Erf

Defined in header <cmath>.

Description

Computes the error function of num.
​The library provides overloads of std::erf for all cv-unqualified floating-point types as the type of the parameter num (since C++23).

​Additional Overloads are provided for all integer types, which are treated as double.

Declarations

C++23

// 1)
/* floating-point-type */ erf( /* floating-point-type */ num );
// 2)
float erff( float num );
// 3)
long double erfl( long double num );

Additional Overloads

// 4)
template< class Integer >
double erf ( Integer num );

C++11

// 1)
float erf ( float num );
// 2)
double erf ( double num );
//3)
long double erf ( long double num );
// 4)
float erff( float num );
// 5)
long double erfl( long double num );

Additional Overloads

// 6)
template< class Integer >
double erf ( Integer num );

Parameters

​num - floating-point or integer value

Return value

If no errors occur, value of the error function of num, that is , math here , is returned. If a range error occurs due to underflow, the correct result (after rounding), that is math here 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, ±0 is returned If the argument is ±∞, ±1 is returned If the argument is NaN, NaN is returned

Notes

Underflow is guaranteed if |num| < DBL_MIN * (std::sqrt(π)/2)

math here is the probability that a measurement whose errors are subject to a normal distribution with standard deviation σ is less than x away from the mean value. The additional overloads are not required to be provided exactly as Additional Overloads. They only need to be sufficient to ensure that for their argument num of integer type, std::erf(num) has the same effect as std::erf(static_cast<double>(num)).

Examples

#include <cmath>
#include <iomanip>
#include <iostream>
 
double phi(double x1, double x2)
{
    return (std::erf(x2 / std::sqrt(2)) - std::erf(x1 / std::sqrt(2))) / 2;
}
 
int main()
{
    std::cout 
        << "Normal variate probabilities:\n"
        << std::fixed 
        << std::setprecision(2);
    for (int n = -4; n < 4; ++n)
        std::cout 
            << "[" << std::setw(2) 
            << n
            << ":" << std::setw(2) 
            << n + 1 << "]: "
            << std::setw(5) 
            << 100 * phi(n, n + 1) << "%\n";
 
    std::cout 
        << "Special values:\n"
        << "erf(-0) = " 
        << std::erf(-0.0) << '\n'
        << "erf(Inf) = " 
        << std::erf(INFINITY) << '\n';
}

Result

Normal variate probabilities:
[-4:-3]:  0.13%
[-3:-2]:  2.14%
[-2:-1]: 13.59%
[-1: 0]: 34.13%
[ 0: 1]: 34.13%
[ 1: 2]: 13.59%
[ 2: 3]:  2.14%
[ 3: 4]:  0.13%
Special values:
erf(-0) = -0.00
erf(Inf) = 1.00