update ast 8.6.2

1 files changed, 0 insertions, 3218 deletions

diff --git a/ast/pcdmap.c b/ast/pcdmap.c
deleted file mode 100644
index 7c043d6..0000000
--- a/ast/pcdmap.c
+++ /dev/null
@@ -1,3218 +0,0 @@
-/*
-*class++
-*  Name:
-*     PcdMap
-
-*  Purpose:
-*     Apply 2-dimensional pincushion/barrel distortion.
-
-*  Constructor Function:
-c     astPcdMap
-f     AST_PCDMAP
-
-*  Description:
-*     A PcdMap is a non-linear Mapping which transforms 2-dimensional
-*     positions to correct for the radial distortion introduced by some
-*     cameras and telescopes. This can take the form either of pincushion
-*     or barrel distortion, and is characterized by a single distortion
-*     coefficient.
-*
-*     A PcdMap is specified by giving this distortion coefficient and the
-*     coordinates of the centre of the radial distortion. The forward
-*     transformation of a PcdMap applies the distortion:
-*
-*        RD = R * ( 1 + C * R * R )
-*
-*     where R is the undistorted radial distance from the distortion
-*     centre (specified by attribute PcdCen), RD is the radial distance
-*     from the same centre in the presence of distortion, and C is the
-*     distortion coefficient (given by attribute Disco).
-*
-*     The inverse transformation of a PcdMap removes the distortion
-*     produced by the forward transformation. The expression used to derive
-*     R from RD is an approximate inverse of the expression above.
-
-*  Inheritance:
-*     The PcdMap class inherits from the Mapping class.
-
-*  Attributes:
-*     In addition to those attributes common to all Mappings, every
-*     PcdMap also has the following attributes:
-*
-*     - Disco: PcdMap pincushion/barrel distortion coefficient
-*     - PcdCen(axis): Centre coordinates of pincushion/barrel distortion
-
-*  Functions:
-c     The PcdMap class does not define any new functions beyond those
-f     The PcdMap class does not define any new routines beyond those
-*     which are applicable to all Mappings.
-
-*  Copyright:
-*     Copyright (C) 1997-2006 Council for the Central Laboratory of the
-*     Research Councils
-
-*  Licence:
-*     This program is free software: you can redistribute it and/or
-*     modify it under the terms of the GNU Lesser General Public
-*     License as published by the Free Software Foundation, either
-*     version 3 of the License, or (at your option) any later
-*     version.
-*
-*     This program is distributed in the hope that it will be useful,
-*     but WITHOUT ANY WARRANTY; without even the implied warranty of
-*     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-*     GNU Lesser General Public License for more details.
-*
-*     You should have received a copy of the GNU Lesser General
-*     License along with this program.  If not, see
-*     <http://www.gnu.org/licenses/>.
-
-*  Authors:
-*     DSB: David Berry (Starlink)
-
-*  History:
-*     18-MAY-1999 (DSB):
-*        Original version.
-*     25-OCT-1999 (DSB):
-*        Fixed memory leak in MapMerge.
-*     8-JAN-2003 (DSB):
-*        Changed private InitVtab method to protected astInitPcdMapVtab
-*        method.
-*     23-AUG-2006 (DSB):
-*        Override astEqual.
-*     23-APR-2015 (DSB):
-*        Improve MapMerge. If a PcdMap can merge with its next-but-one
-*        neighbour, then swap the PcdMap with its neighbour, so that
-*        it is then next its next-but-one neighbour, and then merge the
-*        two Mappings into a single Mapping. Previously, only the swap
-*        was performed - not the merger. And the swap was only performed
-*        if the intervening neighbour could not itself merge. This could
-*        result in an infinite simplification loop, which was detected by
-*        CmpMap and and aborted, resulting in no useful simplification.
-*class--
-*/
-
-/* Module Macros. */
-/* ============== */
-/* Set the name of the class we are implementing. This indicates to
-   the header files that define class interfaces that they should make
-   "protected" symbols available. */
-#define astCLASS PcdMap
-
-/* Include files. */
-/* ============== */
-/* Interface definitions. */
-/* ---------------------- */
-
-#include "globals.h"             /* Thread-safe global data access */
-#include "error.h"               /* Error reporting facilities */
-#include "memory.h"              /* Memory management facilities */
-#include "globals.h"             /* Thread-safe global data access */
-#include "object.h"              /* Base Object class */
-#include "pointset.h"            /* Sets of points/coordinates */
-#include "unitmap.h"             /* Unit mappings */
-#include "zoommap.h"             /* Zoom mappings */
-#include "permmap.h"             /* Axis permutations */
-#include "mapping.h"             /* Coordinate mappings (parent class) */
-#include "channel.h"             /* I/O channels */
-#include "pcdmap.h"              /* Interface definition for this class */
-
-/* Error code definitions. */
-/* ----------------------- */
-#include "ast_err.h"             /* AST error codes */
-
-/* C header files. */
-/* --------------- */
-#include <float.h>
-#include <math.h>
-#include <stdarg.h>
-#include <stddef.h>
-#include <stdio.h>
-#include <string.h>
-
-/* Module Variables. */
-/* ================= */
-
-/* Address of this static variable is used as a unique identifier for
-   member of this class. */
-static int class_check;
-
-/* Pointers to parent class methods which are extended by this class. */
-static AstPointSet *(* parent_transform)( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
-static const char *(* parent_getattrib)( AstObject *, const char *, int * );
-static int (* parent_testattrib)( AstObject *, const char *, int * );
-static void (* parent_clearattrib)( AstObject *, const char *, int * );
-static void (* parent_setattrib)( AstObject *, const char *, int * );
-
-/* Define macros for accessing each item of thread specific global data. */
-#ifdef THREAD_SAFE
-
-/* Define how to initialise thread-specific globals. */
-#define GLOBAL_inits \
-   globals->Class_Init = 0; \
-   globals->GetAttrib_Buff[ 0 ] = 0;
-
-/* Create the function that initialises global data for this module. */
-astMAKE_INITGLOBALS(PcdMap)
-
-/* Define macros for accessing each item of thread specific global data. */
-#define class_init astGLOBAL(PcdMap,Class_Init)
-#define class_vtab astGLOBAL(PcdMap,Class_Vtab)
-#define getattrib_buff astGLOBAL(PcdMap,GetAttrib_Buff)
-
-
-
-/* If thread safety is not needed, declare and initialise globals at static
-   variables. */
-#else
-
-static char getattrib_buff[ 101 ];
-
-
-/* Define the class virtual function table and its initialisation flag
-   as static variables. */
-static AstPcdMapVtab class_vtab;   /* Virtual function table */
-static int class_init = 0;       /* Virtual function table initialised? */
-
-#endif
-
-/* External Interface Function Prototypes. */
-/* ======================================= */
-/* The following functions have public prototypes only (i.e. no
-   protected prototypes), so we must provide local prototypes for use
-   within this module. */
-AstPcdMap *astPcdMapId_( double, const double [2], const char *, ... );
-
-/* Prototypes for Private Member Functions. */
-/* ======================================== */
-
-static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
-static const char *GetAttrib( AstObject *, const char *, int * );
-static double GetDisco( AstPcdMap *, int * );
-static double GetPcdCen( AstPcdMap *, int, int * );
-static int CanMerge( AstMapping *, AstMapping *, int, int, int * );
-static int CanSwap( AstMapping *, AstMapping *, int, int, int * );
-static int Equal( AstObject *, AstObject *, int * );
-static int MapMerge( AstMapping *, int, int, int *, AstMapping ***, int **, int * );
-static int TestAttrib( AstObject *, const char *, int * );
-static int TestDisco( AstPcdMap *, int * );
-static int TestPcdCen( AstPcdMap *, int, int * );
-static void ClearAttrib( AstObject *, const char *, int * );
-static void ClearDisco( AstPcdMap *, int * );
-static void ClearPcdCen( AstPcdMap *, int, int * );
-static void Dump( AstObject *, AstChannel *, int * );
-static void PcdPerm( AstMapping **, int *, int, int * );
-static void PcdZoom( AstMapping **, int *, int, int * );
-static void PermGet( AstPermMap *, int **, int **, double **, int * );
-static void SetAttrib( AstObject *, const char *, int * );
-static void SetDisco( AstPcdMap *, double, int * );
-static void SetPcdCen( AstPcdMap *, int, double, int * );
-
-/* Function Macros */
-/* =============== */
-/* Macros which return the maximum and minimum of two values. */
-#define MAX(aa,bb) ((aa)>(bb)?(aa):(bb))
-#define MIN(aa,bb) ((aa)<(bb)?(aa):(bb))
-
-/* Macro to check for equality of floating point values. We cannot
-compare bad values directory because of the danger of floating point
-exceptions, so bad values are dealt with explicitly. */
-#define EQUAL(aa,bb) (((aa)==AST__BAD)?(((bb)==AST__BAD)?1:0):(((bb)==AST__BAD)?0:(fabs((aa)-(bb))<=1.0E5*MAX((fabs(aa)+fabs(bb))*DBL_EPSILON,DBL_MIN))))
-
-/*
-*
-*  Name:
-*     MAKE_CLEAR
-
-*  Purpose:
-*     Implement a method to clear a single value in a multi-valued attribute.
-
-*  Type:
-*     Private macro.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     MAKE_CLEAR(attr,component,assign,nval)
-
-*  Class Membership:
-*     Defined by the PcdMap class.
-
-*  Description:
-*     This macro expands to an implementation of a private member function of
-*     the form:
-*
-*        static void Clear<Attribute>( AstPcdMap *this, int axis )
-*
-*     and an external interface function of the form:
-*
-*        void astClear<Attribute>_( AstPcdMap *this, int axis )
-*
-*     which implement a method for clearing a single value in a specified
-*     multi-valued attribute for an axis of a PcdMap.
-
-*  Parameters:
-*     attr
-*        The name of the attribute to be cleared, as it appears in the function
-*        name (e.g. PcdCen in "astClearPcdCen").
-*     component
-*        The name of the class structure component that holds the attribute
-*        value.
-*     assign
-*        An expression that evaluates to the value to assign to the component
-*        to clear its value.
-*     nval
-*        Specifies the number of values in the multi-valued attribute. The
-*        "axis" values supplied to the created function should be in the
-*        range zero to (nval - 1).
-
-*  Notes:
-*     -  To avoid problems with some compilers, you should not leave any white
-*     space around the macro arguments.
-*
-*/
-
-/* Define the macro. */
-#define MAKE_CLEAR(attr,component,assign,nval) \
-\
-/* Private member function. */ \
-/* ------------------------ */ \
-static void Clear##attr( AstPcdMap *this, int axis, int *status ) { \
-\
-/* Check the global error status. */ \
-   if ( !astOK ) return; \
-\
-/* Validate the axis index. */ \
-   if( axis < 0 || axis >= nval ){ \
-      astError( AST__AXIIN, "%s(%s): Index (%d) is invalid for attribute " \
-                #attr " - it should be in the range 1 to %d.", status, \
-                "astClear" #attr, astGetClass( this ), \
-                axis + 1, nval ); \
-\
-/* Report an error if the object has been cloned (i.e. has a reference \
-   count that is greater than one). */ \
-   } else if( astGetRefCount( this ) > 1 ) { \
-      astError( AST__IMMUT, "astClear(%s): The " #attr "attribute of " \
-                "the supplied %s cannot be cleared because the %s has " \
-                "been cloned (programming error).", status, \
-                astGetClass(this), astGetClass(this), astGetClass(this) ); \
-\
-/* Assign the "clear" value. */ \
-   } else { \
-      this->component[ axis ] = (assign); \
-   } \
-} \
-\
-/* External interface. */ \
-/* ------------------- */ \
-void astClear##attr##_( AstPcdMap *this, int axis, int *status ) { \
-\
-/* Check the global error status. */ \
-   if ( !astOK ) return; \
-\
-/* Invoke the required method via the virtual function table. */ \
-   (**astMEMBER(this,PcdMap,Clear##attr))( this, axis, status ); \
-}
-
-
-/*
-*
-*  Name:
-*     MAKE_GET
-
-*  Purpose:
-*     Implement a method to get a single value in a multi-valued attribute.
-
-*  Type:
-*     Private macro.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     MAKE_GET(attr,type,bad_value,assign,nval)
-
-*  Class Membership:
-*     Defined by the PcdMap class.
-
-*  Description:
-*     This macro expands to an implementation of a private member function of
-*     the form:
-*
-*        static <Type> Get<Attribute>( AstPcdMap *this, int axis )
-*
-*     and an external interface function of the form:
-*
-*        <Type> astGet<Attribute>_( AstPcdMap *this, int axis )
-*
-*     which implement a method for getting a single value from a specified
-*     multi-valued attribute for an axis of a PcdMap.
