Single.Epsilon Single.Epsilon Single.Epsilon Single.Epsilon Field

定義

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

フィールド値

注釈

Epsilonプロパティの値は、 Singleインスタンスの値がSingleゼロの場合に、数値演算または比較に有意な最小の正の値を反映します。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. たとえば、次のコードは、ゼロとEpsilonが等しくない値であると見なされ、のEpsilon値の0と半分が等しいと見なされることを示しています。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()
   {
      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

より正確には、単精度浮動小数点形式は、符号、23ビットの仮数または有効桁、および8ビットの指数で構成されます。More precisely, the single-precision floating-point format consists of a sign, a 23-bit mantissa or significand, and an 8-bit exponent. 次の例に示すように、0の指数は-126、仮数は0です。As the following example shows, zero has an exponent of -126 and a mantissa of 0. Epsilonの指数部は-126、仮数は1です。Epsilon has an exponent of -126 and a mantissa of 1. これSingle.Epsilonは、が0より大きいSingle最小の正の値であり、可能な最小値を表し、指数が-126 Singleであるの最小値を表すことを意味します。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

ただし、 Epsilonプロパティは、 Single型の有効桁数の一般単位ではなく、値が 0 Singleのインスタンスにのみ適用されます。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.

注意

Epsilonプロパティの値は、浮動小数点演算の丸め処理による相対誤差の上限を表すコンピューターイプシロンと等価ではありません。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、1.4 e-45 です。The value of this constant is 1.4e-45.

意味が低い2つの浮動小数点数は、少なくとも有効桁数が異なるため、等しいと比較できない場合があります。Two apparently equivalent floating-point numbers might not compare equal because of differences in their least significant digits. たとえば、 C#式で(float)1/3 == (float)0.33333は、左辺の除算演算には最大有効桁数があり、右側の定数は指定された桁数だけであるため、等号とは比較されません。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. 2つの浮動小数点数を等しいと見なすことができる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、 Epsilon定数よりも大きい値を使用して、2つの値の差の許容される絶対余白を設定する必要があります。等しいと見なされます。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. (通常、この余白の差は、を超えるEpsilon回数になります)。(Typically, that margin of difference is many times greater than Epsilon.)

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、 Epsilon定数の値が小さすぎて検出できないため、0になります。On ARM systems, the value of the Epsilon constant is too small to be detected, so it equates to zero. 代わりに、1.175494351 E-38 と等しい別のイプシロン値を定義できます。You can define an alternative epsilon value that equals 1.175494351E-38 instead.

適用対象