erf(), erfc(), erff(), erfl(), erfcf(), erfcl() — Calculate error and complementary error functions

Standards

Standards / Extensions	C or C++	Dependencies
SAA XPG4 XPG4.2 C99 Single UNIX Specification, Version 3 C++ TR1 C99	both

Format

SAA:

#include <math.h>

double erf(double x);
double erfc(double x);

Compiler option: LANGLVL(EXTENDED), LANGLVL(SAA), or LANGLVL(SAA2)

XPG4:

#define _XOPEN_SOURCE
#include <math.h>

double erf(double x);
double erfc(double x);

C99:

#define _ISOC99_SOURCE
#include <math.h>

float erff(float x);
long double erfl(long double x);
float erfcf(float x);
long double erfcl(long double x)

C++ TR1 C99:

#define _TR1_C99
#include <math.h>

float erf(float x); 
long double erf(long double x); 
float erfc(float x); 
long double erfc(long double x);

General description

Calculates the error and complementary error functions:

Because the erfc() function calculates the value of 1.0 - erf(x), it is used in place of erf() for large values of x.

Note: The following table shows the viable formats for these functions. See IEEE binary floating-point for more information about IEEE Binary Floating-Point.

Function	SPC	Hex	IEEE
erf	X	X	X
erff		X	X
erfl		X	X
erfc	X	X	X
erfcf		X	X
erfcl		X	X

Returned value

Both erf() and erfc() return the calculated value.

If the correct value would cause underflow, 0 is returned and the value of the macro ERANGE is stored in errno. A range error is returned if x is too large.

Special behavior for IEEE: erf() and erfc() are always successful.

Requirements

This function is exposed by specifying on the compile step either the specific option LANGLVL(LONGLONG) or the general option LANGLVL(EXTENDED).

Example

CELEBE01

⁄* CELEBE01                                      
 
  This example uses &erf. and &erfc. to compute the error                      
   function of two numbers.                                                     
                                                                                
 *⁄                                                                             
#include <stdio.h>                                                              
#include <math.h>                                                               
                                                                                
double smallx, largex, value;                                                   
                                                                                
int main(void)                                                                  
{                                                                               
   smallx = 0.1;                                                                
   largex = 10.0;                                                               
                                                                                
   value = erf(smallx);         ⁄* value = 0.112463 *⁄                          
   printf("Error value for 0.1: %f\n", value);                                  
                                                                                
   value = erfc(largex);        ⁄* value = 2.088488e-45 *⁄                      
   printf("Error value for 10.0: %e\n", value);                                 
}

Output

Error value for 0.1: 0.112463
Error value for 10.0: 2.088488e-45