erf, erff, erfl
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Defined in header
<math.h>
float erff( float arg );
(1)
(since C99)
double erf( double arg );
(2)
(since C99)
long double erfl( long double arg );
(3)
(since C99)
Defined in header
<tgmath.h>
#define erf( arg )
(4)
(since C99)
4) Type-generic macro: If arg has type long double,
erfl is called. Otherwise, if arg has integer type or the type double, erf is called. Otherwise, erff is called.Contents
[edit] Parameters
arg
-
floating-point value
[edit] Return value
If no errors occur, value of the error function of arg, that is \(\frac{2}{\sqrt{\pi} }\int_{0}^{arg}{e^{-{t^2} }\mathsf{d}t}\) 2
√π
∫arg0e-t2
dt, is returned. If a range error occurs due to underflow, the correct result (after rounding), that is \(\frac{2\cdot arg}{\sqrt{\pi} }\)
2*arg
√π
, is returned.
[edit] 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
[edit] Notes
Underflow is guaranteed if |arg| < DBL_MIN *(sqrt (π)/2).
\(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)erf( x
σ√2
) is the probability that a measurement whose errors are subject to a normal distribution with standard deviation \(\sigma\)σ is less than \(x\)x away from the mean value.
[edit] Example
Run this code
#include <math.h> #include <stdio.h> double phi(double x1, double x2) { return (erf(x2 / sqrt (2)) - erf(x1 / sqrt (2))) / 2; } int main(void) { puts ("normal variate probabilities:"); for (int n = -4; n < 4; ++n) printf ("[%2d:%2d]: %5.2f%%\n", n, n + 1, 100 * phi(n, n + 1)); puts ("special values:"); printf ("erf(-0) = %f\n", erf(-0.0)); printf ("erf(Inf) = %f\n", erf(INFINITY)); }
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) = -0.000000 erf(Inf) = 1.000000
[edit] References
- C11 standard (ISO/IEC 9899:2011):
- 7.12.8.1 The erf functions (p: 249)
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- F.10.5.1 The erf functions (p: 525)
- C99 standard (ISO/IEC 9899:1999):
- 7.12.8.1 The erf functions (p: 230)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- F.9.5.1 The erf functions (p: 462)
[edit] See also
C++ documentation for erf
[edit] External links
Weisstein, Eric W. "Erf." From MathWorld — A Wolfram Web Resource.