Single.Epsilon Campo

Definición

Representa el menor valor Single positivo mayor que cero.Represents the smallest positive Single value that is greater than zero. Este campo es constante.This field is constant.

public: float Epsilon = 1.401298E-45;
public const float Epsilon = 1.401298E-45;
val mutable Epsilon : single
Public Const Epsilon As Single  = 1.401298E-45

Valor de campo

Comentarios

El valor de la Epsilon propiedad refleja el valor positivo Single más pequeño que es significativo en operaciones numéricas o comparaciones cuando el valor Single de la instancia es cero.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. Por ejemplo, el código siguiente muestra que cero y Epsilon se consideran valores distintos, mientras que cero y la mitad del valor de Epsilon se consideran iguales.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.

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
Module Example
   Public Sub Main()
      Dim values() As Single = { 0, Single.Epsilon, Single.Epsilon * .5 }
      
      For ctr As Integer = 0 To values.Length - 2
         For ctr2 As Integer = ctr + 1 To values.Length - 1
            Console.WriteLine("{0:r} = {1:r}: {2}", _
                              values(ctr), values(ctr2), _ 
                              values(ctr).Equals(values(ctr2)))
         Next
         Console.WriteLine()
      Next      
   End Sub
End Module
' The example displays the following output:
'       0 = 1.401298E-45: False
'       0 = 0: True
'       
'       1.401298E-45 = 0: False

Más concretamente, el formato de punto flotante de precisión sencilla consta de un signo, una mantisa de 23 bits o un significado y un exponente de 8 bits.More precisely, the single-precision floating-point format consists of a sign, a 23-bit mantissa or significand, and an 8-bit exponent. Como se muestra en el ejemplo siguiente, cero tiene un exponente de-126 y una mantisa de 0.As the following example shows, zero has an exponent of -126 and a mantissa of 0. Epsilontiene un exponente de-126 y una mantisa de 1.Epsilon has an exponent of -126 and a mantissa of 1. Esto significa que Single.Epsilon es el valor positivo Single más pequeño que es mayor que cero y representa el menor valor posible y el menor posible incremento para un Single cuyo exponente es-126.This means that Single.Epsilon is the smallest positive Single value that is greater than zero and represents the smallest possible value and the smallest possible increment for a 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
Module Example
   Public Sub Main()
      Dim values() As Single = { 0.0, Single.Epsilon }
      For Each value In values
         Console.WriteLine(GetComponentParts(value))
         Console.WriteLine()
      Next   
   End Sub

   Private Function GetComponentParts(value As Single) As String
      Dim result As String =  String.Format("{0:R}: ", value)
      Dim indent As Integer =  result.Length

      ' Convert the single to an 8-byte array.
      Dim bytes() As Byte = BitConverter.GetBytes(value)
      Dim formattedSingle As Integer = BitConverter.ToInt32(bytes, 0)

      ' Get the sign bit (byte 3, bit 7).
      result += String.Format("Sign: {0}{1}", 
                              If(formattedSingle >> 31 <> 0, "1 (-)", "0 (+)"),
                              vbCrLf)

      ' Get the exponent (byte 2 bit 7 to byte 3, bits 6)
      Dim exponent As Integer =  (formattedSingle >> 23) And &h000000FF
      Dim adjustment As Integer = If(exponent <> 0, 127, 126)
      result += String.Format("{0}Exponent: 0x{1:X4} ({1}){2}", 
                              New String(" "c, indent), exponent - adjustment,
                              vbCrLf)

      ' Get the significand (bits 0-22)
      Dim significand As Long =  If(exponent <> 0, 
                         (formattedSingle And &h007FFFFF) Or &h800000, 
                         formattedSingle And &h007FFFFF) 
      result += String.Format("{0}Mantissa: 0x{1:X13}{2}", 
                              New String(" "c, indent), significand, vbCrLf)    

      Return result   
   End Function
End Module
' The example displays the following output:
'       0: Sign: 0 (+)
'          Exponent: 0xFFFFFF82 (-126)
'          Mantissa: 0x0000000000000
'       
'       
'       1.401298E-45: Sign: 0 (+)
'                     Exponent: 0xFFFFFF82 (-126)
'                     Mantissa: 0x0000000000001

Sin embargo, Epsilon la propiedad no es una medida general de precisión Single del tipo; solo se aplica a Single las instancias de que tienen un valor de cero.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.

Nota

El valor de la Epsilon propiedad no es equivalente a la máquina épsilon, que representa el límite superior del error relativo debido al redondeo en aritmética de punto flotante.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.

El valor de esta constante es 1.4 e-45.The value of this constant is 1.4e-45.

Dos números de punto flotante aparentemente equivalentes podrían no compararse igual debido a las diferencias en sus dígitos menos significativos.Two apparently equivalent floating-point numbers might not compare equal because of differences in their least significant digits. Por ejemplo, la C# expresión (float)1/3 == (float)0.33333no se compara igual porque la operación de división en el lado izquierdo tiene precisión máxima, mientras que la constante del lado derecho solo es precisa para los dígitos especificados.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. Si crea un algoritmo personalizado que determina si dos números de punto flotante se pueden considerar iguales, debe utilizar un valor mayor que la Epsilon constante para establecer el margen absoluto aceptable de diferencia para que los dos valores sean se consideran iguales.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. (Normalmente, ese margen de diferencia es muchas veces mayor que Epsilon).(Typically, that margin of difference is many times greater than Epsilon.)

Notas de la plataformaPlatform Notes

En los sistemas ARM, el valor de Epsilon la constante es demasiado pequeño para que se detecte, por lo que es igual a cero.On ARM systems, the value of the Epsilon constant is too small to be detected, so it equates to zero. En su lugar, puede definir un valor de épsilon alternativo que sea igual a 1.175494351 E-38.You can define an alternative epsilon value that equals 1.175494351E-38 instead.

Se aplica a