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