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 ε = AMACH(4) is the machine precision.

Figure 5- 4 Plot of erf⁻¹(x)

Comments

Informational error

Type Code

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

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