erf, erff, erfl

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

arg

2

√π

arg
0e^-t2t

2*arg

√π

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

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 (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 (p: 335-337)
• F.9.5.1 The erf functions (p: 462)

See also

erfcerfcferfcl (C99)(C99)(C99)

computes complementary error function (function)

External links

Weisstein, Eric W. "Erf."

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