std::erf, std::erff, std::erfl
Defined in header <cmath> |
||
---|---|---|
float erf ( float arg ); float erff( float arg ); |
(1) | (since C++11) |
double erf ( double arg ); |
(2) | (since C++11) |
long double erf ( long double arg ); long double erfl( long double arg ); |
(3) | (since C++11) |
double erf ( IntegralType 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 ofarg
, that is \(\frac{2}{\sqrt{\pi} }\int_{0}^{arg}{e^{-{t^2} }\mathsf{d}t}\)
2/√π∫
arg0 e -t2
d t, is returned.
If a range error occurs due to underflow, the correct result (after rounding), that is \(\frac{2\cdot arg}{\sqrt{\pi} }\).
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)
\(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)erf(
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)(C++11)(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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