Double precision problems on .NET

Question

I have a simple C# function:

public static double Floor(double value, double step)
{
    return Math.Floor(value / step) * step;
}

That calculates the higher number, lower than or equal to "value", that is multiple of "step". But it lacks precision, as seen in the following tests:

[TestMethod()]
public void FloorTest()
{
    int decimals = 6;
    double value = 5F;
    double step = 2F;
    double expected = 4F;
    double actual = Class.Floor(value, step);
    Assert.AreEqual(expected, actual);
    value = -11.5F;
    step = 1.1F;
    expected = -12.1F;
    actual = Class.Floor(value, step);
    Assert.AreEqual(Math.Round(expected, decimals),Math.Round(actual, decimals));
    Assert.AreEqual(expected, actual);
}

The first and second asserts are ok, but the third fails, because the result is only equal until the 6th decimal place. Why is that? Is there any way to correct this?

Update If I debug the test I see that the values are equal until the 8th decimal place instead of the 6th, maybe because Math.Round introduces some imprecision.

Note In my test code I wrote the "F" suffix (explicit float constant) where I meant "D" (double), so if I change that I can have more precision.

Answer 1

http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems

For example, the non-representability of 0.1 and 0.01 (in binary) means that the result of attempting to square 0.1 is neither 0.01 nor the representable number closest to it.

Only use floating point if you want a machine's interpretation (binary) of number systems. You can't represent 10 cents.

Answer 2

If you omit all the F postfixes (ie -12.1 instead of -12.1F) you will get equality to a few digits more. Your constants (and especially the expected values) are now floats because of the F. If you are doing that on purpose then please explain.

But for the rest i concur with the other answers on comparing double or float values for equality, it's just not reliable.

Answer 3

For the similar issue, I end up using the following implementation which seems to success most of my test case (up to 5 digit precision):

public static double roundValue(double rawValue, double valueTick)
{
    if (valueTick <= 0.0) return 0.0;

    Decimal val = new Decimal(rawValue);
    Decimal step = new Decimal(valueTick);
    Decimal modulo = Decimal.Round(Decimal.Divide(val,step));

    return Decimal.ToDouble(Decimal.Multiply(modulo, step));
}

Answer 4

Floating point arithmetic on computers are not Exact Science :).

If you want exact precision to a predefined number of decimals use Decimal instead of double or accept a minor interval.

Answer 5

Sometimes the result is more precise than you would expect from strict:FP IEEE 754. That's because HW uses more bits for the computation. See C# specification and this article

Java has strictfp keyword and C++ have compiler switches. I miss that option in .NET

Answer 6

I actually sort of wish they hadn't implemented the == operator for floats and doubles. It's almost always the wrong thing to do to ever ask if a double or a float is equal to any other value.