Double 結構
定義
重要
部分資訊涉及發行前產品,在發行之前可能會有大幅修改。 Microsoft 對此處提供的資訊,不做任何明確或隱含的瑕疵擔保。
表示雙精度浮點數。
public value class double : IComparable, IComparable<double>, IConvertible, IEquatable<double>, IFormattable
public value class double : IComparable, IComparable<double>, IConvertible, IEquatable<double>, ISpanFormattable
public value class double : IComparable<double>, IConvertible, IEquatable<double>, IParsable<double>, ISpanParsable<double>, System::Numerics::IAdditionOperators<double, double, double>, System::Numerics::IAdditiveIdentity<double, double>, System::Numerics::IBinaryFloatingPointIeee754<double>, System::Numerics::IBinaryNumber<double>, System::Numerics::IBitwiseOperators<double, double, double>, System::Numerics::IComparisonOperators<double, double, bool>, System::Numerics::IDecrementOperators<double>, System::Numerics::IDivisionOperators<double, double, double>, System::Numerics::IEqualityOperators<double, double, bool>, System::Numerics::IExponentialFunctions<double>, System::Numerics::IFloatingPoint<double>, System::Numerics::IFloatingPointConstants<double>, System::Numerics::IFloatingPointIeee754<double>, System::Numerics::IHyperbolicFunctions<double>, System::Numerics::IIncrementOperators<double>, System::Numerics::ILogarithmicFunctions<double>, System::Numerics::IMinMaxValue<double>, System::Numerics::IModulusOperators<double, double, double>, System::Numerics::IMultiplicativeIdentity<double, double>, System::Numerics::IMultiplyOperators<double, double, double>, System::Numerics::INumber<double>, System::Numerics::INumberBase<double>, System::Numerics::IPowerFunctions<double>, System::Numerics::IRootFunctions<double>, System::Numerics::ISignedNumber<double>, System::Numerics::ISubtractionOperators<double, double, double>, System::Numerics::ITrigonometricFunctions<double>, System::Numerics::IUnaryNegationOperators<double, double>, System::Numerics::IUnaryPlusOperators<double, double>
public value class double : IComparable<double>, IConvertible, IEquatable<double>, IParsable<double>, ISpanParsable<double>, IUtf8SpanFormattable, IUtf8SpanParsable<double>, System::Numerics::IAdditionOperators<double, double, double>, System::Numerics::IAdditiveIdentity<double, double>, System::Numerics::IBinaryFloatingPointIeee754<double>, System::Numerics::IBinaryNumber<double>, System::Numerics::IBitwiseOperators<double, double, double>, System::Numerics::IComparisonOperators<double, double, bool>, System::Numerics::IDecrementOperators<double>, System::Numerics::IDivisionOperators<double, double, double>, System::Numerics::IEqualityOperators<double, double, bool>, System::Numerics::IExponentialFunctions<double>, System::Numerics::IFloatingPoint<double>, System::Numerics::IFloatingPointConstants<double>, System::Numerics::IFloatingPointIeee754<double>, System::Numerics::IHyperbolicFunctions<double>, System::Numerics::IIncrementOperators<double>, System::Numerics::ILogarithmicFunctions<double>, System::Numerics::IMinMaxValue<double>, System::Numerics::IModulusOperators<double, double, double>, System::Numerics::IMultiplicativeIdentity<double, double>, System::Numerics::IMultiplyOperators<double, double, double>, System::Numerics::INumber<double>, System::Numerics::INumberBase<double>, System::Numerics::IPowerFunctions<double>, System::Numerics::IRootFunctions<double>, System::Numerics::ISignedNumber<double>, System::Numerics::ISubtractionOperators<double, double, double>, System::Numerics::ITrigonometricFunctions<double>, System::Numerics::IUnaryNegationOperators<double, double>, System::Numerics::IUnaryPlusOperators<double, double>
public value class double : IComparable, IConvertible, IFormattable
public value class double : IComparable, IComparable<double>, IEquatable<double>, IFormattable
public struct Double : IComparable, IComparable<double>, IConvertible, IEquatable<double>, IFormattable
public readonly struct Double : IComparable, IComparable<double>, IConvertible, IEquatable<double>, IFormattable
public readonly struct Double : IComparable, IComparable<double>, IConvertible, IEquatable<double>, ISpanFormattable