-
-*  Parameters:
-*     attr
-*        The name of the attribute whose value is to be obtained, as it
-*        appears in the function name (e.g. PcdCen in "astGetPcdCen").
-*     type
-*        The C type of the attribute.
-*     bad_value
-*        A constant value to return if the global error status is set, or if
-*        the function fails.
-*     assign
-*        An expression that evaluates to the value to be returned. This can
-*        use the string "axis" to represent the zero-based value index.
-*     nval
-*        Specifies the number of values in the multi-valued attribute. The
-*        "axis" values supplied to the created function should be in the
-*        range zero to (nval - 1).
-
-*  Notes:
-*     -  To avoid problems with some compilers, you should not leave any white
-*     space around the macro arguments.
-*
-*/
-
-/* Define the macro. */
-#define MAKE_GET(attr,type,bad_value,assign,nval) \
-\
-/* Private member function. */ \
-/* ------------------------ */ \
-static type Get##attr( AstPcdMap *this, int axis, int *status ) { \
-   type result;                  /* Result to be returned */ \
-\
-/* Initialise */ \
-   result = (bad_value); \
-\
-/* Check the global error status. */ \
-   if ( !astOK ) return result; \
-\
-/* Validate the axis index. */ \
-   if( axis < 0 || axis >= nval ){ \
-      astError( AST__AXIIN, "%s(%s): Index (%d) is invalid for attribute " \
-                #attr " - it should be in the range 1 to %d.", status, \
-                "astGet" #attr, astGetClass( this ), \
-                axis + 1, nval ); \
-\
-/* Assign the result value. */ \
-   } else { \
-      result = (assign); \
-   } \
-\
-/* Check for errors and clear the result if necessary. */ \
-   if ( !astOK ) result = (bad_value); \
-\
-/* Return the result. */ \
-   return result; \
-} \
-/* External interface. */ \
-/* ------------------- */  \
-type astGet##attr##_( AstPcdMap *this, int axis, int *status ) { \
-\
-/* Check the global error status. */ \
-   if ( !astOK ) return (bad_value); \
-\
-/* Invoke the required method via the virtual function table. */ \
-   return (**astMEMBER(this,PcdMap,Get##attr))( this, axis, status ); \
-}
-
-/*
-*
-*  Name:
-*     MAKE_SET
-
-*  Purpose:
-*     Implement a method to set a single value in a multi-valued attribute.
-
-*  Type:
-*     Private macro.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     MAKE_SET(attr,type,component,assign,nval)
-
-*  Class Membership:
-*     Defined by the PcdMap class.
-
-*  Description:
-*     This macro expands to an implementation of a private member function of
-*     the form:
-*
-*        static void Set<Attribute>( AstPcdMap *this, int axis, <Type> value )
-*
-*     and an external interface function of the form:
-*
-*        void astSet<Attribute>_( AstPcdMap *this, int axis, <Type> value )
-*
-*     which implement a method for setting a single value in a specified
-*     multi-valued attribute for a PcdMap.
-
-*  Parameters:
-*      attr
-*         The name of the attribute to be set, as it appears in the function
-*         name (e.g. PcdCen in "astSetPcdCen").
-*      type
-*         The C type of the attribute.
-*      component
-*         The name of the class structure component that holds the attribute
-*         value.
-*      assign
-*         An expression that evaluates to the value to be assigned to the
-*         component.
-*      nval
-*         Specifies the number of values in the multi-valued attribute. The
-*         "axis" values supplied to the created function should be in the
-*         range zero to (nval - 1).
-
-*  Notes:
-*     -  To avoid problems with some compilers, you should not leave any white
-*     space around the macro arguments.
-*-
-*/
-
-/* Define the macro. */
-#define MAKE_SET(attr,type,component,assign,nval) \
-\
-/* Private member function. */ \
-/* ------------------------ */ \
-static void Set##attr( AstPcdMap *this, int axis, type value, int *status ) { \
-\
-/* Check the global error status. */ \
-   if ( !astOK ) return; \
-\
-/* Validate the axis index. */ \
-   if( axis < 0 || axis >= nval ){ \
-      astError( AST__AXIIN, "%s(%s): Index (%d) is invalid for attribute " \
-                #attr " - it should be in the range 1 to %d.", status, \
-                "astSet" #attr, astGetClass( this ), \
-                axis + 1, nval ); \
-\
-/* Report an error if the object has been cloned (i.e. has a reference \
-   count that is greater than one). */ \
-   } else if( astGetRefCount( this ) > 1 ) { \
-      astError( AST__IMMUT, "astSet(%s): The " #attr "attribute of " \
-                "the supplied %s cannot be changed because the %s has " \
-                "been cloned (programming error).", status, \
-                astGetClass(this), astGetClass(this), astGetClass(this) ); \
-\
-/* Store the new value in the structure component. */ \
-   } else { \
-      this->component[ axis ] = (assign); \
-   } \
-} \
-\
-/* External interface. */ \
-/* ------------------- */ \
-void astSet##attr##_( AstPcdMap *this, int axis, type value, int *status ) { \
-\
-/* Check the global error status. */ \
-   if ( !astOK ) return; \
-\
-/* Invoke the required method via the virtual function table. */ \
-   (**astMEMBER(this,PcdMap,Set##attr))( this, axis, value, status ); \
-}
-
-/*
-*
-*  Name:
-*     MAKE_TEST
-
-*  Purpose:
-*     Implement a method to test if a single value has been set in a
-*     multi-valued attribute.
-
-*  Type:
-*     Private macro.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     MAKE_TEST(attr,assign,nval)
-
-*  Class Membership:
-*     Defined by the PcdMap class.
-
-*  Description:
-*     This macro expands to an implementation of a private member function of
-*     the form:
-*
-*        static int Test<Attribute>( AstPcdMap *this, int axis )
-*
-*     and an external interface function of the form:
-*
-*        int astTest<Attribute>_( AstPcdMap *this, int axis )
-*
-*     which implement a method for testing if a single value in a specified
-*     multi-valued attribute has been set for a class.
-
-*  Parameters:
-*      attr
-*         The name of the attribute to be tested, as it appears in the function
-*         name (e.g. PcdCen in "astTestPcdCen").
-*      assign
-*         An expression that evaluates to 0 or 1, to be used as the returned
-*         value. This can use the string "axis" to represent the zero-based
-*         index of the value within the attribute.
-*      nval
-*         Specifies the number of values in the multi-valued attribute. The
-*         "axis" values supplied to the created function should be in the
-*         range zero to (nval - 1).
-
-*  Notes:
-*     -  To avoid problems with some compilers, you should not leave any white
-*     space around the macro arguments.
-*-
-*/
-
-/* Define the macro. */
-#define MAKE_TEST(attr,assign,nval) \
-\
-/* Private member function. */ \
-/* ------------------------ */ \
-static int Test##attr( AstPcdMap *this, int axis, int *status ) { \
-   int result;                   /* Value to return */ \
-\
-/* Initialise */ \
-   result = 0; \
-\
-/* Check the global error status. */ \
-   if ( !astOK ) return result; \
-\
-\
-/* Validate the axis index. */ \
-   if( axis < 0 || axis >= nval ){ \
-      astError( AST__AXIIN, "%s(%s): Index (%d) is invalid for attribute " \
-                #attr " - it should be in the range 1 to %d.", status, \
-                "astTest" #attr, astGetClass( this ), \
-                axis + 1, nval ); \
-\
-/* Assign the result value. */ \
-   } else { \
-      result = (assign); \
-   } \
-\
-/* Check for errors and clear the result if necessary. */ \
-   if ( !astOK ) result = 0; \
-\
-/* Return the result. */ \
-   return result; \
-} \
-/* External interface. */ \
-/* ------------------- */ \
-int astTest##attr##_( AstPcdMap *this, int axis, int *status ) { \
-\
-/* Check the global error status. */ \
-   if ( !astOK ) return 0; \
-\
-/* Invoke the required method via the virtual function table. */ \
-   return (**astMEMBER(this,PcdMap,Test##attr))( this, axis, status ); \
-}
-
-/* Member functions. */
-/* ================= */
-static int CanMerge( AstMapping *map1, AstMapping *map2, int inv1, int inv2, int *status ){
-/*
-*
-*  Name:
-*     CanMerge
-
-*  Purpose:
-*     Checks if two Mappings can be merged.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     int CanMerge( AstMapping *map1, AstMapping *map2, int inv1, int inv2, int *status )
-
-*  Class Membership:
-*     PcdMap internal utility function.
-
-*  Description:
-*     This function checks the two supplied Mappings to see if they
-*     can be merged into a single Mapping. One of the pair must be a PcdMap.
-
-*  Parameters:
-*     map1
-*        A pointer to the first mapping.
-*     map2
-*        A pointer to the second mapping.
-*     inv1
-*        The invert flag to use with the first mapping.
-*     inv2
-*        The invert flag to use with the second mapping.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     1 if the Mappings can be merged, zero otherwise.
-
-*/
-
-   AstPcdMap  *pcd;          /* Pointer to PcdMap Mapping */
-   AstPcdMap  *pcd2;         /* Pointer to second PcdMap Mapping */
-   AstMapping *nopcd;        /* Pointer to non-PcdMap Mapping */
-   const char *class1;       /* Pointer to map1 class string */
-   const char *class2;       /* Pointer to map2 class string */
-   const char *nopcd_class;  /* Pointer to non-PcdMap class string */
-   int invert[ 2 ];          /* Original invert flags */
-   int ret;                  /* Returned flag */
-
-/* Check the global error status. */
-   if ( !astOK ) return 0;
-
-/* Initialise */
-   ret = 0;
-   pcd = NULL;
-   nopcd = NULL;
-
-/* Temporarily set the Invert attributes of both Mappings to the supplied
-   values. */
-   invert[ 0 ] = astGetInvert( map1 );
-   astSetInvert( map1, inv1 );
-
-   invert[ 1 ] = astGetInvert( map2 );
-   astSetInvert( map2, inv2 );
-
-/* Get the classes of the two mappings. */
-   class1 = astGetClass( map1 );
-   class2 = astGetClass( map2 );
-   if( astOK ){
-
-/* Get pointers to the PcdMap and the non-PcdMap Mapping. */
-      if( !strcmp( class1, "PcdMap" ) ){
-         pcd = (AstPcdMap * ) map1;
-         nopcd = map2;
-         nopcd_class = class2;
-      } else if( !strcmp( class2, "PcdMap" ) ){
-         nopcd = map1;
-         pcd = (AstPcdMap * ) map2;
-         nopcd_class = class1;
-      } else {
-         nopcd_class = "unusable";
-      }
-
-/* The Mappings can merge if the other Mapping is a UnitMap. */
-      if( !strcmp( nopcd_class, "UnitMap" ) ){
-         ret = 1;
-
-/* They can also merge if the other Mapping is also a PcdMap, and is the
-   invert of the other. */
-      } else if( !strcmp( nopcd_class, "PcdMap" ) ){
-         pcd2 = (AstPcdMap *) nopcd;
-
-/* Check the distortion coefficients are equal. */
-         if( EQUAL( astGetDisco( pcd ), astGetDisco( pcd2 ) ) ){
-
-/* Check the axis 0 centres are equal. */
-            if( EQUAL( astGetPcdCen( pcd, 0 ), astGetPcdCen( pcd2, 0 ) ) ){
-
-/* Check the axis 1 centres are equal. */
-               if( EQUAL( astGetPcdCen( pcd, 1 ), astGetPcdCen( pcd2, 1 ) ) ){
-
-/* Check the Invert flags are different. */
-                  if( astGetInvert( pcd ) != astGetInvert( pcd2 ) ){
-
-/* If the Mappings have passed all these tests, they can be merged. */
-                     ret = 1;
-                  }
-               }
-            }
-         }
-      }
-   }
-
-/* Re-instate the original settings of the Invert attributes for the
-   supplied Mappings. */
-   astSetInvert( map1, invert[ 0 ] );
-   astSetInvert( map2, invert[ 1 ] );
-
-/* Return the answer. */
-   return astOK ? ret : 0;
-}
-
-static int CanSwap( AstMapping *map1, AstMapping *map2, int inv1, int inv2, int *status ){
-/*
-*  Name:
-*     CanSwap
-
-*  Purpose:
-*     Determine if two Mappings could be swapped.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     int CanSwap( AstMapping *map1, AstMapping *map2, int inv1, int inv2, int *status )
-
-*  Class Membership:
-*     PcdMap member function
-
-*  Description:
-*     This function returns a flag indicating if the pair of supplied
-*     Mappings could be replaced by an equivalent pair of Mappings from the
-*     same classes as the supplied pair, but in reversed order. Each pair
-*     of Mappings is considered to be compounded in series. The supplied
-*     Mappings are not changed in any way.
