSDB V4, V1, V6, V4
FMOVD 152(R9), F6
WFMDB V4, V4, V7
FMOVD 144(R9), F1
FMOVD 136(R9), F5
WFMADB V4, V1, V6, V1
VLEG $0, 128(R9), V16
FMOVD 120(R9), F6
WFMADB V4, V5, V6, V5
FMOVD 112(R9), F6
WFMADB V1, V7, V5, V1
WFMADB V4, V6, V16, V16
SLD $3, R0, R2
FMOVD 104(R9), F5
WORD $0xED824004 //ldeb %f8,4(%r2,%r4)
BYTE $0x00
BYTE $0x04
LDEBR F3, F3
FMOVD 96(R9), F6
WFMADB V4, V6, V5, V6
FADD F8, F3
WFMADB V7, V6, V16, V6
FMUL F7, F7
FMOVD 88(R9), F5
FMADD F7, F1, F6
WFMADB V4, V5, V3, V16
FMOVD 80(R9), F1
WFSDB V16, V3, V3
MOVD $·powtl<>+0(SB), R3
WFMADB V4, V6, V1, V6
FMADD F5, F4, F3
FMOVD 72(R9), F1
WFMADB V4, V6, V1, V6
WORD $0xED323000 //adb %f3,0(%r2,%r3)
BYTE $0x00
BYTE $0x1A
FMOVD 64(R9), F1
WFMADB V4, V6, V1, V6
MOVD $·pow_xadd<>+0(SB), R2
WFMADB V4, V6, V3, V4
FMOVD 0(R2), F5
WFADB V4, V16, V3
VLEG $0, 56(R9), V20
WFMSDB V2, V3, V5, V3
VLEG $0, 48(R9), V18
WFADB V3, V5, V6
WORD $0xB3CD0023 //lgdr %r2,%f3
WFMSDB V2, V16, V6, V16
FMOVD 40(R9), F1
WFMADB V2, V4, V16, V4
FMOVD 32(R9), F7
WFMDB V4, V4, V3
WFMADB V4, V1, V20, V1
WFMADB V4, V7, V18, V7
VLEG $0, 24(R9), V16
WFMADB V1, V3, V7, V1
FMOVD 16(R9), F5
WFMADB V4, V5, V16, V5
WORD $0xEC4239BC //risbg %r4,%r2,57,128+60,3
BYTE $0x03
BYTE $0x55
WFMADB V3, V1, V5, V1
MOVD $·powtexp<>+0(SB), R3
WORD $0x68343000 //ld %f3,0(%r4,%r3)
FMADD F3, F4, F4
WORD $0xEC52000F //risbgn %r5,%r2,64-64+0,64-64+0+16-1,64-0-16
BYTE $0x30
BYTE $0x59
WFMADB V4, V1, V3, V4
WORD $0xB3CD0026 //lgdr %r2,%f6
WORD $0xB3C10015 //ldgr %f1,%r5
SRAD $48, R2, R2
FMADD F1, F4, F1
RLL $16, R2, R2
ANDW $0x7FFF0000, R2
WORD $0xC22B3F71 //alfi %r2,1064370176
BYTE $0x00
BYTE $0x00
ORW R2, R1, R3
MOVW R3, R6
CMPBLT R6, $0, L43
L1:
FMOVD F1, ret+16(FP)
RET
L43:
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L44
FMOVD F0, F3
L7:
MOVD $·pow_xinf<>+0(SB), R3
FMOVD 0(R3), F5
WFCEDBS V3, V5, V7
BVS L8
WFMDB V3, V2, V6
L8:
WFCEDBS V2, V2, V3
BVS L9
WORD $0xB3120022 //ltdbr %f2,%f2
BEQ L26
MOVW R1, R6
CMPBLT R6, $0, L45
L11:
WORD $0xC0190003 //iilf %r1,262143
BYTE $0xFF
BYTE $0xFF
MOVW R2, R7
MOVW R1, R6
CMPBLE R7, R6, L34
WORD $0xEC1520BF //risbgn %r1,%r5,64-32,128+63,64+0+32
BYTE $0x60
BYTE $0x59
WORD $0xB3CD0026 //lgdr %r2,%f6
MOVD $powiadd<>+0(SB), R3
WORD $0xEC223CBC //risbg %r2,%r2,60,128+60,64-60
BYTE $0x04
BYTE $0x55
WORD $0x5A123000 //a %r1,0(%r2,%r3)
WORD $0xEC51001F //risbgn %r5,%r1,64-64+0,64-64+0+32-1,64-0-32
BYTE $0x20
BYTE $0x59
WORD $0xB3C10015 //ldgr %f1,%r5
FMADD F1, F4, F1
MOVD $powxscale<>+0(SB), R1
WORD $0xED121000 //mdb %f1,0(%r2,%r1)
BYTE $0x00
BYTE $0x1C
BR L1
L42:
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L46
FMOVD F0, F4
L3:
MOVD $·pow_x001a<>+0(SB), R2
WORD $0xED402000 //cdb %f4,0(%r2)
BYTE $0x00
BYTE $0x19
BGE L2
BVS L2
MOVD $·pow_x43f<>+0(SB), R2
WORD $0xED402000 //mdb %f4,0(%r2)
BYTE $0x00
BYTE $0x1C
WORD $0xC0298009 //iilf %r2,2148095317
BYTE $0x55
BYTE $0x55
WORD $0xB3CD0034 //lgdr %r3,%f4
WORD $0xEC3320BF //risbgn %r3,%r3,64-32,128+63,64+0+32
BYTE $0x60
BYTE $0x59
SUBW R3, R2, R3
WORD $0xEC2321AB //risbg %r2,%r3,33,128+43,0
BYTE $0x00
BYTE $0x55
WORD $0xEC333ABF //risbgn %r3,%r3,64-6,128+63,64+44+6