public readonly struct Double : IComparable<double>, IConvertible, IEquatable<double>, IParsable<double>, ISpanParsable<double>, System.Numerics.IAdditionOperators<double,double,double>, System.Numerics.IAdditiveIdentity<double,double>, System.Numerics.IBinaryFloatingPointIeee754<double>, System.Numerics.IBinaryNumber<double>, System.Numerics.IBitwiseOperators<double,double,double>, System.Numerics.IComparisonOperators<double,double,bool>, System.Numerics.IDecrementOperators<double>, System.Numerics.IDivisionOperators<double,double,double>, System.Numerics.IEqualityOperators<double,double,bool>, System.Numerics.IExponentialFunctions<double>, System.Numerics.IFloatingPoint<double>, System.Numerics.IFloatingPointConstants<double>, System.Numerics.IFloatingPointIeee754<double>, System.Numerics.IHyperbolicFunctions<double>, System.Numerics.IIncrementOperators<double>, System.Numerics.ILogarithmicFunctions<double>, System.Numerics.IMinMaxValue<double>, System.Numerics.IModulusOperators<double,double,double>, System.Numerics.IMultiplicativeIdentity<double,double>, System.Numerics.IMultiplyOperators<double,double,double>, System.Numerics.INumber<double>, System.Numerics.INumberBase<double>, System.Numerics.IPowerFunctions<double>, System.Numerics.IRootFunctions<double>, System.Numerics.ISignedNumber<double>, System.Numerics.ISubtractionOperators<double,double,double>, System.Numerics.ITrigonometricFunctions<double>, System.Numerics.IUnaryNegationOperators<double,double>, System.Numerics.IUnaryPlusOperators<double,double>
public readonly struct Double : IComparable<double>, IConvertible, IEquatable<double>, IParsable<double>, ISpanParsable<double>, IUtf8SpanFormattable, IUtf8SpanParsable<double>, System.Numerics.IAdditionOperators<double,double,double>, System.Numerics.IAdditiveIdentity<double,double>, System.Numerics.IBinaryFloatingPointIeee754<double>, System.Numerics.IBinaryNumber<double>, System.Numerics.IBitwiseOperators<double,double,double>, System.Numerics.IComparisonOperators<double,double,bool>, System.Numerics.IDecrementOperators<double>, System.Numerics.IDivisionOperators<double,double,double>, System.Numerics.IEqualityOperators<double,double,bool>, System.Numerics.IExponentialFunctions<double>, System.Numerics.IFloatingPoint<double>, System.Numerics.IFloatingPointConstants<double>, System.Numerics.IFloatingPointIeee754<double>, System.Numerics.IHyperbolicFunctions<double>, System.Numerics.IIncrementOperators<double>, System.Numerics.ILogarithmicFunctions<double>, System.Numerics.IMinMaxValue<double>, System.Numerics.IModulusOperators<double,double,double>, System.Numerics.IMultiplicativeIdentity<double,double>, System.Numerics.IMultiplyOperators<double,double,double>, System.Numerics.INumber<double>, System.Numerics.INumberBase<double>, System.Numerics.IPowerFunctions<double>, System.Numerics.IRootFunctions<double>, System.Numerics.ISignedNumber<double>, System.Numerics.ISubtractionOperators<double,double,double>, System.Numerics.ITrigonometricFunctions<double>, System.Numerics.IUnaryNegationOperators<double,double>, System.Numerics.IUnaryPlusOperators<double,double>
[System.Serializable]
public struct Double : IComparable, IConvertible, IFormattable
[System.Serializable]
[System.Runtime.InteropServices.ComVisible(true)]
public struct Double : IComparable, IComparable<double>, IConvertible, IEquatable<double>, IFormattable
public struct Double : IComparable, IComparable<double>, IEquatable<double>, IFormattable
type double = struct
interface IConvertible
interface IFormattable
type double = struct
interface IConvertible
interface ISpanFormattable
interface IFormattable
type double = struct
interface IConvertible
interface IFormattable
interface IParsable<double>
interface ISpanFormattable
interface ISpanParsable<double>
interface IAdditionOperators<double, double, double>
interface IAdditiveIdentity<double, double>
interface IBinaryFloatingPointIeee754<double>
interface IBinaryNumber<double>
interface IBitwiseOperators<double, double, double>
interface IComparisonOperators<double, double, bool>
interface IEqualityOperators<double, double, bool>
interface IDecrementOperators<double>
interface IDivisionOperators<double, double, double>
interface IIncrementOperators<double>
interface IModulusOperators<double, double, double>
interface IMultiplicativeIdentity<double, double>
interface IMultiplyOperators<double, double, double>
interface INumber<double>
interface INumberBase<double>
interface ISubtractionOperators<double, double, double>
interface IUnaryNegationOperators<double, double>
