twopi

 Procedure Abstract Required_Reading Keywords Declarations Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version

#### 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).
```

```     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

```     W.L. Taber      (JPL)
I.M. Underwood  (JPL)
```

#### Version

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

Fixed the description in the detailed output section
`Wed Apr  5 17:47:40 2017`