mirror of https://github.com/golang/go.git
math: implement fast path for Exp
- using FMA and AVX instructions if available to speed-up Exp calculation on amd64 - using a data table instead of #define'ed constants because these instructions do not support loading floating point immediates. One has to use a memory operand / register. - Benchmark results on Intel(R) Core(TM) i5-5200U CPU @ 2.20GHz: Original vs New (non-FMA path) name old time/op new time/op delta Exp 16.0ns ± 1% 16.1ns ± 3% ~ (p=0.308 n=9+10) Original vs New (FMA path) name old time/op new time/op delta Exp 16.0ns ± 1% 13.7ns ± 2% -14.80% (p=0.000 n=9+10) Change-Id: I3d8986925d82b39b95ee979ae06f59d7e591d02e Reviewed-on: https://go-review.googlesource.com/62590 Reviewed-by: Ilya Tocar <ilya.tocar@intel.com> Reviewed-by: Keith Randall <khr@golang.org> Run-TryBot: Keith Randall <khr@golang.org> TryBot-Result: Gobot Gobot <gobot@golang.org>
This commit is contained in:
Agniva De Sarker
Keith Randall
parent
475df0ebcc
commit
d2f317218b
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@ -21,18 +21,21 @@
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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 T0 1.0
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#define T1 0.5
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#define T2 1.6666666666666666667e-1
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#define T3 4.1666666666666666667e-2
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#define T4 8.3333333333333333333e-3
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#define T5 1.3888888888888888889e-3
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#define T6 1.9841269841269841270e-4
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#define T7 2.4801587301587301587e-5
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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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@ -52,6 +55,8 @@ TEXT ·Exp(SB),NOSPLIT,$0
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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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@ -61,36 +66,37 @@ TEXT ·Exp(SB),NOSPLIT,$0
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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 $T7, X1
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MOVSD exprodata<>+64(SB), X1
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MULSD X0, X1
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ADDSD $T6, X1
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ADDSD exprodata<>+56(SB), X1
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MULSD X0, X1
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ADDSD $T5, X1
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ADDSD exprodata<>+48(SB), X1
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MULSD X0, X1
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ADDSD $T4, X1
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ADDSD exprodata<>+40(SB), X1
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MULSD X0, X1
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ADDSD $T3, X1
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ADDSD exprodata<>+32(SB), X1
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MULSD X0, X1
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ADDSD $T2, X1
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ADDSD exprodata<>+24(SB), X1
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MULSD X0, X1
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ADDSD $T1, X1
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ADDSD exprodata<>+0(SB), X1
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MULSD X0, X1
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ADDSD $T0, X1
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ADDSD exprodata<>+8(SB), X1
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MULSD X1, X0
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MOVSD $2.0, X1
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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 $2.0, X1
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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 $2.0, X1
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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 $2.0, X1
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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 $1.0, X0
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ADDSD exprodata<>+8(SB), X0
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// return fr * 2**exponent
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lastStep:
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MOVL $0x3FF, AX // bias
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ADDL AX, BX
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JLE underflow
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@ -117,3 +123,30 @@ overflow: // return +Inf
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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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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 lastStep
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@ -0,0 +1,11 @@
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// 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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// +build amd64 amd64p32
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package math
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import "internal/cpu"
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var useFMA = cpu.X86.HasAVX && cpu.X86.HasFMA
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