System.Double 结构

项目
01/11/2024

本文提供了此 API 参考文档的补充说明。

值Double类型表示双精度 64 位数字，其值范围为负 1.79769313486232e308 到正 1.79769313486232e308，以及正或负零，PositiveInfinity NegativeInfinity而不是数字（NaN）。它旨在表示非常大的值（如行星或星系之间的距离）或极小（如物质的分子质量（以公斤为单位）和通常不精确（如地球与另一个太阳系的距离）。该Double类型符合二进制浮点算术的 IEC 60559：1989（I企业版E 754）标准。

浮点表示和精度

数据类型 Double 以 64 位二进制格式存储双精度浮点值，如下表所示：

组成部分	Bits
Significand or mantissa	0-51
指数	52-62
符号（0 = 正，1 = 负数）	63

正如小数分数无法精确表示某些小数值（如 1/3 或 Math.PI），二进制分数无法表示某些小数值。例如，1/10（由 .1 精确表示为小数分数）由 .001100110011 表示为二进制分数，模式“0011”重复为无穷大。在这种情况下，浮点值提供它所表示的数字的不精确表示形式。对原始浮点值执行其他数学运算往往会增加其缺乏精度。例如，如果将 .1 乘以 10 并将 .1 乘以 .1 的结果相加 9 倍，则会看到该加法，因为它涉及 8 个运算，因此产生了不太精确的结果。请注意，仅当使用“R”标准数字格式字符串显示这两 Double个值时，这种差异才明显，如有必要，该字符串将显示类型支持Double的所有 17 位精度。

using System;

public class Example13
{
    public static void Main()
    {
        Double value = .1;
        Double result1 = value * 10;
        Double result2 = 0;
        for (int ctr = 1; ctr <= 10; ctr++)
            result2 += value;

        Console.WriteLine(".1 * 10:           {0:R}", result1);
        Console.WriteLine(".1 Added 10 times: {0:R}", result2);
    }
}
// The example displays the following output:
//       .1 * 10:           1
//       .1 Added 10 times: 0.99999999999999989

let value = 0.1
let result1 = value * 10.
let mutable result2 = 0.
for i = 1 to 10 do
    result2 <- result2 + value

printfn $".1 * 10:           {result1:R}"
printfn $".1 Added 10 times: {result2:R}"
// The example displays the following output:
//       .1 * 10:           1
//       .1 Added 10 times: 0.99999999999999989

Module Example14
    Public Sub Main()
        Dim value As Double = 0.1
        Dim result1 As Double = value * 10
        Dim result2 As Double
        For ctr As Integer = 1 To 10
            result2 += value
        Next
        Console.WriteLine(".1 * 10:           {0:R}", result1)
        Console.WriteLine(".1 Added 10 times: {0:R}", result2)
    End Sub
End Module
' The example displays the following output:
'       .1 * 10:           1
'       .1 Added 10 times: 0.99999999999999989

由于某些数字不能完全表示为小数二进制值，因此浮点数只能近似实数。

所有浮点数也有有限数量的有效数字，这也决定了浮点值与实数的近似程度。一个 Double 值最多具有 15 个小数位数的精度，但内部最多保留 17 位数字。这意味着，某些浮点操作可能缺少更改浮点值的精度。下面的示例进行了这方面的演示。它定义非常大的 Double.Epsilon 浮点值，然后向它添加一个四千万的乘积。但是，产品太小，无法修改原始浮点值。其最小有效位数是千分之一，而产品中最重要的数字是 10-309。

using System;

public class Example14
{
    public static void Main()
    {
        Double value = 123456789012.34567;
        Double additional = Double.Epsilon * 1e15;
        Console.WriteLine("{0} + {1} = {2}", value, additional,
                                             value + additional);
    }
}
// The example displays the following output:
//    123456789012.346 + 4.94065645841247E-309 = 123456789012.346

open System

let value = 123456789012.34567
let additional = Double.Epsilon * 1e15
printfn $"{value} + {additional} = {value + additional}"
// The example displays the following output:
//    123456789012.346 + 4.94065645841247E-309 = 123456789012.346

Module Example15
    Public Sub Main()
        Dim value As Double = 123456789012.34567
        Dim additional As Double = Double.Epsilon * 1.0E+15
        Console.WriteLine("{0} + {1} = {2}", value, additional,
                                           value + additional)
    End Sub
End Module
' The example displays the following output:
'   123456789012.346 + 4.94065645841247E-309 = 123456789012.346

浮点数的有限精度有几个后果：

对于特定精度，看起来相等的两个浮点数在进行比较时可能不相等，因为其最小有效位不同。在以下示例中，一系列数字相加，其总数与预期总数进行比较。尽管这两个值看起来是相同的，但对方法的 Equals 调用表示它们不是。

using System;

public class Example10
{
    public static void Main()
    {
        Double[] values = { 10.0, 2.88, 2.88, 2.88, 9.0 };
        Double result = 27.64;
        Double total = 0;
        foreach (var value in values)
            total += value;

        if (total.Equals(result))
            Console.WriteLine("The sum of the values equals the total.");
        else
            Console.WriteLine("The sum of the values ({0}) does not equal the total ({1}).",
                              total, result);
    }
}
// The example displays the following output:
//      The sum of the values (36.64) does not equal the total (36.64).
//
// If the index items in the Console.WriteLine statement are changed to {0:R},
// the example displays the following output:
//       The sum of the values (27.639999999999997) does not equal the total (27.64).

let values = [ 10.0; 2.88; 2.88; 2.88; 9.0 ]
let result = 27.64
let total = List.sum values

if total.Equals result then
    printfn "The sum of the values equals the total."
else
    printfn $"The sum of the values ({total}) does not equal the total ({result})."
// The example displays the following output:
//      The sum of the values (36.64) does not equal the total (36.64).
//
// If the index items in the Console.WriteLine statement are changed to {0:R},
// the example displays the following output:
//       The sum of the values (27.639999999999997) does not equal the total (27.64).

Module Example11
    Public Sub Main()
        Dim values() As Double = {10.0, 2.88, 2.88, 2.88, 9.0}
        Dim result As Double = 27.64
        Dim total As Double
        For Each value In values
            total += value
        Next
        If total.Equals(result) Then
            Console.WriteLine("The sum of the values equals the total.")
        Else
            Console.WriteLine("The sum of the values ({0}) does not equal the total ({1}).",
                           total, result)
        End If
    End Sub
End Module
' The example displays the following output:
'      The sum of the values (36.64) does not equal the total (36.64).   
'
' If the index items in the Console.WriteLine statement are changed to {0:R},
' the example displays the following output:
'       The sum of the values (27.639999999999997) does not equal the total (27.64).

如果将语句中的Console.WriteLine(String, Object, Object)格式项从{0}和{1}更改为{0:R}{1:R}显示这两Double个值的所有有效数字，则很明显，由于加法运算期间精度损失，这两个值不相等。在这种情况下，可以通过调用 Math.Round(Double, Int32) 方法将值舍入 Double 到所需的精度，然后再执行比较来解决该问题。

如果使用小数，则使用浮点数的数学或比较运算可能不会产生相同的结果，因为二进制浮点数可能不等于小数。上一个示例通过显示将 .1 乘以 10 和添加 .1 倍的结果来说明这一点。

当具有小数值的数值操作的准确性很重要时，可以使用 Decimal 该类型而不是 Double 类型。当数值运算的准确性与整数值超出或UInt64类型范围Int64非常重要时，请使用该BigInteger类型。

如果涉及浮点数，则值可能不会往返。如果操作将原始浮点数转换为另一种形式，则表示一个值是往返的，反运算会将转换后的窗体转换回浮点数，而最终的浮点数不等于原始浮点数。往返可能会失败，因为转换中丢失或更改了一个或多个最小有效位数。在以下示例中，三 Double 个值转换为字符串，并保存在文件中。但是，如输出所示，即使值看起来相同，还原的值并不等于原始值。

using System;
using System.IO;

public class Example11
{
    public static void Main()
    {
        StreamWriter sw = new StreamWriter(@".\Doubles.dat");
        Double[] values = { 2.2 / 1.01, 1.0 / 3, Math.PI };
        for (int ctr = 0; ctr < values.Length; ctr++)
        {
            sw.Write(values[ctr].ToString());
            if (ctr != values.Length - 1)
                sw.Write("|");
        }
        sw.Close();

