| Defined in header <cmath> | ||
|---|---|---|
float erfc( float arg ); | (1) | (since C++11) |
double erfc( double arg ); | (2) | (since C++11) |
long double erfc( long double arg ); | (3) | (since C++11) |
double erfc( Integral 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
#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
| (C++11) | error function (function) |
C documentation for erfc | |
External links
Weisstein, Eric W. "Erfc." From MathWorld--A Wolfram Web Resource.
Please login to continue.