/C

# erf, erff, erfl

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)
1-3) Computes the error function of `arg`.
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
0
e-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)