Procedure

     TWOPI ( Twice the value of pi )

     DOUBLE PRECISION FUNCTION TWOPI ( )

Abstract

     Return twice the value of pi (the ratio of the circumference of
     a circle to its diameter).

Required_Reading

     None.

Keywords

     CONSTANTS

Declarations

    None.

Brief_I/O

     The function returns twice the value of pi.

Detailed_Input

     None.

Detailed_Output

     The function returns twice the value of pi (the ratio of
     a circle's circumference to its diameter), determined by
     the ACOS function. That is,

           TWOPI = ACOS ( -1.D0 ) * 2.D0

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     The first time the function is referenced, the value is computed
     as shown above. The value is saved, and returned directly upon
     subsequent reference.

Examples

     The code fragment below illustrates the use of TWOPI.

        C
        C      The longitude of the ascending node is the angle
        C      between the x-axis and the node vector, n.
        C                                              -
        C
               NODE = ACOS ( N(1) / VNORM(N) )

               IF ( NODE .LT. 0.D0 ) THEN
                  NODE = NODE + TWOPI()
               END IF

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)
     I.M. Underwood     (JPL)

Version

    SPICELIB Version 1.0.3, 07-JUL-2020 (JDR)

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.0.2, 28-AUG-1997 (WLT)

        Fixed the description in the detailed output section
        of the header.

    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 (WLT) (IMU)