-
-*  Parameters:
-*     map1
-*        The Mapping to be applied first.
-*     map2
-*        The Mapping to be applied second.
-*     inv1
-*        The invert flag to use with map1. A value of zero causes the forward
-*        mapping to be used, and a non-zero value causes the inverse
-*        mapping to be used.
-*     inv2
-*        The invert flag to use with map2.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     1 if the Mappings could be swapped, 0 otherwise.
-
-*  Notes:
-*     -  One of the supplied pair of Mappings must be a PcdMap.
-*     -  A value of 0 is returned if the two Mappings could be merged into
-*     a single Mapping.
-*     -  A value of 0 is returned if an error has already occurred, or if
-*     this function should fail for any reason.
-*/
-
-/* Local Variables: */
-   AstMapping *nopcd;        /* Pointer to non-PcdMap Mapping */
-   const char *class1;       /* Pointer to map1 class string */
-   const char *class2;       /* Pointer to map2 class string */
-   const char *nopcd_class;  /* Pointer to non-PcdMap class string */
-   double *consts;           /* Pointer to constants array */
-   int *inperm;              /* Pointer to input axis permutation array */
-   int *outperm;             /* Pointer to output axis permutation array */
-   int invert[ 2 ];          /* Original invert flags */
-   int nin;                  /* No. of input coordinates for the PermMap */
-   int nout;                 /* No. of output coordinates for the PermMap */
-   int ret;                  /* Returned flag */
-
-/* Check the global error status. */
-   if ( !astOK ) return 0;
-
-/* Initialise */
-   ret = 0;
-
-/* Temporarily set the Invert attributes of both Mappings to the supplied
-   values. */
-   invert[ 0 ] = astGetInvert( map1 );
-   astSetInvert( map1, inv1 );
-
-   invert[ 1 ] = astGetInvert( map2 );
-   astSetInvert( map2, inv2 );
-
-/* Get the classes of the two mappings. */
-   class1 = astGetClass( map1 );
-   class2 = astGetClass( map2 );
-   if( astOK ){
-
-/* Get a pointer to the non-PcdMap Mapping. */
-      if( !strcmp( class1, "PcdMap" ) ){
-         nopcd = map2;
-         nopcd_class = class2;
-      } else {
-         nopcd = map1;
-         nopcd_class = class1;
-      }
-
-/* If the other Mapping is a ZoomMap, the Mappings can be swapped. */
-      if( !strcmp( nopcd_class, "ZoomMap" ) ){
-         ret = 1;
-
-/* If it is a PermMap, the Mappings can be swapped so long as the PermMap
-   simply swaps the two axes. */
-      } else if( !strcmp( nopcd_class, "PermMap" ) ){
-
-/* Get the number of input and output coordinates for the PermMap. */
-         nin = astGetNin( nopcd );
-         nout = astGetNout( nopcd );
-
-/* Must be 2-dimensional to swap. */
-         if( nin == 2 && nout == 2 ) {
-
-/* Get the axis permutation arrays and constants array for the PermMap. */
-            PermGet( (AstPermMap *) nopcd, &outperm, &inperm, &consts, status );
-            if( astOK ) {
-
-/* If the PermMap simply swaps the 2 axes (in both direction) we can
-   swap the two mappings. */
-               ret = ( outperm[0] == 1 && outperm[1] == 0 &&
-                       inperm[0] == 1 && inperm[1] == 0 );
-
-/* Free the axis permutation and constants arrays. */
-               outperm = (int *) astFree( (void *) outperm );
-               inperm = (int *) astFree( (void *) inperm );
-               consts = (double *) astFree( (void *) consts );
-            }
-         }
-      }
-   }
-
-/* Re-instate the original settings of the Invert attributes for the
-   supplied Mappings. */
-   astSetInvert( map1, invert[ 0 ] );
-   astSetInvert( map2, invert[ 1 ] );
-
-/* Return the answer. */
-   return astOK ? ret : 0;
-}
-
-static void ClearAttrib( AstObject *this_object, const char *attrib, int *status ) {
-/*
-*  Name:
-*     ClearAttrib
-
-*  Purpose:
-*     Clear an attribute value for a PcdMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     void ClearAttrib( AstObject *this, const char *attrib, int *status )
-
-*  Class Membership:
-*     PcdMap member function (over-rides the astClearAttrib protected
-*     method inherited from the Mapping class).
-
-*  Description:
-*     This function clears the value of a specified attribute for a
-*     PcdMap, so that the default value will subsequently be used.
-
-*  Parameters:
-*     this
-*        Pointer to the PcdMap.
-*     attrib
-*        Pointer to a null terminated string specifying the attribute
-*        name.  This should be in lower case with no surrounding white
-*        space.
-*     status
-*        Pointer to the inherited status variable.
-*/
-
-/* Local Variables: */
-   AstPcdMap *this;              /* Pointer to the PcdMap structure */
-   int axis;                     /* Axis number */
-   int len;                      /* Length of attrib string */
-   int nc;                       /* No. characters read by astSscanf */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain a pointer to the PcdMap structure. */
-   this = (AstPcdMap *) this_object;
-
-/* Obtain the length of the "attrib" string. */
-   len = strlen( attrib );
-
-/* Check the attribute name and clear the appropriate attribute. */
-
-/* PcdCen(axis). */
-/* ------------- */
-   if ( nc = 0,
-               ( 1 == astSscanf( attrib, "pcdcen(%d)%n", &axis, &nc ) )
-               && ( nc >= len ) ) {
-      astClearPcdCen( this, axis - 1 );
-
-/* PcdCen. */
-/* ------- */
-   } else if ( !strcmp( attrib, "pcdcen" ) ) {
-      astClearPcdCen( this, 0 );
-      astClearPcdCen( this, 1 );
-
-/* Disco. */
-/* ------ */
-   } else if ( !strcmp( attrib, "disco" ) ) {
-      astClearDisco( this );
-
-/* If the attribute is still not recognised, pass it on to the parent
-   method for further interpretation. */
-   } else {
-      (*parent_clearattrib)( this_object, attrib, status );
-   }
-}
-
-static int Equal( AstObject *this_object, AstObject *that_object, int *status ) {
-/*
-*  Name:
-*     Equal
-
-*  Purpose:
-*     Test if two PcdMaps are equivalent.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     int Equal( AstObject *this, AstObject *that, int *status )
-
-*  Class Membership:
-*     PcdMap member function (over-rides the astEqual protected
-*     method inherited from the astMapping class).
-
-*  Description:
-*     This function returns a boolean result (0 or 1) to indicate whether
-*     two PcdMaps are equivalent.
-
-*  Parameters:
-*     this
-*        Pointer to the first Object (a PcdMap).
-*     that
-*        Pointer to the second Object.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     One if the PcdMaps are equivalent, zero otherwise.
-
-*  Notes:
-*     - A value of zero will be returned if this function is invoked
-*     with the global status set, or if it should fail for any reason.
-*/
-
-/* Local Variables: */
-   AstPcdMap *that;
-   AstPcdMap *this;
-   int result;
-
-/* Initialise. */
-   result = 0;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Obtain pointers to the two PcdMap structures. */
-   this = (AstPcdMap *) this_object;
-   that = (AstPcdMap *) that_object;
-
-/* Check the second object is a PcdMap. We know the first is a
-   PcdMap since we have arrived at this implementation of the virtual
-   function. */
-   if( astIsAPcdMap( that ) ) {
-
-/* Check the Invert flags for the two PcdMaps are equal. */
-      if( astGetInvert( this ) == astGetInvert( that ) ) {
-
-/* Check all the attributes are equal. */
-         if( astEQUAL( this->pcdcen[0], that->pcdcen[0] ) &&
-             astEQUAL( this->pcdcen[1], that->pcdcen[1] ) &&
-             astEQUAL( this->disco, that->disco ) ) {
-            result = 1;
-         }
-      }
-   }
-
-/* If an error occurred, clear the result value. */
-   if ( !astOK ) result = 0;
-
-/* Return the result, */
-   return result;
-}
-
-static const char *GetAttrib( AstObject *this_object, const char *attrib, int *status ) {
-/*
-*  Name:
-*     GetAttrib
-
-*  Purpose:
-*     Get the value of a specified attribute for a PcdMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     const char *GetAttrib( AstObject *this, const char *attrib, int *status )
-
-*  Class Membership:
-*     PcdMap member function (over-rides the protected astGetAttrib
-*     method inherited from the Mapping class).
-
-*  Description:
-*     This function returns a pointer to the value of a specified
-*     attribute for a PcdMap, formatted as a character string.
-
-*  Parameters:
-*     this
-*        Pointer to the PcdMap.
-*     attrib
-*        Pointer to a null terminated string containing the name of
-*        the attribute whose value is required. This name should be in
-*        lower case, with all white space removed.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     - Pointer to a null terminated string containing the attribute
-*     value.
-
-*  Notes:
-*     - The returned string pointer may point at memory allocated
-*     within the PcdMap, or at static memory. The contents of the
-*     string may be over-written or the pointer may become invalid
-*     following a further invocation of the same function or any
-*     modification of the PcdMap. A copy of the string should
-*     therefore be made if necessary.
-*     - A NULL pointer will be returned if this function is invoked
-*     with the global error status set, or if it should fail for any
-*     reason.
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstPcdMap *this;              /* Pointer to the PcdMap structure */
-   const char *result;           /* Pointer value to return */
-   double dval;                  /* Double attribute value */
-   int axis;                     /* Axis number */
-   int len;                      /* Length of attrib string */
-   int nc;                       /* No. characters read by astSscanf */
-
-/* Initialise. */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(this_object);
-
-/* Obtain a pointer to the PcdMap structure. */
-   this = (AstPcdMap *) this_object;
-
-/* Obtain the length of the attrib string. */
-   len = strlen( attrib );
-
-/* Compare "attrib" with each recognised attribute name in turn,
-   obtaining the value of the required attribute. If necessary, write
-   the value into "getattrib_buff" as a null terminated string in an appropriate
-   format.  Set "result" to point at the result string. */
-
-/* Disco. */
-/* ------ */
-   if ( !strcmp( attrib, "disco" ) ) {
-      dval = astGetDisco( this );
-      if ( astOK ) {
-         (void) sprintf( getattrib_buff, "%.*g", AST__DBL_DIG, dval );
-         result = getattrib_buff;
-      }
-
-/* PcdCen(axis). */
-/* ------------- */
-   } else if ( nc = 0,
-               ( 1 == astSscanf( attrib, "pcdcen(%d)%n", &axis, &nc ) )
-               && ( nc >= len ) ) {
-      dval = astGetPcdCen( this, axis - 1 );
-      if ( astOK ) {
-         (void) sprintf( getattrib_buff, "%.*g", AST__DBL_DIG, dval );
-         result = getattrib_buff;
-      }
-
-/* PcdCen. */
-/* ------- */
-   } else if ( !strcmp( attrib, "pcdcen" ) ) {
-      dval = astGetPcdCen( this, 0 );
-      if ( astOK ) {
-         (void) sprintf( getattrib_buff, "%.*g", AST__DBL_DIG, dval );
-         result = getattrib_buff;
-      }
-
-/* If the attribute name was not recognised, pass it on to the parent
-   method for further interpretation. */
-   } else {
-      result = (*parent_getattrib)( this_object, attrib, status );
-   }
-
-/* Return the result. */
-   return result;
-}
-
-void astInitPcdMapVtab_(  AstPcdMapVtab *vtab, const char *name, int *status ) {
-/*
-*+
-*  Name:
-*     astInitPcdMapVtab
-
-*  Purpose:
-*     Initialise a virtual function table for a PcdMap.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     void astInitPcdMapVtab( AstPcdMapVtab *vtab, const char *name )
-
-*  Class Membership:
-*     PcdMap vtab initialiser.
-
-*  Description:
-*     This function initialises the component of a virtual function
-*     table which is used by the PcdMap class.
-
-*  Parameters:
-*     vtab
-*        Pointer to the virtual function table. The components used by
-*        all ancestral classes will be initialised if they have not already
-*        been initialised.
-*     name
-*        Pointer to a constant null-terminated character string which contains
-*        the name of the class to which the virtual function table belongs (it
-*        is this pointer value that will subsequently be returned by the Object
-*        astClass function).
