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go/src/math/exp_s390x.s
Bill O'Farrell 88672de7af math: use SIMD to accelerate additional scalar math functions on s390x 
As necessary, math functions were structured to use stubs, so that they can
be accelerated with assembly on any platform.

Technique used was minimax polynomial approximation using tables of
polynomial coefficients, with argument range reduction.

Benchmark         New     Old     Speedup
BenchmarkAcos     12.2    47.5    3.89
BenchmarkAcosh    18.5    56.2    3.04
BenchmarkAsin     13.1    40.6    3.10
BenchmarkAsinh    19.4    62.8    3.24
BenchmarkAtan     10.1    23      2.28
BenchmarkAtanh    19.1    53.2    2.79
BenchmarkAtan2    16.5    33.9    2.05
BenchmarkCbrt     14.8    58      3.92
BenchmarkErf      10.8    20.1    1.86
BenchmarkErfc     11.2    23.5    2.10
BenchmarkExp      8.77    53.8    6.13
BenchmarkExpm1    10.1    38.3    3.79
BenchmarkLog      13.1    40.1    3.06
BenchmarkLog1p    12.7    38.3    3.02
BenchmarkPowInt   31.7    40.5    1.28
BenchmarkPowFrac  33.1    141     4.26
BenchmarkTan      11.5    30      2.61

Accuracy was tested against a high precision
reference function to determine maximum error.
Note: ulperr is error in "units in the last place"

       max
      ulperr
Acos  1.15
Acosh 1.07
Asin  2.22
Asinh 1.72
Atan  1.41
Atanh 3.00
Atan2 1.45
Cbrt  1.18
Erf   1.29
Erfc  4.82
Exp   1.00
Expm1 2.26
Log   0.94
Log1p 2.39
Tan   3.14

Pow will have 99.99% correctly rounded results with reasonable inputs
producing numeric (non Inf or NaN) results

Change-Id: I850e8cf7b70426e8b54ec49d74acd4cddc8c6cb2
Reviewed-on: https://go-review.googlesource.com/38585
Reviewed-by: Michael Munday <munday@ca.ibm.com>
Run-TryBot: Michael Munday <munday@ca.ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
2017-05-08 19:52:30 +00:00

186 lines
5.0 KiB
ArmAsm
Raw Blame History

// 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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