std::erfc,std::erfcf,std::erfcl (3) Linux Manual Page
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:
See also
erf
erff
erfl error function
(C++11)
(C++11)
(C++11)
External links
Weisstein,_Eric_W._"Erfc." From MathWorld–A Wolfram Web Resource.