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Each URL was manually verified to ensure it did not serve up incorrect content. Change-Id: I4dc846227af95a73ee9a3074d0c379ff0fa955df Reviewed-on: https://go-review.googlesource.com/115798 Reviewed-by: Ian Lance Taylor <iant@golang.org> Run-TryBot: Ian Lance Taylor <iant@golang.org>
160 lines
4.2 KiB
ArmAsm
160 lines
4.2 KiB
ArmAsm
// Copyright 2010 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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// The method is based on a paper by Naoki Shibata: "Efficient evaluation
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// methods of elementary functions suitable for SIMD computation", Proc.
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// of International Supercomputing Conference 2010 (ISC'10), pp. 25 -- 32
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// (May 2010). The paper is available at
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// https://www.springerlink.com/content/340228x165742104/
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//
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// The original code and the constants below are from the author's
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// implementation available at http://freshmeat.net/projects/sleef.
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// The README file says, "The software is in public domain.
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// You can use the software without any obligation."
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//
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// This code is a simplified version of the original.
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#define LN2 0.6931471805599453094172321214581766 // log_e(2)
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#define LOG2E 1.4426950408889634073599246810018920 // 1/LN2
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#define LN2U 0.69314718055966295651160180568695068359375 // upper half LN2
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#define LN2L 0.28235290563031577122588448175013436025525412068e-12 // lower half LN2
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#define PosInf 0x7FF0000000000000
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#define NegInf 0xFFF0000000000000
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#define Overflow 7.09782712893384e+02
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DATA exprodata<>+0(SB)/8, $0.5
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DATA exprodata<>+8(SB)/8, $1.0
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DATA exprodata<>+16(SB)/8, $2.0
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DATA exprodata<>+24(SB)/8, $1.6666666666666666667e-1
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DATA exprodata<>+32(SB)/8, $4.1666666666666666667e-2
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DATA exprodata<>+40(SB)/8, $8.3333333333333333333e-3
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DATA exprodata<>+48(SB)/8, $1.3888888888888888889e-3
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DATA exprodata<>+56(SB)/8, $1.9841269841269841270e-4
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DATA exprodata<>+64(SB)/8, $2.4801587301587301587e-5
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GLOBL exprodata<>+0(SB), RODATA, $72
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// func Exp(x float64) float64
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TEXT ·Exp(SB),NOSPLIT,$0
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// test bits for not-finite
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MOVQ x+0(FP), BX
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MOVQ $~(1<<63), AX // sign bit mask
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MOVQ BX, DX
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ANDQ AX, DX
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MOVQ $PosInf, AX
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CMPQ AX, DX
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JLE notFinite
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// check if argument will overflow
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MOVQ BX, X0
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MOVSD $Overflow, X1
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COMISD X1, X0
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JA overflow
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MOVSD $LOG2E, X1
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MULSD X0, X1
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CVTSD2SL X1, BX // BX = exponent
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CVTSL2SD BX, X1
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CMPB ·useFMA(SB), $1
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JE avxfma
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MOVSD $LN2U, X2
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MULSD X1, X2
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SUBSD X2, X0
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MOVSD $LN2L, X2
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MULSD X1, X2
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SUBSD X2, X0
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// reduce argument
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MULSD $0.0625, X0
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// Taylor series evaluation
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MOVSD exprodata<>+64(SB), X1
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MULSD X0, X1
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ADDSD exprodata<>+56(SB), X1
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MULSD X0, X1
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ADDSD exprodata<>+48(SB), X1
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MULSD X0, X1
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ADDSD exprodata<>+40(SB), X1
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MULSD X0, X1
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ADDSD exprodata<>+32(SB), X1
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MULSD X0, X1
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ADDSD exprodata<>+24(SB), X1
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MULSD X0, X1
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ADDSD exprodata<>+0(SB), X1
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MULSD X0, X1
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ADDSD exprodata<>+8(SB), X1
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MULSD X1, X0
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MOVSD exprodata<>+16(SB), X1
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ADDSD X0, X1
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MULSD X1, X0
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MOVSD exprodata<>+16(SB), X1
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ADDSD X0, X1
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MULSD X1, X0
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MOVSD exprodata<>+16(SB), X1
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ADDSD X0, X1
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MULSD X1, X0
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MOVSD exprodata<>+16(SB), X1
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ADDSD X0, X1
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MULSD X1, X0
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ADDSD exprodata<>+8(SB), X0
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// return fr * 2**exponent
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ldexp:
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ADDL $0x3FF, BX // add bias
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JLE denormal
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CMPL BX, $0x7FF
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JGE overflow
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lastStep:
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SHLQ $52, BX
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MOVQ BX, X1
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MULSD X1, X0
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MOVSD X0, ret+8(FP)
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RET
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notFinite:
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// test bits for -Inf
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MOVQ $NegInf, AX
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CMPQ AX, BX
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JNE notNegInf
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// -Inf, return 0
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underflow: // return 0
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MOVQ $0, ret+8(FP)
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RET
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overflow: // return +Inf
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MOVQ $PosInf, BX
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notNegInf: // NaN or +Inf, return x
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MOVQ BX, ret+8(FP)
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RET
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denormal:
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CMPL BX, $-52
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JL underflow
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ADDL $0x3FE, BX // add bias - 1
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SHLQ $52, BX
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MOVQ BX, X1
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MULSD X1, X0
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MOVQ $1, BX
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JMP lastStep
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avxfma:
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MOVSD $LN2U, X2
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VFNMADD231SD X2, X1, X0
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MOVSD $LN2L, X2
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VFNMADD231SD X2, X1, X0
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// reduce argument
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MULSD $0.0625, X0
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// Taylor series evaluation
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MOVSD exprodata<>+64(SB), X1
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VFMADD213SD exprodata<>+56(SB), X0, X1
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VFMADD213SD exprodata<>+48(SB), X0, X1
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VFMADD213SD exprodata<>+40(SB), X0, X1
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VFMADD213SD exprodata<>+32(SB), X0, X1
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VFMADD213SD exprodata<>+24(SB), X0, X1
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VFMADD213SD exprodata<>+0(SB), X0, X1
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VFMADD213SD exprodata<>+8(SB), X0, X1
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MULSD X1, X0
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VADDSD exprodata<>+16(SB), X0, X1
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MULSD X1, X0
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VADDSD exprodata<>+16(SB), X0, X1
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MULSD X1, X0
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VADDSD exprodata<>+16(SB), X0, X1
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MULSD X1, X0
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VADDSD exprodata<>+16(SB), X0, X1
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VFMADD213SD exprodata<>+8(SB), X1, X0
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JMP ldexp
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