std::log1p,std::log1pf,std::log1pl (3) - Linux Manuals

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

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