double.NaN Equality in MS Test

Question

Why am I getting this result?

[TestMethod]
public void nan_test()
{
    Assert.AreEqual(1, double.NaN, 1E-1); <-- Passes
    Assert.AreEqual(1, double.NaN);       <-- Fails
}

What difference does the delta have in asserting NaN equals a number? Surely it should always return false. I am aware of IsNaN, but that's not useful here (see below).

Background: I have a function returning NaN (erroneously) , it was meant to be a real number but the test still passed. I'm using the delta because it's double precision equality, the original test used 1E-9.

Answer 1

When you use Assert.AreEqual(1, double.NaN), it tries an equality test on the numbers and of course it fails, since double.NaN isn't equal to anything.

When you do Assert.AreEqual(1, double.NaN, 1E-1), it has to do arithmetic on the numbers. Specifically, it computes

Math.Abs((double) (expected - actual)) > delta
Math.Abs(1 - double.NaN) > 1E-1
Math.Abs(double.NaN) > 1E-1 // All arithmetic with double.NaN returns double.NaN
double.NaN > 1E-1 // All comparisons with double.NaN return false (except !=)

which is false. It looks like the actual delta isn't larger than the delta you passed, but only since it is trying to indicate that you cannot perform the comparison.

Moral of the story: the behavior of NaN is pretty crazy (but the best some smart people could come up with). Do your best to check for NaN before performing any computations where you cannot have the error propagate up silently, like this one.

Answer 2

Have a look here: Why does Assert.AreEqual(1.0, double.NaN, 1.0) pass?

Edit:

there is definitely a bug in Assert.AreEqual. in VS 2008's Microsoft.VisualStudio.QualityTools.UnitTestFramework it's coded as

if (Math.Abs((double) (expected - actual)) > delta)
{
    // report error
}

As in your case Math.Abs((double) (expected - actual)) is a double.NaN, the comparison yields false :-)