How to compare floating-point numbers in Scala

This is an excerpt from the Scala Cookbook (partially modified for the internet). This is Recipe 2.5, “Comparing Floating-Point Numbers in Scala.”

Problem

You 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.

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 “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, you quickly learn that 0.1 plus 0.1 is 0.2:

scala> 0.1 + 0.1
res0: Double = 0.2

But 0.1 plus 0.2 isn’t exactly 0.3:

scala> 0.1 + 0.2
res1: 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
res0: 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, 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
    }
}

which you can then invoke 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 it doesn’t look quite right, so it might be better named approximatelyEqual, equalWithinTolerance, or some other name.

See Also

• A Wikipedia article on floating-point accuracy problems
• A Wikipedia article on arbitrary-precision arithmetic
• An Oracle document on what every computer scientist should know about floating-point arithmetic

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