Math.Exp(Double) Metoda

Reference

Definice

Obor názvů:: System

Sestavení:: System.Runtime.Extensions.dll

Sestavení:: System.Runtime.dll

Sestavení:: mscorlib.dll

Sestavení:: netstandard.dll

Zdroj:: Math.cs

Zdroj:: Math.cs

Zdroj:: Math.cs

Důležité

Některé informace platí pro předběžně vydaný produkt, který se může zásadně změnit, než ho výrobce nebo autor vydá. Microsoft neposkytuje žádné záruky, výslovné ani předpokládané, týkající se zde uváděných informací.

Vrátí hodnotu e zvýšenou na zadanou mocninu.

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

Parametry

d: Double

Číslo určující mocninu.

Návraty

Double

Číslo e zvýšené na mocninu d. Pokud d se rovná hodnotě NaN nebo PositiveInfinity, vrátí se tato hodnota. Pokud d je hodnota rovna NegativeInfinity, vrátí se hodnota 0.

Příklady

Následující příklad používá Exp k vyhodnocení určitých exponenciálních a logaritmických identit pro vybrané hodnoty.

// 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

Poznámky

e je matematická konstanta, jejíž hodnota je přibližně 2,71828.

Pow Pomocí metody můžete vypočítat mocniny jiných bází.

Exp je inverzní hodnota k Log.

Tato metoda volá základní modul runtime jazyka C a přesný výsledek nebo platný rozsah vstupu se může v různých operačních systémech nebo architekturách lišit.

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