Std::erf,std::erff,std::erfl (3) Linux Manual Page

std::erf,std::erff,std::erfl – std::erf,std::erff,std::erfl

Synopsis

Defined in header <cmath>
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

External links

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

std::erf,std::erff,std::erfl (3) Linux Manual Page