        Double[] restoredValues = new Double[values.Length];
        StreamReader sr = new StreamReader(@".\Doubles.dat");
        string temp = sr.ReadToEnd();
        string[] tempStrings = temp.Split('|');
        for (int ctr = 0; ctr < tempStrings.Length; ctr++)
            restoredValues[ctr] = Double.Parse(tempStrings[ctr]);

        for (int ctr = 0; ctr < values.Length; ctr++)
            Console.WriteLine("{0} {2} {1}", values[ctr],
                              restoredValues[ctr],
                              values[ctr].Equals(restoredValues[ctr]) ? "=" : "<>");
    }
}
// The example displays the following output:
//       2.17821782178218 <> 2.17821782178218
//       0.333333333333333 <> 0.333333333333333
//       3.14159265358979 <> 3.14159265358979

open System
open System.IO

let values = [ 2.2 / 1.01; 1. / 3.; Math.PI ]

using (new StreamWriter(@".\Doubles.dat")) (fun sw ->
    for i = 0 to values.Length - 1 do
        sw.Write(string values[i])
        if i <> values.Length - 1 then
            sw.Write "|")

using (new StreamReader(@".\Doubles.dat")) (fun sr ->
    let temp = sr.ReadToEnd()
    let tempStrings = temp.Split '|'

    let restoredValues =
        [ for i = 0 to tempStrings.Length - 1 do
              Double.Parse tempStrings[i] ]

    for i = 0 to values.Length - 1 do
        printfn $"""{values[i]} {if values[ i ].Equals restoredValues[i] then "=" else "<>"} {restoredValues[i]}""")

// The example displays the following output:
//       2.17821782178218 <> 2.17821782178218
//       0.333333333333333 <> 0.333333333333333
//       3.14159265358979 <> 3.14159265358979

Imports System.IO

Module Example12
    Public Sub Main()
        Dim sw As New StreamWriter(".\Doubles.dat")
        Dim values() As Double = {2.2 / 1.01, 1.0 / 3, Math.PI}
        For ctr As Integer = 0 To values.Length - 1
            sw.Write(values(ctr).ToString())
            If ctr <> values.Length - 1 Then sw.Write("|")
        Next
        sw.Close()

        Dim restoredValues(values.Length - 1) As Double
        Dim sr As New StreamReader(".\Doubles.dat")
        Dim temp As String = sr.ReadToEnd()
        Dim tempStrings() As String = temp.Split("|"c)
        For ctr As Integer = 0 To tempStrings.Length - 1
            restoredValues(ctr) = Double.Parse(tempStrings(ctr))
        Next

        For ctr As Integer = 0 To values.Length - 1
            Console.WriteLine("{0} {2} {1}", values(ctr),
                           restoredValues(ctr),
                           If(values(ctr).Equals(restoredValues(ctr)), "=", "<>"))
        Next
    End Sub
End Module
' The example displays the following output:
'       2.17821782178218 <> 2.17821782178218
'       0.333333333333333 <> 0.333333333333333
'       3.14159265358979 <> 3.14159265358979

在这种情况下，可以使用“G17” 标准数值格式字符串来成功对值进行舍入，以保留值的完整精度 Double ，如以下示例所示。

using System;
using System.IO;

public class Example12
{
    public static void Main()
    {
        StreamWriter sw = new StreamWriter(@".\Doubles.dat");
        Double[] values = { 2.2 / 1.01, 1.0 / 3, Math.PI };
        for (int ctr = 0; ctr < values.Length; ctr++)
            sw.Write("{0:G17}{1}", values[ctr], ctr < values.Length - 1 ? "|" : "");

        sw.Close();

        Double[] restoredValues = new Double[values.Length];
        StreamReader sr = new StreamReader(@".\Doubles.dat");
        string temp = sr.ReadToEnd();
        string[] tempStrings = temp.Split('|');
        for (int ctr = 0; ctr < tempStrings.Length; ctr++)
            restoredValues[ctr] = Double.Parse(tempStrings[ctr]);

        for (int ctr = 0; ctr < values.Length; ctr++)
            Console.WriteLine("{0} {2} {1}", values[ctr],
                              restoredValues[ctr],
                              values[ctr].Equals(restoredValues[ctr]) ? "=" : "<>");
    }
}
// The example displays the following output:
//       2.17821782178218 = 2.17821782178218
//       0.333333333333333 = 0.333333333333333
//       3.14159265358979 = 3.14159265358979

open System
open System.IO

let values = [ 2.2 / 1.01; 1. / 3.; Math.PI ]

using (new StreamWriter(@".\Doubles.dat")) (fun sw -> 
    for i = 0 to values.Length - 1 do
        sw.Write $"""{values[i]:G17}{if i < values.Length - 1 then "|" else ""}""")

using (new StreamReader(@".\Doubles.dat")) (fun sr ->
    let temp = sr.ReadToEnd()
    let tempStrings = temp.Split '|'
    
    let restoredValues = 
      [ for i = 0 to tempStrings.Length - 1 do
            Double.Parse tempStrings[i] ]

    for i = 0 to values.Length - 1 do
        printfn $"""{restoredValues[i]} {if values[i].Equals restoredValues[i] then "=" else "<>"} {values[i]}""")

// The example displays the following output:
//       2.17821782178218 = 2.17821782178218
//       0.333333333333333 = 0.333333333333333
//       3.14159265358979 = 3.14159265358979

Imports System.IO

Module Example13
    Public Sub Main()
        Dim sw As New StreamWriter(".\Doubles.dat")
        Dim values() As Double = {2.2 / 1.01, 1.0 / 3, Math.PI}
        For ctr As Integer = 0 To values.Length - 1
            sw.Write("{0:G17}{1}", values(ctr),
                  If(ctr < values.Length - 1, "|", ""))
        Next
        sw.Close()

        Dim restoredValues(values.Length - 1) As Double
        Dim sr As New StreamReader(".\Doubles.dat")
        Dim temp As String = sr.ReadToEnd()
        Dim tempStrings() As String = temp.Split("|"c)
        For ctr As Integer = 0 To tempStrings.Length - 1
            restoredValues(ctr) = Double.Parse(tempStrings(ctr))
        Next

        For ctr As Integer = 0 To values.Length - 1
            Console.WriteLine("{0} {2} {1}", values(ctr),
                           restoredValues(ctr),
                           If(values(ctr).Equals(restoredValues(ctr)), "=", "<>"))
        Next
    End Sub
End Module
' The example displays the following output:
'       2.17821782178218 = 2.17821782178218
'       0.333333333333333 = 0.333333333333333
'       3.14159265358979 = 3.14159265358979

重要

与值一起使用 Double 时，在某些情况下，“R”格式说明符无法成功往返原始值。若要确保 Double 值成功往返，请使用“G17”格式说明符。

Single 值的精度小于 Double 值。 Single转换为看似等效Double的值通常不等于Double值，因为精度差异。在以下示例中，将相同的除法运算结果分配给一 Double 个值和一个 Single 值。将 Single 值强制转换为 a 之后，两个 Double值的比较表明它们不相等。

using System;

public class Example9
{
    public static void Main()
    {
        Double value1 = 1 / 3.0;
        Single sValue2 = 1 / 3.0f;
        Double value2 = (Double)sValue2;
        Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2,
                                            value1.Equals(value2));
    }
}
// The example displays the following output:
//        0.33333333333333331 = 0.3333333432674408: False

open System

let value1 = 1. / 3.
let sValue2 = 1f /3f

let value2 = double sValue2
printfn $"{value1:R} = {value2:R}: {value1.Equals value2}"
// The example displays the following output:
//        0.33333333333333331 = 0.3333333432674408: False

Module Example10
    Public Sub Main()
        Dim value1 As Double = 1 / 3
        Dim sValue2 As Single = 1 / 3
        Dim value2 As Double = CDbl(sValue2)
        Console.WriteLine("{0} = {1}: {2}", value1, value2, value1.Equals(value2))
    End Sub
End Module
' The example displays the following output:
'       0.33333333333333331 = 0.3333333432674408: False

若要避免此问题，请使用 Double 代替 Single 数据类型，或使用 Round 该方法，使两个值具有相同的精度。

此外，由于类型的精度Double损失，具有Double值的算术和赋值运算的结果可能因平台略有不同。例如，分配文本 Double 值的结果可能与 .NET 的 32 位和 64 位版本不同。下面的示例演示了当文本值 -4.423060424772E-305 和值为 -4.4233060424772E-305 Double 的变量时，这种差异。请注意，本例中方法的结果 Parse(String) 不会导致精度损失。

double value = -4.42330604244772E-305;

double fromLiteral = -4.42330604244772E-305;
double fromVariable = value;
double fromParse = Double.Parse("-4.42330604244772E-305");

