Sqrt function (Newton's method) using the Google's GO language... Exercise 43...

output.txt

http://tour.golang.org/#43

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:

To begin with, just repeat that calculation 10 times and see how close you get to the answer for various values (1, 2, 3, ...).

The approximation function for the SQRT function returns the given values for the SQRT(4)...

2.5
2.05
2.000609756097561
2.0000000929222947
2.000000000000002
2
2
2
2
2

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

sqrt.go

package main

import (
	"fmt"
)

var p = 0.0

func Sqrt(x float64) float64 {
	z := 1.0
	for p - z != 0 { 
		z = newton(z, x)
		p = newton(z, x)
	}
	return z
}

func newton(z, x float64) float64 {
	return z - ( ((z*z) - x) / (2*z) )
}

func main() {
	fmt.Println(Sqrt(4))
}

it does not work with 2, because p - z will never be equal to 0 even if it gets close to it.

Change the import to be:

import (
    "fmt"
    "math"
)

And the for statement to be:

for math.Abs(p - z) > 0.000001 { 

And it will work.

Bueno mejoran el código inicial:

`package main

import (
"fmt"
"math"
)

func Sqrt(x float64) float64 {
var z, p float64
p = 0
z = 2
for math.Abs(p-z) > 0.000001 {
p = z
z = newton(z, x)
}
return z
}

func newton(z, x float64) float64 {
return z - (((z * z) - x) / (2 * z))
}

func main() {
x:= 90000.0
fmt.Println(Sqrt(x))
fmt.Println(math.Sqrt(x))
}
`