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88672de7af
As necessary, math functions were structured to use stubs, so that they can
be accelerated with assembly on any platform.
Technique used was minimax polynomial approximation using tables of
polynomial coefficients, with argument range reduction.
Benchmark New Old Speedup
BenchmarkAcos 12.2 47.5 3.89
BenchmarkAcosh 18.5 56.2 3.04
BenchmarkAsin 13.1 40.6 3.10
BenchmarkAsinh 19.4 62.8 3.24
BenchmarkAtan 10.1 23 2.28
BenchmarkAtanh 19.1 53.2 2.79
BenchmarkAtan2 16.5 33.9 2.05
BenchmarkCbrt 14.8 58 3.92
BenchmarkErf 10.8 20.1 1.86
BenchmarkErfc 11.2 23.5 2.10
BenchmarkExp 8.77 53.8 6.13
BenchmarkExpm1 10.1 38.3 3.79
BenchmarkLog 13.1 40.1 3.06
BenchmarkLog1p 12.7 38.3 3.02
BenchmarkPowInt 31.7 40.5 1.28
BenchmarkPowFrac 33.1 141 4.26
BenchmarkTan 11.5 30 2.61
Accuracy was tested against a high precision
reference function to determine maximum error.
Note: ulperr is error in "units in the last place"
max
ulperr
Acos 1.15
Acosh 1.07
Asin 2.22
Asinh 1.72
Atan 1.41
Atanh 3.00
Atan2 1.45
Cbrt 1.18
Erf 1.29
Erfc 4.82
Exp 1.00
Expm1 2.26
Log 0.94
Log1p 2.39
Tan 3.14
Pow will have 99.99% correctly rounded results with reasonable inputs
producing numeric (non Inf or NaN) results
Change-Id: I850e8cf7b70426e8b54ec49d74acd4cddc8c6cb2
Reviewed-on: https://go-review.googlesource.com/38585
Reviewed-by: Michael Munday <munday@ca.ibm.com>
Run-TryBot: Michael Munday <munday@ca.ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
111 lines
2.8 KiB
ArmAsm
111 lines
2.8 KiB
ArmAsm
// Copyright 2017 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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#include "textflag.h"
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// Minimax polynomial approximations
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DATA ·tanrodataL13<> + 0(SB)/8, $0.181017336383229927e-07
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DATA ·tanrodataL13<> + 8(SB)/8, $-.256590857271311164e-03
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DATA ·tanrodataL13<> + 16(SB)/8, $-.464359274328689195e+00
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DATA ·tanrodataL13<> + 24(SB)/8, $1.0
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DATA ·tanrodataL13<> + 32(SB)/8, $-.333333333333333464e+00
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DATA ·tanrodataL13<> + 40(SB)/8, $0.245751217306830032e-01
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DATA ·tanrodataL13<> + 48(SB)/8, $-.245391301343844510e-03
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DATA ·tanrodataL13<> + 56(SB)/8, $0.214530914428992319e-01
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DATA ·tanrodataL13<> + 64(SB)/8, $0.108285667160535624e-31
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DATA ·tanrodataL13<> + 72(SB)/8, $0.612323399573676480e-16
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DATA ·tanrodataL13<> + 80(SB)/8, $0.157079632679489656e+01
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DATA ·tanrodataL13<> + 88(SB)/8, $0.636619772367581341e+00
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GLOBL ·tanrodataL13<> + 0(SB), RODATA, $96
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// Constants
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DATA ·tanxnan<> + 0(SB)/8, $0x7ff8000000000000
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GLOBL ·tanxnan<> + 0(SB), RODATA, $8
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DATA ·tanxlim<> + 0(SB)/8, $0x432921fb54442d19
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GLOBL ·tanxlim<> + 0(SB), RODATA, $8
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DATA ·tanxadd<> + 0(SB)/8, $0xc338000000000000
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GLOBL ·tanxadd<> + 0(SB), RODATA, $8
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// Tan returns the tangent of the radian argument.
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//
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// Special cases are:
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// Tan(±0) = ±0
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// Tan(±Inf) = NaN
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// Tan(NaN) = NaN
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// The algorithm used is minimax polynomial approximation using a table of
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// polynomial coefficients determined with a Remez exchange algorithm.
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TEXT ·tanAsm(SB), NOSPLIT, $0-16
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FMOVD x+0(FP), F0
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//specail case Tan(±0) = ±0
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FMOVD $(0.0), F1
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FCMPU F0, F1
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BEQ atanIsZero
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MOVD $·tanrodataL13<>+0(SB), R5
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WORD $0xB3120000 //ltdbr %f0,%f0
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BLTU L10
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FMOVD F0, F2
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L2:
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MOVD $·tanxlim<>+0(SB), R1
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WORD $0xED201000 //cdb %f2,0(%r1)
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BYTE $0x00
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BYTE $0x19
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BGE L11
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BVS L11
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MOVD $·tanxadd<>+0(SB), R1
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FMOVD 88(R5), F6
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FMOVD 0(R1), F4
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WFMSDB V0, V6, V4, V6
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FMOVD 80(R5), F1
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FADD F6, F4
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FMOVD 72(R5), F2
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FMSUB F1, F4, F0
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FMOVD 64(R5), F3
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WFMADB V4, V2, V0, V2
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FMOVD 56(R5), F1
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WFMADB V4, V3, V2, V4
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FMUL F2, F2
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VLEG $0, 48(R5), V18
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WORD $0xB3CD0016 //lgdr %r1,%f6
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FMOVD 40(R5), F5
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FMOVD 32(R5), F3
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FMADD F1, F2, F3
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FMOVD 24(R5), F1
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FMOVD 16(R5), F7
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FMOVD 8(R5), F0
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WFMADB V2, V7, V1, V7
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WFMADB V2, V0, V5, V0
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WFMDB V2, V2, V1
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FMOVD 0(R5), F5
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WFLCDB V4, V16
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WFMADB V2, V5, V18, V5
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WFMADB V1, V0, V7, V0
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WORD $0xA7110001 //tmll %r1,1
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WFMADB V1, V5, V3, V1
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BNE L12
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WFDDB V0, V1, V0
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WFMDB V2, V16, V2
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WFMADB V2, V0, V4, V0
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WORD $0xB3130000 //lcdbr %f0,%f0
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FMOVD F0, ret+8(FP)
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RET
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L12:
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WFMSDB V2, V1, V0, V2
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WFMDB V16, V2, V2
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FDIV F2, F0
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FMOVD F0, ret+8(FP)
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RET
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L11:
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MOVD $·tanxnan<>+0(SB), R1
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FMOVD 0(R1), F0
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FMOVD F0, ret+8(FP)
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RET
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L10:
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WORD $0xB3130020 //lcdbr %f2,%f0
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BR L2
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atanIsZero:
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FMOVD F0, ret+8(FP)
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RET
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