std:: log1p, std:: log1pf, std:: log1pl

Parameters

Return value

If no errors occur ln(1+num) is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a pole error 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 .

Domain error occurs if num is less than -1 .

Pole error may occur if num is -1 .

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 and FE_DIVBYZERO is raised.
• If the argument is less than -1, NaN is returned and FE_INVALID is raised.
• 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.

The additional overloads are not required to be provided exactly as (A) . They only need to be sufficient to ensure that for their first argument num1 and second argument num2 :

Example

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

log1p(0) = 0
Interest earned in 2 days on $100, compounded daily at 1%
    on a 30/360 calendar = 0.00555563
log(1+1e-16) = 0, but log1p(1e-16) = 1e-16
log1p(-0) = -0
log1p(+Inf) = inf
log1p(-1) = -inf
    errno == ERANGE: Result too large
    FE_DIVBYZERO raised

See also