# std::erf,std::erff,std::erfl (3) - Linux Man Pages

## NAME

std::erf,std::erff,std::erfl - std::erf,std::erff,std::erfl

## Synopsis

float erf ( float arg ); (1) (since C++11)
float erff( float arg );
double erf ( double arg ); (2) (since C++11)
long double erf ( long double arg ); (3) (since C++11)
long double erfl( long double arg );
double erf ( IntegralType arg ); (4) (since C++11)

1-3) Computes the error_function of 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 error function of arg, that is

2

π

∫arg
0e-t2
dt, is returned.

If a range error occurs due to underflow, the correct result (after rounding), that is

2*arg

π

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 |arg| < DBL_MIN*(sqrt(π)/2)
erf(

x
σ

2

) 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.

## Example

The following example calculates the probability that a normal variate is on the interval (x1, x2)
// Run this code

#include <iostream>
#include <cmath>
#include <iomanip>
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';
}

## Output:

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

Weisstein,_Eric_W._"Erf." From MathWorld--A Wolfram Web Resource.