ERFCI

This function evaluates the inverse complementary error function.

Function Return Value

ERFCI — Function value. (Output)

Required Arguments

X — Argument for which the function value is desired. (Input)

FORTRAN 90 Interface

Generic: ERFCI (X)

Specific: The specific interface names are S_ERFCI and D_ERFCI.

FORTRAN 77 Interface

Single: ERFCI (X)

Double: The double precision function name is DERFCI.

Description

The function ERFCI(X) computes the inverse of the complementary error function erfc x, defined in ERFC.

The function ERFCI(X) is defined for 0 < x < 2. If xmax < x < 2, then the answer will be less accurate than half precision. Very approximately,

 

Where ɛ = AMACH(4) is the machine precision.

 

Figure 1,  Plot of erfc‑1(x)

Comments

Informational Error

 

Type

Code

Description

3

2

Result of ERFCI(X) is accurate to less than one‑half precision because the argument is too close to 2.0.

Example

In this example, erfc‑1(erfc(1.0)) is computed and printed.

 

USE ERFCI_INT

USE ERFC_INT

USE UMACH_INT

 

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = ERFC(1.0)

VALUE = ERFCI(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' ERFCI(', F6.3, ') = ', F6.3)

END

Output

 

ERFCI( 0.157) = 1.000