| Defined in header <cmath> | ||
|---|---|---|
float erf( float arg ); | (1) | (since C++11) |
double erf( double arg ); | (2) | (since C++11) |
long double erf( long double arg ); | (3) | (since C++11) |
double erf( Integral arg ); | (4) | (since C++11) |
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).
#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
See also
| (C++11) | complementary error function (function) |
C documentation for erf | |
External links
Weisstein, Eric W. "Erf." From MathWorld--A Wolfram Web Resource.
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