Double.Epsilon Double.Epsilon Double.Epsilon Double.Epsilon Field

定義

ゼロより大きい最小の Double 値を表します。Represents the smallest positive Double value that is greater than zero. このフィールドは定数です。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

フィールド値

注釈

値、Epsilonプロパティには、最小の正の値が反映されます。Double数値演算または比較で重要である値との値、Doubleインスタンスは 0 です。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. たとえば、次のコードに示すが 0 とEpsilonが等しくない値であると見なされますの値の半にEpsilon等しいと見なされます。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

浮動正確には、ポイント、記号、52 ビット仮数または仮数部、および 11 ビット指数の形式で構成されます。More precisely, the floating point format consists of a sign, a 52-bit mantissa or significand, and an 11-bit exponent. 次の例に示すように、0 には、-1022 の指数と 0 の仮数部があります。As the following example shows, zero has an exponent of -1022 and a mantissa of 0. Epsilon -1022 の指数と 1 の仮数部があります。Epsilon has an exponent of -1022 and a mantissa of 1. つまり、Epsilonが最小のDouble値 0 を超えると、最小有効値との最小の可能な増分値を表します、Doubleが指数部が-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

ただし、Epsilonプロパティは有効桁数の一般的なメジャーではありません、 Double ; 入力のみに適用されるDoubleゼロの値または-1022 の指数部を持つインスタンス。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.

注意

値、Epsilonプロパティが浮動小数点演算の丸め処理のための相対的なエラーの上限を表すマシン epsilon に相当します。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.

この定数の値は 4.94065645841247e-324。The value of this constant is 4.94065645841247e-324.

2 つの等しい浮動小数点数が等しくない有効桁数の違いがあるため。Two apparently equivalent floating-point numbers might not compare equal because of differences in their least significant digits. たとえば、c# の式(double)1/3 == (double)0.33333が等しくないため、右側にある定数は、指定した数字のみに正確なときに、左側にある除算演算が最大有効桁数。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. 2 つの浮動小数点数値を等しくないと見なすかどうかを決定するカスタム アルゴリズムを作成する場合はお勧めしません、アルゴリズムの値を作成、Epsilonの差の絶対値の許容を確立するために定数等しいと見なされる 2 つの値。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. (通常は、相違点の余白が数倍Epsilon)。2 つの倍精度浮動小数点値を比較する方法の詳細については、次を参照してください。DoubleEquals(Double)します。(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).

プラットフォームに関する注意事項Platform Notes

ARM システムでは、値、Epsilon定数が 0 と同じですを検出するには小さすぎます。On ARM systems, the value of the Epsilon constant is too small to be detected, so it equates to zero. 2.2250738585072014E に相当する代替 epsilon 値を定義することができます-308 代わりにします。You can define an alternative epsilon value that equals 2.2250738585072014E-308 instead.

適用対象