interface IUnaryPlusOperators<double, double>
interface IExponentialFunctions<double>
interface IFloatingPointConstants<double>
interface IFloatingPoint<double>
interface ISignedNumber<double>
interface IFloatingPointIeee754<double>
interface IHyperbolicFunctions<double>
interface ILogarithmicFunctions<double>
interface IPowerFunctions<double>
interface IRootFunctions<double>
interface ITrigonometricFunctions<double>
interface IMinMaxValue<double>
type double = struct
interface IConvertible
interface IFormattable
interface IParsable<double>
interface ISpanFormattable
interface ISpanParsable<double>
interface IAdditionOperators<double, double, double>
interface IAdditiveIdentity<double, double>
interface IBinaryFloatingPointIeee754<double>
interface IBinaryNumber<double>
interface IBitwiseOperators<double, double, double>
interface IComparisonOperators<double, double, bool>
interface IEqualityOperators<double, double, bool>
interface IDecrementOperators<double>
interface IDivisionOperators<double, double, double>
interface IIncrementOperators<double>
interface IModulusOperators<double, double, double>
interface IMultiplicativeIdentity<double, double>
interface IMultiplyOperators<double, double, double>
interface INumber<double>
interface INumberBase<double>
interface ISubtractionOperators<double, double, double>
interface IUnaryNegationOperators<double, double>
interface IUnaryPlusOperators<double, double>
interface IUtf8SpanParsable<double>
interface IExponentialFunctions<double>
interface IFloatingPointConstants<double>
interface IFloatingPoint<double>
interface ISignedNumber<double>
interface IFloatingPointIeee754<double>
interface IHyperbolicFunctions<double>
interface ILogarithmicFunctions<double>
interface IPowerFunctions<double>
interface IRootFunctions<double>
interface ITrigonometricFunctions<double>
interface IMinMaxValue<double>
interface IUtf8SpanFormattable
[<System.Serializable>]
type double = struct
interface IFormattable
interface IConvertible
[<System.Serializable>]
[<System.Runtime.InteropServices.ComVisible(true)>]
type double = struct
interface IFormattable
interface IConvertible
type double = struct
interface IFormattable
Public Structure Double
Implements IComparable, IComparable(Of Double), IConvertible, IEquatable(Of Double), IFormattable
Public Structure Double
Implements IComparable, IComparable(Of Double), IConvertible, IEquatable(Of Double), ISpanFormattable
Public Structure Double
Implements IAdditionOperators(Of Double, Double, Double), IAdditiveIdentity(Of Double, Double), IBinaryFloatingPointIeee754(Of Double), IBinaryNumber(Of Double), IBitwiseOperators(Of Double, Double, Double), IComparable(Of Double), IComparisonOperators(Of Double, Double, Boolean), IConvertible, IDecrementOperators(Of Double), IDivisionOperators(Of Double, Double, Double), IEqualityOperators(Of Double, Double, Boolean), IEquatable(Of Double), IExponentialFunctions(Of Double), IFloatingPoint(Of Double), IFloatingPointConstants(Of Double), IFloatingPointIeee754(Of Double), IHyperbolicFunctions(Of Double), IIncrementOperators(Of Double), ILogarithmicFunctions(Of Double), IMinMaxValue(Of Double), IModulusOperators(Of Double, Double, Double), IMultiplicativeIdentity(Of Double, Double), IMultiplyOperators(Of Double, Double, Double), INumber(Of Double), INumberBase(Of Double), IParsable(Of Double), IPowerFunctions(Of Double), IRootFunctions(Of Double), ISignedNumber(Of Double), ISpanParsable(Of Double), ISubtractionOperators(Of Double, Double, Double), ITrigonometricFunctions(Of Double), IUnaryNegationOperators(Of Double, Double), IUnaryPlusOperators(Of Double, Double)
Public Structure Double
Implements IAdditionOperators(Of Double, Double, Double), IAdditiveIdentity(Of Double, Double), IBinaryFloatingPointIeee754(Of Double), IBinaryNumber(Of Double), IBitwiseOperators(Of Double, Double, Double), IComparable(Of Double), IComparisonOperators(Of Double, Double, Boolean), IConvertible, IDecrementOperators(Of Double), IDivisionOperators(Of Double, Double, Double), IEqualityOperators(Of Double, Double, Boolean), IEquatable(Of Double), IExponentialFunctions(Of Double), IFloatingPoint(Of Double), IFloatingPointConstants(Of Double), IFloatingPointIeee754(Of Double), IHyperbolicFunctions(Of Double), IIncrementOperators(Of Double), ILogarithmicFunctions(Of Double), IMinMaxValue(Of Double), IModulusOperators(Of Double, Double, Double), IMultiplicativeIdentity(Of Double, Double), IMultiplyOperators(Of Double, Double, Double), INumber(Of Double), INumberBase(Of Double), IParsable(Of Double), IPowerFunctions(Of Double), IRootFunctions(Of Double), ISignedNumber(Of Double), ISpanParsable(Of Double), ISubtractionOperators(Of Double, Double, Double), ITrigonometricFunctions(Of Double), IUnaryNegationOperators(Of Double, Double), IUnaryPlusOperators(Of Double, Double), IUtf8SpanFormattable, IUtf8SpanParsable(Of Double)
