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# Single.Epsilon champ

.NET Framework (current version)

Date de publication : novembre 2016

Représente la valeur Single positive la plus petite qui est supérieure à zéro. Ce champ est constant.

Espace de noms:   System
Assembly:  mscorlib (dans mscorlib.dll)

## Syntaxe

```public const float Epsilon
```

#### Valeur de champ

Type: System.Single

## Notes

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

```using System;

public class Example
{
public static void Main()
{
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++)
{
Console.WriteLine("{0:r} = {1:r}: {2}",
values[ctr], values[ctr2],
values[ctr].Equals(values[ctr2]));
}
Console.WriteLine();
}
}
}
// The example displays the following output:
//       0 = 1.401298E-45: False
//       0 = 0: True
//
//       1.401298E-45 = 0: False
```

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. F:System.Single.Epsilon has an exponent of -126 and a mantissa of 1. This means that F:System.Single.Epsilon is the smallest positive T:System.Single value that is greater than zero and represents the smallest possible value and the smallest possible increment for a T:System.Single whose exponent is -126.

```using System;

public class Example
{
public static void Main()
{
float[] values = { 0.0f, Single.Epsilon };
foreach (var value in values) {
Console.WriteLine(GetComponentParts(value));
Console.WriteLine();
}
}

private static string GetComponentParts(float value)
{
string result = String.Format("{0:R}: ", value);
int indent = result.Length;

// Convert the single to a 4-byte array.
byte[] bytes = BitConverter.GetBytes(value);
int formattedSingle = BitConverter.ToInt32(bytes, 0);

// Get the sign bit (byte 3, bit 7).
result += String.Format("Sign: {0}\n",
(formattedSingle >> 31) != 0 ? "1 (-)" : "0 (+)");

// Get the exponent (byte 2 bit 7 to byte 3, bits 6)
int exponent =  (formattedSingle >> 23) & 0x000000FF;
int adjustment = (exponent != 0) ? 127 : 126;
result += String.Format("{0}Exponent: 0x{1:X4} ({1})\n", new String(' ', indent), exponent - adjustment);

// Get the significand (bits 0-22)
long significand = exponent != 0 ?
((formattedSingle & 0x007FFFFF) | 0x800000) :
(formattedSingle & 0x007FFFFF);
result += String.Format("{0}Mantissa: 0x{1:X13}\n", new String(' ', indent), significand);
return result;
}
}
//       // The example displays the following output:
//       0: Sign: 0 (+)
//          Exponent: 0xFFFFFF82 (-126)
//          Mantissa: 0x0000000000000
//
//
//       1.401298E-45: Sign: 0 (+)
//                     Exponent: 0xFFFFFF82 (-126)
//                     Mantissa: 0x0000000000001
```

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

Remarque

The value of the F: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 F: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 F:System.Single.Epsilon.)

### Platform Notes

On ARM systems, the value of the F: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.

## Informations de version

Plateforme Windows universelle
Disponible depuis 8
.NET Framework
Disponible depuis 1.1
Bibliothèque de classes portable
Pris en charge dans : plateformes .NET portables
Silverlight
Disponible depuis 2.0
Silverlight pour Windows Phone
Disponible depuis 7.0
Windows Phone
Disponible depuis 8.1

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