-*-
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstObjectVtab *object;        /* Pointer to Object component of Vtab */
-   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
-
-/* Check the local error status. */
-   if ( !astOK ) return;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* Initialize the component of the virtual function table used by the
-   parent class. */
-   astInitMappingVtab( (AstMappingVtab *) vtab, name );
-
-/* Store a unique "magic" value in the virtual function table. This
-   will be used (by astIsAPcdMap) to determine if an object belongs
-   to this class.  We can conveniently use the address of the (static)
-   class_check variable to generate this unique value. */
-   vtab->id.check = &class_check;
-   vtab->id.parent = &(((AstMappingVtab *) vtab)->id);
-
-/* Initialise member function pointers. */
-/* ------------------------------------ */
-/* Store pointers to the member functions (implemented here) that provide
-   virtual methods for this class. */
-   vtab->ClearDisco = ClearDisco;
-   vtab->SetDisco = SetDisco;
-   vtab->GetDisco = GetDisco;
-   vtab->TestDisco = TestDisco;
-   vtab->ClearPcdCen = ClearPcdCen;
-   vtab->SetPcdCen = SetPcdCen;
-   vtab->GetPcdCen = GetPcdCen;
-   vtab->TestPcdCen = TestPcdCen;
-
-/* Save the inherited pointers to methods that will be extended, and
-   replace them with pointers to the new member functions. */
-   object = (AstObjectVtab *) vtab;
-   mapping = (AstMappingVtab *) vtab;
-
-   parent_clearattrib = object->ClearAttrib;
-   object->ClearAttrib = ClearAttrib;
-   parent_getattrib = object->GetAttrib;
-   object->GetAttrib = GetAttrib;
-   parent_setattrib = object->SetAttrib;
-   object->SetAttrib = SetAttrib;
-   parent_testattrib = object->TestAttrib;
-   object->TestAttrib = TestAttrib;
-   object->Equal = Equal;
-
-   parent_transform = mapping->Transform;
-   mapping->Transform = Transform;
-
-/* Store replacement pointers for methods which will be over-ridden by
-   new member functions implemented here. */
-   mapping->MapMerge = MapMerge;
-
-/* Declare the class dump function.*/
-   astSetDump( vtab, Dump, "PcdMap", "Apply pincushion distortion" );
-
-/* If we have just initialised the vtab for the current class, indicate
-   that the vtab is now initialised, and store a pointer to the class
-   identifier in the base "object" level of the vtab. */
-   if( vtab == &class_vtab ) {
-      class_init = 1;
-      astSetVtabClassIdentifier( vtab, &(vtab->id) );
-   }
-}
-
-static int MapMerge( AstMapping *this, int where, int series, int *nmap,
-                     AstMapping ***map_list, int **invert_list, int *status ) {
-/*
-*  Name:
-*     MapMerge
-
-*  Purpose:
-*     Simplify a sequence of Mappings containing a PcdMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "mapping.h"
-*     int MapMerge( AstMapping *this, int where, int series, int *nmap,
-*                   AstMapping ***map_list, int **invert_list, int *status )
-
-*  Class Membership:
-*     PcdMap method (over-rides the protected astMapMerge method
-*     inherited from the Mapping class).
-
-*  Description:
-*     This function attempts to simplify a sequence of Mappings by
-*     merging a nominated PcdMap in the sequence with its neighbours,
-*     so as to shorten the sequence if possible.
-*
-*     In many cases, simplification will not be possible and the
-*     function will return -1 to indicate this, without further
-*     action.
-*
-*     In most cases of interest, however, this function will either
-*     attempt to replace the nominated PcdMap with a Mapping which it
-*     considers simpler, or to merge it with the Mappings which
-*     immediately precede it or follow it in the sequence (both will
-*     normally be considered). This is sufficient to ensure the
-*     eventual simplification of most Mapping sequences by repeated
-*     application of this function.
-*
-*     In some cases, the function may attempt more elaborate
-*     simplification, involving any number of other Mappings in the
-*     sequence. It is not restricted in the type or scope of
-*     simplification it may perform, but will normally only attempt
-*     elaborate simplification in cases where a more straightforward
-*     approach is not adequate.
-
-*  Parameters:
-*     this
-*        Pointer to the nominated PcdMap which is to be merged with
-*        its neighbours. This should be a cloned copy of the PcdMap
-*        pointer contained in the array element "(*map_list)[where]"
-*        (see below). This pointer will not be annulled, and the
-*        PcdMap it identifies will not be modified by this function.
-*     where
-*        Index in the "*map_list" array (below) at which the pointer
-*        to the nominated PcdMap resides.
-*     series
-*        A non-zero value indicates that the sequence of Mappings to
-*        be simplified will be applied in series (i.e. one after the
-*        other), whereas a zero value indicates that they will be
-*        applied in parallel (i.e. on successive sub-sets of the
-*        input/output coordinates).
-*     nmap
-*        Address of an int which counts the number of Mappings in the
-*        sequence. On entry this should be set to the initial number
-*        of Mappings. On exit it will be updated to record the number
-*        of Mappings remaining after simplification.
-*     map_list
-*        Address of a pointer to a dynamically allocated array of
-*        Mapping pointers (produced, for example, by the astMapList
-*        method) which identifies the sequence of Mappings. On entry,
-*        the initial sequence of Mappings to be simplified should be
-*        supplied.
-*
-*        On exit, the contents of this array will be modified to
-*        reflect any simplification carried out. Any form of
-*        simplification may be performed. This may involve any of: (a)
-*        removing Mappings by annulling any of the pointers supplied,
-*        (b) replacing them with pointers to new Mappings, (c)
-*        inserting additional Mappings and (d) changing their order.
-*
-*        The intention is to reduce the number of Mappings in the
-*        sequence, if possible, and any reduction will be reflected in
-*        the value of "*nmap" returned. However, simplifications which
-*        do not reduce the length of the sequence (but improve its
-*        execution time, for example) may also be performed, and the
-*        sequence might conceivably increase in length (but normally
-*        only in order to split up a Mapping into pieces that can be
-*        more easily merged with their neighbours on subsequent
-*        invocations of this function).
-*
-*        If Mappings are removed from the sequence, any gaps that
-*        remain will be closed up, by moving subsequent Mapping
-*        pointers along in the array, so that vacated elements occur
-*        at the end. If the sequence increases in length, the array
-*        will be extended (and its pointer updated) if necessary to
-*        accommodate any new elements.
-*
-*        Note that any (or all) of the Mapping pointers supplied in
-*        this array may be annulled by this function, but the Mappings
-*        to which they refer are not modified in any way (although
-*        they may, of course, be deleted if the annulled pointer is
-*        the final one).
-*     invert_list
-*        Address of a pointer to a dynamically allocated array which,
-*        on entry, should contain values to be assigned to the Invert
-*        attributes of the Mappings identified in the "*map_list"
-*        array before they are applied (this array might have been
-*        produced, for example, by the astMapList method). These
-*        values will be used by this function instead of the actual
-*        Invert attributes of the Mappings supplied, which are
-*        ignored.
-*
-*        On exit, the contents of this array will be updated to
-*        correspond with the possibly modified contents of the
-*        "*map_list" array.  If the Mapping sequence increases in
-*        length, the "*invert_list" array will be extended (and its
-*        pointer updated) if necessary to accommodate any new
-*        elements.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     If simplification was possible, the function returns the index
-*     in the "map_list" array of the first element which was
-*     modified. Otherwise, it returns -1 (and makes no changes to the
-*     arrays supplied).
-
-*  Notes:
-*     - A value of -1 will be returned if this function is invoked
-*     with the global error status set, or if it should fail for any
-*     reason.
-*/
-
-/* Local Variables: */
-   AstMapping **maplt;   /* New mappings list pointer */
-   AstMapping *map2;     /* First mapping to check */
-   AstMapping *newmap;   /* Pointer to replacement Mapping */
-   AstMapping *mc[2];    /* Copies of supplied Mappings to swap */
-   AstMapping *smc0;     /* Simplied Mapping */
-   AstMapping *smc1;     /* Simplied Mapping */
-   const char *class1;   /* Pointer to first Mapping class string */
-   const char *class2;   /* Pointer to second Mapping class string */
-   const char *nclass;   /* Pointer to neighbouring Mapping class */
-   int i1;               /* Index of first PcdMap to merge */
-   int i2;               /* Index of last PcdMap to merge */
-   int i;                /* Loop counter */
-   int ic[2];            /* Copies of supplied invert flags to swap */
-   int invert;           /* Should the inverted Mapping be used? */
-   int *invlt;           /* New invert flags list pointer */
-   int nmapt;            /* No. of Mappings in list */
-   int nstep1;           /* No. of Mappings backwards to next mergable Mapping */
-   int nstep2;           /* No. of Mappings forward to next mergable Mapping */
-   int result;           /* Result value to return */
-   int swaphi;           /* Can PcdMap be swapped with higher neighbour? */
-   int swaplo;           /* Can PcdMap be swapped with lower neighbour? */
-
-/* Initialise. */
-   result = -1;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Initialise variables to avoid "used of uninitialised variable"
-   messages from dumb compilers. */
-   i1 = 0;
-   i2 = 0;
-
-/* First of all, see if the PcdMap can be replaced by a simpler Mapping,
-   without reference to the neighbouring Mappings in the list.           */
-/* ======================================================================*/
-/* If the distortion coefficient in the PcdMap is zero, the PcdMap can be
-   replaced by a UnitMap. */
-   if( EQUAL( astGetDisco( (AstPcdMap *) ( *map_list )[ where ] ), 0.0 ) ){
-
-/* Annul the PcdMap pointer in the list and replace it with a UnitMap
-   pointer, and indicate that the forward transformation of the returned
-   UnitMap should be used. */
-      (void) astAnnul( ( *map_list )[ where ] );
-      ( *map_list )[ where ] = (AstMapping *) astUnitMap( 2, "", status );
-      ( *invert_list )[ where ] = 0;
-
-/* Return the index of the first modified element. */
-      result = where;
-
-/* If the PcdMap itself could not be simplified, see if it can be merged
-   with the Mappings on either side of it in the list. */
-   } else {
-
-/* Store the classes of the neighbouring Mappings in the list. */
-       class1 = ( where > 0 ) ? astGetClass( ( *map_list )[ where - 1 ] ) : NULL;
-       class2 = ( where < *nmap - 1 ) ? astGetClass( ( *map_list )[ where + 1 ] ) : NULL;
-
-/* In series. */
-/* ========== */
-      if ( series ) {
-
-/* We first look to see if the PcdMap can be merged with one of its
-   neighbours, resulting in a reduction of one in the number of Mappings
-   in the list. A PcdMap can only merge directly with its own inverse, or
-   a UnitMap. */
-         if( class1 && CanMerge(  ( *map_list )[ where - 1 ],
-                                  ( *map_list )[ where ],
-                                  ( *invert_list )[ where - 1 ],
-                                  ( *invert_list )[ where ], status ) ){
-            nclass = class1;
-            i1 = where - 1;
-            i2 = where;
-
-         } else if( class2 && CanMerge(  ( *map_list )[ where ],
-                                  ( *map_list )[ where + 1 ],
-                                  ( *invert_list )[ where ],
-                                  ( *invert_list )[ where + 1 ], status ) ){
-            nclass = class2;
-            i1 = where;
-            i2 = where + 1;
-
-         } else {
-            nclass = NULL;
-         }
-
-/* If the PcdMap can merge with one of its neighbours, create the merged
-   Mapping. */
-         if( nclass ){
-
-/* If the neighbour is a PcdMap, it must be the inverse of the nominated
-   Mapping, and so they merge to form a UnitMap. */
-            if( !strcmp( nclass, "PcdMap" ) ){
-               newmap = (AstMapping *) astUnitMap( 2, "", status );
-               invert = 0;
-
-/* If the neighbour is a UnitMap, they merge to form a clone of the
-   nominated PcdMap. */
-            } else {
-               newmap = (AstMapping *) astClone( ( *map_list )[ where ] );
-               invert = ( *invert_list )[ where ];
-            }
-
-/* If succesfull... */
-            if( astOK ){
-
-/* Annul the first of the two Mappings, and replace it with the merged
-   Mapping. Also set the invert flag. */
-               (void) astAnnul( ( *map_list )[ i1 ] );
-               ( *map_list )[ i1 ] = newmap;
-               ( *invert_list )[ i1 ] = invert;
-
-/* Annul the second of the two Mappings, and shuffle down the rest of the
-   list to fill the gap. */
-               (void) astAnnul( ( *map_list )[ i2 ] );
-               for ( i = i2 + 1; i < *nmap; i++ ) {
-                  ( *map_list )[ i - 1 ] = ( *map_list )[ i ];
-                  ( *invert_list )[ i - 1 ] = ( *invert_list )[ i ];
-               }
-
-/* Clear the vacated element at the end. */
-               ( *map_list )[ *nmap - 1 ] = NULL;
-               ( *invert_list )[ *nmap - 1 ] = 0;
-
-/* Decrement the Mapping count and return the index of the first
-   modified element. */
-               ( *nmap )--;
-               result = i1;
-
-            }
-
-/* If the PcdMap could not merge directly with either of its neighbours,
-   we consider whether it would be worthwhile to swap the PcdMap with
-   either of its neighbours. This can only be done for certain classes
-   of Mapping (ZoomMaps & some PermMaps), and will usually require both
-   Mappings to be modified (unless they are commutative). The advantage of
-   swapping the order of the Mappings is that it may result in the PcdMap
-   being adjacent to a Mapping with which it can merge directly on the next
-   invocation of this function, thus reducing the number of Mappings
-   in the list. */
-         } else {
-
-/* Set a flag if we could swap the PcdMap with its higher neighbour. */
-            if( where + 1 < *nmap ){
-               swaphi = CanSwap(  ( *map_list )[ where ],
-                                  ( *map_list )[ where + 1 ],
-                                  ( *invert_list )[ where ],
-                                  ( *invert_list )[ where + 1 ], status );
-            } else {
-               swaphi = 0;
-            }
-
-/* If so, step through each of the Mappings which follow the PcdMap,
-   looking for a Mapping with which the PcdMap could merge directly. Stop
-   when such a Mapping is found, or if a Mapping is found with which the
-   PcdMap could definitely not swap. Note the number of Mappings which
-   separate the PcdMap from the Mapping with which it could merge (if
-   any). */
-            nstep2 = -1;
-            if( swaphi ){
-               for( i2 = where + 1; i2 < *nmap; i2++ ){
-
-/* See if we may be able to merge with this Mapping. If so, note the number
-   of steps between the two Mappings and leave the loop. */
-                  nclass = astGetClass( ( *map_list )[ i2 ] );
-
-                  if( !strcmp( nclass, "UnitMap" ) ||
-                      !strcmp( nclass, "PcdMap" ) ){
-                     nstep2 = i2 - where - 1;
-                     break;
-                  }
-
-/* If there is no chance that we can swap with this Mapping, leave the loop
-   with -1 for the number of steps to indicate that no merging is possible.