Console.WriteLine("Double value from literal: {0,29:R}", fromLiteral);
Console.WriteLine("Double value from variable: {0,28:R}", fromVariable);
Console.WriteLine("Double value from Parse method: {0,24:R}", fromParse);
// On 32-bit versions of the .NET Framework, the output is:
//    Double value from literal:        -4.42330604244772E-305
//    Double value from variable:       -4.42330604244772E-305
//    Double value from Parse method:   -4.42330604244772E-305
//
// On other versions of the .NET Framework, the output is:
//    Double value from literal:      -4.4233060424477198E-305
//    Double value from variable:     -4.4233060424477198E-305
//    Double value from Parse method:   -4.42330604244772E-305

let value = -4.42330604244772E-305

let fromLiteral = -4.42330604244772E-305
let fromVariable = value
let fromParse = Double.Parse "-4.42330604244772E-305"

printfn $"Double value from literal: {fromLiteral,29:R}"
printfn $"Double value from variable: {fromVariable,28:R}"
printfn $"Double value from Parse method: {fromParse,24:R}"
// On 32-bit versions of the .NET Framework, the output is:
//    Double value from literal:        -4.42330604244772E-305
//    Double value from variable:       -4.42330604244772E-305
//    Double value from Parse method:   -4.42330604244772E-305
//
// On other versions of the .NET Framework, the output is:
//    Double value from literal:      -4.4233060424477198E-305
//    Double value from variable:     -4.4233060424477198E-305
//    Double value from Parse method:   -4.42330604244772E-305

Dim value As Double = -4.4233060424477198E-305

Dim fromLiteral As Double = -4.4233060424477198E-305
Dim fromVariable As Double = value
Dim fromParse As Double = Double.Parse("-4.42330604244772E-305")

Console.WriteLine("Double value from literal: {0,29:R}", fromLiteral)
Console.WriteLine("Double value from variable: {0,28:R}", fromVariable)
Console.WriteLine("Double value from Parse method: {0,24:R}", fromParse)
' On 32-bit versions of the .NET Framework, the output is:
'    Double value from literal:        -4.42330604244772E-305
'    Double value from variable:       -4.42330604244772E-305
'    Double value from Parse method:   -4.42330604244772E-305
'
' On other versions of the .NET Framework, the output is:
'    Double value from literal:        -4.4233060424477198E-305
'    Double value from variable:       -4.4233060424477198E-305
'    Double value from Parse method:     -4.42330604244772E-305

测试相等性

若要视为相等，两 Double 个值必须表示相同的值。但是，由于值之间的精度差异，或者由于一个或两个值的精度损失，预期相同的浮点值通常因最小有效位数的差异而不相等。因此，调用 Equals 方法以确定两个值是否相等，或调用 CompareTo 该方法来确定两 Double 个值之间的关系，通常会产生意外的结果。在下面的示例中，这一点显而易见，其中两个明显相等 Double 的值结果不相等，因为第一个值具有 15 位精度，而第二个值有 17 位。

using System;

public class Example
{
   public static void Main()
   {
      double value1 = .333333333333333;
      double value2 = 1.0/3;
      Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2));
   }
}
// The example displays the following output:
//        0.333333333333333 = 0.33333333333333331: False

open System

let value1 = 0.333333333333333
let value2 = 1. / 3.
printfn $"{value1:R} = {value2:R}: {value1.Equals value2}"
// The example displays the following output:
//        0.333333333333333 = 0.33333333333333331: False

Module Example1
    Public Sub Main()
        Dim value1 As Double = 0.333333333333333
        Dim value2 As Double = 1 / 3
        Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2))
    End Sub
End Module
' The example displays the following output:
'       0.333333333333333 = 0.33333333333333331: False

遵循不同代码路径且以不同方式操作的计算值通常证明不相等。在下面的示例中，一个 Double 值是平方的，然后计算平方根以还原原始值。第二个 Double 乘以 3.51，在结果的平方根除以 3.51 以还原原始值之前。尽管这两个值似乎完全相同，但对方法的 Equals(Double) 调用表示它们不相等。使用“R”标准格式字符串返回一个结果字符串，该字符串显示每个 Double 值的所有有效数字显示第二个值小于第一个值 .0000000000001。

using System;

public class Example1
{
    public static void Main()
    {
        double value1 = 100.10142;
        value1 = Math.Sqrt(Math.Pow(value1, 2));
        double value2 = Math.Pow(value1 * 3.51, 2);
        value2 = Math.Sqrt(value2) / 3.51;
        Console.WriteLine("{0} = {1}: {2}\n",
                          value1, value2, value1.Equals(value2));
        Console.WriteLine("{0:R} = {1:R}", value1, value2);
    }
}
// The example displays the following output:
//    100.10142 = 100.10142: False
//
//    100.10142 = 100.10141999999999

open System

let value1 = 
    Math.Pow(100.10142, 2)
    |> sqrt

let value2 = 
    let v = pown (value1 * 3.51) 2
    (Math.Sqrt v) / 3.51

printfn $"{value1} = {value2}: {value1.Equals value2}\n"
printfn $"{value1:R} = {value2:R}"
// The example displays the following output:
//    100.10142 = 100.10142: False
//
//    100.10142 = 100.10141999999999

Module Example2
    Public Sub Main()
        Dim value1 As Double = 100.10142
        value1 = Math.Sqrt(Math.Pow(value1, 2))
        Dim value2 As Double = Math.Pow(value1 * 3.51, 2)
        value2 = Math.Sqrt(value2) / 3.51
        Console.WriteLine("{0} = {1}: {2}",
                        value1, value2, value1.Equals(value2))
        Console.WriteLine()
        Console.WriteLine("{0:R} = {1:R}", value1, value2)
    End Sub
End Module
' The example displays the following output:
'    100.10142 = 100.10142: False
'    
'    100.10142 = 100.10141999999999

如果精度损失可能会影响比较结果，则可以采用以下任一替代方法来调用 Equals 或 CompareTo 方法：

Math.Round调用该方法以确保这两个值具有相同的精度。以下示例修改前面的示例以使用此方法，以便两个小数部分值等效。

using System;

public class Example2
{
    public static void Main()
    {
        double value1 = .333333333333333;
        double value2 = 1.0 / 3;
        int precision = 7;
        value1 = Math.Round(value1, precision);
        value2 = Math.Round(value2, precision);
        Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2));
    }
}
// The example displays the following output:
//        0.3333333 = 0.3333333: True

open System

let v1 = 0.333333333333333
let v2 = 1. / 3.
let precision = 7
let value1 = Math.Round(v1, precision)
let value2 = Math.Round(v2, precision)
printfn $"{value1:R} = {value2:R}: {value1.Equals value2}"
// The example displays the following output:
//        0.3333333 = 0.3333333: True

Module Example3
    Public Sub Main()
        Dim value1 As Double = 0.333333333333333
        Dim value2 As Double = 1 / 3
        Dim precision As Integer = 7
        value1 = Math.Round(value1, precision)
        value2 = Math.Round(value2, precision)
        Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2))
    End Sub
End Module
' The example displays the following output:
'       0.3333333 = 0.3333333: True

精度问题仍适用于中点值的舍入。有关更多信息，请参见 Math.Round(Double, Int32, MidpointRounding) 方法。

测试近似相等性而不是相等性。这要求定义两个值可能有所不同但仍相等的绝对量，或者定义一个相对量，较小的值可以从较大的值中分离。

警告

Double.Epsilon 在测试相等性时，有时用作两 Double 个值之间的距离的绝对度量值。但是， Double.Epsilon 度量可添加到其值为零的最小可能值，或从 Double 中减去该值。对于大多数正值和负 Double 值，该值 Double.Epsilon 太小，无法检测到。因此，除值为零的值外，我们不建议在测试中使用相等性。

以下示例使用后一种方法来定义测试两个 IsApproximatelyEqual 值之间的相对差异的方法。它还比较了对 IsApproximatelyEqual 方法和方法 Equals(Double) 的调用结果。

using System;

public class Example3
{
    public static void Main()
    {
        double one1 = .1 * 10;
        double one2 = 0;
        for (int ctr = 1; ctr <= 10; ctr++)
            one2 += .1;

        Console.WriteLine("{0:R} = {1:R}: {2}", one1, one2, one1.Equals(one2));
        Console.WriteLine("{0:R} is approximately equal to {1:R}: {2}",
                          one1, one2,
                          IsApproximatelyEqual(one1, one2, .000000001));
    }

    static bool IsApproximatelyEqual(double value1, double value2, double epsilon)
    {
        // If they are equal anyway, just return True.
        if (value1.Equals(value2))
            return true;

        // Handle NaN, Infinity.
        if (Double.IsInfinity(value1) | Double.IsNaN(value1))
            return value1.Equals(value2);
        else if (Double.IsInfinity(value2) | Double.IsNaN(value2))
            return value1.Equals(value2);