BYTE $0x72
BYTE $0x59
WORD $0xE303C000 //llgc %r0,0(%r3,%r12)
BYTE $0x00
BYTE $0x90
SLD $3, R0, R3
WORD $0x5A234000 //a %r2,0(%r3,%r4)
BYTE $0x18 //lr %r3,%r2
BYTE $0x32
WORD $0xEC83001F //risbgn %r8,%r3,64-64+0,64-64+0+32-1,64-0-32
BYTE $0x20
BYTE $0x59
ADDW $0x4000000, R3
BLEU L5
WORD $0xEC3328BF //risbg %r3,%r3,64-24,128+63,64+32+24
BYTE $0x78
BYTE $0x55
ORW $0x45000000, R3
BR L2
L9:
WFCEDBS V0, V0, V4
BVS L35
FMOVD F2, F1
BR L1
L46:
WORD $0xB3130040 //lcdbr %f4,%f0
BR L3
L44:
WORD $0xB3130030 //lcdbr %f3,%f0
BR L7
L35:
FMOVD F0, F1
BR L1
L26:
FMOVD 8(R9), F1
BR L1
L34:
FMOVD 8(R9), F4
L19:
WORD $0xB3120066 //ltdbr %f6,%f6
BLEU L47
L18:
WFMDB V4, V5, V1
BR L1
L5:
WORD $0xEC3321B2 //risbg %r3,%r3,33,128+50,64-1
BYTE $0x3F
BYTE $0x55
WORD $0xC23B4000 //alfi %r3,1073741824
BYTE $0x00
BYTE $0x00
RLL $24, R3, R3
ORW $0x45000000, R3
BR L2
L45:
WFCEDBS V0, V0, V4
BVS L35
WORD $0xB3120000 //ltdbr %f0,%f0
BLEU L48
FMOVD 8(R9), F4
L12:
MOVW R2, R6
CMPBLT R6, $0, L19
FMUL F4, F1
BR L1
L47:
BLT L40
WFCEDBS V0, V0, V2
BVS L49
L16:
MOVD ·pow_xnan<>+0(SB), R1
WORD $0xB3C10001 //ldgr %f0,%r1
WFMDB V4, V0, V1
BR L1
L48:
WORD $0xB3CD0030 //lgdr %r3,%f0
WORD $0xEC1320BF //risbgn %r1,%r3,64-32,128+63,64+0+32
BYTE $0x60
BYTE $0x59
MOVW R1, R6
CMPBEQ R6, $0, L29
WORD $0xB3120022 //ltdbr %f2,%f2
BLTU L50
FMOVD F2, F4
L14:
MOVD $·pow_x433<>+0(SB), R1
FMOVD 0(R1), F7
WFCHDBS V4, V7, V3
BEQ L15
WFADB V7, V4, V3
FSUB F7, F3
WFCEDBS V4, V3, V3
BEQ L15
WORD $0xB3120000 //ltdbr %f0,%f0
FMOVD 8(R9), F4
BNE L16
L13:
WORD $0xB3120022 //ltdbr %f2,%f2
BLT L18
L40:
FMOVD $0, F0
WFMDB V4, V0, V1
BR L1
L49:
WFMDB V0, V4, V1
BR L1
L29:
FMOVD 8(R9), F4
BR L13
L15:
MOVD $·pow_x434<>+0(SB), R1
FMOVD 0(R1), F7
WFCHDBS V4, V7, V3
BEQ L32
WFADB V7, V4, V3
FSUB F7, F3
WFCEDBS V4, V3, V4
BEQ L32
FMOVD 0(R9), F4
L17:
WORD $0xB3120000 //ltdbr %f0,%f0
BNE L12
BR L13
L32:
FMOVD 8(R9), F4
BR L17
L50:
WORD $0xB3130042 //lcdbr %f4,%f2
BR L14
xIsOne: // Pow(1, y) = 1 for any y
yIsOne: // Pow(x, 1) = x for any x
posInfGeZero: // Pow(+Inf, y) = +Inf for y > 0
MOVD R1, ret+16(FP)
RET
yIsNan: // Pow(NaN, y) = NaN
ltZeroInt: // Pow(x, y) = NaN for finite x < 0 and finite non-integer y
MOVD $NaN, R2
MOVD R2, ret+16(FP)
RET
negOnePosInf: // Pow(-1, ±Inf) = 1
negOneNegInf:
MOVD $PosOne, R3
MOVD R3, ret+16(FP)
RET
negZeroOddInt:
MOVD $NegInf, R3
MOVD R3, ret+16(FP)
RET
zeroNotOdd: // Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
posZeroLtZero: // special case Pow(+0, y < 0) = +Inf
zeroNegInf: // Pow(±0, -Inf) = +Inf
MOVD $PosInf, R3
MOVD R3, ret+16(FP)
RET
gtOnePosInf: //Pow(x, +Inf) = +Inf for |x| > 1
ltNegOnePosInf:
MOVD R2, ret+16(FP)
RET
yIsZero: //Pow(x, ±0) = 1 for any x
MOVD $PosOne, R4
MOVD R4, ret+16(FP)
RET
negZeroOddIntGtZero: // Pow(-0, y) = -0 for y an odd integer > 0
MOVD $NegZero, R3
MOVD R3, ret+16(FP)
RET
zeroNotOddGtZero: // Pow(±0, y) = +0 for finite y > 0 and not an odd integer
MOVD $0, ret+16(FP)
RET

11
src/math/pow_stub.s Normal file
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@ -0,0 +1,11 @@
// 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.
