Math.Exp(Double) Méthode

Référence

Définition

Espace de noms:: System

Assembly:: System.Runtime.Extensions.dll

Assembly:: System.Runtime.dll

Assembly:: mscorlib.dll

Assembly:: netstandard.dll

Source:: Math.cs

Source:: Math.cs

Source:: Math.cs

Important

Certaines informations portent sur la préversion du produit qui est susceptible d’être en grande partie modifiée avant sa publication. Microsoft exclut toute garantie, expresse ou implicite, concernant les informations fournies ici.

Retourne e élevé à la puissance spécifiée.

public:
 static double Exp(double d);

public static double Exp (double d);

static member Exp : double -> double

Public Shared Function Exp (d As Double) As Double

Paramètres

d: Double

Nombre spécifiant une puissance.

Retours

Double

Nombre e élevé à la puissance d. Si d est égal à NaN ou PositiveInfinity, cette valeur est retournée. Si d est égal à NegativeInfinity, 0 est retourné.

Exemples

L’exemple suivant utilise Exp pour évaluer certaines identités exponentielles et logarithmiques pour les valeurs sélectionnées.

// Example for the Math::Exp( double ) method.
using namespace System;

// Evaluate logarithmic/exponential identity with a given argument.
void UseLnExp( double arg )
{
   
   // Evaluate e ^ ln(X) == ln(e ^ X) == X.
   Console::WriteLine( "\n      Math::Exp(Math::Log({0})) == {1:E16}\n"
   "      Math::Log(Math::Exp({0})) == {2:E16}", arg, Math::Exp( Math::Log( arg ) ), Math::Log( Math::Exp( arg ) ) );
}


// Evaluate exponential identities that are functions of two arguments.
void UseTwoArgs( double argX, double argY )
{
   
   // Evaluate (e ^ X) * (e ^ Y) == e ^ (X + Y).
   Console::WriteLine( "\nMath::Exp({0}) * Math::Exp({1}) == {2:E16}"
   "\n           Math::Exp({0} + {1}) == {3:E16}", argX, argY, Math::Exp( argX ) * Math::Exp( argY ), Math::Exp( argX + argY ) );
   
   // Evaluate (e ^ X) ^ Y == e ^ (X * Y).
   Console::WriteLine( " Math::Pow(Math::Exp({0}), {1}) == {2:E16}"
   "\n           Math::Exp({0} * {1}) == {3:E16}", argX, argY, Math::Pow( Math::Exp( argX ), argY ), Math::Exp( argX * argY ) );
   
   // Evaluate X ^ Y == e ^ (Y * ln(X)).
   Console::WriteLine( "            Math::Pow({0}, {1}) == {2:E16}"
   "\nMath::Exp({1} * Math::Log({0})) == {3:E16}", argX, argY, Math::Pow( argX, argY ), Math::Exp( argY * Math::Log( argX ) ) );
}

int main()
{
   Console::WriteLine( "This example of Math::Exp( double ) "
   "generates the following output.\n" );
   Console::WriteLine( "Evaluate [e ^ ln(X) == ln(e ^ X) == X] "
   "with selected values for X:" );
   UseLnExp( 0.1 );
   UseLnExp( 1.2 );
   UseLnExp( 4.9 );
   UseLnExp( 9.9 );
   Console::WriteLine( "\nEvaluate these identities with "
   "selected values for X and Y:" );
   Console::WriteLine( "   (e ^ X) * (e ^ Y) == e ^ (X + Y)" );
   Console::WriteLine( "   (e ^ X) ^ Y == e ^ (X * Y)" );
   Console::WriteLine( "   X ^ Y == e ^ (Y * ln(X))" );
   UseTwoArgs( 0.1, 1.2 );
   UseTwoArgs( 1.2, 4.9 );
   UseTwoArgs( 4.9, 9.9 );
}

/*
This example of Math::Exp( double ) generates the following output.

Evaluate [e ^ ln(X) == ln(e ^ X) == X] with selected values for X:

      Math::Exp(Math::Log(0.1)) == 1.0000000000000001E-001
      Math::Log(Math::Exp(0.1)) == 1.0000000000000008E-001

      Math::Exp(Math::Log(1.2)) == 1.2000000000000000E+000
      Math::Log(Math::Exp(1.2)) == 1.2000000000000000E+000

      Math::Exp(Math::Log(4.9)) == 4.9000000000000012E+000
      Math::Log(Math::Exp(4.9)) == 4.9000000000000004E+000

      Math::Exp(Math::Log(9.9)) == 9.9000000000000004E+000
      Math::Log(Math::Exp(9.9)) == 9.9000000000000004E+000

