How to compare floating-point numbers in Scala

Scala FAQ: I need to compare two floating-point numbers in Scala, but as in some other programming languages, two floating-point numbers that should be equivalent may not be; how do I comparison floating-point numbers?

Solution

As in Java and many other languages, you solve this problem by creating a method that lets you specify the precision for your comparison. The following Scala “approximately equals” method demonstrates the approach:

def ~=(x: Double, y: Double, precision: Double) = {
    if ((x - y).abs < precision) true else false
}

You can use this method like this:

scala> val a = 0.3
a: Double = 0.3

scala> val b = 0.1 + 0.2
b: Double = 0.30000000000000004

scala> ~=(a, b, 0.0001)
res0: Boolean = true

scala> ~=(b, a, 0.0001)
res1: Boolean = true

Discussion

When you begin working with floating-point numbers in programming, you quickly learn that 0.1 plus 0.1 is 0.2:

scala> 0.1 + 0.1
res2: Double = 0.2

But 0.1 plus 0.2 isn’t exactly 0.3:

scala> 0.1 + 0.2
res3: Double = 0.30000000000000004

This subtle inaccuracy makes comparing two floating-point numbers a real problem:

scala> val a = 0.3
a: Double = 0.3

scala> val b = 0.1 + 0.2
b: Double = 0.30000000000000004

scala> a == b
res4: Boolean = false

As a result, you end up writing your own functions to compare floating-point numbers with a precision (or tolerance).

As you saw in Recipe 1.11 of the Scala Cookbook, you can define an implicit conversion to add a method like this to the Double class. This makes the following code very readable:

if (a ~= b) ...

Or, you can add the same method to a utilities object, if you prefer:

object MathUtils {
    def ~=(x: Double, y: Double, precision: Double) = {
        if ((x - y).abs < precision) true else false
    }
}

You can then invoke that method like a static method in Java:

println(MathUtils.~=(a, b, 0.000001))

With an implicit conversion, the name ~= is very readable, but in a utilities object like this that name doesn’t look right, so it might be better named approximatelyEqual, equalWithinTolerance, or some other name.

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