        // Handle zero to avoid division by zero
        double divisor = Math.Max(value1, value2);
        if (divisor.Equals(0))
            divisor = Math.Min(value1, value2);

        return Math.Abs((value1 - value2) / divisor) <= epsilon;
    }
}
// The example displays the following output:
//       1 = 0.99999999999999989: False
//       1 is approximately equal to 0.99999999999999989: True

open System

let isApproximatelyEqual (value1: double) (value2: double) (epsilon: double) =
    // If they are equal anyway, just return True.
    if value1.Equals value2 then 
        true
    else
        // Handle NaN, Infinity.
        if Double.IsInfinity value1 || Double.IsNaN value1 then 
            value1.Equals value2
        elif Double.IsInfinity value2 || Double.IsNaN value2 then
            value1.Equals value2
        else
            // Handle zero to avoid division by zero
            let divisor = max value1 value2
            let divisor = 
                if divisor.Equals 0 then
                    min value1 value2
                else 
                    divisor
            abs ((value1 - value2) / divisor) <= epsilon

let one1 = 0.1 * 10.
let mutable one2 = 0.
for _ = 1 to 10 do
    one2 <- one2 + 0.1

printfn $"{one1:R} = {one2:R}: {one1.Equals one2}"
printfn $"{one1:R} is approximately equal to {one2:R}: {isApproximatelyEqual one1 one2 0.000000001}"

// The example displays the following output:
//       1 = 0.99999999999999989: False
//       1 is approximately equal to 0.99999999999999989: True

Module Example4
    Public Sub Main()
        Dim one1 As Double = 0.1 * 10
        Dim one2 As Double = 0
        For ctr As Integer = 1 To 10
            one2 += 0.1
        Next
        Console.WriteLine("{0:R} = {1:R}: {2}", one1, one2, one1.Equals(one2))
        Console.WriteLine("{0:R} is approximately equal to {1:R}: {2}",
                        one1, one2,
                        IsApproximatelyEqual(one1, one2, 0.000000001))
    End Sub

    Function IsApproximatelyEqual(value1 As Double, value2 As Double,
                                 epsilon As Double) As Boolean
        ' If they are equal anyway, just return True.
        If value1.Equals(value2) Then Return True

        ' Handle NaN, Infinity.
        If Double.IsInfinity(value1) Or Double.IsNaN(value1) Then
            Return value1.Equals(value2)
        ElseIf Double.IsInfinity(value2) Or Double.IsNaN(value2) Then
            Return value1.Equals(value2)
        End If

        ' Handle zero to avoid division by zero
        Dim divisor As Double = Math.Max(value1, value2)
        If divisor.Equals(0) Then
            divisor = Math.Min(value1, value2)
        End If

        Return Math.Abs((value1 - value2) / divisor) <= epsilon
    End Function
End Module
' The example displays the following output:
'       1 = 0.99999999999999989: False
'       1 is approximately equal to 0.99999999999999989: True

浮点值和异常

与整数类型的操作不同，在溢出或非法操作（如除以零）的情况下引发异常，具有浮点值的操作不会引发异常。相反，在异常情况下，浮点运算的结果为零、正无穷大、负无穷大或非数字（NaN）：

如果浮点操作的结果对于目标格式太小，则结果为零。当两个非常小的数字相乘时，可能会出现这种情况，如以下示例所示。

using System;

public class Example6
{
    public static void Main()
    {
        Double value1 = 1.1632875981534209e-225;
        Double value2 = 9.1642346778e-175;
        Double result = value1 * value2;
        Console.WriteLine("{0} * {1} = {2}", value1, value2, result);
        Console.WriteLine("{0} = 0: {1}", result, result.Equals(0.0));
    }
}
// The example displays the following output:
//       1.16328759815342E-225 * 9.1642346778E-175 = 0
//       0 = 0: True

let value1 = 1.1632875981534209e-225
let value2 = 9.1642346778e-175
let result = value1 * value2
printfn $"{value1} * {value2} = {result}"
printfn $"{result} = 0: {result.Equals 0.0}"
// The example displays the following output:
//       1.16328759815342E-225 * 9.1642346778E-175 = 0
//       0 = 0: True

Module Example7
    Public Sub Main()
        Dim value1 As Double = 1.1632875981534209E-225
        Dim value2 As Double = 9.1642346778E-175
        Dim result As Double = value1 * value2
        Console.WriteLine("{0} * {1} = {2}", value1, value2, result)
        Console.WriteLine("{0} = 0: {1}", result, result.Equals(0.0))
    End Sub
End Module
' The example displays the following output:
'       1.16328759815342E-225 * 9.1642346778E-175 = 0
'       0 = 0: True

如果浮点运算结果的大小超过目标格式的范围，则操作的结果是 PositiveInfinity 或 NegativeInfinity，适合结果的符号。溢出Double.MaxValue PositiveInfinity的操作的结果，以及溢出Double.MinValue的操作的结果，NegativeInfinity如以下示例所示。

using System;

public class Example7
{
    public static void Main()
    {
        Double value1 = 4.565e153;
        Double value2 = 6.9375e172;
        Double result = value1 * value2;
        Console.WriteLine("PositiveInfinity: {0}",
                           Double.IsPositiveInfinity(result));
        Console.WriteLine("NegativeInfinity: {0}\n",
                          Double.IsNegativeInfinity(result));

        value1 = -value1;
        result = value1 * value2;
        Console.WriteLine("PositiveInfinity: {0}",
                           Double.IsPositiveInfinity(result));
        Console.WriteLine("NegativeInfinity: {0}",
                          Double.IsNegativeInfinity(result));
    }
}

// The example displays the following output:
//       PositiveInfinity: True
//       NegativeInfinity: False
//
//       PositiveInfinity: False
//       NegativeInfinity: True

open System

let value1 = 4.565e153
let value2 = 6.9375e172
let result = value1 * value2
printfn $"PositiveInfinity: {Double.IsPositiveInfinity result}"
printfn $"NegativeInfinity: {Double.IsNegativeInfinity result}\n"

let value3 = - value1
let result2 = value2 * value3
printfn $"PositiveInfinity: {Double.IsPositiveInfinity result2}"
printfn $"NegativeInfinity: {Double.IsNegativeInfinity result2}"

// The example displays the following output:
//       PositiveInfinity: True
//       NegativeInfinity: False
//
//       PositiveInfinity: False
//       NegativeInfinity: True

Module Example8
    Public Sub Main()
        Dim value1 As Double = 4.565E+153
        Dim value2 As Double = 6.9375E+172
        Dim result As Double = value1 * value2
        Console.WriteLine("PositiveInfinity: {0}",
                         Double.IsPositiveInfinity(result))
        Console.WriteLine("NegativeInfinity: {0}",
                        Double.IsNegativeInfinity(result))
        Console.WriteLine()
        value1 = -value1
        result = value1 * value2
        Console.WriteLine("PositiveInfinity: {0}",
                         Double.IsPositiveInfinity(result))
        Console.WriteLine("NegativeInfinity: {0}",
                        Double.IsNegativeInfinity(result))
    End Sub
End Module
' The example displays the following output:
'       PositiveInfinity: True
'       NegativeInfinity: False
'       
'       PositiveInfinity: False
'       NegativeInfinity: True

PositiveInfinity 此外，除法结果为零，正分红， NegativeInfinity 除数为零，负股息的结果为零。

如果浮点操作无效，则操作的结果为 NaN。例如， NaN 以下操作的结果：
- 除以零，股息为零。请注意，除法的其他事例为零会导致或 PositiveInfinity NegativeInfinity。
- 具有无效输入的任何浮点操作。例如，使用负值调用 Math.Sqrt 方法将 NaN返回，调用 Math.Acos 方法的值大于一个或小于负值。
- 具有其值为 Double.NaN的参数的任何操作。

