| 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.Parameters
| arg | - | floating point value |
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
#include <stdio.h>
#include <math.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
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)
See also
| (C99)(C99)(C99) | computes complementary error function (function) |
C++ documentation for erf | |
External links
Weisstein, Eric W. "Erf." From MathWorld--A Wolfram Web Resource.
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