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
\(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)

2
√
π

∫∞
arge^-t2
dt or \({\small 1-\operatorname{erf}(arg)}\)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

See also

erf
erff
erfl error function
(C++11) (function)
(C++11)
(C++11)

External links

Weisstein, Eric W. "Erfc." From MathWorld--A Wolfram Web Resource.