Evaluate these identities with selected values for X and Y:
   (e ^ X) * (e ^ Y) == e ^ (X + Y)
   (e ^ X) ^ Y == e ^ (X * Y)
   X ^ Y == e ^ (Y * ln(X))

Math::Exp(0.1) * Math::Exp(1.2) == 3.6692966676192444E+000
           Math::Exp(0.1 + 1.2) == 3.6692966676192444E+000
 Math::Pow(Math::Exp(0.1), 1.2) == 1.1274968515793757E+000
           Math::Exp(0.1 * 1.2) == 1.1274968515793757E+000
            Math::Pow(0.1, 1.2) == 6.3095734448019331E-002
Math::Exp(1.2 * Math::Log(0.1)) == 6.3095734448019344E-002

Math::Exp(1.2) * Math::Exp(4.9) == 4.4585777008251705E+002
           Math::Exp(1.2 + 4.9) == 4.4585777008251716E+002
 Math::Pow(Math::Exp(1.2), 4.9) == 3.5780924170885260E+002
           Math::Exp(1.2 * 4.9) == 3.5780924170885277E+002
            Math::Pow(1.2, 4.9) == 2.4433636334442981E+000
Math::Exp(4.9 * Math::Log(1.2)) == 2.4433636334442981E+000

Math::Exp(4.9) * Math::Exp(9.9) == 2.6764450551890982E+006
           Math::Exp(4.9 + 9.9) == 2.6764450551891015E+006
 Math::Pow(Math::Exp(4.9), 9.9) == 1.1684908531676833E+021
           Math::Exp(4.9 * 9.9) == 1.1684908531676829E+021
            Math::Pow(4.9, 9.9) == 6.8067718210957060E+006
Math::Exp(9.9 * Math::Log(4.9)) == 6.8067718210956985E+006
*/

// Example for the Math.Exp( double ) method.
using System;

class ExpDemo
{
    public static void Main()
    {
        Console.WriteLine(
            "This example of Math.Exp( double ) " +
            "generates the following output.\n" );
        Console.WriteLine(
            "Evaluate [e ^ ln(X) == ln(e ^ X) == X] " +
            "with selected values for X:" );

        UseLnExp(0.1);
        UseLnExp(1.2);
        UseLnExp(4.9);
        UseLnExp(9.9);

        Console.WriteLine(
            "\nEvaluate these identities with " +
            "selected values for X and Y:" );
        Console.WriteLine( "   (e ^ X) * (e ^ Y) == e ^ (X + Y)" );
        Console.WriteLine( "   (e ^ X) ^ Y == e ^ (X * Y)" );
        Console.WriteLine( "   X ^ Y == e ^ (Y * ln(X))" );

        UseTwoArgs(0.1, 1.2);
        UseTwoArgs(1.2, 4.9);
        UseTwoArgs(4.9, 9.9);
    }

    // Evaluate logarithmic/exponential identity with a given argument.
    static void UseLnExp(double arg)
    {
        // Evaluate e ^ ln(X) == ln(e ^ X) == X.
        Console.WriteLine(
            "\n      Math.Exp(Math.Log({0})) == {1:E16}\n" +
            "      Math.Log(Math.Exp({0})) == {2:E16}",
            arg, Math.Exp(Math.Log(arg)), Math.Log(Math.Exp(arg)) );
    }

    // Evaluate exponential identities that are functions of two arguments.
    static void UseTwoArgs(double argX, double argY)
    {
        // Evaluate (e ^ X) * (e ^ Y) == e ^ (X + Y).
        Console.WriteLine(
            "\nMath.Exp({0}) * Math.Exp({1}) == {2:E16}" +
            "\n          Math.Exp({0} + {1}) == {3:E16}",
            argX, argY, Math.Exp(argX) * Math.Exp(argY),
            Math.Exp(argX + argY) );

        // Evaluate (e ^ X) ^ Y == e ^ (X * Y).
        Console.WriteLine(
            " Math.Pow(Math.Exp({0}), {1}) == {2:E16}" +
            "\n          Math.Exp({0} * {1}) == {3:E16}",
            argX, argY, Math.Pow(Math.Exp(argX), argY),
            Math.Exp(argX * argY) );

        // Evaluate X ^ Y == e ^ (Y * ln(X)).
        Console.WriteLine(
            "           Math.Pow({0}, {1}) == {2:E16}" +
            "\nMath.Exp({1} * Math.Log({0})) == {3:E16}",
            argX, argY, Math.Pow(argX, argY),
            Math.Exp(argY * Math.Log(argX)) );
    }
}

/*
This example of Math.Exp( double ) generates the following output.