// +build 386 amd64 amd64p32 arm
#include "textflag.h"
TEXT ·Pow(SB),NOSPLIT,$0
JMP ·pow(SB)

21
src/math/stubs_arm64.s
View file

@ -12,15 +12,33 @@ TEXT ·Asin(SB),NOSPLIT,$0
TEXT ·Acos(SB),NOSPLIT,$0
B ·acos(SB)
TEXT ·Asinh(SB),NOSPLIT,$0
B ·asinh(SB)
TEXT ·Acosh(SB),NOSPLIT,$0
B ·acosh(SB)
TEXT ·Atan2(SB),NOSPLIT,$0
B ·atan2(SB)
TEXT ·Atan(SB),NOSPLIT,$0
B ·atan(SB)
TEXT ·Atanh(SB),NOSPLIT,$0
B ·atanh(SB)
TEXT ·Exp2(SB),NOSPLIT,$0
B ·exp2(SB)
TEXT ·Erf(SB),NOSPLIT,$0
B ·erf(SB)
TEXT ·Erfc(SB),NOSPLIT,$0
B ·erfc(SB)
TEXT ·Cbrt(SB),NOSPLIT,$0
B ·cbrt(SB)
TEXT ·Cosh(SB),NOSPLIT,$0
B ·cosh(SB)
@ -71,3 +89,6 @@ TEXT ·Tan(SB),NOSPLIT,$0
TEXT ·Tanh(SB),NOSPLIT,$0
B ·tanh(SB)
TEXT ·Pow(SB),NOSPLIT,$0
B ·pow(SB)

21
src/math/stubs_mips64x.s
View file

@ -12,12 +12,21 @@ TEXT ·Asin(SB),NOSPLIT,$0
TEXT ·Acos(SB),NOSPLIT,$0
JMP ·acos(SB)
TEXT ·Asinh(SB),NOSPLIT,$0
JMP ·asinh(SB)
TEXT ·Acosh(SB),NOSPLIT,$0
JMP ·acosh(SB)
TEXT ·Atan2(SB),NOSPLIT,$0
JMP ·atan2(SB)
TEXT ·Atan(SB),NOSPLIT,$0
JMP ·atan(SB)
TEXT ·Atanh(SB),NOSPLIT,$0
JMP ·atanh(SB)
TEXT ·Dim(SB),NOSPLIT,$0
JMP ·dim(SB)
@ -27,6 +36,12 @@ TEXT ·Min(SB),NOSPLIT,$0
TEXT ·Max(SB),NOSPLIT,$0
JMP ·max(SB)
TEXT ·Erf(SB),NOSPLIT,$0
JMP ·erf(SB)
TEXT ·Erfc(SB),NOSPLIT,$0
JMP ·erfc(SB)
TEXT ·Exp2(SB),NOSPLIT,$0
JMP ·exp2(SB)
@ -95,3 +110,9 @@ TEXT ·Tan(SB),NOSPLIT,$0
TEXT ·Tanh(SB),NOSPLIT,$0
JMP ·tanh(SB)
TEXT ·Cbrt(SB),NOSPLIT,$0
JMP ·cbrt(SB)
TEXT ·Pow(SB),NOSPLIT,$0
JMP ·pow(SB)

21
src/math/stubs_mipsx.s
View file

@ -12,12 +12,21 @@ TEXT ·Asin(SB),NOSPLIT,$0
TEXT ·Acos(SB),NOSPLIT,$0
JMP ·acos(SB)
TEXT ·Asinh(SB),NOSPLIT,$0
JMP ·asinh(SB)
TEXT ·Acosh(SB),NOSPLIT,$0
JMP ·acosh(SB)
TEXT ·Atan2(SB),NOSPLIT,$0
JMP ·atan2(SB)
TEXT ·Atan(SB),NOSPLIT,$0
JMP ·atan(SB)
TEXT ·Atanh(SB),NOSPLIT,$0
JMP ·atanh(SB)
TEXT ·Dim(SB),NOSPLIT,$0
JMP ·dim(SB)
@ -27,6 +36,12 @@ TEXT ·Min(SB),NOSPLIT,$0
TEXT ·Max(SB),NOSPLIT,$0
JMP ·max(SB)
TEXT ·Erf(SB),NOSPLIT,$0
JMP ·erf(SB)
TEXT ·Erfc(SB),NOSPLIT,$0
JMP ·erfc(SB)
TEXT ·Exp2(SB),NOSPLIT,$0
JMP ·exp2(SB)
@ -93,3 +108,9 @@ TEXT ·Tan(SB),NOSPLIT,$0
TEXT ·Tanh(SB),NOSPLIT,$0
JMP ·tanh(SB)
TEXT ·Cbrt(SB),NOSPLIT,$0
JMP ·cbrt(SB)
TEXT ·Pow(SB),NOSPLIT,$0
JMP ·pow(SB)

22
src/math/stubs_ppc64x.s
View file

@ -12,12 +12,21 @@ TEXT ·Asin(SB),NOSPLIT,$0
TEXT ·Acos(SB),NOSPLIT,$0
BR ·acos(SB)
TEXT ·Asinh(SB),NOSPLIT,$0
BR ·asinh(SB)
TEXT ·Acosh(SB),NOSPLIT,$0
BR ·acosh(SB)
TEXT ·Atan2(SB),NOSPLIT,$0
BR ·atan2(SB)
TEXT ·Atan(SB),NOSPLIT,$0
BR ·atan(SB)
TEXT ·Atanh(SB),NOSPLIT,$0
BR ·atanh(SB)
TEXT ·Dim(SB),NOSPLIT,$0
BR ·dim(SB)
@ -27,6 +36,12 @@ TEXT ·Min(SB),NOSPLIT,$0
TEXT ·Max(SB),NOSPLIT,$0
BR ·max(SB)
TEXT ·Erf(SB),NOSPLIT,$0
BR ·erf(SB)
TEXT ·Erfc(SB),NOSPLIT,$0
BR ·erfc(SB)
TEXT ·Exp2(SB),NOSPLIT,$0
BR ·exp2(SB)
@ -83,3 +98,10 @@ TEXT ·Tan(SB),NOSPLIT,$0
TEXT ·Tanh(SB),NOSPLIT,$0
BR ·tanh(SB)
TEXT ·Cbrt(SB),NOSPLIT,$0
BR ·cbrt(SB)
TEXT ·Pow(SB),NOSPLIT,$0
BR ·pow(SB)

423
src/math/stubs_s390x.s
