std::log1p,std::log1pf,std::log1pl(3)

NAME
std::log1p,std::log1pf,std::log1pl - std::log1p,std::log1pf,std::log1pl

Synopsis
   Defined in header <cmath>
   float log1p ( float arg ); (1) (since C++11)
   float log1pf( float arg );
   double log1p ( double arg ); (2) (since C++11)
   long double log1p ( long double arg ); (3) (since C++11)
   long double log1pl( long double arg );
   double log1p ( IntegralType arg ); (4) (since C++11)
   1-3) Computes the natural (base e) logarithm of 1+arg. This function is more precise
   than the expression std::log(1+arg) 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 ln(1+arg) 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 arg is less than -1.
   Pole error may occur if arg 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.

Example
// Run this code
 #include <iostream>
 #include <cfenv>
 #include <cmath>
 #include <cerrno>
 #include <cstring>
 // #pragma STDC FENV_ACCESS ON
 int main()
 {
     std::cout << "log1p(0) = " << log1p(0) << '\n'
               << "Interest earned in 2 days on 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)
               << " 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";
 }

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

See also
   log
   logf computes natural (base e) logarithm (\({\small \ln{x} }\)ln(x))
   logl (function)
   (C++11)
   (C++11)
   log10
   log10f computes common (base 10) logarithm (\({\small \log_{10}{x} }\)log[10](x))
   log10l (function)
   (C++11)
   (C++11)
   log2
   log2f
   log2l base 2 logarithm of the given number (\({\small \log_{2}{x} }\)log[2](x))
   (C++11) (function)
   (C++11)
   (C++11)
   expm1
   expm1f
   expm1l returns e raised to the given power, minus one (\({\small e^x-1}\)e^x-1)
   (C++11) (function)
   (C++11)
   (C++11)