abesto · August 26, 2012 09:27 · Aug 26, 2012
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+/*
+A Tour of Go: page 44
+http://tour.golang.org/#44
+
+Exercise: Loops and Functions
+
+As a simple way to play with functions and loops, implement the square root function using Newton's method.
+
+In this case, Newton's method is to approximate Sqrt(x) by picking a starting point z and then repeating: z - (z*z - x) / (2 * z)
+
+
+To begin with, just repeat that calculation 10 times and see how close you get to the answer for various values (1, 2, 3, ...).
+
+Next, change the loop condition to stop once the value has stopped changing (or only changes by a very small delta). See if that's more or fewer iterations. How close are you to the math.Sqrt?
+
+Hint: to declare and initialize a floating point value, give it floating point syntax or use a conversion:
+
+	z := float64(1)
+	z := 1.0
+*/
+
+package main
+
+import (
+	"fmt"
+	"math"
+)
+
+const DELTA = 0.0000001
+const INITIAL_Z = 100.0
+
+func Sqrt(x float64) (z float64) {
+    z = INITIAL_Z
+
+    step := func() float64 {
+    	return z - (z*z - x) / (2 * z)
+    }
+
+    for zz := step(); math.Abs(zz - z) > DELTA
+    {
+    	z = zz
+	zz = step()
+    }
+    return
+}
+
+func main() {
+	fmt.Println(Sqrt(500))
+	fmt.Println(math.Sqrt(500))
+}
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