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

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.

Answer 2

If you want precision, use System.Decimal. If you want speed, use System.Double (or System.Float). Floating point numbers are not "infinite precision" numbers, and therefore asserting equality must include a tolerance. As long as your numbers have a reasonable number of significant digits, this is ok.

• If you're looking to do math on very large AND very small numbers, don't use float or double.
• If you need infinite precision, don't use float or double.
• If you are aggregating a very large number of values, don't use float or double (the errors will compound themselves).
• If you need speed and size, use float or double.

See this answer (also by me) for a detailed analysis of how precision affects the outcome of your mathematical operations.

Answer 3

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 4

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 5

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 6

Check the answers to this question: Is it safe to check floating point values for equality to 0?

Really, just check for "within tolerance of..."

Answer 7

floats and doubles cannot accurately store all numbers. This is a limitation with the IEEE floating point system. In order to have faithful precision you need to use a more advanced math library.

If you don't need precision past a certain point, then perhaps decimal will work better for you. It has a higher precision than double.

Answer 8

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 9

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));
}