std::erfc, std::erfcf, std::erfcl
Defined in header <cmath> |
||
---|---|---|
float erfc ( float arg ); float erfcf( float arg ); |
(1) | (since C++11) |
double erfc ( double arg ); |
(2) | (since C++11) |
long double erfc ( long double arg ); long double erfcl( long double arg ); |
(3) | (since C++11) |
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 ofarg
, that is \(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)
2/√π∫
∞arg e -t2
d t 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
#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)(C++11)(C++11)
|
error function (function) |
C documentation for erfc |
External links
Weisstein, Eric W. "Erfc." From MathWorld--A Wolfram Web Resource.
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