ch3: add exercise3.8

Author: linehk

ch3/exercise3.8/mandelbrot.go

@@ -0,0 +1,90 @@
+package mandelbrot
+
+import (
+	"image/color"
+	"math"
+	"math/big"
+	"math/cmplx"
+)
+
+func mandelbrot64(z complex128) color.Color {
+	const iterations = 200
+	const contrast = 15
+	var v complex64
+	for n := uint8(0); n < iterations; n++ {
+		v = v*v + complex64(z)
+		if cmplx.Abs(complex128(v)) > 2 {
+			if n > 50 {
+				return color.RGBA{100, 0, 0, 255}
+			}
+			scale := math.Log(float64(n)) / math.Log(float64(iterations))
+			return color.RGBA{0, 0, 255 - uint8(scale*255), 255}
+		}
+	}
+	return color.Black
+}
+
+func mandelbrot128(z complex128) color.Color {
+	const iterations = 200
+	const contrast = 15
+	var v complex128
+	for n := uint8(0); n < iterations; n++ {
+		v = v*v + z
+		if cmplx.Abs(v) > 2 {
+			if n > 50 {
+				return color.RGBA{100, 0, 0, 255}
+			}
+			scale := math.Log(float64(n)) / math.Log(float64(iterations))
+			return color.RGBA{0, 0, 255 - uint8(scale*255), 255}
+		}
+	}
+	return color.Black
+}
+
+func mandelbrotBigFloat(z complex128) color.Color {
+	const iterations = 200
+	const contrast = 15
+	zR := (&big.Float{}).SetFloat64(real(z))
+	zI := (&big.Float{}).SetFloat64(imag(z))
+	var vR, vI = &big.Float{}, &big.Float{}
+	for i := uint8(0); i < iterations; i++ {
+		vR2, vI2 := &big.Float{}, &big.Float{}
+		vR2.Mul(vR, vR).Sub(vR2, (&big.Float{}).Mul(vI, vI)).Add(vR2, zR)
+		vI2.Mul(vR, vI).Mul(vI2, big.NewFloat(2)).Add(vI2, zI)
+		vR, vI = vR2, vI2
+		squareSum := &big.Float{}
+		squareSum.Mul(vR, vR).Add(squareSum, (&big.Float{}).Mul(vI, vI))
+		if squareSum.Cmp(big.NewFloat(4)) == 1 {
+			if i > 50 {
+				return color.RGBA{100, 0, 0, 255}
+			}
+			scale := math.Log(float64(i)) / math.Log(float64(iterations))
+			return color.RGBA{0, 0, 255 - uint8(scale*255), 255}
+		}
+	}
+	return color.Black
+}
+
+func mandelbrotBigRat(z complex128) color.Color {
+	const iterations = 200
+	const contrast = 15
+	zR := (&big.Rat{}).SetFloat64(real(z))
+	zI := (&big.Rat{}).SetFloat64(imag(z))
+	var vR, vI = &big.Rat{}, &big.Rat{}
+	for i := uint8(0); i < iterations; i++ {
+		vR2, vI2 := &big.Rat{}, &big.Rat{}
+		vR2.Mul(vR, vR).Sub(vR2, (&big.Rat{}).Mul(vI, vI)).Add(vR2, zR)
+		vI2.Mul(vR, vI).Mul(vI2, big.NewRat(2, 1)).Add(vI2, zI)
+		vR, vI = vR2, vI2
+		squareSum := &big.Rat{}
+		squareSum.Mul(vR, vR).Add(squareSum, (&big.Rat{}).Mul(vI, vI))
+		if squareSum.Cmp(big.NewRat(4, 1)) == 1 {
+			if i > 50 {
+				return color.RGBA{100, 0, 0, 255}
+			}
+			scale := math.Log(float64(i)) / math.Log(float64(iterations))
+			return color.RGBA{0, 0, 255 - uint8(scale*255), 255}
+		}
+	}
+	return color.Black
+}

ch3/exercise3.8/mandelbrot_test.go

@@ -0,0 +1,38 @@
+package mandelbrot
+
+import (
+	"image/color"
+	"testing"
+)
+
+func bench(b *testing.B, f func(complex128) color.Color) {
+	for i := 0; i < b.N; i++ {
+		f(complex(float64(i), float64(i)))
+	}
+}
+
+func BenchmarkMandelbrotComplex64(b *testing.B) {
+	bench(b, mandelbrot64)
+}
+
+func BenchmarkMandelbrotComplex128(b *testing.B) {
+	bench(b, mandelbrot128)
+}
+
+func BenchmarkMandelbrotBigFloat(b *testing.B) {
+	bench(b, mandelbrotBigFloat)
+}
+
+func BenchmarkMandelbrotBigRat(b *testing.B) {
+	bench(b, mandelbrotBigRat)
+}
+
+/*
+goos: darwin
+goarch: amd64
+pkg: github.com/linehk/gopl/ch3/exercise3.8
+BenchmarkMandelbrotComplex64-8    	20000000	        57.9 ns/op
+BenchmarkMandelbrotComplex128-8   	20000000	        56.5 ns/op
+BenchmarkMandelbrotBigFloat-8     	 2000000	       590 ns/op
+BenchmarkMandelbrotBigRat-8       	 1000000	      1334 ns/op
+*/