Evaluate [e ^ ln(X) == ln(e ^ X) == X] with selected values for X:

      Math.Exp(Math.Log(0.1)) == 1.0000000000000001E-001
      Math.Log(Math.Exp(0.1)) == 1.0000000000000008E-001

      Math.Exp(Math.Log(1.2)) == 1.2000000000000000E+000
      Math.Log(Math.Exp(1.2)) == 1.2000000000000000E+000

      Math.Exp(Math.Log(4.9)) == 4.9000000000000012E+000
      Math.Log(Math.Exp(4.9)) == 4.9000000000000004E+000

      Math.Exp(Math.Log(9.9)) == 9.9000000000000004E+000
      Math.Log(Math.Exp(9.9)) == 9.9000000000000004E+000

Evaluate these identities with selected values for X and Y:
   (e ^ X) * (e ^ Y) == e ^ (X + Y)
   (e ^ X) ^ Y == e ^ (X * Y)
   X ^ Y == e ^ (Y * ln(X))

Math.Exp(0.1) * Math.Exp(1.2) == 3.6692966676192444E+000
          Math.Exp(0.1 + 1.2) == 3.6692966676192444E+000
 Math.Pow(Math.Exp(0.1), 1.2) == 1.1274968515793757E+000
          Math.Exp(0.1 * 1.2) == 1.1274968515793757E+000
           Math.Pow(0.1, 1.2) == 6.3095734448019331E-002
Math.Exp(1.2 * Math.Log(0.1)) == 6.3095734448019344E-002

Math.Exp(1.2) * Math.Exp(4.9) == 4.4585777008251705E+002
          Math.Exp(1.2 + 4.9) == 4.4585777008251716E+002
 Math.Pow(Math.Exp(1.2), 4.9) == 3.5780924170885260E+002
          Math.Exp(1.2 * 4.9) == 3.5780924170885277E+002
           Math.Pow(1.2, 4.9) == 2.4433636334442981E+000
Math.Exp(4.9 * Math.Log(1.2)) == 2.4433636334442981E+000

Math.Exp(4.9) * Math.Exp(9.9) == 2.6764450551890982E+006
          Math.Exp(4.9 + 9.9) == 2.6764450551891015E+006
 Math.Pow(Math.Exp(4.9), 9.9) == 1.1684908531676833E+021
          Math.Exp(4.9 * 9.9) == 1.1684908531676829E+021
           Math.Pow(4.9, 9.9) == 6.8067718210957060E+006
Math.Exp(9.9 * Math.Log(4.9)) == 6.8067718210956985E+006
*/

// Example for the Math.Exp( double ) method.
// The exp function may be used instead.

open System
printfn "This example of Math.Exp( double ) generates the following output.\n"
printfn "Evaluate [e ^ ln(X) = ln(e ^ X) = X] with selected values for X:"

// Evaluate logarithmic/exponential identity with a given argument.
let useLnExp arg =
    // Evaluate e ^ ln(X) = ln(e ^ X) = X.
    printfn $"\n      Math.Exp(Math.Log({arg})) = {Math.Exp(Math.Log arg):E16}\n      Math.Log(Math.Exp({arg})) = {Math.Log(Math.Exp arg):E16}"

// Evaluate exponential identities that are functions of two arguments.
let useTwoArgs argX argY =
    // Evaluate (e ^ X) * (e ^ Y) = e ^ (X + Y).
    printfn $"""
Math.Exp({argX}) * Math.Exp({argY}) = {Math.Exp argX * Math.Exp argY:E16}" +
          Math.Exp({argX} + {argY}) = {Math.Exp(argX + argY):E16}"""

    // Evaluate (e ^ X) ^ Y = e ^ (X * Y).
    printfn $" Math.Pow(Math.Exp({argX}), {argY}) = {Math.Pow(Math.Exp argX, argY):E16}\n          Math.Exp({argX} * {argY}) = {Math.Exp(argX * argY):E16}"