View file

@ -4,27 +4,9 @@
#include "textflag.h"
TEXT ·Asin(SB),NOSPLIT,$0
BR ·asin(SB)
TEXT ·Acos(SB),NOSPLIT,$0
BR ·acos(SB)
TEXT ·Atan2(SB),NOSPLIT,$0
BR ·atan2(SB)
TEXT ·Atan(SB),NOSPLIT,$0
BR ·atan(SB)
TEXT ·Exp2(SB),NOSPLIT,$0
BR ·exp2(SB)
TEXT ·Expm1(SB),NOSPLIT,$0
BR ·expm1(SB)
TEXT ·Exp(SB),NOSPLIT,$0
BR ·exp(SB)
TEXT ·Frexp(SB),NOSPLIT,$0
BR ·frexp(SB)
@ -37,12 +19,6 @@ TEXT ·Ldexp(SB),NOSPLIT,$0
TEXT ·Log2(SB),NOSPLIT,$0
BR ·log2(SB)
TEXT ·Log1p(SB),NOSPLIT,$0
BR ·log1p(SB)
TEXT ·Log(SB),NOSPLIT,$0
BR ·log(SB)
TEXT ·Modf(SB),NOSPLIT,$0
BR ·modf(SB)
@ -52,9 +28,6 @@ TEXT ·Mod(SB),NOSPLIT,$0
TEXT ·Remainder(SB),NOSPLIT,$0
BR ·remainder(SB)
TEXT ·Tan(SB),NOSPLIT,$0
BR ·tan(SB)
//if go assembly use vector instruction
TEXT ·hasVectorFacility(SB),NOSPLIT,$24-1
MOVD $x-24(SP), R1
@ -77,129 +50,463 @@ novector:
RET
TEXT ·Log10(SB),NOSPLIT,$0
MOVD log10vectorfacility+0x00(SB),R1
MOVD ·log10vectorfacility+0x00(SB),R1
BR (R1)
TEXT ·log10TrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $log10vectorfacility+0x00(SB), R1
MOVD $·log10vectorfacility+0x00(SB), R1
MOVD $·log10(SB), R2
MOVD R2, 0(R1)
BR ·log10(SB)
vectorimpl:
MOVD $log10vectorfacility+0x00(SB), R1
MOVD $·log10vectorfacility+0x00(SB), R1
MOVD $·log10Asm(SB), R2
MOVD R2, 0(R1)
BR ·log10Asm(SB)
GLOBL log10vectorfacility+0x00(SB), NOPTR, $8
DATA log10vectorfacility+0x00(SB)/8, $·log10TrampolineSetup(SB)
GLOBL ·log10vectorfacility+0x00(SB), NOPTR, $8
DATA ·log10vectorfacility+0x00(SB)/8, $·log10TrampolineSetup(SB)
TEXT ·Cos(SB),NOSPLIT,$0
MOVD cosvectorfacility+0x00(SB),R1
MOVD ·cosvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·cosTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $cosvectorfacility+0x00(SB), R1
MOVD $·cosvectorfacility+0x00(SB), R1
MOVD $·cos(SB), R2
MOVD R2, 0(R1)
BR ·cos(SB)
vectorimpl:
MOVD $cosvectorfacility+0x00(SB), R1
MOVD $·cosvectorfacility+0x00(SB), R1
MOVD $·cosAsm(SB), R2
MOVD R2, 0(R1)
BR ·cosAsm(SB)
GLOBL cosvectorfacility+0x00(SB), NOPTR, $8
DATA cosvectorfacility+0x00(SB)/8, $·cosTrampolineSetup(SB)
GLOBL ·cosvectorfacility+0x00(SB), NOPTR, $8
DATA ·cosvectorfacility+0x00(SB)/8, $·cosTrampolineSetup(SB)
TEXT ·Cosh(SB),NOSPLIT,$0
MOVD coshvectorfacility+0x00(SB),R1
MOVD ·coshvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·coshTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $coshvectorfacility+0x00(SB), R1
MOVD $·coshvectorfacility+0x00(SB), R1
MOVD $·cosh(SB), R2
MOVD R2, 0(R1)
BR ·cosh(SB)
vectorimpl:
MOVD $coshvectorfacility+0x00(SB), R1
MOVD $·coshvectorfacility+0x00(SB), R1
MOVD $·coshAsm(SB), R2
MOVD R2, 0(R1)
BR ·coshAsm(SB)
GLOBL coshvectorfacility+0x00(SB), NOPTR, $8
DATA coshvectorfacility+0x00(SB)/8, $·coshTrampolineSetup(SB)
GLOBL ·coshvectorfacility+0x00(SB), NOPTR, $8
DATA ·coshvectorfacility+0x00(SB)/8, $·coshTrampolineSetup(SB)
TEXT ·Sin(SB),NOSPLIT,$0
MOVD sinvectorfacility+0x00(SB),R1