Public Structure Double
Implements IComparable, IConvertible, IFormattable
Public Structure Double
Implements IComparable, IComparable(Of Double), IEquatable(Of Double), IFormattable
- 繼承
- 屬性
- 實作
-
IComparable IComparable<Double> IConvertible IEquatable<Double> IFormattable ISpanFormattable IComparable<TSelf> IEquatable<TSelf> IParsable<Double> IParsable<TSelf> ISpanParsable<Double> ISpanParsable<TSelf> IAdditionOperators<Double,Double,Double> IAdditionOperators<TSelf,TSelf,TSelf> IAdditiveIdentity<Double,Double> IAdditiveIdentity<TSelf,TSelf> IBinaryFloatingPointIeee754<Double> IBinaryNumber<Double> IBinaryNumber<TSelf> IBitwiseOperators<Double,Double,Double> IBitwiseOperators<TSelf,TSelf,TSelf> IComparisonOperators<Double,Double,Boolean> IComparisonOperators<TSelf,TSelf,Boolean> IDecrementOperators<Double> IDecrementOperators<TSelf> IDivisionOperators<Double,Double,Double> IDivisionOperators<TSelf,TSelf,TSelf> IEqualityOperators<Double,Double,Boolean> IEqualityOperators<TSelf,TOther,TResult> IEqualityOperators<TSelf,TSelf,Boolean> IExponentialFunctions<Double> IExponentialFunctions<TSelf> IFloatingPoint<Double> IFloatingPoint<TSelf> IFloatingPointConstants<Double> IFloatingPointConstants<TSelf> IFloatingPointIeee754<Double> IFloatingPointIeee754<TSelf> IHyperbolicFunctions<Double> IHyperbolicFunctions<TSelf> IIncrementOperators<Double> IIncrementOperators<TSelf> ILogarithmicFunctions<Double> ILogarithmicFunctions<TSelf> IMinMaxValue<Double> IModulusOperators<Double,Double,Double> IModulusOperators<TSelf,TSelf,TSelf> IMultiplicativeIdentity<Double,Double> IMultiplicativeIdentity<TSelf,TSelf> IMultiplyOperators<Double,Double,Double> IMultiplyOperators<TSelf,TSelf,TSelf> INumber<Double> INumber<TSelf> INumberBase<Double> INumberBase<TSelf> IPowerFunctions<Double> IPowerFunctions<TSelf> IRootFunctions<Double> IRootFunctions<TSelf> ISignedNumber<Double> ISignedNumber<TSelf> ISubtractionOperators<Double,Double,Double> ISubtractionOperators<TSelf,TSelf,TSelf> ITrigonometricFunctions<Double> ITrigonometricFunctions<TSelf> IUnaryNegationOperators<Double,Double> IUnaryNegationOperators<TSelf,TSelf> IUnaryPlusOperators<Double,Double> IUnaryPlusOperators<TSelf,TSelf> IUtf8SpanFormattable IUtf8SpanParsable<Double> IUtf8SpanParsable<TSelf>
範例
下列程式碼範例說明 如何使用 Double :
// The Temperature class stores the temperature as a Double
// and delegates most of the functionality to the Double
// implementation.
public ref class Temperature: public IComparable, public IFormattable
{
// IComparable.CompareTo implementation.
public:
virtual int CompareTo( Object^ obj )
{
if (obj == nullptr) return 1;
if (dynamic_cast<Temperature^>(obj) )
{
Temperature^ temp = (Temperature^)(obj);
return m_value.CompareTo( temp->m_value );
}
throw gcnew ArgumentException( "object is not a Temperature" );
}
// IFormattable.ToString implementation.
virtual String^ ToString( String^ format, IFormatProvider^ provider )
{
if ( format != nullptr )
{
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]
static Temperature^ Parse( String^ s, NumberStyles styles, IFormatProvider^ provider )
{
Temperature^ temp = gcnew Temperature;
if ( s->TrimEnd(nullptr)->EndsWith( "'F" ) )
{
temp->Value = Double::Parse( s->Remove( s->LastIndexOf( '\'' ), 2 ), styles, provider );
}
else
if ( s->TrimEnd(nullptr)->EndsWith( "'C" ) )
{
temp->Celsius = Double::Parse( s->Remove( s->LastIndexOf( '\'' ), 2 ), styles, provider );
}
else
{
temp->Value = Double::Parse( s, styles, provider );
}
return temp;
}
protected:
double m_value;
public:
property double Value
{
double get()
{
return m_value;
}
void set( double value )
{
m_value = value;
}
}
property double Celsius
{
double get()
{
return (m_value - 32.0) / 1.8;
}
void set( double value )
{
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.
