Exercises 03.12 - 04.02

ex02.03-02.05/popcount.go

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+// Copyright © 2016 Alan A. A. Donovan & Brian W. Kernighan.
+// License: https://creativecommons.org/licenses/by-nc-sa/4.0/
+
+// See page 45.
+
+// (Package doc comment intentionally malformed to demonstrate golint.)
+//!+
+package popcount
+
+// pc[i] is the population count of i.
+var pc [256]byte
+
+func init() {
+	for i := range pc {
+		pc[i] = pc[i/2] + byte(i&1)
+	}
+}
+
+// PopCountExpression returns the population count (number of set bits) of x.
+func PopCountExpression(x uint64) int {
+	return int(pc[byte(x>>(0*8))] +
+		pc[byte(x>>(1*8))] +
+		pc[byte(x>>(2*8))] +
+		pc[byte(x>>(3*8))] +
+		pc[byte(x>>(4*8))] +
+		pc[byte(x>>(5*8))] +
+		pc[byte(x>>(6*8))] +
+		pc[byte(x>>(7*8))])
+}
+
+// Ex 02.03
+// PopCountLoop returns the population count (number of set bits) of x.
+func PopCountLoop(x uint64) int {
+	var popCount byte
+	for i := uint(0); i < 64; i += 8 {
+		popCount += pc[byte(x>>i)]
+	}
+	return int(popCount)
+}
+
+// Ex 02.04
+// PopCountLoop returns the population count (number of set bits) of x.
+func PopCountShift(x uint64) int {
+	var popCount uint64
+	for x != 0 {
+		popCount += x & 1
+		x = x >> 1
+	}
+	return int(popCount)
+}
+
+// Ex 02.05
+func PopCountClear(x uint64) int {
+	var popCount int
+	for x != 0 {
+		x = x & (x - 1)
+		popCount++
+	}
+	return popCount
+}
+
+//!-

ex02.03-02.05/popcount_test.go

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+// Copyright © 2016 Alan A. A. Donovan & Brian W. Kernighan.
+// License: https://creativecommons.org/licenses/by-nc-sa/4.0/
+
+package popcount
+
+import (
+	"testing"
+)
+
+// -- Benchmarks --
+
+func BenchmarkPopCountExpression(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		PopCountExpression(0x1234567890ABCDEF)
+	}
+}
+
+func BenchmarkPopCountLoop(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		PopCountLoop(0x1234567890ABCDEF)
+	}
+}
+
+func BenchmarkPopCountShift(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		PopCountClear(0x1234567890ABCDEF)
+	}
+}
+
+func BenchmarkPopCountClear(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		PopCountShift(0x1234567890ABCDEF)
+	}
+}
+
+// Go 1.6, 2.67GHz Xeon
+// $ go test -cpu=4 -bench=. gopl.io/ch2/popcount
+// BenchmarkPopCount-4                  200000000         6.30 ns/op
+// BenchmarkBitCount-4                  300000000         4.15 ns/op
+// BenchmarkPopCountByClearing-4        30000000         45.2 ns/op
+// BenchmarkPopCountByShifting-4        10000000        153 ns/op
+//
+// Go 1.6, 2.5GHz Intel Core i5
+// $ go test -cpu=4 -bench=. gopl.io/ch2/popcount
+// BenchmarkPopCount-4                  200000000         7.52 ns/op
+// BenchmarkBitCount-4                  500000000         3.36 ns/op
+// BenchmarkPopCountByClearing-4        50000000         34.3 ns/op
+// BenchmarkPopCountByShifting-4        20000000        108 ns/op
+//
+// Go 1.7, 3.5GHz Xeon
+// $ go test -cpu=4 -bench=. gopl.io/ch2/popcount
+// BenchmarkPopCount-12                 2000000000        0.28 ns/op
+// BenchmarkBitCount-12                 2000000000        0.27 ns/op
+// BenchmarkPopCountByClearing-12       100000000        18.5 ns/op
+// BenchmarkPopCountByShifting-12       20000000         70.1 ns/op

