Std::expm1,std::expm1f,std::expm1l (3) Linux Manual Page

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

Synopsis

Defined in header <cmath>
float expm1 ( float arg ); (1) (since C++11)
float expm1f( float arg );
double expm1 ( double arg ); (2) (since C++11)
long double expm1 ( long double arg ); (3) (since C++11)
long double expm1l( long double arg );
double expm1 ( IntegralType 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

// Run this code

#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

std::expm1,std::expm1f,std::expm1l (3) Linux Manual Page