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(Nothing).EndsWith("'F") Then
temp.Value = Double.Parse(s.Remove(s.LastIndexOf("'"c), 2), styles, provider)
Else
If s.TrimEnd(Nothing).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
備註
實 Double 值型別代表雙精確度 64 位數位,其值範圍從負 1.79769313486232e308 到正數 1.79769313486232e308,以及正數或負零、、 PositiveInfinityNegativeInfinity 和 不是數位 (NaN) 。 其目的在於表示極大型 (的值,例如行星之間的距離或) 或極小的 (,例如) ) 的分子品質,而且通常是不精確的 (,例如從地球到另一個太陽能系統的距離) 。 此 Double 類型符合二進位浮點算術的 IEC 60559:1989 (IEEE 754) 標準。
本主題包含下列章節:
Floating-Point 標記法和精確度
Double資料類型會以 64 位二進位格式儲存雙精確度浮點值,如下表所示:
部分 | Bits |
---|---|
Significand 或 mantissa | 0-51 |
指數 | 52-62 |
符號 (0 = 正數,1 = 負) | 63 |
就如同小數分數無法精確地表示某些小數值 (,例如 1/3 或 Math.PI) ,二進位分數無法代表某些小數值。 例如,以十進位分數以 .1 精確表示的 1/10 是以 .001100110011 表示為二進位分數,而模式 「0011」 會重複到無限大。 在此情況下,浮點值會提供其所代表數位的不精確標記法。 在原始浮點值上執行其他數學運算通常會增加其缺乏精確度。 例如,如果我們比較將 .1 乘以 10 的結果,並將 .1 加到 .1 九次,我們會看到加法,因為它涉及 8 個以上的作業,所以會產生較不精確的結果。 請注意,只有在我們使用 「R」標準數值格式字串來顯示這兩 Double 個值時,才會明顯顯示此差異,必要時會顯示類型支援 Double 的所有 17 位數有效位數。
using System;
public class Example
{
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 Example
Public Sub Main()
Dim value As Double = .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
由於某些數位無法完全表示為小數二進位值,因此浮點數只能近似實數。
所有浮點數也有有限的有效位數,這也決定浮點值近似實數的精確度。 Double值最多可有 15 個小數位數的有效位數,雖然內部會維護最多 17 位數。 這表示某些浮點運算可能缺少變更浮點值的精確度。 下列範例提供說明。 它會定義非常大的浮點值,然後將 的乘 Double.Epsilon 積和一個四進階加入其中。 不過,產品太小而無法修改原始浮點值。 其最小有效位數為千分之一,而產品中最有效位數為10-309。
using System;
public class Example
{
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 Example
Public Sub Main()
Dim value As Double = 123456789012.34567
Dim additional As Double = Double.Epsilon * 1e15
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
浮點數的有限有效位數有數個結果:
對特定有效位數相等的兩個浮點數,可能因為它們的最低有效位數不同,而不相等。 在下列範例中,一連串的數位會加在一起,而且其總計會與其預期的總計進行比較。 雖然這兩個值似乎相同,但是對 方法的
Equals
呼叫表示它們不是。using System; public class Example { 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 Example 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).
