log2sum.go

package main

import (
	"math"
	"testing"
)

func Log2Sum(logx, logy float64) float64 {
	if logx < logy {
		logx, logy = logy, logx
	}
	if logx-logy < 2 {
		p := 1 - math.Exp2(logy-logx)
		p2 := p * p
		return 1 + logx - (p/2+p2/8+p2*p/24+p2*p2/64)/math.Ln2
	}
	p := math.Exp2(logy - logx)
	p2 := p * p
	return logx + (p-p2/2+p2*p/3-p2*p2/4)/math.Ln2
}

func slowLog2Sum(logx, logy float64) float64 {
	return math.Log2(math.Pow(2, logx) + math.Pow(2, logy))
}

func TestLog2Sum(t *testing.T) {
	for x := 1; x < 200; x++ {
		for y := 1; y < 200; y++ {
			logx := math.Log2(float64(x))
			logy := math.Log2(float64(y))
			a := Log2Sum(logx, logy)
			b := slowLog2Sum(logx, logy)
			if math.Abs(a-b) >= 0.005 {
				t.Errorf("Log2(%d + %d) = %f, want %f", x, y, a, b)
			}
		}
	}

	for x := float64(1); x < 2e9; x *= 10 {
		for y := float64(1); y < 2e9; y *= 10 {
			logx := math.Log2(x)
			logy := math.Log2(y)
			a := Log2Sum(logx, logy)
			b := slowLog2Sum(logx, logy)
			if math.Abs(a-b) >= 0.00001 {
				t.Errorf("Log2(%f + %f) = %f, want %f", x, y, a, b)
			}
		}
	}
}

func BenchmarkLog2Sum(b *testing.B) {
	x, y := math.Log2(50), math.Log2(200)
	for i := 0; i < b.N; i++ {
		Log2Sum(x, y)
	}
}

func BenchmarkSlowLog2Sum(b *testing.B) {
	x, y := math.Log2(50), math.Log2(200)
	for i := 0; i < b.N; i++ {
		slowLog2Sum(x, y)
	}
}