/*****************************************************************************
*                                                                            *
*   ERFCINV.SPL  Copyright (C) 2001 DSP Development Corporation              *
*                               All Rights Reserved                          *
*                                                                            *
*   Author:      Randy Race                                                  *
*                                                                            *
*   Synopsis:    Returns inverse incomplete error function                   *
*                                                                            *
*   Revisions:    6 Dec 2001  RRR  Creation                                  *
*                                                                            *
*****************************************************************************/

#if @HELP_ERFCINV

    ERFCINV

    Purpose: Returns the inverse incomplete error function

    Syntax:  ERFCINV(y)

                 y - real or series


    Returns: A real or series, the inverse incomplete error function
             x where y = erfc(x) for 0 <= y <= 2 and -inf <= x <= inf.


    Example:
             erfcinv(.2)

             returns 0.90619381, the inverse incomplete error function of 0.2.

             erfc(erfcinv(.2))

             returns 0.2, indicating that ERFC and ERFCINV are inverse
             functions.

    Remarks:
             ERFCINV uses the built-in INVPROBN function to find the Z value
             for a given a probability value of a normal distribution.

             erfc(erfcinv(x)) == x

             erfcinv(x) == -invprobn(x/2) / sqrt(2)

    See Also:
             Erf
             Erfc
             Erfinv
             Invprobn
             Probn
#endif



/* inverse incomplete error function */
erfcinv(x)
{
        /* use inverse normal CDF */
        return(-invprobn(x / 2) / sqrt(2));
}