erfc_inverse

Evaluates the real inverse complementary error function erfc-1 (x).

Synopsis

#include <imsl.h>

float imsl_f_erfc_inverse (float x)

The type double function is imsl_d_erfc_inverse.

Required Arguments

float x (Input)
Point at which the inverse complementary error function is to be evaluated. The argument x must be in the range 0 < x < 2.

Return Value

The value of the inverse complementary error function.

Description

The inverse complementary error function y = erfc-1 (x) is such that x = erfc (y) where

 

 

Figure 1,  Plot of erfc-1(x)

Example

Evaluate the inverse complementary error function at x = 1/2.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

float x = 0.5;

float ans;

 

ans = imsl_f_erf_inverse(x);

printf("inverse erf(%f) = %f\n", x, ans);

}

Output

 

inverse erfc(0.500000) = 0.476936

Alert Errors

IMSL_LARGE_ARG_UNDERFLOW	The argument x must not be so large that the result underflows. Very approximately, x should be less than
	where ɛ is the machine precision.

Warning Errors

IMSL_LARGE_ARG_WARN

|x| should be less than where ɛ is the machine precision, to prevent the answer from being less accurate than half precision.

Fatal Errors

IMSL_ERF_ALGORITHM	The algorithm failed to converge.
IMSL_SMALL_ARG_OVERFLOW	The computation of must not overflow.
IMSL_REAL_OUT_OF_RANGE	The function is defined only for 0 < x < 2.