如果您將 語句中的 Console.WriteLine(String, Object, Object) 格式專案從
{0}
和{1}
變更為{0:R}
,{1:R}
以顯示兩 Double 個值的所有有效位數,則清楚表示這兩個值在加法作業期間遺失有效位數不相等。 在此情況下,您可以藉由呼叫 Math.Round(Double, Int32) 方法來將值四舍 Double 五入到所需的精確度,再執行比較,來解決此問題。如果使用十進位數,則使用浮點數的數學或比較運算可能不會產生相同的結果,因為二進位浮點數可能不等於小數。 上一個範例說明如何顯示將 .1 乘以 10 並加 .1 次的結果。
當數值運算中具有小數值的精確度很重要時,您可以使用 Decimal 而非 Double 類型。 當數值運算中具有超出 或 UInt64 類型範圍 Int64 之整數值的精確度很重要時,請使用 BigInteger 類型。
如果涉及浮點數,則值可能不會來回。 如果作業將原始浮點數轉換成另一個表單,反向運算會將轉換後的表單轉換為浮點數,而最終浮點數不等於原始浮點數,則值會說為來回。 因為轉換中遺失或變更一或多個最小有效位數,所以來回行程可能會失敗。 在下列範例中,三 Double 個值會轉換成字串,並儲存在檔案中。 不過,如輸出所示,即使值看起來相同,還原的值不等於原始值。
using System; using System.IO; public class Example { 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 Example 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
在此情況下,可以使用 「G17」 標準數值格式字串 來成功四捨五入,以保留值的完整精確度 Double ,如下列範例所示。
using System; using System.IO; public class Example { 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 Example 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
Single 值的有效位數小於 Double 值。 Single轉換成看似相等 Double 的值通常不等於值, Double 因為精確度的差異。 在下列範例中,相同的除法運算結果會指派給 Double 和 Single 值。 將 Single 值轉換成 Double 之後,兩個值的比較會顯示它們不相等。
using System; public class Example { 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 Example 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
若要避免這個問題,請使用 DoubleSingle 取代資料類型,或使用 Round 方法,讓這兩個值具有相同的精確度。
此外,具有值的算術和指派運算 Double 結果可能會因型別的精確度 Double 遺失而因平臺而略有不同。 例如,指派常 Double 值的結果可能與 32 位和 64 位版本的.NET Framework不同。 下列範例說明當常值 -4.42330604244772E-305 和值為 -4.42330604244772E-305 Double 的變數時,這項差異。 請注意,在此情況下,方法的結果 Parse(String) 不會因為精確度遺失而受到影響。
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 = -4.42330604244772E-305
Dim fromLiteral As Double = -4.42330604244772E-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
測試是否相等
若要視為相等,兩 Double 個值必須代表相同的值。 不過,由於值之間的精確度差異,或因為一或兩個值遺失有效位數,因此預期相同的浮點值通常因為其最小有效位數的差異而不相等。 因此,呼叫 Equals 方法以判斷兩個值是否相等,或呼叫 CompareTo 方法來判斷兩 Double 個值之間的關聯性,通常會產生非預期的結果。 這在下列範例中很明顯,其中兩個明顯相等 Double 的值會變成不相等,因為第一個有 15 位數的有效位數,而第二個數字有 17。
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 Example
Public Sub Main()
Dim value1 As Double = .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
遵循不同程式碼路徑且以不同方式操作的匯出值,通常證明不相等。 在下列範例中,一個 Double 值是平方,然後計算平方根來還原原始值。 第二 Double 個乘以 3.51,並在結果平方根除以 3.51 之前平方以還原原始值。 雖然這兩個值似乎相同,但是對 方法的 Equals(Double) 呼叫表示它們不相等。 使用 「R」 標準格式字串傳回結果字串,其中顯示每個 Double 值的所有有效位數,顯示第二個值是 .0000000000001小於第一個值。
using System;
public class Example
{
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 Example
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
如果遺失精確度可能會影響比較的結果,您可以採用下列任何替代方法來呼叫 Equals 或 CompareTo 方法:
Math.Round呼叫 方法,以確保這兩個值具有相同的精確度。 下列範例會修改先前的範例,以使用此方法,讓兩個小數值相等。
using System; public class Example { 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 Example Public Sub Main() Dim value1 As Double = .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
精確度的問題仍適用于中間點值的四捨五入。 如需詳細資訊,請參閱 Math.Round(Double, Int32, MidpointRounding) 方法。
測試近似相等,而不是相等。 這需要您定義兩個值可以相異但仍然相等的絕對數量,或定義較小的值可以從較大的值除以相等的相對數量。