    // Evaluate X ^ Y = e ^ (Y * ln(X)).
    printfn $"           Math.Pow({argX}, {argY}) = {Math.Pow(argX, argY):E16}\nMath.Exp({argY} * Math.Log({argX})) = {Math.Exp(argY * Math.Log argX):E16}"

useLnExp 0.1
useLnExp 1.2
useLnExp 4.9
useLnExp 9.9

printfn "\nEvaluate these identities with selected values for X and Y:"
printfn "   (e ^ X) * (e ^ Y) = e ^ (X + Y)"
printfn "   (e ^ X) ^ Y = e ^ (X * Y)"
printfn "   X ^ Y = e ^ (Y * ln(X))"

useTwoArgs 0.1 1.2
useTwoArgs 1.2 4.9
useTwoArgs 4.9 9.9

// This example of Math.Exp( double ) generates the following output.
//
// Evaluate [e ^ ln(X) = ln(e ^ X) = X] with selected values for X:
//
//       Math.Exp(Math.Log(0.1)) = 1.0000000000000001E-001
//       Math.Log(Math.Exp(0.1)) = 1.0000000000000008E-001
//
//       Math.Exp(Math.Log(1.2)) = 1.2000000000000000E+000
//       Math.Log(Math.Exp(1.2)) = 1.2000000000000000E+000
//
//       Math.Exp(Math.Log(4.9)) = 4.9000000000000012E+000
//       Math.Log(Math.Exp(4.9)) = 4.9000000000000004E+000
//
//       Math.Exp(Math.Log(9.9)) = 9.9000000000000004E+000
//       Math.Log(Math.Exp(9.9)) = 9.9000000000000004E+000
//
// Evaluate these identities with selected values for X and Y:
//    (e ^ X) * (e ^ Y) = e ^ (X + Y)
//    (e ^ X) ^ Y = e ^ (X * Y)
//    X ^ Y = e ^ (Y * ln(X))
//
// Math.Exp(0.1) * Math.Exp(1.2) = 3.6692966676192444E+000
//           Math.Exp(0.1 + 1.2) = 3.6692966676192444E+000
//  Math.Pow(Math.Exp(0.1), 1.2) = 1.1274968515793757E+000
//           Math.Exp(0.1 * 1.2) = 1.1274968515793757E+000
//            Math.Pow(0.1, 1.2) = 6.3095734448019331E-002
// Math.Exp(1.2 * Math.Log(0.1)) = 6.3095734448019344E-002
//
// Math.Exp(1.2) * Math.Exp(4.9) = 4.4585777008251705E+002
//           Math.Exp(1.2 + 4.9) = 4.4585777008251716E+002
//  Math.Pow(Math.Exp(1.2), 4.9) = 3.5780924170885260E+002
//           Math.Exp(1.2 * 4.9) = 3.5780924170885277E+002
//            Math.Pow(1.2, 4.9) = 2.4433636334442981E+000
// Math.Exp(4.9 * Math.Log(1.2)) = 2.4433636334442981E+000
//
// Math.Exp(4.9) * Math.Exp(9.9) = 2.6764450551890982E+006
//           Math.Exp(4.9 + 9.9) = 2.6764450551891015E+006
//  Math.Pow(Math.Exp(4.9), 9.9) = 1.1684908531676833E+021
//           Math.Exp(4.9 * 9.9) = 1.1684908531676829E+021
//            Math.Pow(4.9, 9.9) = 6.8067718210957060E+006
// Math.Exp(9.9 * Math.Log(4.9)) = 6.8067718210956985E+006

' Example for the Math.Exp( Double ) method.
Module ExpDemo
   
    Sub Main()
        Console.WriteLine( _
            "This example of Math.Exp( Double ) " & _
            "generates the following output." & vbCrLf)
        Console.WriteLine( _
            "Evaluate [e ^ ln(X) == ln(e ^ X) == X] " & _
            "with selected values for X:")

        UseLnExp(0.1)
        UseLnExp(1.2)
        UseLnExp(4.9)
        UseLnExp(9.9)
          
        Console.WriteLine( vbCrLf & _
            "Evaluate these identities with selected values for X and Y:")
        Console.WriteLine("   (e ^ X) * (e ^ Y) = e ^ (X + Y)")
        Console.WriteLine("   (e ^ X) ^ Y = e ^ (X * Y)")
        Console.WriteLine("   X ^ Y = e ^ (Y * ln(X))")
          
        UseTwoArgs(0.1, 1.2)
        UseTwoArgs(1.2, 4.9)
        UseTwoArgs(4.9, 9.9)
    End Sub
       
    ' Evaluate logarithmic/exponential identity with a given argument.
    Sub UseLnExp(arg As Double)

        ' Evaluate e ^ ln(X) = ln(e ^ X) = X.
        Console.WriteLine( _
            vbCrLf & "      Math.Exp(Math.Log({0})) = {1:E16}" + _
            vbCrLf & "      Math.Log(Math.Exp({0})) = {2:E16}", _
            arg, Math.Exp(Math.Log(arg)), Math.Log(Math.Exp(arg)))
    End Sub
       