类型转换

结构 Double 不定义任何显式或隐式转换运算符;而是由编译器实现转换。

任何基元数值类型的 Double 值的转换都是一种扩大转换，因此不需要显式强制转换运算符或调用转换方法，除非编译器显式要求它。例如，C# 编译器需要转换运算符才能从中 Decimal 转换， Double而 Visual Basic 编译器则不需要转换运算符。以下示例将其他基元数值类型的最小值或最大值转换为。Double

using System;

public class Example4
{
    public static void Main()
    {
        dynamic[] values = { Byte.MinValue, Byte.MaxValue, Decimal.MinValue,
                           Decimal.MaxValue, Int16.MinValue, Int16.MaxValue,
                           Int32.MinValue, Int32.MaxValue, Int64.MinValue,
                           Int64.MaxValue, SByte.MinValue, SByte.MaxValue,
                           Single.MinValue, Single.MaxValue, UInt16.MinValue,
                           UInt16.MaxValue, UInt32.MinValue, UInt32.MaxValue,
                           UInt64.MinValue, UInt64.MaxValue };
        double dblValue;
        foreach (var value in values)
        {
            if (value.GetType() == typeof(Decimal))
                dblValue = (Double)value;
            else
                dblValue = value;
            Console.WriteLine("{0} ({1}) --> {2:R} ({3})",
                              value, value.GetType().Name,
                              dblValue, dblValue.GetType().Name);
        }
    }
}
// The example displays the following output:
//    0 (Byte) --> 0 (Double)
//    255 (Byte) --> 255 (Double)
//    -79228162514264337593543950335 (Decimal) --> -7.9228162514264338E+28 (Double)
//    79228162514264337593543950335 (Decimal) --> 7.9228162514264338E+28 (Double)
//    -32768 (Int16) --> -32768 (Double)
//    32767 (Int16) --> 32767 (Double)
//    -2147483648 (Int32) --> -2147483648 (Double)
//    2147483647 (Int32) --> 2147483647 (Double)
//    -9223372036854775808 (Int64) --> -9.2233720368547758E+18 (Double)
//    9223372036854775807 (Int64) --> 9.2233720368547758E+18 (Double)
//    -128 (SByte) --> -128 (Double)
//    127 (SByte) --> 127 (Double)
//    -3.402823E+38 (Single) --> -3.4028234663852886E+38 (Double)
//    3.402823E+38 (Single) --> 3.4028234663852886E+38 (Double)
//    0 (UInt16) --> 0 (Double)
//    65535 (UInt16) --> 65535 (Double)
//    0 (UInt32) --> 0 (Double)
//    4294967295 (UInt32) --> 4294967295 (Double)
//    0 (UInt64) --> 0 (Double)
//    18446744073709551615 (UInt64) --> 1.8446744073709552E+19 (Double)

open System

let values: obj[] = 
    [| Byte.MinValue; Byte.MaxValue; Decimal.MinValue
       Decimal.MaxValue; Int16.MinValue; Int16.MaxValue
       Int32.MinValue; Int32.MaxValue; Int64.MinValue
       Int64.MaxValue; SByte.MinValue; SByte.MaxValue
       Single.MinValue; Single.MaxValue; UInt16.MinValue
       UInt16.MaxValue; UInt32.MinValue, UInt32.MaxValue
       UInt64.MinValue; UInt64.MaxValue |]

for value in values do
    let dblValue = value :?> double
    printfn $"{value} ({value.GetType().Name}) --> {dblValue:R} ({dblValue.GetType().Name})"
// The example displays the following output:
//    0 (Byte) --> 0 (Double)
//    255 (Byte) --> 255 (Double)
//    -79228162514264337593543950335 (Decimal) --> -7.9228162514264338E+28 (Double)
//    79228162514264337593543950335 (Decimal) --> 7.9228162514264338E+28 (Double)
//    -32768 (Int16) --> -32768 (Double)
//    32767 (Int16) --> 32767 (Double)
//    -2147483648 (Int32) --> -2147483648 (Double)
//    2147483647 (Int32) --> 2147483647 (Double)
//    -9223372036854775808 (Int64) --> -9.2233720368547758E+18 (Double)
//    9223372036854775807 (Int64) --> 9.2233720368547758E+18 (Double)
//    -128 (SByte) --> -128 (Double)
//    127 (SByte) --> 127 (Double)
//    -3.402823E+38 (Single) --> -3.4028234663852886E+38 (Double)
//    3.402823E+38 (Single) --> 3.4028234663852886E+38 (Double)
//    0 (UInt16) --> 0 (Double)
//    65535 (UInt16) --> 65535 (Double)
//    0 (UInt32) --> 0 (Double)
//    4294967295 (UInt32) --> 4294967295 (Double)
//    0 (UInt64) --> 0 (Double)
//    18446744073709551615 (UInt64) --> 1.8446744073709552E+19 (Double)

Module Example5
    Public Sub Main()
        Dim values() As Object = {Byte.MinValue, Byte.MaxValue, Decimal.MinValue,
                                 Decimal.MaxValue, Int16.MinValue, Int16.MaxValue,
                                 Int32.MinValue, Int32.MaxValue, Int64.MinValue,
                                 Int64.MaxValue, SByte.MinValue, SByte.MaxValue,
                                 Single.MinValue, Single.MaxValue, UInt16.MinValue,
                                 UInt16.MaxValue, UInt32.MinValue, UInt32.MaxValue,
                                 UInt64.MinValue, UInt64.MaxValue}
        Dim dblValue As Double
        For Each value In values
            dblValue = value
            Console.WriteLine("{0} ({1}) --> {2:R} ({3})",
                           value, value.GetType().Name,
                           dblValue, dblValue.GetType().Name)
        Next
    End Sub
End Module
' The example displays the following output:
'    0 (Byte) --> 0 (Double)
'    255 (Byte) --> 255 (Double)
'    -79228162514264337593543950335 (Decimal) --> -7.9228162514264338E+28 (Double)
'    79228162514264337593543950335 (Decimal) --> 7.9228162514264338E+28 (Double)
'    -32768 (Int16) --> -32768 (Double)
'    32767 (Int16) --> 32767 (Double)
'    -2147483648 (Int32) --> -2147483648 (Double)
'    2147483647 (Int32) --> 2147483647 (Double)
'    -9223372036854775808 (Int64) --> -9.2233720368547758E+18 (Double)
'    9223372036854775807 (Int64) --> 9.2233720368547758E+18 (Double)
'    -128 (SByte) --> -128 (Double)
'    127 (SByte) --> 127 (Double)
'    -3.402823E+38 (Single) --> -3.4028234663852886E+38 (Double)
'    3.402823E+38 (Single) --> 3.4028234663852886E+38 (Double)
'    0 (UInt16) --> 0 (Double)
'    65535 (UInt16) --> 65535 (Double)
'    0 (UInt32) --> 0 (Double)
'    4294967295 (UInt32) --> 4294967295 (Double)
'    0 (UInt64) --> 0 (Double)
'    18446744073709551615 (UInt64) --> 1.8446744073709552E+19 (Double)

此外，值Single、值以及Single.NegativeInfinity分别转换为 Double.NaN、Double.PositiveInfinity和Double.NegativeInfinity。 Single.PositiveInfinity Single.NaN

请注意，将某些数值类型的值转换为 Double 值可能涉及精度损失。如示例所示，在将精度和Decimal Int64 UInt64值转换为Double值时，可能会丢失精度。

将值转换为 Double 任何其他基元数值数据类型的值是缩小转换，需要强制转换运算符（在 C#中）、转换方法（在 Visual Basic 中）或对方法的 Convert 调用。超出目标数据类型范围的值（由目标类型的 MinValue 和 MaxValue 属性定义）的行为如下表所示。

目标类型	Result
任何整型	OverflowException如果在检查上下文中发生转换，则会出现异常。如果转换发生在未检查上下文（C# 中的默认值），则转换操作会成功，但值溢出。
Decimal	异常 OverflowException 。
Single	Single.NegativeInfinity 表示负值。 Single.PositiveInfinity 表示正值。

此外，Double.NaN Double.PositiveInfinity在Double.NegativeInfinity检查上下文中引发转换为整数的转换OverflowException，但这些值在未转换到未检查上下文中的整数时溢出。对于转换到 Decimal的转换，它们始终会引发一个 OverflowException。对于转换，Single它们分别转换为Single.NaN和Single.PositiveInfinity Single.NegativeInfinity转换。

精度损失可能是将值转换为另一个 Double 数值类型造成的。如果转换为任何整型类型，如示例中所示的输出，当值舍入（如 Visual Basic 中）或截断（如 C# 中）时 Double ，小数部分将丢失。对于转换到 Decimal 值和 Single 值，该值 Double 在目标数据类型中可能没有精确的表示形式。

