| title | description | ms.date | dev_langs | |||
|---|---|---|---|---|---|---|
System.Single.Epsilon property |
Learn about the System.Single.Epsilon property. |
01/24/2024 |
|
[!INCLUDE context]
The value of the xref:System.Single.Epsilon property reflects the smallest positive xref:System.Single value that is significant in numeric operations or comparisons when the value of the xref:System.Single instance is zero. For example, the following code shows that zero and xref:System.Single.Epsilon are considered to be unequal values, whereas zero and half the value of xref:System.Single.Epsilon are considered to be equal.
:::code language="csharp" source="./snippets/System/Single/Epsilon/csharp/epsilon.cs" interactive="try-dotnet" id="Snippet5"::: :::code language="fsharp" source="./snippets/System/Single/Epsilon/fsharp/epsilon.fs" id="Snippet5"::: :::code language="vb" source="./snippets/System/Single/Epsilon/vb/epsilon.vb" id="Snippet5":::
More precisely, the single-precision floating-point format consists of a sign, a 23-bit mantissa or significand, and an 8-bit exponent. As the following example shows, zero has an exponent of -126 and a mantissa of 0. xref:System.Single.Epsilon has an exponent of -126 and a mantissa of 1. This means that xref:System.Single.Epsilon?displayProperty=nameWithType is the smallest positive xref:System.Single value that is greater than zero and represents the smallest possible value and the smallest possible increment for a xref:System.Single whose exponent is -126.
:::code language="csharp" source="./snippets/System/Single/Epsilon/csharp/epsilon1.cs" interactive="try-dotnet" id="Snippet6"::: :::code language="fsharp" source="./snippets/System/Single/Epsilon/fsharp/epsilon1.fs" id="Snippet6"::: :::code language="vb" source="./snippets/System/Single/Epsilon/vb/epsilon1.vb" id="Snippet6":::
However, the xref:System.Single.Epsilon property is not a general measure of precision of the xref:System.Single type; it applies only to xref:System.Single instances that have a value of zero.
Note
The value of the xref:System.Single.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 xref:System.Single.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 xref:System.Single.Epsilon.)
On ARM systems, the value of the xref:System.Single.Epsilon constant is too small to be detected, so it equates to zero. You can define an alternative epsilon value that equals 1.175494351E-38 instead.