main.go

/* https://tour.golang.org/flowcontrol/8
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)
Original formula: https://tour.golang.org/content/img/newton.png

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"
)

// Newton's method
func nextZn(z, x float64) float64 {
	return z - (z*z-x)/(2*z)
}

func Sqrt(x float64) float64 {
	z := nextZn(2, x)
	for zn, delta := z, z; delta > 0.00001; z = zn {
		zn = nextZn(z, x)
		delta = z - zn
	}
	return z
}

func main() {
	fmt.Println(Sqrt(33))
	// fmt.Println(math.Sqrt(33))
}