以下示例将一些 Double 值转换为其他几个数值类型。转换发生在 Visual Basic（默认值）、C# 中的检查上下文中（由于检查关键字 (keyword)），以及 F# 中（由于已选中模块）。该示例的输出显示了两个检查未检查上下文中转换的结果。可以通过使用/removeintchecks+编译器开关、C# 注释掉语句，在 F# 中通过注释掉checkedopen Checked语句，在 Visual Basic 中执行未检查上下文中的转换。

using System;

public class Example5
{
    public static void Main()
    {
        Double[] values = { Double.MinValue, -67890.1234, -12345.6789,
                          12345.6789, 67890.1234, Double.MaxValue,
                          Double.NaN, Double.PositiveInfinity,
                          Double.NegativeInfinity };
        checked
        {
            foreach (var value in values)
            {
                try
                {
                    Int64 lValue = (long)value;
                    Console.WriteLine("{0} ({1}) --> {2} (0x{2:X16}) ({3})",
                                      value, value.GetType().Name,
                                      lValue, lValue.GetType().Name);
                }
                catch (OverflowException)
                {
                    Console.WriteLine("Unable to convert {0} to Int64.", value);
                }
                try
                {
                    UInt64 ulValue = (ulong)value;
                    Console.WriteLine("{0} ({1}) --> {2} (0x{2:X16}) ({3})",
                                      value, value.GetType().Name,
                                      ulValue, ulValue.GetType().Name);
                }
                catch (OverflowException)
                {
                    Console.WriteLine("Unable to convert {0} to UInt64.", value);
                }
                try
                {
                    Decimal dValue = (decimal)value;
                    Console.WriteLine("{0} ({1}) --> {2} ({3})",
                                      value, value.GetType().Name,
                                      dValue, dValue.GetType().Name);
                }
                catch (OverflowException)
                {
                    Console.WriteLine("Unable to convert {0} to Decimal.", value);
                }
                try
                {
                    Single sValue = (float)value;
                    Console.WriteLine("{0} ({1}) --> {2} ({3})",
                                      value, value.GetType().Name,
                                      sValue, sValue.GetType().Name);
                }
                catch (OverflowException)
                {
                    Console.WriteLine("Unable to convert {0} to Single.", value);
                }
                Console.WriteLine();
            }
        }
    }
}
// The example displays the following output for conversions performed
// in a checked context:
//       Unable to convert -1.79769313486232E+308 to Int64.
//       Unable to convert -1.79769313486232E+308 to UInt64.
//       Unable to convert -1.79769313486232E+308 to Decimal.
//       -1.79769313486232E+308 (Double) --> -Infinity (Single)
//
//       -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
//       Unable to convert -67890.1234 to UInt64.
//       -67890.1234 (Double) --> -67890.1234 (Decimal)
//       -67890.1234 (Double) --> -67890.13 (Single)
//
//       -12345.6789 (Double) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
//       Unable to convert -12345.6789 to UInt64.
//       -12345.6789 (Double) --> -12345.6789 (Decimal)
//       -12345.6789 (Double) --> -12345.68 (Single)
//
//       12345.6789 (Double) --> 12345 (0x0000000000003039) (Int64)
//       12345.6789 (Double) --> 12345 (0x0000000000003039) (UInt64)
//       12345.6789 (Double) --> 12345.6789 (Decimal)
//       12345.6789 (Double) --> 12345.68 (Single)
//
//       67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
//       67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
//       67890.1234 (Double) --> 67890.1234 (Decimal)
//       67890.1234 (Double) --> 67890.13 (Single)
//
//       Unable to convert 1.79769313486232E+308 to Int64.
//       Unable to convert 1.79769313486232E+308 to UInt64.
//       Unable to convert 1.79769313486232E+308 to Decimal.
//       1.79769313486232E+308 (Double) --> Infinity (Single)
//
//       Unable to convert NaN to Int64.
//       Unable to convert NaN to UInt64.
//       Unable to convert NaN to Decimal.
//       NaN (Double) --> NaN (Single)
//
//       Unable to convert Infinity to Int64.
//       Unable to convert Infinity to UInt64.
//       Unable to convert Infinity to Decimal.
//       Infinity (Double) --> Infinity (Single)
//
//       Unable to convert -Infinity to Int64.
//       Unable to convert -Infinity to UInt64.
//       Unable to convert -Infinity to Decimal.
//       -Infinity (Double) --> -Infinity (Single)
// The example displays the following output for conversions performed
// in an unchecked context:
//       -1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       -1.79769313486232E+308 (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
//       Unable to convert -1.79769313486232E+308 to Decimal.
//       -1.79769313486232E+308 (Double) --> -Infinity (Single)
//
//       -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
//       -67890.1234 (Double) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
//       -67890.1234 (Double) --> -67890.1234 (Decimal)
//       -67890.1234 (Double) --> -67890.13 (Single)
//
//       -12345.6789 (Double) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
//       -12345.6789 (Double) --> 18446744073709539271 (0xFFFFFFFFFFFFCFC7) (UInt64)
//       -12345.6789 (Double) --> -12345.6789 (Decimal)
//       -12345.6789 (Double) --> -12345.68 (Single)
//
//       12345.6789 (Double) --> 12345 (0x0000000000003039) (Int64)
//       12345.6789 (Double) --> 12345 (0x0000000000003039) (UInt64)
//       12345.6789 (Double) --> 12345.6789 (Decimal)
//       12345.6789 (Double) --> 12345.68 (Single)
//
//       67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
//       67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
//       67890.1234 (Double) --> 67890.1234 (Decimal)
//       67890.1234 (Double) --> 67890.13 (Single)
//
//       1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       1.79769313486232E+308 (Double) --> 0 (0x0000000000000000) (UInt64)
//       Unable to convert 1.79769313486232E+308 to Decimal.
//       1.79769313486232E+308 (Double) --> Infinity (Single)
//
//       NaN (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       NaN (Double) --> 0 (0x0000000000000000) (UInt64)
//       Unable to convert NaN to Decimal.
//       NaN (Double) --> NaN (Single)
//
//       Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       Infinity (Double) --> 0 (0x0000000000000000) (UInt64)
//       Unable to convert Infinity to Decimal.
//       Infinity (Double) --> Infinity (Single)
//
//       -Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       -Infinity (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
//       Unable to convert -Infinity to Decimal.
//       -Infinity (Double) --> -Infinity (Single)

open System
open Checked

let values = 
    [| Double.MinValue; -67890.1234; -12345.6789
       12345.6789; 67890.1234; Double.MaxValue
       Double.NaN; Double.PositiveInfinity;
       Double.NegativeInfinity |]

for value in values do
    try
        let lValue = int64 value
        printfn $"{value} ({value.GetType().Name}) --> {lValue} (0x{lValue:X16}) ({lValue.GetType().Name})"
    with :? OverflowException ->
        printfn $"Unable to convert {value} to Int64."
    try
        let ulValue = uint64 value
        printfn $"{value} ({value.GetType().Name}) --> {ulValue} (0x{ulValue:X16}) ({ulValue.GetType().Name})"
    with :? OverflowException ->
        printfn $"Unable to convert {value} to UInt64."
    try
        let dValue = decimal value
        printfn $"{value} ({value.GetType().Name}) --> {dValue} ({dValue.GetType().Name})"
    with :? OverflowException ->
        printfn $"Unable to convert {value} to Decimal."
    try
        let sValue = float32 value
        printfn $"{value} ({value.GetType().Name}) --> {sValue} ({sValue.GetType().Name})"
    with :? OverflowException ->
        printfn $"Unable to convert {value} to Single."
    printfn ""
// The example displays the following output for conversions performed
// in a checked context:
//       Unable to convert -1.79769313486232E+308 to Int64.
//       Unable to convert -1.79769313486232E+308 to UInt64.
//       Unable to convert -1.79769313486232E+308 to Decimal.
//       -1.79769313486232E+308 (Double) --> -Infinity (Single)
//
//       -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
//       Unable to convert -67890.1234 to UInt64.
//       -67890.1234 (Double) --> -67890.1234 (Decimal)
//       -67890.1234 (Double) --> -67890.13 (Single)
//
//       -12345.6789 (Double) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
//       Unable to convert -12345.6789 to UInt64.
//       -12345.6789 (Double) --> -12345.6789 (Decimal)
//       -12345.6789 (Double) --> -12345.68 (Single)
//
//       12345.6789 (Double) --> 12345 (0x0000000000003039) (Int64)
//       12345.6789 (Double) --> 12345 (0x0000000000003039) (UInt64)
//       12345.6789 (Double) --> 12345.6789 (Decimal)
//       12345.6789 (Double) --> 12345.68 (Single)
//
//       67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
//       67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
//       67890.1234 (Double) --> 67890.1234 (Decimal)
//       67890.1234 (Double) --> 67890.13 (Single)
//
//       Unable to convert 1.79769313486232E+308 to Int64.
//       Unable to convert 1.79769313486232E+308 to UInt64.
//       Unable to convert 1.79769313486232E+308 to Decimal.
//       1.79769313486232E+308 (Double) --> Infinity (Single)
//
//       Unable to convert NaN to Int64.
//       Unable to convert NaN to UInt64.
//       Unable to convert NaN to Decimal.
//       NaN (Double) --> NaN (Single)
//
//       Unable to convert Infinity to Int64.
//       Unable to convert Infinity to UInt64.
//       Unable to convert Infinity to Decimal.
//       Infinity (Double) --> Infinity (Single)
//
//       Unable to convert -Infinity to Int64.
//       Unable to convert -Infinity to UInt64.
//       Unable to convert -Infinity to Decimal.
//       -Infinity (Double) --> -Infinity (Single)
// The example displays the following output for conversions performed
// in an unchecked context:
//       -1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       -1.79769313486232E+308 (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
//       Unable to convert -1.79769313486232E+308 to Decimal.
//       -1.79769313486232E+308 (Double) --> -Infinity (Single)
//
//       -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
//       -67890.1234 (Double) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
//       -67890.1234 (Double) --> -67890.1234 (Decimal)
//       -67890.1234 (Double) --> -67890.13 (Single)
//
//       -12345.6789 (Double) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
//       -12345.6789 (Double) --> 18446744073709539271 (0xFFFFFFFFFFFFCFC7) (UInt64)
//       -12345.6789 (Double) --> -12345.6789 (Decimal)
//       -12345.6789 (Double) --> -12345.68 (Single)
//
//       12345.6789 (Double) --> 12345 (0x0000000000003039) (Int64)
//       12345.6789 (Double) --> 12345 (0x0000000000003039) (UInt64)
//       12345.6789 (Double) --> 12345.6789 (Decimal)
//       12345.6789 (Double) --> 12345.68 (Single)
//
//       67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
//       67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
//       67890.1234 (Double) --> 67890.1234 (Decimal)
//       67890.1234 (Double) --> 67890.13 (Single)
//
//       1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       1.79769313486232E+308 (Double) --> 0 (0x0000000000000000) (UInt64)
//       Unable to convert 1.79769313486232E+308 to Decimal.
//       1.79769313486232E+308 (Double) --> Infinity (Single)
//
//       NaN (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       NaN (Double) --> 0 (0x0000000000000000) (UInt64)
//       Unable to convert NaN to Decimal.
//       NaN (Double) --> NaN (Single)
//
//       Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       Infinity (Double) --> 0 (0x0000000000000000) (UInt64)
//       Unable to convert Infinity to Decimal.
//       Infinity (Double) --> Infinity (Single)
//
//       -Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
//       -Infinity (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
//       Unable to convert -Infinity to Decimal.
//       -Infinity (Double) --> -Infinity (Single)

