std::expm1,std::expm1f,std::expm1l(3)

NAME
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

See also
   exp
   expf returns e raised to the given power (\({\small e^x}\)e^x)
   expl (function)
   (C++11)
   (C++11)
   exp2
   exp2f
   exp2l returns 2 raised to the given power (\({\small 2^x}\)2^x)
   (C++11) (function)
   (C++11)
   (C++11)
   log1p
   log1pf natural logarithm (to base e) of 1 plus the given number (\({\small
   log1pl \ln{(1+x)} }\)ln(1+x))
   (C++11) (function)
   (C++11)
   (C++11)