Double.Epsilon Campo

Definición

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

public: double Epsilon = 4.94065645841247E-324;
public const double Epsilon = 4.94065645841247E-324;
val mutable Epsilon : double
Public Const Epsilon As Double  = 4.94065645841247E-324

Valor de campo

Comentarios

El valor de la propiedad Epsilon refleja el valor positivo Double más pequeño que es significativo en operaciones numéricas o comparaciones cuando el valor de la instancia de Double es cero.The value of the Epsilon property reflects the smallest positive Double value that is significant in numeric operations or comparisons when the value of the Double 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()
   {
      double[] values = { 0, Double.Epsilon, Double.Epsilon * .5 };
      
      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 = 4.94065645841247E-324: False
//       0 = 0: True
//       
//       4.94065645841247E-324 = 0: False
Module Example
   Public Sub Main()
      Dim values() As Double = { 0, Double.Epsilon, Double.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 = 4.94065645841247E-324: False
'       0 = 0: True
'       
'       4.94065645841247E-324 = 0: False

Más concretamente, el formato de punto flotante consta de un signo, una mantisa de 52 bits o una mantisa y un exponente de 11 bits.More precisely, the floating point format consists of a sign, a 52-bit mantissa or significand, and an 11-bit exponent. Como se muestra en el ejemplo siguiente, cero tiene un exponente de-1022 y una mantisa de 0.As the following example shows, zero has an exponent of -1022 and a mantissa of 0. Epsilon tiene un exponente de-1022 y una mantisa de 1.Epsilon has an exponent of -1022 and a mantissa of 1. Esto significa que Epsilon es el valor Double positivo más pequeño mayor que cero y representa el menor valor posible y el menor posible incremento para un @no__t 2 cuyo exponente es-1022.This means that Epsilon is the smallest positive Double value greater than zero and represents the smallest possible value and the smallest possible increment for a Double whose exponent is -1022.

using System;

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

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

      // Convert the double to an 8-byte array.
      byte[] bytes = BitConverter.GetBytes(value);
      // Get the sign bit (byte 7, bit 7).
      result += String.Format("Sign: {0}\n", 
                              (bytes[7] & 0x80) == 0x80 ? "1 (-)" : "0 (+)");

      // Get the exponent (byte 6 bits 4-7 to byte 7, bits 0-6)
      int exponent = (bytes[7] & 0x07F) << 4;
      exponent = exponent | ((bytes[6] & 0xF0) >> 4);  
      int adjustment = exponent != 0 ? 1023 : 1022;
      result += String.Format("{0}Exponent: 0x{1:X4} ({1})\n", new String(' ', indent), exponent - adjustment);

      // Get the significand (bits 0-51)
      long significand = ((bytes[6] & 0x0F) << 48); 
      significand = significand | ((long) bytes[5] << 40);
      significand = significand | ((long) bytes[4] << 32);
      significand = significand | ((long) bytes[3] << 24);
      significand = significand | ((long) bytes[2] << 16);
      significand = significand | ((long) bytes[1] << 8);
      significand = significand | bytes[0];    
      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: 0xFFFFFC02 (-1022)
//          Mantissa: 0x0000000000000
//       
//       
//       4.94065645841247E-324: Sign: 0 (+)
//                              Exponent: 0xFFFFFC02 (-1022)
//                              Mantissa: 0x0000000000001
Module Example
   Public Sub Main()
      Dim values() As Double = { 0.0, Double.Epsilon }
      For Each value In values
         Console.WriteLine(GetComponentParts(value))
         Console.WriteLine()
      Next   
   End Sub

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

      ' Convert the double to an 8-byte array.
      Dim bytes() As Byte = BitConverter.GetBytes(value)
      ' Get the sign bit (byte 7, bit 7).
      result += String.Format("Sign: {0}{1}", 
                              If((bytes(7) And &H80) = &H80, "1 (-)", "0 (+)"),
                              vbCrLf)

      ' Get the exponent (byte 6 bits 4-7 to byte 7, bits 0-6)
      Dim exponent As Integer =  (bytes(7) And &H07F) << 4
      exponent = exponent Or ((bytes(6) And &HF0) >> 4)  
      Dim adjustment As Integer = If(exponent <> 0, 1023, 1022)
      result += String.Format("{0}Exponent: 0x{1:X4} ({1}){2}", 
                              New String(" "c, indent), exponent - adjustment,
                              vbCrLf)

      ' Get the significand (bits 0-51)
      Dim significand As Long =  ((bytes(6) And &H0F) << 48) 
      significand = significand Or (bytes(5) << 40)
      significand = significand Or (bytes(4) << 32)
      significand = significand Or (bytes(3) << 24)
      significand = significand Or (bytes(2) << 16)
      significand = significand Or (bytes(1) << 8)
      significand = significand Or bytes(0)    
      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: 0xFFFFFC02 (-1022)
'          Mantissa: 0x0000000000000
'       
'       
'       4.94065645841247E-324: Sign: 0 (+)
'                              Exponent: 0xFFFFFC02 (-1022)
'                              Mantissa: 0x0000000000001

Sin embargo, la propiedad Epsilon no es una medida general de precisión del tipo Double; solo se aplica a las instancias de @no__t 2 que tienen un valor de cero o un exponente de-1022.However, the Epsilon property is not a general measure of precision of the Double type; it applies only to Double instances that have a value of zero or an exponent of -1022.

Nota

El valor de la propiedad Epsilon 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 94065645841247e e-324.The value of this constant is 4.94065645841247e-324.

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 (double)1/3 == (double)0.33333 no se compara igual porque la operación de división en el lado izquierdo tiene precisión máxima, mientras que la constante del lado derecho solo es exacta en los dígitos especificados.For example, the C# expression, (double)1/3 == (double)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, no se recomienda basar el algoritmo en el valor de la constante Epsilon para establecer el margen de diferencia absoluto aceptable para los dos valores que se consideran iguales.If you create a custom algorithm that determines whether two floating-point numbers can be considered equal, we do not recommend that you base your algorithm on the value of 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). Para obtener información sobre cómo comparar dos valores de punto flotante de precisión doble, vea Double y Equals(Double).(Typically, that margin of difference is many times greater than Epsilon.) For information about comparing two double-precision floating-point values, see Double and Equals(Double).

Notas de la plataformaPlatform Notes

En los sistemas ARM, el valor de la constante Epsilon 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 2.2250738585072014 E-308.You can define an alternative epsilon value that equals 2.2250738585072014E-308 instead.

Se aplica a