Module Example6
    Public Sub Main()
        Dim values() As Double = {Double.MinValue, -67890.1234, -12345.6789,
                                 12345.6789, 67890.1234, Double.MaxValue,
                                 Double.NaN, Double.PositiveInfinity,
                                 Double.NegativeInfinity}
        For Each value In values
            Try
                Dim lValue As Int64 = CLng(value)
                Console.WriteLine("{0} ({1}) --> {2} (0x{2:X16}) ({3})",
                               value, value.GetType().Name,
                               lValue, lValue.GetType().Name)
            Catch e As OverflowException
                Console.WriteLine("Unable to convert {0} to Int64.", value)
            End Try
            Try
                Dim ulValue As UInt64 = CULng(value)
                Console.WriteLine("{0} ({1}) --> {2} (0x{2:X16}) ({3})",
                               value, value.GetType().Name,
                               ulValue, ulValue.GetType().Name)
            Catch e As OverflowException
                Console.WriteLine("Unable to convert {0} to UInt64.", value)
            End Try
            Try
                Dim dValue As Decimal = CDec(value)
                Console.WriteLine("{0} ({1}) --> {2} ({3})",
                               value, value.GetType().Name,
                               dValue, dValue.GetType().Name)
            Catch e As OverflowException
                Console.WriteLine("Unable to convert {0} to Decimal.", value)
            End Try
            Try
                Dim sValue As Single = CSng(value)
                Console.WriteLine("{0} ({1}) --> {2} ({3})",
                               value, value.GetType().Name,
                               sValue, sValue.GetType().Name)
            Catch e As OverflowException
                Console.WriteLine("Unable to convert {0} to Single.", value)
            End Try
            Console.WriteLine()
        Next
    End Sub
End Module
' The example displays the following output for conversions performed
' in a checked context:
'       Unable to convert -1.79769313486232E+308 to Int64.
'       Unable to convert -1.79769313486232E+308 to UInt64.
'       Unable to convert -1.79769313486232E+308 to Decimal.
'       -1.79769313486232E+308 (Double) --> -Infinity (Single)
'
'       -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
'       Unable to convert -67890.1234 to UInt64.
'       -67890.1234 (Double) --> -67890.1234 (Decimal)
'       -67890.1234 (Double) --> -67890.13 (Single)
'
'       -12345.6789 (Double) --> -12346 (0xFFFFFFFFFFFFCFC6) (Int64)
'       Unable to convert -12345.6789 to UInt64.
'       -12345.6789 (Double) --> -12345.6789 (Decimal)
'       -12345.6789 (Double) --> -12345.68 (Single)
'
'       12345.6789 (Double) --> 12346 (0x000000000000303A) (Int64)
'       12345.6789 (Double) --> 12346 (0x000000000000303A) (UInt64)
'       12345.6789 (Double) --> 12345.6789 (Decimal)
'       12345.6789 (Double) --> 12345.68 (Single)
'
'       67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
'       67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
'       67890.1234 (Double) --> 67890.1234 (Decimal)
'       67890.1234 (Double) --> 67890.13 (Single)
'
'       Unable to convert 1.79769313486232E+308 to Int64.
'       Unable to convert 1.79769313486232E+308 to UInt64.
'       Unable to convert 1.79769313486232E+308 to Decimal.
'       1.79769313486232E+308 (Double) --> Infinity (Single)
'
'       Unable to convert NaN to Int64.
'       Unable to convert NaN to UInt64.
'       Unable to convert NaN to Decimal.
'       NaN (Double) --> NaN (Single)
'
'       Unable to convert Infinity to Int64.
'       Unable to convert Infinity to UInt64.
'       Unable to convert Infinity to Decimal.
'       Infinity (Double) --> Infinity (Single)
'
'       Unable to convert -Infinity to Int64.
'       Unable to convert -Infinity to UInt64.
'       Unable to convert -Infinity to Decimal.
'       -Infinity (Double) --> -Infinity (Single)
' The example displays the following output for conversions performed
' in an unchecked context:
'       -1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
'       -1.79769313486232E+308 (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
'       Unable to convert -1.79769313486232E+308 to Decimal.
'       -1.79769313486232E+308 (Double) --> -Infinity (Single)
'
'       -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
'       -67890.1234 (Double) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
'       -67890.1234 (Double) --> -67890.1234 (Decimal)
'       -67890.1234 (Double) --> -67890.13 (Single)
'
'       -12345.6789 (Double) --> -12346 (0xFFFFFFFFFFFFCFC6) (Int64)
'       -12345.6789 (Double) --> 18446744073709539270 (0xFFFFFFFFFFFFCFC6) (UInt64)
'       -12345.6789 (Double) --> -12345.6789 (Decimal)
'       -12345.6789 (Double) --> -12345.68 (Single)
'
'       12345.6789 (Double) --> 12346 (0x000000000000303A) (Int64)
'       12345.6789 (Double) --> 12346 (0x000000000000303A) (UInt64)
'       12345.6789 (Double) --> 12345.6789 (Decimal)
'       12345.6789 (Double) --> 12345.68 (Single)
'
'       67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
'       67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
'       67890.1234 (Double) --> 67890.1234 (Decimal)
'       67890.1234 (Double) --> 67890.13 (Single)
'
'       1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
'       1.79769313486232E+308 (Double) --> 0 (0x0000000000000000) (UInt64)
'       Unable to convert 1.79769313486232E+308 to Decimal.
'       1.79769313486232E+308 (Double) --> Infinity (Single)
'
'       NaN (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
'       NaN (Double) --> 0 (0x0000000000000000) (UInt64)
'       Unable to convert NaN to Decimal.
'       NaN (Double) --> NaN (Single)
'
'       Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
'       Infinity (Double) --> 0 (0x0000000000000000) (UInt64)
'       Unable to convert Infinity to Decimal.
'       Infinity (Double) --> Infinity (Single)
'
'       -Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
'       -Infinity (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
'       Unable to convert -Infinity to Decimal.
'       -Infinity (Double) --> -Infinity (Single)

有关数值类型的转换的详细信息，请参阅 .NET 中的类型转换和类型转换表。

浮点功能

结构和 Double 相关类型提供在以下方面执行操作的方法：

值的比较。可以调用 Equals 该方法来确定两 Double 个值是相等的，还是 CompareTo 确定两个值之间的关系的方法。

该 Double 结构还支持一组完整的比较运算符。例如，可以测试相等性或不相等性，或者确定一个值是否大于或等于另一个值。如果其中一个操作数不是数值 Double类型，则会在执行比较之前将其转换为数值 Double 类型。

警告

由于精度差异，预期相等的两 Double 个值可能不相等，这会影响比较结果。有关比较两 Double个值的详细信息，请参阅“测试相等性”部分。

还可以调用IsNaN这些特殊值的、IsInfinity和IsPositiveInfinity IsNegativeInfinity方法来测试这些特殊值。
数学运算。常见的算术运算（如加法、减法、乘法和除法）由语言编译器和公共中间语言（CIL）指令实现，而不是由 Double 方法实现。如果数学运算中的其中一个操作数是非数值类型 Double，则会在执行该操作之前将其转换为一个 Double 操作数。操作的结果也是一个 Double 值。

