erfc(), erfcf(), erfcl()

Updated: April 19, 2023

Complementary error function

Synopsis:

#include <math.h>

double erfc ( double x );

float erfcf ( float x );

long double erfcl( long double x );

Arguments:

x
The number for which you want to compute the complementary error function.

Library:

libm
The general-purpose math library.
libm-sve
(QNX Neutrino 7.1 or later) A library that optimizes the code for ARMv8.2 chips that have Scalable Vector Extension hardware.

Your system requirements will determine how you should work with these libraries:

Note: Compile your program with the -fno-builtin option to prevent the compiler from using a built-in version of the function.

Description:

The erfc(), erfcf(), and erfcl() functions calculate the complementary error function of x (i.e., the result of the error function, erf(), subtracted from 1.0). This is useful because the error function isn't very accurate when x is large.

The erf() function computes:

This equality is true: erfc(-x) = 2 - erfc(x)

To check for error situations, use feclearexcept() and fetestexcept(). For example:

Returns:

The value of the error function.

If x is: These functions return: Errors:
±0.0 1.0
A value that would cause underflow 0.0 FE_UNDERFLOW
-Inf 2.0
Inf 0.0
NaN NaN

These functions raise FE_INEXACT if the FPU reports that the result can't be exactly represented as a floating-point number.

Classification:

C11, POSIX 1003.1

Safety:  
Cancellation point No
Interrupt handler Yes
Signal handler Yes
Thread Yes