-   PcdMaps can swap with ZoomMaps and some PermMaps. */
-                  if( strcmp( nclass, "ZoomMap" ) &&
-                      strcmp( nclass, "PermMap" ) ) {
-                     break;
-                  }
-
-               }
-
-            }
-
-/* Do the same working forward from the PcdMap towards the start of the map
-   list. */
-            if( where > 0 ){
-               swaplo = CanSwap(  ( *map_list )[ where - 1 ],
-                                  ( *map_list )[ where ],
-                                  ( *invert_list )[ where - 1 ],
-                                  ( *invert_list )[ where ], status );
-            } else {
-               swaplo = 0;
-            }
-
-            nstep1 = -1;
-            if( swaplo ){
-               for( i1 = where - 1; i1 >= 0; i1-- ){
-
-                  nclass = astGetClass( ( *map_list )[ i1 ] );
-
-                  if( !strcmp( nclass, "UnitMap" ) ||
-                      !strcmp( nclass, "PcdMap" ) ){
-                     nstep1 = where - 1 - i1;
-                     break;
-                  }
-
-                  if( strcmp( nclass, "ZoomMap" ) &&
-                      strcmp( nclass, "PermMap" ) ) {
-                     break;
-                  }
-
-               }
-
-            }
-
-/* Choose which neighbour to swap with so that the PcdMap moves towards the
-   nearest Mapping with which it can merge. */
-            if( nstep1 != -1 && ( nstep2 == -1 || nstep2 > nstep1 ) ){
-               nclass = class1;
-               i1 = where - 1;
-               i2 = where;
-            } else if( nstep2 != -1 ){
-               nclass = class2;
-               i1 = where;
-               i2 = where + 1;
-            } else {
-               nclass = NULL;
-            }
-
-/* If there is a target Mapping in the list with which the PcdMap could
-   merge, replace the supplied Mappings with swapped Mappings to bring a
-   PcdMap closer to the target Mapping. */
-            if( nclass ){
-
-/* Swap the Mappings. */
-               if( !strcmp( nclass, "ZoomMap" ) ){
-                  PcdZoom( (*map_list) + i1, (*invert_list) + i1, where - i1, status );
-
-               } else if( !strcmp( nclass, "PermMap" ) ){
-                  PcdPerm( (*map_list) + i1, (*invert_list) + i1, where - i1, status );
-               }
-
-/* And then merge them. */
-               if( where == i1 && where + 1 < *nmap ) {    /* Merging upwards */
-                  map2 = astClone( (*map_list)[ where + 1 ] );
-                  nmapt = *nmap - where - 1;
-                  maplt = *map_list + where + 1;
-                  invlt = *invert_list + where + 1;
-
-                  (void) astMapMerge( map2, 0, series, &nmapt, &maplt, &invlt );
-                  map2 = astAnnul( map2 );
-                  *nmap = where + 1 + nmapt;
-
-               } else if( where - 2 >= 0 ) {               /* Merging downwards */
-                  map2 = astClone( (*map_list)[ where - 2 ] );
-                  nmapt = *nmap - where + 2;
-                  maplt = *map_list + where - 2 ;
-                  invlt = *invert_list + where - 2;
-
-                  (void) astMapMerge( map2, 0, series, &nmapt, &maplt, &invlt );
-                  map2 = astAnnul( map2 );
-                  *nmap = where - 2 + nmapt;
-               }
-
-               result = i1;
-
-/* If there is no Mapping available for merging, it may still be
-   advantageous to swap with a neighbour because the swapped Mapping may
-   be simpler than the original Mappings. */
-            } else if( swaphi || swaplo ) {
-
-/* Try swapping with each possible neighbour in turn. */
-               for( i = 0; i < 2; i++ ) {
-
-/*  Set up the class and pointers for the mappings to be swapped, first
-    the lower neighbour, then the upper neighbour. */
-                  if( i == 0 && swaplo ){
-                     nclass = class1;
-                     i1 = where - 1;
-                     i2 = where;
-
-                  } else if( i == 1 && swaphi ){
-                     nclass = class2;
-                     i1 = where;
-                     i2 = where + 1;
-
-                  } else {
-                     nclass = NULL;
-                  }
-
-/* If we have a Mapping to swap with... */
-                  if( nclass ) {
-
-/* Take copies of the Mapping and Invert flag arrays so we do not change
-   the supplied values. */
-                     mc[ 0 ] = (AstMapping *) astCopy( ( (*map_list) + i1 )[0] );
-                     mc[ 1 ] = (AstMapping *) astCopy( ( (*map_list) + i1 )[1] );
-                     ic[ 0 ] = ( (*invert_list) + i1 )[0];
-                     ic[ 1 ] = ( (*invert_list) + i1 )[1];
-
-/* Swap these Mappings. */
-                     if( !strcmp( nclass, "ZoomMap" ) ){
-                        PcdZoom( mc, ic, where - i1, status );
-                     } else if( !strcmp( nclass, "PermMap" ) ){
-                        PcdPerm( mc, ic, where - i1, status );
-                     }
-
-/* If neither of the swapped Mappings can be simplified further, then there
-   is no point in swapping the Mappings, so just annul the map copies. */
-                     smc0 = astSimplify( mc[0] );
-                     smc1 = astSimplify( mc[1] );
-
-                     if( astGetClass( smc0 ) == astGetClass( mc[0] ) &&
-                         astGetClass( smc1 ) == astGetClass( mc[1] ) ) {
-
-                        mc[ 0 ] = (AstMapping *) astAnnul( mc[ 0 ] );
-                        mc[ 1 ] = (AstMapping *) astAnnul( mc[ 1 ] );
-
-/* If one or both of the swapped Mappings could be simplified, then annul
-   the supplied Mappings and return the swapped mappings, storing the index
-   of the first modified Mapping. */
-                     } else {
-                        (void ) astAnnul( ( (*map_list) + i1 )[0] );
-                        (void ) astAnnul( ( (*map_list) + i1 )[1] );
-
-                        ( (*map_list) + i1 )[0] = mc[ 0 ];
-                        ( (*map_list) + i1 )[1] = mc[ 1 ];
-
-                        ( (*invert_list) + i1 )[0] = ic[ 0 ];
-                        ( (*invert_list) + i1 )[1] = ic[ 1 ];
-
-                        result = i1;
-                        break;
-                     }
-
-/* Annul the simplied Mappings */
-                     smc0 = astAnnul( smc0 );
-                     smc1 = astAnnul( smc1 );
-
-                  }
-               }
-            }
-         }
-
-/* In parallel. */
-/* ============ */
-/* PcdMaps cannot combine in parallel with any other Mappings. */
-      }
-   }
-
-/* Return the result. */
-   return result;
-}
-
-static void PermGet( AstPermMap *map, int **outperm, int **inperm,
-                     double **consts, int *status ){
-/*
-*  Name:
-*     PermGet
-
-*  Purpose:
-*     Get the axis permutation and constants array for a PermMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     void PermGet( AstPermMap *map, int **outperm, int **inperm,
-*                   double **const, int *status )
-
-*  Class Membership:
-*     PcdMap member function
-
-*  Description:
-*     This function returns axis permutation and constants arrays which can
-*     be used to create a PermMap which is equivalent to the supplied PermMap.
-
-*  Parameters:
-*     map
-*        The PermMap.
-*     outperm
-*        An address at which to return a popinter to an array of ints
-*        holding the output axis permutation array. The array should be
-*        released using astFree when no longer needed.
-*     inperm
-*        An address at which to return a popinter to an array of ints
-*        holding the input axis permutation array. The array should be
-*        released using astFree when no longer needed.
-*     consts
-*        An address at which to return a popinter to an array of doubles
-*        holding the constants array. The array should be released using
-*        astFree when no longer needed.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Notes:
-*     -  NULL pointers are returned if an error has already occurred, or if
-*     this function should fail for any reason.
