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11/18/2011

Single.Epsilon Field

Microsoft Silverlight will reach end of support after October 2021. Learn more.

Represents the smallest positive Single value greater than zero. This field is constant.

Namespace: System
Assembly: mscorlib (in mscorlib.dll)

Syntax

'Declaration
Public Const Epsilon As Single

public const float Epsilon

Remarks

The value of the Epsilon property reflects the smallest positive Single value that is significant in numeric operations or comparisons when the value of the Single instance is zero. For example, the following code shows that zero and Epsilon are considered to be unequal values, whereas zero and half the value of Epsilon are considered to be equal.

Module Example
   Public Sub Demo(ByVal outputBlock As System.Windows.Controls.TextBlock)
      Dim values() As Single = {0, Single.Epsilon, Single.Epsilon * 0.5}

      For ctr As Integer = 0 To values.Length - 2
         For ctr2 As Integer = ctr + 1 To values.Length - 1
            outputBlock.Text += String.Format("{0:r} = {1:r}: {2}", _
                              values(ctr), values(ctr2), _
                              values(ctr).Equals(values(ctr2))) & vbCrLf
         Next
         outputBlock.Text &= vbCrLf
      Next
   End Sub
End Module
' The example displays the following output:
'       0 = 1.401298E-45: False
'       0 = 0: True
'       
'       1.401298E-45 = 0: False

using System;

public class Example
{
   public static void Demo(System.Windows.Controls.TextBlock outputBlock)
   {
      float[] values = { 0f, Single.Epsilon, Single.Epsilon * .5f };

      for (int ctr = 0; ctr <= values.Length - 2; ctr++)
      {
         for (int ctr2 = ctr + 1; ctr2 <= values.Length - 1; ctr2++)
         {
            outputBlock.Text += String.Format("{0:r} = {1:r}: {2}",
                              values[ctr], values[ctr2],
                              values[ctr].Equals(values[ctr2])) + "\n";
         }
         outputBlock.Text += "\n";
      }
   }
}
// The example displays the following output:
//       0 = 1.401298E-45: False
//       0 = 0: True
//       
//       1.401298E-45 = 0: False

However, the Epsilon property is not a general measure of precision of the Single type; it applies only to Single instances that have a value of zero.

Note:
The value of the Epsilon property is not equivalent to machine epsilon, which represents the upper bound of the relative error due to rounding in floating-point arithmetic.

The value of this constant is 1.4e-45.

Two apparently equivalent floating-point numbers might not compare equal because of differences in their least significant digits. For example, the C# expression, (float)1/3 == (float)0.33333, does not compare equal because the division operation on the left side has maximum precision while the constant on the right side is precise only to the specified digits. If you create a custom algorithm that determines whether two floating-point numbers can be considered equal, you must use a value that is greater than the Epsilon constant to establish the acceptable absolute margin of difference for the two values to be considered equal. (Typically, that margin of difference is many times greater than Epsilon.)

Version Information

Silverlight

Supported in: 5, 4, 3

Silverlight for Windows Phone

Supported in: Windows Phone OS 7.1, Windows Phone OS 7.0

XNA Framework

Supported in: Xbox 360, Windows Phone OS 7.0

Platforms

For a list of the operating systems and browsers that are supported by Silverlight, see Supported Operating Systems and Browsers.

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