std:: expm1, std:: expm1f, std:: expm1l

Parameters

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.

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 < num .

The additional overloads are not required to be provided exactly as (A) . They only need to be sufficient to ensure that for their argument num of integer type, std :: expm1 ( num ) has the same effect as std :: expm1 ( static_cast < double > ( num ) ) .

Example

#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";
}

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

See also