-*/
-
-/* Local Variables: */
-   AstPointSet *pset1;       /* PointSet holding input positions for PermMap */
-   AstPointSet *pset2;       /* PointSet holding output positions for PermMap */
-   double **ptr1;            /* Pointer to pset1 data */
-   double **ptr2;            /* Pointer to pset2 data */
-   double *cnst;             /* Pointer to constants array */
-   double cn;                /* Potential new constant value */
-   double ip;                /* Potential output axis index */
-   double op;                /* Potential input axis index */
-   int *inprm;               /* Pointer to input axis permutation array */
-   int *outprm;              /* Pointer to output axis permutation array */
-   int i;                    /* Axis count */
-   int nc;                   /* Number of constants stored so far */
-   int nin;                  /* No. of input coordinates for the PermMap */
-   int nout;                 /* No. of output coordinates for the PermMap */
-
-/* Initialise. */
-   if( outperm ) *outperm = NULL;
-   if( inperm ) *inperm = NULL;
-   if( consts ) *consts = NULL;
-
-/* Check the global error status and the supplied pointers. */
-   if ( !astOK || !outperm || !inperm || !consts ) return;
-
-/* Initialise variables to avoid "used of uninitialised variable"
-   messages from dumb compilers. */
-   nc = 0;
-
-/* Get the number of input and output axes for the supplied PermMap. */
-   nin = astGetNin( map );
-   nout = astGetNout( map );
-
-/* Allocate the memory for the returned arrays. */
-   outprm = (int *) astMalloc( sizeof( int )* (size_t) nout );
-   inprm = (int *) astMalloc( sizeof( int )* (size_t) nin );
-   cnst = (double *) astMalloc( sizeof( double )* (size_t) ( nout + nin ) );
-
-/* Returned the pointers to these arrays.*/
-   *outperm = outprm;
-   *inperm = inprm;
-   *consts = cnst;
-
-/* Create two PointSets, each holding two points, which can be used for
-   input and output positions with the PermMap. */
-   pset1 = astPointSet( 2, nin, "", status );
-   pset2 = astPointSet( 2, nout, "", status );
-
-/* Set up the two input positions to be [0,1,2...] and [-1,-1,-1,...]. The
-   first position is used to enumerate the axes, and the second is used to
-   check for constant axis values. */
-   ptr1 = astGetPoints( pset1 );
-   if( astOK ){
-      for( i = 0; i < nin; i++ ){
-         ptr1[ i ][ 0 ] = ( double ) i;
-         ptr1[ i ][ 1 ] = -1.0;
-      }
-   }
-
-/* Use the PermMap to transform these positions in the forward direction. */
-   (void) astTransform( map, pset1, 1, pset2 );
-
-/* Look at the mapped positions to determine the output axis permutation
-   array. */
-   ptr2 = astGetPoints( pset2 );
-   if( astOK ){
-
-/* No constant axis valeus found yet. */
-      nc = 0;
-
-/* Do each output axis. */
-      for( i = 0; i < nout; i++ ){
-
-/* If the output axis value is copied from an input axis value, the index
-   of the appropriate input axis will be in the mapped first position. */
-         op = ptr2[ i ][ 0 ];
-
-/* If the output axis value is assigned a constant value, the result of
-   mapping the two different input axis values will be the same. */
-         cn = ptr2[ i ][ 1 ];
-         if( op == cn ) {
-
-/* We have found another constant. Store it in the constants array, and
-   store the index of the constant in the output axis permutation array. */
-            cnst[ nc ] = cn;
-            outprm[ i ] = -( nc + 1 );
-            nc++;
-
-/* If the output axis values are different, then the output axis value
-   must be copied from the input axis value. */
-         } else {
-            outprm[ i ] = (int) ( op + 0.5 );
-         }
-      }
-   }
-
-/* Now do the same thing to determine the input permutation array. */
-   if( astOK ){
-      for( i = 0; i < nout; i++ ){
-         ptr2[ i ][ 0 ] = ( double ) i;
-         ptr2[ i ][ 1 ] = -1.0;
-      }
-   }
-
-   (void) astTransform( map, pset2, 0, pset1 );
-
-   if( astOK ){
-
-      for( i = 0; i < nin; i++ ){
-
-         ip = ptr1[ i ][ 0 ];
-         cn = ptr1[ i ][ 1 ];
-         if( ip == cn ) {
-
-            cnst[ nc ] = cn;
-            inprm[ i ] = -( nc + 1 );
-            nc++;
-
-         } else {
-            inprm[ i ] = (int) ( ip + 0.5 );
-         }
-      }
-   }
-
-/* Annul the PointSets. */
-   pset1 = astAnnul( pset1 );
-   pset2 = astAnnul( pset2 );
-
-/* If an error has occurred, attempt to free the returned arrays. */
-   if( !astOK ) {
-      *outperm = (int *) astFree( (void *) *outperm );
-      *inperm = (int *) astFree( (void *) *inperm );
-      *consts = (double *) astFree( (void *) *consts );
-   }
-
-/* Return. */
-   return;
-}
-
-static void SetAttrib( AstObject *this_object, const char *setting, int *status ) {
-/*
-*  Name:
-*     SetAttrib
-
-*  Purpose:
-*     Set an attribute value for a PcdMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     void SetAttrib( AstObject *this, const char *setting, int *status )
-
-*  Class Membership:
-*     PcdMap member function (over-rides the astSetAttrib protected
-*     method inherited from the Mapping class).
-
-*  Description:
-*     This function assigns an attribute value for a PcdMap, the
-*     attribute and its value being specified by means of a string of
-*     the form:
-*
-*        "attribute= value "
-*
-*     Here, "attribute" specifies the attribute name and should be in
-*     lower case with no white space present. The value to the right
-*     of the "=" should be a suitable textual representation of the
-*     value to be assigned and this will be interpreted according to
-*     the attribute's data type.  White space surrounding the value is
-*     only significant for string attributes.
-
-*  Parameters:
-*     this
-*        Pointer to the PcdMap.
-*     setting
-*        Pointer to a null terminated string specifying the new attribute
-*        value.
-*     status
-*        Pointer to the inherited status variable.
-*/
-
-/* Local Variables: */
-   AstPcdMap *this;              /* Pointer to the PcdMap structure */
-   double dval;                  /* Double attribute value */
-   int axis;                     /* Index for the axis */
-   int len;                      /* Length of setting string */
-   int nc;                       /* Number of characters read by astSscanf */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain a pointer to the PcdMap structure. */
-   this = (AstPcdMap *) this_object;
-
-/* Obtain the length of the setting string. */
-   len = (int) strlen( setting );
-
-/* Test for each recognised attribute in turn, using "astSscanf" to parse
-   the setting string and extract the attribute value (or an offset to
-   it in the case of string values). In each case, use the value set
-   in "nc" to check that the entire string was matched. Once a value
-   has been obtained, use the appropriate method to set it. */
-
-/* Disco. */
-/* ------ */
-   if ( nc = 0,
-        ( 1 == astSscanf( setting, "disco= %lg %n", &dval, &nc ) )
-        && ( nc >= len ) ) {
-      astSetDisco( this, dval );
-
-/* PcdCen(axis). */
-/* ------------ */
-   } else if ( nc = 0,
-               ( 2 == astSscanf( setting, "pcdcen(%d)= %lg %n",
-                              &axis, &dval, &nc ) )
-               && ( nc >= len ) ) {
-      astSetPcdCen( this, axis - 1, dval );
-
-/* PcdCen. */
-/* ------- */
-   } else if ( nc = 0,
-        ( 1 == astSscanf( setting, "pcdcen= %lg %n", &dval, &nc ) )
-        && ( nc >= len ) ) {
-      astSetPcdCen( this, 0, dval );
-      astSetPcdCen( this, 1, dval );
-
-/* If the attribute is still not recognised, pass it on to the parent
-   method for further interpretation. */
-   } else {
-      (*parent_setattrib)( this_object, setting, status );
-   }
-
-}
-
-static int TestAttrib( AstObject *this_object, const char *attrib, int *status ) {
-/*
-*  Name:
-*     TestAttrib
-
-*  Purpose:
-*     Test if a specified attribute value is set for a PcdMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     int TestAttrib( AstObject *this, const char *attrib, int *status )
-
-*  Class Membership:
-*     PcdMap member function (over-rides the astTestAttrib protected
-*     method inherited from the Mapping class).
-
-*  Description:
-*     This function returns a boolean result (0 or 1) to indicate whether
-*     a value has been set for one of a PcdMap's attributes.
-
-*  Parameters:
-*     this
-*        Pointer to the PcdMap.
-*     attrib
-*        Pointer to a null terminated string specifying the attribute
-*        name.  This should be in lower case with no surrounding white
-*        space.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     One if a value has been set, otherwise zero.
-
-*  Notes:
-*     - A value of zero will be returned if this function is invoked
-*     with the global status set, or if it should fail for any reason.
-*/
-
-/* Local Variables: */
-   AstPcdMap *this;              /* Pointer to the PcdMap structure */
-   int axis;                     /* Axis number */
-   int len;                      /* Length of attrib string */
-   int nc;                       /* No. characters read by astSscanf */
-   int result;                   /* Result value to return */
-
-/* Initialise. */
-   result = 0;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Obtain a pointer to the PcdMap structure. */
-   this = (AstPcdMap *) this_object;
-
-/* Obtain the length of the attrib string. */
-   len = strlen( attrib );
-
-/* Check the attribute name and test the appropriate attribute. */
-
-/* Disco. */
-/* ------ */
-   if ( !strcmp( attrib, "disco" ) ) {
-      result = astTestDisco( this );
-
-/* PcdCen. */
-/* ------- */
-   } else if ( !strcmp( attrib, "pcdcen" ) ) {
-      result = astTestPcdCen( this, 0 );
-
-/* PcdCen(axis). */
-/* ---------- */
-   } else if ( nc = 0,
-               ( 1 == astSscanf( attrib, "pcdcen(%d)%n", &axis, &nc ) )
-               && ( nc >= len ) ) {
-      result = astTestPcdCen( this, axis - 1 );
-
-/* If the attribute is still not recognised, pass it on to the parent
-   method for further interpretation. */
-   } else {
-      result = (*parent_testattrib)( this_object, attrib, status );
-   }
-
-/* Return the result, */
-   return result;
-}
-
-static AstPointSet *Transform( AstMapping *this, AstPointSet *in,
-                               int forward, AstPointSet *out, int *status ) {
-/*
-*  Name:
-*     Transform
-
-*  Purpose:
-*     Apply a PcdMap to transform a set of points.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
-*                             int forward, AstPointSet *out, int *status )
-
-*  Class Membership:
-*     PcdMap member function (over-rides the astTransform protected
-*     method inherited from the Mapping class).
-
-*  Description:
-*     This function takes a PcdMap and a set of points encapsulated in a
-*     PointSet and transforms the points so as to map them into the
-*     required window.
-
-*  Parameters:
-*     this
-*        Pointer to the PcdMap.
-*     in
-*        Pointer to the PointSet holding the input coordinate data.
-*     forward
-*        A non-zero value indicates that the forward coordinate transformation
-*        should be applied, while a zero value requests the inverse
-*        transformation.
-*     out
-*        Pointer to a PointSet which will hold the transformed (output)
-*        coordinate values. A NULL value may also be given, in which case a
-*        new PointSet will be created by this function.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     Pointer to the output (possibly new) PointSet.
-
-*  Notes:
-*     -  A null pointer will be returned if this function is invoked with the
-*     global error status set, or if it should fail for any reason.
-*     -  The number of coordinate values per point in the input PointSet must
-*     match the number of coordinates for the PcdMap being applied.
-*     -  If an output PointSet is supplied, it must have space for sufficient
-*     number of points and coordinate values per point to accommodate the
-*     result. Any excess space will be ignored.
-*/
-
-/* Local Variables: */
-   AstPointSet *result;          /* Pointer to output PointSet */
-   AstPcdMap *map;               /* Pointer to PcdMap to be applied */
-   double **ptr_in;              /* Pointer to input coordinate data */
-   double **ptr_out;             /* Pointer to output coordinate data */
-   double *axin_0;               /* Pointer to next input axis 0 value */
-   double *axin_1;               /* Pointer to next input axis 1 value */
-   double *axout_0;              /* Pointer to next output axis 0 value */
-   double *axout_1;              /* Pointer to next output axis 1 value */
-   int npoint;                   /* Number of points */
-   int point;                    /* Loop counter for points */
-   double dx;                    /* Undistorted X increment from centre  */
-   double dy;                    /* Undistorted Y increment from centre */
-   double dxp;                   /* Distorted X increment from centre  */
-   double dyp;                   /* Distorted Y increment from centre */
-   double disco;                 /* Distortion coefficient */
-   double cen0;                  /* Centre of distortion on axis 0 */
-   double cen1;                  /* Centre of distortion on axis 1 */
-   double cr2;                   /* Constant */
-   double a;                     /* Constant */
-   double cr2a2;                 /* Constant */
-   double f;                     /* Expansion factor */
-
-/* Check the global error status. */
-   if ( !astOK ) return NULL;
-
-/* Obtain a pointer to the PcdMap. */
-   map = (AstPcdMap *) this;
-
-/* Apply the parent mapping using the stored pointer to the Transform member
-   function inherited from the parent Mapping class. This function validates
-   all arguments and generates an output PointSet if necessary, but does not
-   actually transform any coordinate values. */
-   result = (*parent_transform)( this, in, forward, out, status );
-
-/* We will now extend the parent astTransform method by performing the
-   calculations needed to generate the output coordinate values. */
-
-/* Determine the numbers of points and coordinates per point from the input
-   PointSet and obtain pointers for accessing the input and output coordinate
-   values. */
-   npoint = astGetNpoint( in );
-   ptr_in = astGetPoints( in );
-   ptr_out = astGetPoints( result );
-
-/* Determine whether to apply the forward or inverse mapping, according to the
-   direction specified and whether the mapping has been inverted. */
-   if ( astGetInvert( map ) ) forward = !forward;
-
-/* Get the distortion coefficient and centre. */
-   disco = astGetDisco( map );
-   cen0 = astGetPcdCen( map, 0 );
-   cen1 = astGetPcdCen( map, 1 );
-
-/* Perform coordinate arithmetic. */
-/* ------------------------------ */
-   if( astOK ){
-
-/* Store pointers to the first input and output values on both axes. */
-      axin_0 = ptr_in[ 0 ];
-      axin_1 = ptr_in[ 1 ];
-      axout_0 = ptr_out[ 0 ];
-      axout_1 = ptr_out[ 1 ];
-
-/* First deal with forward transformations. */
-      if( forward ){
-
-         for( point = 0; point < npoint; point++ ){
-            if( *axin_0 != AST__BAD && *axin_1 != AST__BAD ){
-               dx = ( *axin_0 - cen0 );
-               dy = ( *axin_1 - cen1 );
-               f = 1.0 + disco*( dx*dx + dy*dy );
-               dxp = dx*f;
-               dyp = dy*f;
-               *(axout_0++) = dxp + cen0;
-               *(axout_1++) = dyp + cen1;
-
-            } else {
-               *(axout_0++) = AST__BAD;
-               *(axout_1++) = AST__BAD;
-            }
-            axin_0++;
-            axin_1++;
-         }
-
-/* Now deal with inverse transformations. */
-      } else {
-
-         for( point = 0; point < npoint; point++ ){
-            if( *axin_0 != AST__BAD && *axin_1 != AST__BAD ){
-               dxp = ( *axin_0 - cen0 );
-               dyp = ( *axin_1 - cen1 );
-
-               cr2 = disco*( dxp*dxp + dyp*dyp );
-               a = ( 2.0*cr2 + 1.0 )/( 3.0*cr2 + 1.0 );
-               cr2a2 = cr2*a*a;
-               f = ( 2.0*cr2a2*a + 1.0 )/( 3.0*cr2a2 + 1.0 );
-
-               dx = dxp*f;
-               dy = dyp*f;
-
-/* The above approximate inverse is taken from SLA_UNPCD. If more accuracy
-c   is needed, the following code can be uncommented to iterate to a better
-c   solution.
