Procedure

     DATANH  ( Double precision arc hyperbolic tangent )

     DOUBLE PRECISION FUNCTION  DATANH ( X )

Abstract

     Return the inverse hyperbolic tangent of a double precision
     argument.

Required_Reading

     None.

Keywords

     HYPERBOLIC
     MATH

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   X

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     X          I   Number whose inverse hyperbolic tangent is
                    desired.

     The function returns the inverse hyperbolic tangent of a double
     precision number.

Detailed_Input

     X        is any double precision.

              X must be within the range -1 < X < +1.

Detailed_Output

     The function returns the inverse hyperbolic tangent of the double
     precision number X.

Parameters

     None.

Exceptions

     1)  If X is not between -1.0 and 1.0, the error
         SPICE(INVALIDARGUMENT) is signaled.

Files

     None.

Particulars

     This function simply implements the definition of the inverse
     hyperbolic tangent as follows:

        DATANH = 0.5D0 * DLOG ( (1+X) / (1-X) )

     If the input value is not valid, an error is signaled.

Examples

     The following table gives a few values for X and the resulting
     value of DATANH.

         X                       DATANH(X)
        ----------------------------------------------
        -0.2000000000000000     -0.2027325540540822
        -0.1000000000000000     -0.1003353477310756
         0.0000000000000000E+00  0.0000000000000000E+00
         0.1000000000000000      0.1003353477310756
         0.2000000000000000      0.2027325540540822
         0.4000000000000000      0.4236489301936018
        0.8000000000000000       1.098612288668110

Restrictions

     1)  The value of the input variable X must be between -1.0 and
         1.0, otherwise an error is signaled.

Literature_References

     [1]  W.H. Beyer, "CRC Standard Mathematical Tables," CRC Press,
          1987.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     H.A. Neilan        (JPL)
     W.M. Owen          (JPL)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.2.0, 17-JUN-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.1.0, 17-MAY-1994 (HAN)

        Set the default function value to either 0, 0.0D0, .FALSE.,
        or blank depending on the type of the function.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 31-JAN-1990 (WMO)