Has value changed by a very small amount?

Getting Help Code Review
1

Playing with exercise from A Tour of Go

"Next, change the loop condition to stop once the value has stopped changing (or only changes by a very small amount). "

v1 := 1.7320508075688772
v2 := 1.7320508075688774

How do I determine if difference between v1 and v2 is a very small amount?

2

That depends. By what amount does the value change in which th loop shall continue? How large would you consider an amount to be, that is not very small?

1 Like
3

Okay, thanks for questions :slight_smile: made it simple:

if v2 - v1 >= 0.0 && v2 - v1 <= 0.00001 {
// …
}

4

Looks fine to me.

5

But what if v2 - v1 < 0.0?

A common pattern is to check if math.Abs(v2 - v1) <= epsilon where epsilon is the biggest difference which shall be considered as “only small change”, 0.00001 in your case.

2 Likes
6

Thank you for the hint. I assumed that v2 must be always greater than v1 in terms of used algorithm.
Anyway, I’ve rewritten code according to your comment:

package main

import (
	"fmt"
	"math"
)

// determination of small change amount
const epsilon = 0.000001

func Sqrt(x float64) float64 {
	z := x / 2
	z2 := z
	var diff float64

	for i := 0; i < 10; i++ {
		z -= (z*z - x) / (2 * z)

		diff = z2 - z
		// instead of math.Abs(diff)
		if diff < 0 {
			diff *= -1
		}

		fmt.Println(i+1, "; z=", z, "; z2 - z=", z2, "-", z, "=", diff)

		if diff <= epsilon {
			break
		}

		z2 = z
	}

	return z
}

func main() {
	x := 3.0
	fmt.Println(Sqrt(x), "Sqrt(", x, ")")
	fmt.Println(math.Sqrt(x), "math.Sqrt(", x, ")")
}