-c
-c               fl = 1.0 + disco*( dx*dx + dy*dy );
-c               dx = dxp/fl;
-c               dy = dyp/fl;
-c
-c               df = fabs( fl );
-c               while( df > fabs( fl*1.0E-6 ) ){
-c                  f = 1.0 + disco*( dx*dx + dy*dy );
-c                  df = fabs( f - fl );
-c                  fl = f;
-c
-c                  dx = dxp/f;
-c                  dy = dyp/f;
-c               }
-*/
-               *(axout_0++) = dx + cen0;
-               *(axout_1++) = dy + cen1;
-
-            } else {
-               *(axout_0++) = AST__BAD;
-               *(axout_1++) = AST__BAD;
-            }
-            axin_0++;
-            axin_1++;
-         }
-
-      }
-
-   }
-
-/* Return a pointer to the output PointSet. */
-   return result;
-}
-
-static void PcdZoom( AstMapping **maps, int *inverts, int ipc, int *status ){
-/*
-*  Name:
-*     PcdZoom
-
-*  Purpose:
-*     Swap a PcdMap and a ZoomMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     void PcdZoom( AstMapping **maps, int *inverts, int ipc, int *status )
-
-*  Class Membership:
-*     PcdMap member function
-
-*  Description:
-*     A list of two Mappings is supplied containing a PcdMap and a
-*     ZoomMap. These Mappings are annulled, and replaced with
-*     another pair of Mappings consisting of a PcdMap and a ZoomMap
-*     in the opposite order. These Mappings are chosen so that their
-*     combined effect is the same as the original pair of Mappings.
-
-*  Parameters:
-*     maps
-*        A pointer to an array of two Mapping pointers.
-*     inverts
-*        A pointer to an array of two invert flags.
-*     ipc
-*        The index within "maps" of the PcdMap.
-*     status
-*        Pointer to the inherited status variable.
-
-*/
-
-/* Local Variables: */
-   AstPcdMap *pm2;               /* Pointer to the returned PcdMap */
-   AstPcdMap *pm;                /* Pointer to the supplied PcdMap */
-   AstZoomMap *zm2;              /* Pointer to the returned ZoomMap */
-   AstZoomMap *zm;               /* Pointer to the supplied ZoomMap */
-   double cen[2];                /* New distortion centre */
-   double disc;                  /* Distortion coeff. for returned PcdMap */
-   double disco;                 /* Distortion coeff. for supplied PcdMap */
-   double xcen;                  /* Axis 0 centre for supplied PcdMap */
-   double ycen;                  /* Axis 1 centre for supplied PcdMap */
-   double zoom;                  /* Zoom factor for supplied ZoomMap */
-   int old_pinv;                 /* Invert value for the supplied PcdMap */
-   int old_zinv;                 /* Invert value for the supplied ZoomMap */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Store pointers to the supplied PcdMap and the ZoomMap. */
-   pm = (AstPcdMap *) maps[ ipc ];
-   zm = (AstZoomMap *) maps[ 1 - ipc ];
-
-/* Temporarily set the Invert attribute of the supplied Mappings to the
-   supplied values. */
-   old_pinv = astGetInvert( pm );
-   astSetInvert( pm, inverts[ ipc ] );
-
-   old_zinv = astGetInvert( zm );
-   astSetInvert( zm, inverts[ 1 - ipc ] );
-
-/* Get the zoom factor from the ZoomMap. */
-   zoom = astGetZoom( zm );
-
-/* Get the distortion coefficient from the PcdMap. */
-   disco = astGetDisco( pm );
-
-/* Get the distortion centre from the PcdMap. */
-   xcen = astGetPcdCen( pm, 0 );
-   ycen = astGetPcdCen( pm, 1 );
-
-/* Re-instate the original value of the Invert attributes of the supplied
-   Mappings. */
-   astSetInvert( pm, old_pinv );
-   astSetInvert( zm, old_zinv );
-
-/* Create the returned ZoomMap. */
-   zm2 = astZoomMap( 2, zoom, "", status );
-
-/* Find the attributes of the returned PcdMap. If the PCD map is applied
-   first... */
-   if( ipc == 0 ) {
-      cen[ 0 ] = xcen*zoom;
-      cen[ 1 ] = ycen*zoom;
-      disc = disco/(zoom*zoom);
-
-/* If the PCD map is applied second... */
-   } else {
-      cen[ 0 ] = xcen/zoom;
-      cen[ 1 ] = ycen/zoom;
-      disc = disco*zoom*zoom;
-   }
-
-/* Create the returned PcdMap. */
-   pm2 = astPcdMap( disc, cen, "", status );
-   if( inverts[ ipc ] ) astInvert( pm2 );
-
-/* Replace the supplied Mappings with the ones created above, swapping the
-   order. */
-   if( astOK ){
-      (void) astAnnul( pm );
-      (void) astAnnul( zm );
-
-      maps[ 1 - ipc ] = (AstMapping *) pm2;
-      inverts[ 1 - ipc  ] = inverts[ ipc ];
-
-      maps[ ipc ] = (AstMapping *) zm2;
-      inverts[ ipc ] = 0;
-
-   }
-
-/* Return. */
-   return;
-}
-
-static void PcdPerm( AstMapping **maps, int *inverts, int ipc, int *status ){
-/*
-*  Name:
-*     PcdPerm
-
-*  Purpose:
-*     Swap a PcdMap and a PermMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     void PcdPerm( AstMapping **maps, int *inverts, int ipc, int *status )
-
-*  Class Membership:
-*     PcdMap member function
-
-*  Description:
-*     A list of two Mappings is supplied containing a PcdMap and a
-*     PermMap. These Mappings are annulled, and replaced with
-*     another pair of Mappings consisting of a PcdMap and a PermMap
-*     in the opposite order. These Mappings are chosen so that their
-*     combined effect is the same as the original pair of Mappings.
-
-*  Parameters:
-*     maps
-*        A pointer to an array of two Mapping pointers.
-*     inverts
-*        A pointer to an array of two invert flags.
-*     ipc
-*        The index within "maps" of the PcdMap.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Notes:
-*     -  It should have been checked previously that the PermMap simply
-*     swaps axes 0 and 1. This is the only sort of PermMap which can be
-*     used here.
-
-*/
-
-   AstPermMap *rm;               /* Pointer to the supplied PermMap */
-   AstPermMap *rm2;              /* Pointer to the returned PermMap */
-   AstPcdMap *pm;                /* Pointer to the supplied PcdMap */
-   AstPcdMap *pm2;               /* Pointer to the returned PcdMap */
-   double cen[2];                /* Centre for new PcdMap */
-   double disco;                 /* Distortion coeff. for supplied PcdMap */
-   double xcen;                  /* Axis 0 centre for supplied PcdMap */
-   double ycen;                  /* Axis 1 centre for supplied PcdMap */
-   int old_rinv;                 /* Invert value for the supplied PermMap */
-   int old_pinv;                 /* Invert value for the supplied PcdMap */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Store pointers to the supplied PcdMap and the PermMap. */
-   pm = (AstPcdMap *) maps[ ipc ];
-   rm = (AstPermMap *) maps[ 1 - ipc ];
-
-/* Temporarily set the Invert attribute of the supplied Mappings to the
-   supplied values. */
-   old_pinv = astGetInvert( pm );
-   astSetInvert( pm, inverts[ ipc ] );
-
-   old_rinv = astGetInvert( rm );
-   astSetInvert( rm, inverts[ 1 - ipc ] );
-
-/* Get the distortion coefficient from the PcdMap. */
-   disco = astGetDisco( pm );
-
-/* Get the distortion centre from the PcdMap. */
-   xcen = astGetPcdCen( pm, 0 );
-   ycen = astGetPcdCen( pm, 1 );
-
-/* Re-instate the original value of the Invert attributes of the supplied
-   Mappings. */
-   astSetInvert( pm, old_pinv );
-   astSetInvert( rm, old_rinv );
-
-/* Create the returned PermMap (unchanged). */
-   rm2 = astClone( rm );
-
-/* Create the returned PcdMap. */
-   cen[ 0 ] = ycen;
-   cen[ 1 ] = xcen;
-   pm2 = astPcdMap( disco, cen, "", status );
-   if( inverts[ ipc ] ) astInvert( pm2 );
-
-/* Replace the supplied Mappings with the ones created above, swapping the
-   order. */
-   if( astOK ){
-      (void) astAnnul( pm );
-      (void) astAnnul( rm );
-
-      old_pinv = inverts[ ipc ];
-
-      maps[ ipc ] = (AstMapping *) rm2;
-      inverts[ ipc ] = inverts[ 1 - ipc ];
-
-      maps[ 1 - ipc ] = (AstMapping *) pm2;
-      inverts[ 1 - ipc  ] = old_pinv;
-   }
-
-/* Return. */
-   return;
-}
-
-/* Functions which access class attributes. */
-/* ---------------------------------------- */
-/* Implement member functions to access the attributes associated with
-   this class using the macros defined for this purpose in the
-   "object.h" file. For a description of each attribute, see the class
-   interface (in the associated .h file). */
-/*
-*att++
-*  Name:
-*     Disco
-
-*  Purpose:
-*     PcdMap pincushion/barrel distortion coefficient.
-
-*  Type:
-*     Public attribute.
-
-*  Synopsis:
-*     Double precision.
-
-*  Description:
-*     This attribute specifies the pincushion/barrel distortion coefficient
-*     used by a PcdMap. This coefficient is set when the PcdMap is created,
-*     but may later be modified. If the attribute is cleared, its default
-*     value is zero, which gives no distortion. For pincushion distortion,
-*     the value should be positive. For barrel distortion, it should be
-*     negative.
-*
-*     Note that the forward transformation of a PcdMap applies the
-*     distortion specified by this attribute and the inverse
-*     transformation removes this distortion. If the PcdMap is inverted
-c     (e.g. using astInvert), then the forward transformation will
-f     (e.g. using AST_INVERT), then the forward transformation will
-*     remove the distortion and the inverse transformation will apply
-*     it. The distortion itself will still be given by the same value of
-*     Disco.
-*
-*     Note, the value of this attribute may changed only if the PcdMap
-*     has no more than one reference. That is, an error is reported if the
-*     PcdMap has been cloned, either by including it within another object
-*     such as a CmpMap or FrameSet or by calling the
-c     astClone
-f     AST_CLONE
-*     function.
-
-*  Applicability:
-*     PcdMap
-*        All PcdMaps have this attribute.
-
-*att--
-*/
-/* This ia a double value with a value of AST__BAD when undefined but
-   yielding a default of 0.0. */
-astMAKE_CLEAR1(PcdMap,Disco,disco,AST__BAD)
-astMAKE_GET(PcdMap,Disco,double,0.0,( ( this->disco == AST__BAD ) ?
-                                      0.0 : this->disco ))
-astMAKE_SET1(PcdMap,Disco,double,disco,value)
-astMAKE_TEST(PcdMap,Disco,( this->disco != AST__BAD ))
-
-
-/*
-*att++
-*  Name:
-*     PcdCen(axis)
-
-*  Purpose:
-*     Centre coordinates of pincushion/barrel distortion.
-
-*  Type:
-*     Public attribute.
-
-*  Synopsis:
-*     Floating point.
