Expm1

Defined in header <cmath>.

Description

Computes the e (Euler's number, 2.7182818...) raised to the given power num, minus 1.0. This function is more accurate than the expression std::exp(num) - 1.0 if num is close to zero. The library provides overloads of std::expm1 for all cv-unqualified floating-point types as the type of the parameter num.

Declarations

C++23

// 1)
/* floating-point-type */ expm1( /* floating-point-type */ num );
// 2)
float expm1f( float num );
// 3)
long double expm1l( long double num );

Additional Overloads

// 4)
template< class Integer >
double expm1 ( Integer num );

C++11

// 1)
float expm1 ( float num );
// 2)
double expm1 ( double num );
// 3)
long double expm1 ( long double num );
// 4)
float expm1f( float num );
// 5)
long double expm1l( long double num );

Additional Overloads

// 6)
template< class Integer >
double expm1 ( Integer num );

Parameters

​num - floating-point or integer value

Return value

If no errors occur e^num -1 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, it is returned, unmodified
• If the argument is -∞, -1 is returned
• If the argument is +∞, +∞ is returned
• If the argument is NaN, NaN is returned

Examples

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
int main()
{
    std::cout 
        << "expm1(1) = " 
        << std::expm1(1) << '\n'
        << "Interest earned in 2 days on $100, compounded daily at 1%\n"
        << "    on a 30/360 calendar = "
        << 100 * std::expm1(2 * std::log1p(0.01 / 360)) << '\n'
        << "exp(1e-16)-1 = " 
        << std::exp(1e-16) - 1
        << ", but expm1(1e-16) = " 
        << std::expm1(1e-16) << '\n';
 
    // special values
    std::cout 
        << "expm1(-0) = " 
        << std::expm1(-0.0) << '\n'
        << "expm1(-Inf) = " 
        << std::expm1(-INFINITY) << '\n';
 
    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout 
        << "expm1(710) = " 
        << std::expm1(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

expm1(1) = 1.71828
Interest earned in 2 days on $100, compounded daily at 1%
    on a 30/360 calendar = 0.00555563
exp(1e-16)-1 = 0, but expm1(1e-16) = 1e-16
expm1(-0) = -0
expm1(-Inf) = -1
expm1(710) = inf
errno == ERANGE: Result too large
FE_OVERFLOW raised