std::expm1

Defined in header `<cmath>`
float expm1( float arg );	(1)	(since C++11)
double expm1( double arg );	(2)	(since C++11)
long double expm1( long double arg );	(3)	(since C++11)
double expm1( Integral arg );	(4)	(since C++11)

1-3) Computes the e (Euler's number, 2.7182818) raised to the given power arg, minus 1.0. This function is more accurate than the expression std::exp(arg)-1.0 if arg is close to zero.

4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2) (the argument is cast to double).

Parameters

arg

value of floating-point or Integral type

Return value

If no errors occur earg
-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

Notes

The functions std::expm1 and std::log1p are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)n
-1 can be expressed as std::expm1(n * std::log1p(x)). These functions also simplify writing accurate inverse hyperbolic functions.

For IEEE-compatible type double, overflow is guaranteed if 709.8 < arg.

Example

#include <iostream>
#include <cmath>
#include <cerrno>
#include <cstring>
#include <cfenv>
#pragma STDC FENV_ACCESS ON
int main()
{
    std::cout << "expm1(1) = " << std::expm1(1) << '\n'
              << "Interest earned in 2 days on 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 output:

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

exp	returns e raised to the given power (e^x) (function)
exp2 (C++11)	returns 2 raised to the given power (2^x) (function)
log1p (C++11)	natural logarithm (to base e) of 1 plus the given number (ln(1+x)) (function)
C documentation for `expm1`