MOVD ·sinvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·sinTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $sinvectorfacility+0x00(SB), R1
MOVD $·sinvectorfacility+0x00(SB), R1
MOVD $·sin(SB), R2
MOVD R2, 0(R1)
BR ·sin(SB)
vectorimpl:
MOVD $sinvectorfacility+0x00(SB), R1
MOVD $·sinvectorfacility+0x00(SB), R1
MOVD $·sinAsm(SB), R2
MOVD R2, 0(R1)
BR ·sinAsm(SB)
GLOBL sinvectorfacility+0x00(SB), NOPTR, $8
DATA sinvectorfacility+0x00(SB)/8, $·sinTrampolineSetup(SB)
GLOBL ·sinvectorfacility+0x00(SB), NOPTR, $8
DATA ·sinvectorfacility+0x00(SB)/8, $·sinTrampolineSetup(SB)
TEXT ·Sinh(SB),NOSPLIT,$0
MOVD sinhvectorfacility+0x00(SB),R1
MOVD ·sinhvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·sinhTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $sinhvectorfacility+0x00(SB), R1
MOVD $·sinhvectorfacility+0x00(SB), R1
MOVD $·sinh(SB), R2
MOVD R2, 0(R1)
BR ·sinh(SB)
vectorimpl:
MOVD $sinhvectorfacility+0x00(SB), R1
MOVD $·sinhvectorfacility+0x00(SB), R1
MOVD $·sinhAsm(SB), R2
MOVD R2, 0(R1)
BR ·sinhAsm(SB)
GLOBL sinhvectorfacility+0x00(SB), NOPTR, $8
DATA sinhvectorfacility+0x00(SB)/8, $·sinhTrampolineSetup(SB)
GLOBL ·sinhvectorfacility+0x00(SB), NOPTR, $8
DATA ·sinhvectorfacility+0x00(SB)/8, $·sinhTrampolineSetup(SB)
TEXT ·Tanh(SB),NOSPLIT,$0
MOVD tanhvectorfacility+0x00(SB),R1
MOVD ·tanhvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·tanhTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $tanhvectorfacility+0x00(SB), R1
MOVD $·tanhvectorfacility+0x00(SB), R1
MOVD $·tanh(SB), R2
MOVD R2, 0(R1)
BR ·tanh(SB)
vectorimpl:
MOVD $tanhvectorfacility+0x00(SB), R1
MOVD $·tanhvectorfacility+0x00(SB), R1
MOVD $·tanhAsm(SB), R2
MOVD R2, 0(R1)
BR ·tanhAsm(SB)
GLOBL tanhvectorfacility+0x00(SB), NOPTR, $8
DATA tanhvectorfacility+0x00(SB)/8, $·tanhTrampolineSetup(SB)
GLOBL ·tanhvectorfacility+0x00(SB), NOPTR, $8
DATA ·tanhvectorfacility+0x00(SB)/8, $·tanhTrampolineSetup(SB)
TEXT ·Log1p(SB),NOSPLIT,$0
MOVD ·log1pvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·log1pTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·log1pvectorfacility+0x00(SB), R1
MOVD $·log1p(SB), R2
MOVD R2, 0(R1)
BR ·log1p(SB)
vectorimpl:
MOVD $·log1pvectorfacility+0x00(SB), R1
MOVD $·log1pAsm(SB), R2
MOVD R2, 0(R1)
BR ·log1pAsm(SB)
GLOBL ·log1pvectorfacility+0x00(SB), NOPTR, $8
DATA ·log1pvectorfacility+0x00(SB)/8, $·log1pTrampolineSetup(SB)
TEXT ·Atanh(SB),NOSPLIT,$0
MOVD ·atanhvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·atanhTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·atanhvectorfacility+0x00(SB), R1
MOVD $·atanh(SB), R2
MOVD R2, 0(R1)
BR ·atanh(SB)
vectorimpl:
MOVD $·atanhvectorfacility+0x00(SB), R1
MOVD $·atanhAsm(SB), R2
MOVD R2, 0(R1)
BR ·atanhAsm(SB)
GLOBL ·atanhvectorfacility+0x00(SB), NOPTR, $8
DATA ·atanhvectorfacility+0x00(SB)/8, $·atanhTrampolineSetup(SB)
TEXT ·Acos(SB),NOSPLIT,$0
MOVD ·acosvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·acosTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·acosvectorfacility+0x00(SB), R1
