Trading Space for Time

Is there any way to make these two functions run faster?

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// linear2sRGB is a sRGB encoder
func linear2sRGB(v float64) float64 {
	if v <= 0.0031308 {
		v *= 12.92
	} else {
		v = 1.055*math.Pow(v, 1/2.4) - 0.055
	}
	return v
}

// sRGB2linear is a sRGB decoder
func sRGB2linear(v float64) float64 {
	if v <= 0.04045 {
		v /= 12.92
	} else {
		v = math.Pow((v+0.055)/1.055, 2.4)
	}
	return v
}

Here’s a straightforward optimization: lookup table + linear interpolation:

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// Linear2sRGB converts linear inputs to sRGB space.
func Linear2sRGB(v float64) float64 {
	i := v * lutSize
	ifloor := int(i) & (lutSize - 1)
	v0 := lin2sRGBLUT[ifloor]
	v1 := lin2sRGBLUT[ifloor+1]
	i -= float64(ifloor)
	return v0*(1.0-i) + v1*i
}

func linear2sRGB(v float64) float64 {
	if v <= 0.0031308 {
		v *= 12.92
	} else {
		v = 1.055*math.Pow(v, 1/2.4) - 0.055
	}
	return v
}

const lutSize = 1024 // keep a power of 2

var lin2sRGBLUT [lutSize + 1]float64

func init() {
	for i := range lin2sRGBLUT[:lutSize] {
		lin2sRGBLUT[i] = linear2sRGB(float64(i) / lutSize)
	}
	lin2sRGBLUT[lutSize] = lin2sRGBLUT[lutSize-1]
}

func BenchmarkLinear2sRGB(b *testing.B) {
	for i := 0; i < b.N; i++ {
		for j := 0.0; j <= 1.0; j += 0.01 {
			convert.Linear2sRGB(j)
		}
	}
}

The benchmark shows approximately 98% runtime performance improvement after optimization.

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name           old time/op  new time/op  delta
Linear2sRGB-6  6.38µs ± 0%  0.14µs ± 0%  -97.87%  (p=0.000 n=10+8)

有什么办法能够让这两个函数跑得更快吗？

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// linear2sRGB is a sRGB encoder
func linear2sRGB(v float64) float64 {
	if v <= 0.0031308 {
		v *= 12.92
	} else {
		v = 1.055*math.Pow(v, 1/2.4) - 0.055
	}
	return v
}

// sRGB2linear is a sRGB decoder
func sRGB2linear(v float64) float64 {
	if v <= 0.04045 {
		v /= 12.92
	} else {
		v = math.Pow((v+0.055)/1.055, 2.4)
	}
	return v
}

这里介绍一个很平凡的优化方案: lookup table + 线性插值:

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// Linear2sRGB converts linear inputs to sRGB space.
func Linear2sRGB(v float64) float64 {
	i := v * lutSize
	ifloor := int(i) & (lutSize - 1)
	v0 := lin2sRGBLUT[ifloor]
	v1 := lin2sRGBLUT[ifloor+1]
	i -= float64(ifloor)
	return v0*(1.0-i) + v1*i
}

func linear2sRGB(v float64) float64 {
	if v <= 0.0031308 {
		v *= 12.92
	} else {
		v = 1.055*math.Pow(v, 1/2.4) - 0.055
	}
	return v
}

const lutSize = 1024 // keep a power of 2

var lin2sRGBLUT [lutSize + 1]float64

func init() {
	for i := range lin2sRGBLUT[:lutSize] {
		lin2sRGBLUT[i] = linear2sRGB(float64(i) / lutSize)
	}
	lin2sRGBLUT[lutSize] = lin2sRGBLUT[lutSize-1]
}

func BenchmarkLinear2sRGB(b *testing.B) {
	for i := 0; i < b.N; i++ {
		for j := 0.0; j <= 1.0; j += 0.01 {
			convert.Linear2sRGB(j)
		}
	}
}

基准测试显示，优化后的运行时性能提升约为 98%。

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name           old time/op  new time/op  delta
Linear2sRGB-6  6.38µs ± 0%  0.14µs ± 0%  -97.87%  (p=0.000 n=10+8)