std::erfc,std::erfcf,std::erfcl (3) - Linux Manuals

std::erfc,std::erfcf,std::erfcl: std::erfc,std::erfcf,std::erfcl

NAME

std::erfc,std::erfcf,std::erfcl - std::erfc,std::erfcf,std::erfcl

Synopsis

Defined in header <cmath>
float erfc ( float arg ); (1) (since C++11)
float erfcf( float arg );
double erfc ( double arg ); (2) (since C++11)
long double erfc ( long double arg ); (3) (since C++11)
long double erfcl( long double arg );
double erfc ( IntegralType arg ); (4) (since C++11)

1-3) Computes the complementary_error_function of arg, that is 1.0-erf(arg), but without loss of precision for large arg
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 a floating-point or Integral_type

Return value

If no errors occur, value of the complementary error function of arg, that is

2

√
π

∫∞
arge-t2
dt or 1-erf(arg), 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 is returned
* If the argument is -∞, 2 is returned
* If the argument is NaN, NaN is returned

Notes

For the IEEE-compatible type double, underflow is guaranteed if arg > 26.55.

Example

// Run this code

  #include <iostream>
  #include <cmath>
  #include <iomanip>
  double normalCDF(double x) // Phi(-∞, x) aka N(x)
  {
      return std::erfc(-x/std::sqrt(2))/2;
  }
  int main()
  {
      std::cout << "normal cumulative distribution function:\n"
                << std::fixed << std::setprecision(2);
      for(double n=0; n<1; n+=0.1)
          std::cout << "normalCDF(" << n << ") " << 100*normalCDF(n) << "%\n";

      std::cout << "special values:\n"
                << "erfc(-Inf) = " << std::erfc(-INFINITY) << '\n'
                << "erfc(Inf) = " << std::erfc(INFINITY) << '\n';
  }

Output:

  normal cumulative distribution function:
  normalCDF(0.00) 50.00%
  normalCDF(0.10) 53.98%
  normalCDF(0.20) 57.93%
  normalCDF(0.30) 61.79%
  normalCDF(0.40) 65.54%
  normalCDF(0.50) 69.15%
  normalCDF(0.60) 72.57%
  normalCDF(0.70) 75.80%
  normalCDF(0.80) 78.81%
  normalCDF(0.90) 81.59%
  normalCDF(1.00) 84.13%
  special values:
  erfc(-Inf) = 2.00
  erfc(Inf) = 0.00

External links

Weisstein,_Eric_W._"Erfc." From MathWorld--A Wolfram Web Resource.