警告
Double.Epsilon 在測試是否相等時,有時會當做兩 Double 個值之間距離的絕對量值。 不過, Double.Epsilon 測量可以加入或減去 Double 其值為零的 最小可能值。 對於大部分的正值和負 Double 值,的值 Double.Epsilon 太小而無法偵測。 因此,除了零的值以外,我們不建議在測試中使用是否相等。
下列範例會使用後者方法來定義方法,以測試兩個
IsApproximatelyEqual
值之間的相對差異。 它也會對比呼叫IsApproximatelyEqual
方法和 Equals(Double) 方法的結果。using System; public class Example { 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 Example Public Sub Main() Dim one1 As Double = .1 * 10 Dim one2 As Double = 0 For ctr As Integer = 1 To 10 one2 += .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, .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) Else If Double.IsInfinity(value2) Or Double.IsNaN(value2) 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
Floating-Point 值和例外狀況
不同于整數型別的作業,若發生溢位或不合法的作業,例如除以零,則具有浮點值的作業不會擲回例外狀況。 相反地,在例外情況下,浮點運算的結果為零、正無限大、負無限大,或非數位 (NaN) :
如果浮點運算的結果對目的地格式而言太小,則結果為零。 當兩個非常小的數位相乘時,就會發生這種情況,如下列範例所示。
using System; public class Example { 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 Example 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
如果浮點運算的結果大小超過目的格式的範圍,則作業的結果會 PositiveInfinity 是 或 NegativeInfinity ,適用于結果的正負號。 溢位 Double.MaxValue 作業的結果為 PositiveInfinity ,而溢位 Double.MinValue 作業的結果為 NegativeInfinity ,如下列範例所示。
using System; public class Example { 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 Example Public Sub Main() Dim value1 As Double = 4.565e153 Dim value2 As Double = 6.9375e172 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 也會產生除以零為正數的除數,以及 NegativeInfinity 零除以負數除數的結果。
如果浮點運算無效,作業的結果為 NaN 。 例如, NaN 下列作業的結果:
- 除以零除數為零。 請注意,除以零的其他案例會導致 PositiveInfinity 或 NegativeInfinity 。
任何具有無效輸入的浮點運算。 例如,使用負值呼叫 Math.Sqrt 方法會 NaN 傳回 ,如同使用大於一或小於負值的值呼叫 Math.Acos 方法一樣。
具有其值為 Double.NaN 之引數的任何作業。
類型轉換和 Double 結構
結構 Double 不會定義任何明確或隱含轉換運算子,而是由編譯器實作轉換。
將任何基本數值型 Double 別的值轉換成 是擴輾轉換,因此不需要明確轉換運算子或呼叫轉換方法,除非編譯器明確要求轉換方法。 例如,C# 編譯器需要轉換運算子,才能從 Decimal 轉換成 Double ,而 Visual Basic 編譯器則不需要。 下列範例會將其他基本數數值型別的最小值或最大值轉換為 Double 。
using System;
public class Example
{
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 Example
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, Single 、、 和 Single.NegativeInfinity 的值 Single.PositiveInfinitySingle.NaN 會分別轉換成 Double.NaN 、 Double.PositiveInfinity 和 Double.NegativeInfinity 。
請注意,將某些數值型 Double 別的值轉換成值,可能會牽涉到精確度遺失。 如範例所示,將 、 Int64 和 UInt64 值轉換成 Decimal 值 Double 時,可能會遺失有效位數。
將值轉換成 Double 任何其他基本數值資料類型的值是縮小轉換,而且需要 C#) 中的轉換運算子 (、Visual Basic) 中的轉換方法 (,或呼叫 Convert 方法。 超出目標資料類型範圍的值,這些資料類型是由目標型別的 MinValue
和 MaxValue
屬性所定義,其行為如下表所示。
目標類型 | 結果 |
---|---|
任何整數類型 | OverflowException如果轉換發生在已檢查的內容中,則為例外狀況。 如果在未核取的內容中發生轉換, (C#) 中的預設值,轉換作業就會成功,但值溢位。 |
Decimal | OverflowException 例外狀況。 |
Single | Single.NegativeInfinity 為負值。 Single.PositiveInfinity 為正值。 |
此外, Double.NaN 、 Double.PositiveInfinity 和 Double.NegativeInfinity 會擲回 OverflowException ,以便轉換成已檢查內容中的整數,但這些值會在未核取的內容中轉換成整數時溢位。 若要轉換成 Decimal ,它們一律會擲回 OverflowException 。 若要轉換成 Single ,它們分別轉換成 Single.NaN 、 Single.PositiveInfinity 和 Single.NegativeInfinity 。