ex03.01-03.04/main.go

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+// Copyright © 2016 Alan A. A. Donovan & Brian W. Kernighan.
+// License: https://creativecommons.org/licenses/by-nc-sa/4.0/
+
+// See page 58.
+//!+
+
+// Surface computes an SVG rendering of a 3-D surface function.
+package main
+
+import (
+	"errors"
+	"fmt"
+	"math"
+	"os"
+)
+
+const (
+	width, height = 600, 320            // canvas size in pixels
+	cells         = 100                 // number of grid cells
+	xyrange       = 30.0                // axis ranges (-xyrange..+xyrange)
+	xyscale       = width / 2 / xyrange // pixels per x or y unit
+	zscale        = height * 0.4        // pixels per z unit
+	angle         = math.Pi / 6         // angle of x, y axes (=30°)
+)
+
+var sin30, cos30 = math.Sin(angle), math.Cos(angle) // sin(30°), cos(30°)
+
+func main() {
+	if len(os.Args) > 1 {
+		switch os.Args[1] {
+		// case "eggcrate":
+		// 	graph(eggcrate)
+		// case "moguls":
+		// 	graph(moguls)
+		// case "saddle":
+		// 	graph(saddle)
+		default:
+			graph(wave)
+		}
+	}
+	graph(wave)
+}
+
+func graph(f func(i, j float64) (float64, error)) {
+	fmt.Printf("<svg xmlns='http://www.w3.org/2000/svg' "+
+		"style='stroke: grey; fill: white; stroke-width: 0.7' "+
+		"width='%d' height='%d'>", width, height)
+	for i := 0; i < cells; i++ {
+		for j := 0; j < cells; j++ {
+			ax, ay, err := corner(i+1, j, f)
+			if err != nil {
+				continue
+			}
+			bx, by, err := corner(i, j, f)
+			if err != nil {
+				continue
+			}
+			cx, cy, err := corner(i, j+1, f)
+			if err != nil {
+				continue
+			}
+			dx, dy, err := corner(i+1, j+1, f)
+			if err != nil {
+				continue
+			}
+			fmt.Printf("<polygon points='%g,%g %g,%g %g,%g %g,%g'/>\n",
+				ax, ay, bx, by, cx, cy, dx, dy)
+		}
+	}
+	fmt.Println("</svg>")
+}
+
+func corner(i, j int, f func(i, j float64) (float64, error)) (float64, float64, error) {
+	// Find point (x,y) at corner of cell (i,j).
+	x := xyrange * (float64(i)/cells - 0.5)
+	y := xyrange * (float64(j)/cells - 0.5)
+
+	// Compute surface height z.
+	z, err := f(x, y)
+	if err != nil {
+		return x, y, err
+	}
+
+	// Project (x,y,z) isometrically onto 2-D SVG canvas (sx,sy).
+	sx := width/2 + (x-y)*cos30*xyscale
+	sy := height/2 + (x+y)*sin30*xyscale - z*zscale
+	return sx, sy, nil
+}
+
+func wave(x, y float64) (float64, error) {
+	r := math.Hypot(x, y) // distance from (0,0)
+	r = math.Sin(r) / r
+	if math.IsNaN(r) {
+		return r, errors.New("Result is NaN")
+	}
+	if math.IsInf(r, 0) {
+		return r, errors.New("Result overflows float64")
+	}
+	return r, nil
+}
+
+func eggcrate(x, y float64) (float64, error) {
+	r := 4 * (math.Pow(math.Sin(x), 2) + math.Pow(math.Sin(y), 2))
+	// r := (x * x) + (y * y) + 25*(math.Pow(math.Sin(x), 2)+math.Pow(math.Sin(y), 2))
+	if math.IsNaN(r) {
+		return r, errors.New("Result is NaN")
+	}
+	if math.IsInf(r, 0) {
+		return r, errors.New("Result overflows float64")
+	}
+	return r, nil
+}
+
+//!-