    ' Evaluate exponential identities that are functions of two arguments.
    Sub UseTwoArgs(argX As Double, argY As Double)

        ' Evaluate (e ^ X) * (e ^ Y) = e ^ (X + Y).
        Console.WriteLine( _
            vbCrLf & "Math.Exp({0}) * Math.Exp({1}) = {2:E16}" + _
            vbCrLf & "          Math.Exp({0} + {1}) = {3:E16}", _
            argX, argY, Math.Exp(argX) * Math.Exp(argY), _
            Math.Exp((argX + argY)))
          
        ' Evaluate (e ^ X) ^ Y = e ^ (X * Y).
        Console.WriteLine( _
            " Math.Pow(Math.Exp({0}), {1}) = {2:E16}" + _
            vbCrLf & "          Math.Exp({0} * {1}) = {3:E16}", _
            argX, argY, Math.Pow(Math.Exp(argX), argY), _
            Math.Exp((argX * argY)))
          
        ' Evaluate X ^ Y = e ^ (Y * ln(X)).
        Console.WriteLine( _
            "           Math.Pow({0}, {1}) = {2:E16}" + _
            vbCrLf & "Math.Exp({1} * Math.Log({0})) = {3:E16}", _
            argX, argY, Math.Pow(argX, argY), _
            Math.Exp((argY * Math.Log(argX))))

    End Sub
End Module 'ExpDemo

' This example of Math.Exp( Double ) generates the following output.
' 
' Evaluate [e ^ ln(X) == ln(e ^ X) == X] with selected values for X:
' 
'       Math.Exp(Math.Log(0.1)) = 1.0000000000000001E-001
'       Math.Log(Math.Exp(0.1)) = 1.0000000000000008E-001
' 
'       Math.Exp(Math.Log(1.2)) = 1.2000000000000000E+000
'       Math.Log(Math.Exp(1.2)) = 1.2000000000000000E+000
' 
'       Math.Exp(Math.Log(4.9)) = 4.9000000000000012E+000
'       Math.Log(Math.Exp(4.9)) = 4.9000000000000004E+000
' 
'       Math.Exp(Math.Log(9.9)) = 9.9000000000000004E+000
'       Math.Log(Math.Exp(9.9)) = 9.9000000000000004E+000
' 
' Evaluate these identities with selected values for X and Y:
'    (e ^ X) * (e ^ Y) = e ^ (X + Y)
'    (e ^ X) ^ Y = e ^ (X * Y)
'    X ^ Y = e ^ (Y * ln(X))
' 
' Math.Exp(0.1) * Math.Exp(1.2) = 3.6692966676192444E+000
'           Math.Exp(0.1 + 1.2) = 3.6692966676192444E+000
'  Math.Pow(Math.Exp(0.1), 1.2) = 1.1274968515793757E+000
'           Math.Exp(0.1 * 1.2) = 1.1274968515793757E+000
'            Math.Pow(0.1, 1.2) = 6.3095734448019331E-002
' Math.Exp(1.2 * Math.Log(0.1)) = 6.3095734448019344E-002
' 
' Math.Exp(1.2) * Math.Exp(4.9) = 4.4585777008251705E+002
'           Math.Exp(1.2 + 4.9) = 4.4585777008251716E+002
'  Math.Pow(Math.Exp(1.2), 4.9) = 3.5780924170885260E+002
'           Math.Exp(1.2 * 4.9) = 3.5780924170885277E+002
'            Math.Pow(1.2, 4.9) = 2.4433636334442981E+000
' Math.Exp(4.9 * Math.Log(1.2)) = 2.4433636334442981E+000
' 
' Math.Exp(4.9) * Math.Exp(9.9) = 2.6764450551890982E+006
'           Math.Exp(4.9 + 9.9) = 2.6764450551891015E+006
'  Math.Pow(Math.Exp(4.9), 9.9) = 1.1684908531676833E+021
'           Math.Exp(4.9 * 9.9) = 1.1684908531676829E+021
'            Math.Pow(4.9, 9.9) = 6.8067718210957060E+006
' Math.Exp(9.9 * Math.Log(4.9)) = 6.8067718210956985E+006

Remarques

e est une constante mathématique dont la valeur est d’environ 2,71828.

Utilisez la Pow méthode pour calculer les puissances d’autres bases.

Exp est l’inverse de Log.

Cette méthode appelle le runtime C sous-jacent, et le résultat exact ou la plage d’entrée valide peut différer d’un système d’exploitation ou d’une architecture à l’autre.

S’applique à

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