可以通过调用static类中的 System.Math （Shared在 Visual Basic）方法中执行其他数学运算。它包括常用于算术（如Math.Abs、Math.Sign和）、几何（如Math.Cos和Math.Sin）和Math.Sqrt微积分（如Math.Log）的其他方法。

还可以操作值 Double 中的单个位。该方法 BitConverter.DoubleToInt64Bits 在 Double 64 位整数中保留值的位模式。该方法 BitConverter.GetBytes(Double) 在字节数组中返回其位模式。
舍入。舍入通常用作减少因浮点表示和精度问题导致的值差异的影响的技术。可以通过调用Math.Round方法来舍入Double值。
格式设置。可以通过调用ToString方法或使用复合格式设置功能将值转换为Double其字符串表示形式。有关如何设置格式字符串控制浮点值的字符串表示形式的信息，请参阅标准数字格式字符串和自定义数字格式字符串主题。
分析字符串。可以通过调用Parse或TryParse方法将浮点值的Double字符串表示形式转换为值。如果分析操作失败，该方法 Parse 将引发异常，而 TryParse 该方法返回 false。

类型转换。该 Double 结构为 IConvertible 接口提供了一个显式接口实现，该接口支持在任意两种标准 .NET 数据类型之间进行转换。语言编译器还支持将所有其他标准数值类型的 Double 值隐式转换为值。将任何标准数值类型的值转换为 a Double 是一种扩大转换，不需要强制转换运算符或转换方法的用户，

但是，转换 Int64 和 Single 值可能涉及精度损失。下表列出了每种类型的精度差异：

类型	最大精度	内部精度
Double	15	17
Int64	19 位十进制数字	19 位十进制数字
Single	7 位十进制数字	9 位十进制数字

精度问题最常影响 Single 转换为 Double 值的值。在下面的示例中，由相同除法运算生成的两个值不相等，因为其中一个值是转换为 a Double的单精度浮点值。

using System;

public class Example13
{
    public static void Main()
    {
        Double value = .1;
        Double result1 = value * 10;
        Double result2 = 0;
        for (int ctr = 1; ctr <= 10; ctr++)
            result2 += value;

        Console.WriteLine(".1 * 10:           {0:R}", result1);
        Console.WriteLine(".1 Added 10 times: {0:R}", result2);
    }
}
// The example displays the following output:
//       .1 * 10:           1
//       .1 Added 10 times: 0.99999999999999989

let value = 0.1
let result1 = value * 10.
let mutable result2 = 0.
for i = 1 to 10 do
    result2 <- result2 + value

printfn $".1 * 10:           {result1:R}"
printfn $".1 Added 10 times: {result2:R}"
// The example displays the following output:
//       .1 * 10:           1
//       .1 Added 10 times: 0.99999999999999989

Module Example14
    Public Sub Main()
        Dim value As Double = 0.1
        Dim result1 As Double = value * 10
        Dim result2 As Double
        For ctr As Integer = 1 To 10
            result2 += value
        Next
        Console.WriteLine(".1 * 10:           {0:R}", result1)
        Console.WriteLine(".1 Added 10 times: {0:R}", result2)
    End Sub
End Module
' The example displays the following output:
'       .1 * 10:           1
'       .1 Added 10 times: 0.99999999999999989

示例

下面的代码示例演示了以下用法 Double：

// The Temperature class stores the temperature as a Double
// and delegates most of the functionality to the Double
// implementation.
public class Temperature : IComparable, IFormattable
{
    // IComparable.CompareTo implementation.
    public int CompareTo(object obj) {
        if (obj == null) return 1;

        Temperature temp = obj as Temperature;
        if (obj != null)
            return m_value.CompareTo(temp.m_value);
        else
            throw new ArgumentException("object is not a Temperature");	
    }

    // IFormattable.ToString implementation.
    public string ToString(string format, IFormatProvider provider) {
        if( format != null ) {
            if( format.Equals("F") ) {
                return String.Format("{0}'F", this.Value.ToString());
            }
            if( format.Equals("C") ) {
                return String.Format("{0}'C", this.Celsius.ToString());
            }
        }

        return m_value.ToString(format, provider);
    }

    // Parses the temperature from a string in the form
    // [ws][sign]digits['F|'C][ws]
    public static Temperature Parse(string s, NumberStyles styles, IFormatProvider provider) {
        Temperature temp = new Temperature();

        if( s.TrimEnd(null).EndsWith("'F") ) {
            temp.Value = Double.Parse( s.Remove(s.LastIndexOf('\''), 2), styles, provider);
        }
        else if( s.TrimEnd(null).EndsWith("'C") ) {
            temp.Celsius = Double.Parse( s.Remove(s.LastIndexOf('\''), 2), styles, provider);
        }
        else {
            temp.Value = Double.Parse(s, styles, provider);
        }

        return temp;
    }

    // The value holder
    protected double m_value;

    public double Value {
        get {
            return m_value;
        }
        set {
            m_value = value;
        }
    }

    public double Celsius {
        get {
            return (m_value-32.0)/1.8;
        }
        set {
            m_value = 1.8*value+32.0;
        }
    }
}

// The Temperature class stores the temperature as a Double
// and delegates most of the functionality to the Double
// implementation.
type Temperature() =
    member val Value = 0. with get, set

    member this.Celsius
        with get () = (this.Value - 32.) / 1.8
        and set (value) =
            this.Value <- 1.8 * value + 32.

    // Parses the temperature from a string in the form
    // [ws][sign]digits['F|'C][ws]
    static member Parse(s: string, styles: NumberStyles, provider: IFormatProvider) =
        let temp = Temperature()

        if s.TrimEnd(null).EndsWith "'F" then
            temp.Value <- Double.Parse(s.Remove(s.LastIndexOf '\'', 2), styles, provider)
        elif s.TrimEnd(null).EndsWith "'C" then
            temp.Celsius <- Double.Parse(s.Remove(s.LastIndexOf '\'', 2), styles, provider)
        else
            temp.Value <- Double.Parse(s, styles, provider)
        temp

    interface IComparable with
        // IComparable.CompareTo implementation.
        member this.CompareTo(obj: obj) =
            match obj with 
            | null -> 1
            | :? Temperature as temp ->
                this.Value.CompareTo temp.Value
            | _ ->
                invalidArg "obj" "object is not a Temperature"

    interface IFormattable with
        // IFormattable.ToString implementation.
        member this.ToString(format: string, provider: IFormatProvider) =
            match format with
            | "F" ->
                $"{this.Value}'F"
            | "C" ->
                $"{this.Celsius}'C"
            | _ ->
                this.Value.ToString(format, provider)

' Temperature class stores the value as Double
' and delegates most of the functionality 
' to the Double implementation.
Public Class Temperature
    Implements IComparable, IFormattable

    Public Overloads Function CompareTo(ByVal obj As Object) As Integer _
        Implements IComparable.CompareTo

        If TypeOf obj Is Temperature Then
            Dim temp As Temperature = CType(obj, Temperature)

            Return m_value.CompareTo(temp.m_value)
        End If

        Throw New ArgumentException("object is not a Temperature")
    End Function

    Public Overloads Function ToString(ByVal format As String, ByVal provider As IFormatProvider) As String _
        Implements IFormattable.ToString

        If Not (format Is Nothing) Then
            If format.Equals("F") Then
                Return [String].Format("{0}'F", Me.Value.ToString())
            End If
            If format.Equals("C") Then
                Return [String].Format("{0}'C", Me.Celsius.ToString())
            End If
        End If

        Return m_value.ToString(format, provider)
    End Function

    ' Parses the temperature from a string in form
    ' [ws][sign]digits['F|'C][ws]
    Public Shared Function Parse(ByVal s As String, ByVal styles As NumberStyles, ByVal provider As IFormatProvider) As Temperature
        Dim temp As New Temperature()

        If s.TrimEnd().EndsWith("'F") Then
            temp.Value = Double.Parse(s.Remove(s.LastIndexOf("'"c), 2), styles, provider)
        Else
            If s.TrimEnd().EndsWith("'C") Then
                temp.Celsius = Double.Parse(s.Remove(s.LastIndexOf("'"c), 2), styles, provider)
            Else
                temp.Value = Double.Parse(s, styles, provider)
            End If
        End If
        Return temp
    End Function

    ' The value holder
    Protected m_value As Double

    Public Property Value() As Double
        Get
            Return m_value
        End Get
        Set(ByVal Value As Double)
            m_value = Value
        End Set
    End Property

    Public Property Celsius() As Double
        Get
            Return (m_value - 32) / 1.8
        End Get
        Set(ByVal Value As Double)
            m_value = Value * 1.8 + 32
        End Set
    End Property
End Class