MOVD $·acos(SB), R2
MOVD R2, 0(R1)
BR ·acos(SB)
vectorimpl:
MOVD $·acosvectorfacility+0x00(SB), R1
MOVD $·acosAsm(SB), R2
MOVD R2, 0(R1)
BR ·acosAsm(SB)
GLOBL ·acosvectorfacility+0x00(SB), NOPTR, $8
DATA ·acosvectorfacility+0x00(SB)/8, $·acosTrampolineSetup(SB)
TEXT ·Asin(SB),NOSPLIT,$0
MOVD ·asinvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·asinTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·asinvectorfacility+0x00(SB), R1
MOVD $·asin(SB), R2
MOVD R2, 0(R1)
BR ·asin(SB)
vectorimpl:
MOVD $·asinvectorfacility+0x00(SB), R1
MOVD $·asinAsm(SB), R2
MOVD R2, 0(R1)
BR ·asinAsm(SB)
GLOBL ·asinvectorfacility+0x00(SB), NOPTR, $8
DATA ·asinvectorfacility+0x00(SB)/8, $·asinTrampolineSetup(SB)
TEXT ·Asinh(SB),NOSPLIT,$0
MOVD ·asinhvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·asinhTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·asinhvectorfacility+0x00(SB), R1
MOVD $·asinh(SB), R2
MOVD R2, 0(R1)
BR ·asinh(SB)
vectorimpl:
MOVD $·asinhvectorfacility+0x00(SB), R1
MOVD $·asinhAsm(SB), R2
MOVD R2, 0(R1)
BR ·asinhAsm(SB)
GLOBL ·asinhvectorfacility+0x00(SB), NOPTR, $8
DATA ·asinhvectorfacility+0x00(SB)/8, $·asinhTrampolineSetup(SB)
TEXT ·Acosh(SB),NOSPLIT,$0
MOVD ·acoshvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·acoshTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·acoshvectorfacility+0x00(SB), R1
MOVD $·acosh(SB), R2
MOVD R2, 0(R1)
BR ·acosh(SB)
vectorimpl:
MOVD $·acoshvectorfacility+0x00(SB), R1
MOVD $·acoshAsm(SB), R2
MOVD R2, 0(R1)
BR ·acoshAsm(SB)
GLOBL ·acoshvectorfacility+0x00(SB), NOPTR, $8
DATA ·acoshvectorfacility+0x00(SB)/8, $·acoshTrampolineSetup(SB)
TEXT ·Erf(SB),NOSPLIT,$0
MOVD ·erfvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·erfTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·erfvectorfacility+0x00(SB), R1
MOVD $·erf(SB), R2
MOVD R2, 0(R1)
BR ·erf(SB)
vectorimpl:
MOVD $·erfvectorfacility+0x00(SB), R1
MOVD $·erfAsm(SB), R2
MOVD R2, 0(R1)
BR ·erfAsm(SB)
GLOBL ·erfvectorfacility+0x00(SB), NOPTR, $8
DATA ·erfvectorfacility+0x00(SB)/8, $·erfTrampolineSetup(SB)
TEXT ·Erfc(SB),NOSPLIT,$0
MOVD ·erfcvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·erfcTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·erfcvectorfacility+0x00(SB), R1
MOVD $·erfc(SB), R2
MOVD R2, 0(R1)
BR ·erfc(SB)
vectorimpl:
MOVD $·erfcvectorfacility+0x00(SB), R1
MOVD $·erfcAsm(SB), R2
MOVD R2, 0(R1)
BR ·erfcAsm(SB)
GLOBL ·erfcvectorfacility+0x00(SB), NOPTR, $8
DATA ·erfcvectorfacility+0x00(SB)/8, $·erfcTrampolineSetup(SB)
TEXT ·Atan(SB),NOSPLIT,$0
MOVD ·atanvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·atanTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·atanvectorfacility+0x00(SB), R1
MOVD $·atan(SB), R2
MOVD R2, 0(R1)
BR ·atan(SB)
vectorimpl:
MOVD $·atanvectorfacility+0x00(SB), R1
MOVD $·atanAsm(SB), R2
MOVD R2, 0(R1)
BR ·atanAsm(SB)
GLOBL ·atanvectorfacility+0x00(SB), NOPTR, $8
