How to get a -0 result in floating point calculations and distinguish it from +0 in C#?

Question

The MSDN documentation mentions that double type includes negative zero. However, both -1.0 / double.PositiveInfinity and -double.Epsilon / 2 appear to return normal 0 (and compare equal to it). How can I get -0?

Answer 1

One way is to use the BitConverter.GetBytes. If you check the bytes, you will see that the sign bit for the value is actually set indicating that its negative.

byte[] zeroBytes = BitConverter.GetBytes(zero);
byte[] negZeroBytes = BitConverter.GetBytes(negZero);

bool sameBytes = zeroBytes[7] == negZeroBytes[7];

Answer 2

Negative zero is to do with the way that the number is stored in binary, not any real achievable result from a mathematical calculation.

In floating point storage, the topmost bit is often used to denote sign. This leaves 31 bits for data (in a 32bit floating point value) so there are actually two representations for zero.

00000000 00000000 00000000 00000000
Or
00000000 00000000 00000000 00000001

Both represent zero, but one with the sign bit set to negative.

Naturally, this would normally occur when you incremented the highest possible positive number, it would overflow back to negative zero.

In .net however I think by default the type does overflow checks and will throw an exception rather than let you overflow, so the only way to really archive this value is by setting it directly. Also, -0 should always compare equal to +0.

There is more about it on Wikipeida

Answer 3

Here is a practical example of differentiating between the two without examining the bits. MSDN links here and here assisted me in constructing this example.

static void Main(string[] args)
{
    float a = 5 / float.NegativeInfinity;
    float b = 5 / float.PositiveInfinity;
    float c = 1 / a;
    float d = 1 / b;
    Console.WriteLine(a);
    Console.WriteLine(b);
    Console.WriteLine(c);
    Console.WriteLine(d);
}

Output:

0
0
-Infinity
Infinity

Take note that -0 and 0 both look the same for comparisons, output, etc. But if you divide 1 by them, you get a -Infinity or Infinity, depending on which zero you have.

Answer 4

Try this. If pz is positive zero and nz is negative zero:

Double.PositiveInfinity/pz => Double.PositiveInfinity
Double.PositiveInfinity/nz => Double.NegativeInfinity

I got this from ECMA C# specification.

You can obtain negative zero by dividing any positive number by negative infinity:

10.0/Double.NegativeInfinity

Answer 5

After checking, I see that -1.0 / double.PositiveInfinity does return -0. Indeed, 1.0 / (-1.0 / double.PositiveInfinity) returns -infinity.