請注意,精確度遺失可能會導致將值轉換成另一個 Double 數數值型別。 在轉換成任何整數型別的情況下,如範例所示,當值如 Visual Basic) 四捨五入 (或截斷 (為 C#) 時 Double ,小陣列件會遺失。 針對 和 DecimalSingle 值的轉換, Double 值在目標資料類型中可能沒有精確的標記法。
下列範例會將一些 Double 值轉換成數個其他數數值型別。 轉換發生在 Visual Basic 中檢查的內容中, (預設) 、C# (,因為 checked 關鍵字) ,而 F# (是因為 Checked 模組) 。 範例的輸出會顯示在已核取未核取內容中轉換的結果。 您可以在 Visual Basic 中未核取的內容中執行轉換,方法是使用 /removeintchecks+
編譯器參數進行編譯、在 C# 中透過批註化 checked
語句,以及在 F# 中將 語句加上批註 open Checked
。
using System;
public class Example
{
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 Example
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)
如需數數值型別轉換的詳細資訊,請參閱.NET Framework和類型轉換資料表中的類型轉換。
Floating-Point 功能
結構和 Double 相關類型提供方法,以在下欄區域中執行作業:
值的比較。 您可以呼叫 Equals 方法來判斷兩 Double 個值是否相等,或 CompareTo 呼叫 方法來判斷兩個值之間的關聯性。
結構 Double 也支援一組完整的比較運算子。 例如,您可以測試是否相等或不相等,或判斷某個值是否大於或等於另一個值。 如果其中一個運算元是 以外的 Double 數數值型別,則會先轉換成 Double ,再執行比較。
您也可以呼叫 IsNaN 、 IsInfinity 、 IsPositiveInfinity 和 IsNegativeInfinity 方法來測試這些特殊值。
數學運算。 常見的算數運算,例如加法、減法、乘法和除法,都是由語言編譯器和 Common Intermediate Language (CIL) 指令實作,而不是由 Double 方法實作。 如果數學運算中的其中一個運算元是 以外的 Double 數數值型別,則會在執行 Double 作業之前轉換為 。 作業的結果也是 Double 值。
您可以在 Visual Basic 中呼叫
static
(Shared
) 方法, System.Math 以執行其他數學運算。 其中包含常用於算術 (的其他方法,例如 Math.Abs 、 Math.Sign 和 Math.Sqrt) 、幾何 (,例如 Math.Cos 和 Math.Sin) ,以及微數 (,例如 Math.Log) 。您也可以操作 值中的 Double 個別位。 方法 BitConverter.DoubleToInt64Bits 會在 Double 64 位整數中保留值的位模式。 方法 BitConverter.GetBytes(Double) 會在位元組陣列中傳回其位模式。
四捨五入。 四捨五入通常用來做為減少浮點表示和精確度問題所造成值間差異影響的技術。 您可以藉由呼叫 Math.Round 方法來四捨五入 Double 值。
格式化。 您可以呼叫 方法或使用複合格式功能, ToString 將值轉換成 Double 其字串表示。 如需格式字串如何控制浮點值的字串表示的詳細資訊,請參閱 標準數值格式字串 和 自訂數值格式字串 主題。
剖析字串。 您可以藉由呼叫 Parse 或 TryParse 方法,將浮點值的字串表示轉換為 Double 值。 如果剖析作業失敗,方法 Parse 會擲回例外狀況,而 方法會 TryParse 傳
false
回 。類型轉換。 結構 Double 會為 介面提供明確的介面實作 IConvertible ,可支援在任兩個標準.NET Framework資料類型之間進行轉換。 語言編譯器也支援將所有其他標準數數值型別的 Double 值隱含轉換成值。 將任何標準數值型 Double 別的值轉換成 是擴輾轉換,而且不需要轉型運算子或轉換方法的使用者。
不過,和 Single 值的 Int64 轉換可能會牽涉到精確度遺失。 下表列出每種類型的有效位數差異:
類型 最大有效位數 內部有效位數 Double 15 17 Int64 19 個小數位數 19 個小數位數 Single 7 個小數位數 9 個小數位數 有效位數的問題最常影響 Single 轉換成 Double 值的值。 在下列範例中,相同除法運算所產生的兩個值不相等,因為其中一個值是轉換成 Double 的單精確度浮點值。
using System; public class Example { 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 Example Public Sub Main() Dim value As Double = .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
欄位
E |
表示常數所指定的自然對數基底,e. |
Epsilon |
代表大於零的最小正 Double 值。 這個欄位為常數。 |
MaxValue |
表示 Double 最大的可能值。 這個欄位為常數。 |
MinValue |
表示 Double 最小的可能值。 這個欄位為常數。 |
NaN |
代表不是數字 ( |
NegativeInfinity |
表示負無限大。 這個欄位為常數。 |
NegativeZero |
表示負數零 (-0) 。 |
Pi |
代表圓周率,由常數 π 指定。 |
PositiveInfinity |
表示正無限大。 這個欄位為常數。 |
Tau |
代表單一回合中的弧度數目,由常數 τ 指定。 |
方法
運算子
Equality(Double, Double) |
傳回值,該值表示兩個指定的 Double 值是否相等。 |
GreaterThan(Double, Double) | |
GreaterThanOrEqual(Double, Double) | |
Inequality(Double, Double) |
傳回值,該值表示兩個指定的 Double 值是否不相等。 |
LessThan(Double, Double) | |
LessThanOrEqual(Double, Double) |
明確介面實作
適用於
執行緒安全性
此類型的所有成員都是安全線程。 看似修改實例狀態的成員,實際上會傳回以新值初始化的新實例。 如同任何其他類型,讀取和寫入包含此類型實例的共用變數必須受到鎖定保護,以確保執行緒安全。