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

 

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Defined in header <cmath>
	(1)
float       erfc (float num ); double      erfc (double num ); longdouble erfc (longdouble num );			(until C++23)
/*floating-point-type*/             erfc (/*floating-point-type*/ num );			(since C++23) (constexpr since C++26)
float       erfcf(float num );		(2)	(since C++11) (constexpr since C++26)
longdouble erfcl(longdouble num );		(3)	(since C++11) (constexpr since C++26)
SIMD overload(since C++26)
Defined in header <simd>
template</*math-floating-point*/ V > constexpr/*deduced-simd-t*/<V>             erfc (const V& v_num );		(S)	(since C++26)
Additional overloads(since C++11)
Defined in header <cmath>
template<class Integer > double      erfc ( Integer num );		(A)	(constexpr since C++26)

1-3) Computes the complementary error function of num, that is 1.0-std::erf(num), but without loss of precision for large num. The library provides overloads of std::erfc for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise std::erfc on v_num. (See math-floating-point and deduced-simd-t for their definitions.)

(since C++26)

A) Additional overloads are provided for all integer types, which are treated as double.

(since C++11)

Parameters

num

-

floating-point or integer value

Return value

If no errors occur, value of the complementary error function of num, that is \(\frac{2}{\sqrt{\pi} }\int_{num}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)

2

√π

∫∞
nume^-t2
dt or \({\small 1-\operatorname{erf}(num)}\)1-erf(num), 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 num >26.55.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::erfc(num) has the same effect as std::erfc(static_cast<double>(num)).

Example

Run this code

#include <cmath>#include <iomanip>#include <iostream>   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

erferfferfl (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.