DATA ·atanvectorfacility+0x00(SB)/8, $·atanTrampolineSetup(SB)
TEXT ·Atan2(SB),NOSPLIT,$0
MOVD ·atan2vectorfacility+0x00(SB),R1
BR (R1)
TEXT ·atan2TrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·atan2vectorfacility+0x00(SB), R1
MOVD $·atan2(SB), R2
MOVD R2, 0(R1)
BR ·atan2(SB)
vectorimpl:
MOVD $·atan2vectorfacility+0x00(SB), R1
MOVD $·atan2Asm(SB), R2
MOVD R2, 0(R1)
BR ·atan2Asm(SB)
GLOBL ·atan2vectorfacility+0x00(SB), NOPTR, $8
DATA ·atan2vectorfacility+0x00(SB)/8, $·atan2TrampolineSetup(SB)
TEXT ·Cbrt(SB),NOSPLIT,$0
MOVD ·cbrtvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·cbrtTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·cbrtvectorfacility+0x00(SB), R1
MOVD $·cbrt(SB), R2
MOVD R2, 0(R1)
BR ·cbrt(SB)
vectorimpl:
MOVD $·cbrtvectorfacility+0x00(SB), R1
MOVD $·cbrtAsm(SB), R2
MOVD R2, 0(R1)
BR ·cbrtAsm(SB)
GLOBL ·cbrtvectorfacility+0x00(SB), NOPTR, $8
DATA ·cbrtvectorfacility+0x00(SB)/8, $·cbrtTrampolineSetup(SB)
TEXT ·Log(SB),NOSPLIT,$0
MOVD ·logvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·logTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·logvectorfacility+0x00(SB), R1
MOVD $·log(SB), R2
MOVD R2, 0(R1)
BR ·log(SB)
vectorimpl:
MOVD $·logvectorfacility+0x00(SB), R1
MOVD $·logAsm(SB), R2
MOVD R2, 0(R1)
BR ·logAsm(SB)
GLOBL ·logvectorfacility+0x00(SB), NOPTR, $8
DATA ·logvectorfacility+0x00(SB)/8, $·logTrampolineSetup(SB)
TEXT ·Tan(SB),NOSPLIT,$0
MOVD ·tanvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·tanTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·tanvectorfacility+0x00(SB), R1
MOVD $·tan(SB), R2
MOVD R2, 0(R1)
BR ·tan(SB)
vectorimpl:
MOVD $·tanvectorfacility+0x00(SB), R1
MOVD $·tanAsm(SB), R2
MOVD R2, 0(R1)
BR ·tanAsm(SB)
GLOBL ·tanvectorfacility+0x00(SB), NOPTR, $8
DATA ·tanvectorfacility+0x00(SB)/8, $·tanTrampolineSetup(SB)
TEXT ·Exp(SB),NOSPLIT,$0
MOVD ·expvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·expTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·expvectorfacility+0x00(SB), R1
MOVD $·exp(SB), R2
MOVD R2, 0(R1)
BR ·exp(SB)
vectorimpl:
MOVD $·expvectorfacility+0x00(SB), R1
MOVD $·expAsm(SB), R2
MOVD R2, 0(R1)
BR ·expAsm(SB)
GLOBL ·expvectorfacility+0x00(SB), NOPTR, $8
DATA ·expvectorfacility+0x00(SB)/8, $·expTrampolineSetup(SB)
TEXT ·Expm1(SB),NOSPLIT,$0
MOVD ·expm1vectorfacility+0x00(SB),R1
BR (R1)
TEXT ·expm1TrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·expm1vectorfacility+0x00(SB), R1
MOVD $·expm1(SB), R2
MOVD R2, 0(R1)
BR ·expm1(SB)
vectorimpl:
MOVD $·expm1vectorfacility+0x00(SB), R1
MOVD $·expm1Asm(SB), R2
MOVD R2, 0(R1)
BR ·expm1Asm(SB)
GLOBL ·expm1vectorfacility+0x00(SB), NOPTR, $8
DATA ·expm1vectorfacility+0x00(SB)/8, $·expm1TrampolineSetup(SB)
TEXT ·Pow(SB),NOSPLIT,$0
MOVD ·powvectorfacility+0x00(SB),R1
BR (R1)
TEXT ·powTrampolineSetup(SB),NOSPLIT, $0
MOVB ·hasVX(SB), R1
CMPBEQ R1, $1, vectorimpl // vectorfacility = 1, vector supported
MOVD $·powvectorfacility+0x00(SB), R1
MOVD $·pow(SB), R2
