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Exp

Defined in header <cmath>.

Description

Computes e (Euler's number, 2.7182818...) raised to the given power num.
The library provides overloads of std::exp for all cv-unqualified floating-point types as the type of the parameter num.

Declarations

// 1)
/* floating-point-type */ exp( /* floating-point-type */ num );
// 2)
float expf( float num );
// 3)
long double expl( long double num );
Additional Overloads
// 4)
template< class Integer >
double exp ( Integer num );

Parameters

num - floating-point or integer value

Return value

If no errors occur, the base-e exponential of num is returned.

If a range error due to overflow occurs, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

If the argument is ±0, 1 is returned If the argument is -∞, +0 is returned If the argument is +∞, +∞ is returned If the argument is NaN, NaN is returned

Notes

For IEEE-compatible type double, overflow is guaranteed if 709.8 < num, and underflow is guaranteed if num < -708.4.

The additional overloads are not required to be provided exactly as Additional Overloads. They only need to be sufficient to ensure that for their argument num of integer type,
std::exp(num) has the same effect as std::exp(static_cast<double>(num)).

Examples

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
#include <iomanip>

// #pragma STDC FENV_ACCESS ON

int main()
{
std::cout
<< "exp(1) = e¹ = "
<< std::setprecision(16) << std::exp(1) << '\n'
<< "FV of $100, continuously compounded at 3% for 1 year = "
<< std::setprecision(6)
<< 100 * std::exp(0.03) << '\n';

// special values
std::cout
<< "exp(-0) = "
<< std::exp(-0.0) << '\n'
<< "exp(-Inf) = "
<< std::exp(-INFINITY) << '\n';

// error handling
errno = 0;
std::feclearexcept(FE_ALL_EXCEPT);

std::cout
<< "exp(710) = "
<< std::exp(710) << '\n';

if (errno == ERANGE)
std::cout
<< "errno == ERANGE: "
<< std::strerror(errno) << '\n';
if (std::fetestexcept(FE_OVERFLOW))
std::cout
<< "FE_OVERFLOW raised\n";
}
Possible Result
exp(1) = e¹ = 2.718281828459045
FV of $100, continuously compounded at 3% for 1 year = 103.045
exp(-0) = 1
exp(-Inf) = 0
exp(710) = inf
errno == ERANGE: Numerical result out of range
FE_OVERFLOW raised

Exp

Defined in header <cmath>.

Description

Computes e (Euler's number, 2.7182818...) raised to the given power num.
The library provides overloads of std::exp for all cv-unqualified floating-point types as the type of the parameter num.

Declarations

// 1)
/* floating-point-type */ exp( /* floating-point-type */ num );
// 2)
float expf( float num );
// 3)
long double expl( long double num );
Additional Overloads
// 4)
template< class Integer >
double exp ( Integer num );

Parameters

num - floating-point or integer value

Return value

If no errors occur, the base-e exponential of num is returned.

If a range error due to overflow occurs, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

If the argument is ±0, 1 is returned If the argument is -∞, +0 is returned If the argument is +∞, +∞ is returned If the argument is NaN, NaN is returned

Notes

For IEEE-compatible type double, overflow is guaranteed if 709.8 < num, and underflow is guaranteed if num < -708.4.

The additional overloads are not required to be provided exactly as Additional Overloads. They only need to be sufficient to ensure that for their argument num of integer type,
std::exp(num) has the same effect as std::exp(static_cast<double>(num)).

Examples

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
#include <iomanip>

// #pragma STDC FENV_ACCESS ON

int main()
{
std::cout
<< "exp(1) = e¹ = "
<< std::setprecision(16) << std::exp(1) << '\n'
<< "FV of $100, continuously compounded at 3% for 1 year = "
<< std::setprecision(6)
<< 100 * std::exp(0.03) << '\n';

// special values
std::cout
<< "exp(-0) = "
<< std::exp(-0.0) << '\n'
<< "exp(-Inf) = "
<< std::exp(-INFINITY) << '\n';

// error handling
errno = 0;
std::feclearexcept(FE_ALL_EXCEPT);

std::cout
<< "exp(710) = "
<< std::exp(710) << '\n';

if (errno == ERANGE)
std::cout
<< "errno == ERANGE: "
<< std::strerror(errno) << '\n';
if (std::fetestexcept(FE_OVERFLOW))
std::cout
<< "FE_OVERFLOW raised\n";
}
Possible Result
exp(1) = e¹ = 2.718281828459045
FV of $100, continuously compounded at 3% for 1 year = 103.045
exp(-0) = 1
exp(-Inf) = 0
exp(710) = inf
errno == ERANGE: Numerical result out of range
FE_OVERFLOW raised