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Showing content from https://en.cppreference.com/w/cpp/algorithm/../ranges/../numeric/math/erfc.html below:

std::erfc, std::erfcf, std::erfcl - cppreference.com

(1) float       erfc ( float num );

double      erfc ( double num );

long double erfc ( long double 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)

long double erfcl( long double num );

(3) (since C++11)
(constexpr since C++26) template< /*math-floating-point*/ V >

constexpr /*deduced-simd-t*/<V>

            erfc ( const V& v_num ); (S) (since C++26)

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)

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

(since C++11) [edit] Parameters num - floating-point or integer value [edit] Return value

If no errors occur, value of the complementary error function of

num

, that is

\(\frac{2}{\sqrt{\pi} }\int_{num}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)∫∞
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.

[edit] Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

[edit] 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)).

[edit] Example 
#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
[edit] See also [edit] External links

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