MOVD R2, 0(R1)
BR ·pow(SB)
vectorimpl:
MOVD $·powvectorfacility+0x00(SB), R1
MOVD $·powAsm(SB), R2
MOVD R2, 0(R1)
BR ·powAsm(SB)
GLOBL ·powvectorfacility+0x00(SB), NOPTR, $8
DATA ·powvectorfacility+0x00(SB)/8, $·powTrampolineSetup(SB)

110
src/math/tan_s390x.s Normal file
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// 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 approximations
DATA ·tanrodataL13<> + 0(SB)/8, $0.181017336383229927e-07
DATA ·tanrodataL13<> + 8(SB)/8, $-.256590857271311164e-03
DATA ·tanrodataL13<> + 16(SB)/8, $-.464359274328689195e+00
DATA ·tanrodataL13<> + 24(SB)/8, $1.0
DATA ·tanrodataL13<> + 32(SB)/8, $-.333333333333333464e+00
DATA ·tanrodataL13<> + 40(SB)/8, $0.245751217306830032e-01
DATA ·tanrodataL13<> + 48(SB)/8, $-.245391301343844510e-03
DATA ·tanrodataL13<> + 56(SB)/8, $0.214530914428992319e-01
DATA ·tanrodataL13<> + 64(SB)/8, $0.108285667160535624e-31
DATA ·tanrodataL13<> + 72(SB)/8, $0.612323399573676480e-16
DATA ·tanrodataL13<> + 80(SB)/8, $0.157079632679489656e+01
DATA ·tanrodataL13<> + 88(SB)/8, $0.636619772367581341e+00
GLOBL ·tanrodataL13<> + 0(SB), RODATA, $96
// Constants
DATA ·tanxnan<> + 0(SB)/8, $0x7ff8000000000000
GLOBL ·tanxnan<> + 0(SB), RODATA, $8
DATA ·tanxlim<> + 0(SB)/8, $0x432921fb54442d19
GLOBL ·tanxlim<> + 0(SB), RODATA, $8
DATA ·tanxadd<> + 0(SB)/8, $0xc338000000000000
GLOBL ·tanxadd<> + 0(SB), RODATA, $8
// Tan returns the tangent of the radian argument.
//
// Special cases are:
// Tan(±0) = ±0
// Tan(±Inf) = NaN
// Tan(NaN) = NaN
// The algorithm used is minimax polynomial approximation using a table of
// polynomial coefficients determined with a Remez exchange algorithm.
TEXT ·tanAsm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
//specail case Tan(±0) = ±0
FMOVD $(0.0), F1
FCMPU F0, F1
BEQ atanIsZero
MOVD $·tanrodataL13<>+0(SB), R5
WORD $0xB3120000 //ltdbr %f0,%f0
BLTU L10
FMOVD F0, F2
L2:
MOVD $·tanxlim<>+0(SB), R1
WORD $0xED201000 //cdb %f2,0(%r1)
BYTE $0x00
BYTE $0x19
BGE L11
BVS L11
MOVD $·tanxadd<>+0(SB), R1
FMOVD 88(R5), F6
FMOVD 0(R1), F4
WFMSDB V0, V6, V4, V6
FMOVD 80(R5), F1
FADD F6, F4
FMOVD 72(R5), F2
FMSUB F1, F4, F0
FMOVD 64(R5), F3
WFMADB V4, V2, V0, V2
FMOVD 56(R5), F1
WFMADB V4, V3, V2, V4
FMUL F2, F2
VLEG $0, 48(R5), V18
WORD $0xB3CD0016 //lgdr %r1,%f6
FMOVD 40(R5), F5
FMOVD 32(R5), F3
FMADD F1, F2, F3
FMOVD 24(R5), F1
FMOVD 16(R5), F7
FMOVD 8(R5), F0
WFMADB V2, V7, V1, V7
WFMADB V2, V0, V5, V0
WFMDB V2, V2, V1
FMOVD 0(R5), F5
WFLCDB V4, V16
WFMADB V2, V5, V18, V5
WFMADB V1, V0, V7, V0
WORD $0xA7110001 //tmll %r1,1
WFMADB V1, V5, V3, V1
BNE L12
WFDDB V0, V1, V0
WFMDB V2, V16, V2
WFMADB V2, V0, V4, V0
WORD $0xB3130000 //lcdbr %f0,%f0
FMOVD F0, ret+8(FP)
RET
L12:
WFMSDB V2, V1, V0, V2
WFMDB V16, V2, V2
FDIV F2, F0
FMOVD F0, ret+8(FP)
RET
L11:
MOVD $·tanxnan<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
L10:
WORD $0xB3130020 //lcdbr %f2,%f0
BR L2
atanIsZero:
FMOVD F0, ret+8(FP)
RET