-
-*  Description:
-*     This attribute specifies the centre of the pincushion/barrel
-*     distortion implemented by a PcdMap. It takes a separate value for
-*     each axis of the PcdMap so that, for instance, the settings
-*     "PcdCen(1)=345.0,PcdCen(2)=-104.4" specify that the pincushion
-*     distortion is centred at positions of 345.0 and -104.4 on axes 1 and 2
-*     respectively. This attribute is set when a PcdMap is created, but may
-*     later be modified. If the attribute is cleared, the default value for
-*     both axes is zero.
-*
-*     Note, the value of this attribute may changed only if the PcdMap
-*     has no more than one reference. That is, an error is reported if the
-*     PcdMap has been cloned, either by including it within another object
-*     such as a CmpMap or FrameSet or by calling the
-c     astClone
-f     AST_CLONE
-*     function.
-
-*  Applicability:
-*     PcdMap
-*        All PcdMaps have this attribute.
-
-*  Notes:
-*     - If no axis is specified, (e.g. "PcdCen" instead of
-*     "PcdCen(2)"), then a "set" or "clear" operation will affect
-*     the attribute value of both axes, while a "get" or "test"
-*     operation will use just the PcdCen(1) value.
-*att--
-*/
-/* The centre of the distortion. AST__BAD is stored if no value has been
-   supplied, resulting in default values of zero being used. */
-MAKE_CLEAR(PcdCen,pcdcen,AST__BAD,2)
-MAKE_SET(PcdCen,double,pcdcen,value,2)
-MAKE_TEST(PcdCen,( this->pcdcen[axis] != AST__BAD ),2)
-MAKE_GET(PcdCen,double,0.0,(( this->pcdcen[axis] == AST__BAD ) ?
-                              0.0 : this->pcdcen[axis] ),2)
-
-/* Copy constructor. */
-/* ----------------- */
-/* No copy constructor is needed, as a byte-by-byte copy suffices. */
-
-/* Destructor. */
-/* ----------- */
-/* No destructor is needed as no memory, etc. needs freeing. */
-
-/* Dump function. */
-/* -------------- */
-static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
-/*
-*  Name:
-*     Dump
-
-*  Purpose:
-*     Dump function for PcdMap objects.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     void Dump( AstObject *this, AstChannel *channel, int *status )
-
-*  Description:
-*     This function implements the Dump function which writes out data
-*     for the PcdMap class to an output Channel.
-
-*  Parameters:
-*     this
-*        Pointer to the PcdMap whose data are being written.
-*     channel
-*        Pointer to the Channel to which the data are being written.
-*     status
-*        Pointer to the inherited status variable.
-*/
-
-/* Local Variables: */
-   AstPcdMap *this;              /* Pointer to the PcdMap structure */
-   double dval;                  /* Attribute value */
-   int set;                      /* Is a value set? */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain a pointer to the PcdMap structure. */
-   this = (AstPcdMap *) this_object;
-
-/* Write out values representing the instance variables for the
-   PcdMap class.  Accompany these with appropriate comment strings,
-   possibly depending on the values being written.*/
-
-/* In the case of attributes, we first use the appropriate (private)
-   Test...  member function to see if they are set. If so, we then use
-   the (private) Get... function to obtain the value to be written
-   out.
-
-   For attributes which are not set, we use the astGet... method to
-   obtain the value instead. This will supply a default value
-   (possibly provided by a derived class which over-rides this method)
-   which is more useful to a human reader as it corresponds to the
-   actual default attribute value.  Since "set" will be zero, these
-   values are for information only and will not be read back. */
-
-/* PcdCen(0). */
-/* ---------- */
-   set = TestPcdCen( this, 0, status );
-   dval = set ? GetPcdCen( this, 0, status ) : astGetPcdCen( this, 0 );
-   astWriteDouble( channel, "PcdCn0", set, 1, dval, "Distortion centre on first axis" );
-
-/* PcdCen(1). */
-/* ---------- */
-   set = TestPcdCen( this, 1, status );
-   dval = set ? GetPcdCen( this, 1, status ) : astGetPcdCen( this, 1 );
-   astWriteDouble( channel, "PcdCn1", set, 1, dval, "Distortion centre on second axis" );
-
-/* Disco. */
-/* ------ */
-   set = TestDisco( this, status );
-   dval = set ? GetDisco( this, status ) : astGetDisco( this );
-   astWriteDouble( channel, "Disco", set, 1, dval, "Distortion coefficient" );
-
-}
-
-/* Standard class functions. */
-/* ========================= */
-/* Implement the astIsAPcdMap and astCheckPcdMap functions using the macros
-   defined for this purpose in the "object.h" header file. */
-astMAKE_ISA(PcdMap,Mapping)
-astMAKE_CHECK(PcdMap)
-
-AstPcdMap *astPcdMap_( double disco, const double pcdcen[2],
-                       const char *options, int *status, ...) {
-/*
-*++
-*  Name:
-c     astPcdMap
-f     AST_PCDMAP
-
-*  Purpose:
-*     Create a PcdMap.
-
-*  Type:
-*     Public function.
-
-*  Synopsis:
-c     #include "pcdmap.h"
-c     AstPcdMap *astPcdMap( double disco, const double pcdcen[2],
-c                           const char *options, ... )
-f     RESULT = AST_PCDMAP( DISCO, PCDCEN, OPTIONS, STATUS )
-
-*  Class Membership:
-*     PcdMap constructor.
-
-*  Description:
-*     This function creates a new PcdMap and optionally initialises its
-*     attributes.
-*
-*     A PcdMap is a non-linear Mapping which transforms 2-dimensional
-*     positions to correct for the radial distortion introduced by some
-*     cameras and telescopes. This can take the form either of pincushion
-*     or barrel distortion, and is characterized by a single distortion
-*     coefficient.
-*
-*     A PcdMap is specified by giving this distortion coefficient and the
-*     coordinates of the centre of the radial distortion. The forward
-*     transformation of a PcdMap applies the distortion:
-*
-*        RD = R * ( 1 + C * R * R )
-*
-*     where R is the undistorted radial distance from the distortion
-*     centre (specified by attribute PcdCen), RD is the radial distance
-*     from the same centre in the presence of distortion, and C is the
-*     distortion coefficient (given by attribute Disco).
-*
-*     The inverse transformation of a PcdMap removes the distortion
-*     produced by the forward transformation. The expression used to derive
-*     R from RD is an approximate inverse of the expression above, obtained
-*     from two iterations of the Newton-Raphson method. The mismatch between
-*     the forward and inverse expressions is negligible for astrometric
-*     applications (to reach 1 milliarcsec at the edge of the Anglo-Australian
-*     Telescope triplet or a Schmidt field would require field diameters of
-*     2.4 and 42 degrees respectively).
-*
-c     If a PcdMap is inverted (e.g. using astInvert) then the roles of the
-f     If a PcdMap is inverted (e.g. using AST_INVERT) then the roles of the
-*     forward and inverse transformations are reversed; the forward
-*     transformation will remove the distortion, and the inverse
-*     transformation will apply it.
-
-*  Parameters:
-c     disco
-f     DISCO = DOUBLE PRECISION (Given)
-*        The distortion coefficient. Negative values give barrel
-*        distortion, positive values give pincushion distortion, and
-*        zero gives no distortion.
-c     pcdcen
-f     PCDCEN( 2 ) = DOUBLE PRECISION (Given)
-c        A 2-element array containing the coordinates of the centre of the
-f        An array containing the coordinates of the centre of the
-*        distortion.
-c     options
-f     OPTIONS = CHARACTER * ( * ) (Given)
-c        Pointer to a null-terminated string containing an optional
-c        comma-separated list of attribute assignments to be used for
-c        initialising the new PcdMap. The syntax used is identical to
-c        that for the astSet function and may include "printf" format
-c        specifiers identified by "%" symbols in the normal way.
-f        A character string containing an optional comma-separated
-f        list of attribute assignments to be used for initialising the
-f        new PcdMap. The syntax used is identical to that for the
-f        AST_SET routine.
-c     ...
-c        If the "options" string contains "%" format specifiers, then
-c        an optional list of additional arguments may follow it in
-c        order to supply values to be substituted for these
-c        specifiers. The rules for supplying these are identical to
-c        those for the astSet function (and for the C "printf"
-c        function).
-f     STATUS = INTEGER (Given and Returned)
-f        The global status.
-
-*  Returned Value:
-c     astPcdMap()
-f     AST_PCDMAP = INTEGER
-*        A pointer to the new PcdMap.
-
-*  Notes:
-*     - A null Object pointer (AST__NULL) will be returned if this
-c     function is invoked with the AST error status set, or if it
-f     function is invoked with STATUS set to an error value, or if it
-*     should fail for any reason.
-
-*  Status Handling:
-*     The protected interface to this function includes an extra
-*     parameter at the end of the parameter list descirbed above. This
-*     parameter is a pointer to the integer inherited status
-*     variable: "int *status".
-
-*--
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstPcdMap *new;              /* Pointer to new PcdMap */
-   va_list args;                /* Variable argument list */
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* Check the global status. */
-   if ( !astOK ) return NULL;
-
-/* Initialise the PcdMap, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitPcdMap( NULL, sizeof( AstPcdMap ), !class_init, &class_vtab,
-                        "PcdMap", disco, pcdcen );
-
-/* If successful, note that the virtual function table has been
-   initialised. */
-   if ( astOK ) {
-      class_init = 1;
-
-/* Obtain the variable argument list and pass it along with the options string
-   to the astVSet method to initialise the new PcdMap's attributes. */
-      va_start( args, status );
-      astVSet( new, options, NULL, args );
-      va_end( args );
-
-/* If an error occurred, clean up by deleting the new object. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return a pointer to the new PcdMap. */
-   return new;
-}
-
-AstPcdMap *astPcdMapId_( double disco, const double pcdcen[2],
-                         const char *options, ... ) {
-/*
-*  Name:
-*     astPcdMapId_
-
-*  Purpose:
-*     Create a PcdMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     AstPcdMap *astPcdMapId_( double disco, const double pcdcen[2],
-*                              const char *options, ... )
-
-*  Class Membership:
-*     PcdMap constructor.
-
-*  Description:
-*     This function implements the external (public) interface to the
-*     astPcdMap constructor function. It returns an ID value (instead
-*     of a true C pointer) to external users, and must be provided
-*     because astPcdMap_ has a variable argument list which cannot be
-*     encapsulated in a macro (where this conversion would otherwise
-*     occur).
-*
-*     The variable argument list also prevents this function from
-*     invoking astPcdMap_ directly, so it must be a re-implementation
-*     of it in all respects, except for the final conversion of the
-*     result to an ID value.
-
-*  Parameters:
-*     As for astPcdMap_.
-
-*  Returned Value:
-*     The ID value associated with the new PcdMap.
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstPcdMap *new;              /* Pointer to new PcdMap */
-   va_list args;                /* Variable argument list */
-
-   int *status;                  /* Pointer to inherited status value */
-
-/* Get a pointer to the inherited status value. */
-   status = astGetStatusPtr;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* Check the global status. */
-   if ( !astOK ) return NULL;
-
-/* Initialise the PcdMap, allocating memory and initialising the
-   virtual function table as well if necessary. */
-   new = astInitPcdMap( NULL, sizeof( AstPcdMap ), !class_init, &class_vtab,
-                        "PcdMap", disco, pcdcen );
-
-/* If successful, note that the virtual function table has been
-   initialised. */
-   if ( astOK ) {
-      class_init = 1;
-
-/* Obtain the variable argument list and pass it along with the options string
-   to the astVSet method to initialise the new PcdMap's attributes. */
-      va_start( args, options );
-      astVSet( new, options, NULL, args );
-      va_end( args );
-
-/* If an error occurred, clean up by deleting the new object. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return an ID value for the new PcdMap. */
-   return astMakeId( new );
-}
-
-AstPcdMap *astInitPcdMap_( void *mem, size_t size, int init,
-                           AstPcdMapVtab *vtab, const char *name,
-                           double disco, const double pcdcen[2], int *status ){
-/*
-*+
-*  Name:
-*     astInitPcdMap
-
-*  Purpose:
-*     Initialise a PcdMap.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     AstPcdMap *astInitPcdMap( void *mem, size_t size, int init,
-*                               AstPcdMapVtab *vtab, const char *name,
-*                               double disco, const double pcdcen[2] )
-
-*  Class Membership:
-*     PcdMap initialiser.
-
-*  Description:
-*     This function is provided for use by class implementations to initialise
-*     a new PcdMap object. It allocates memory (if necessary) to accommodate
-*     the PcdMap plus any additional data associated with the derived class.
-*     It then initialises a PcdMap structure at the start of this memory. If
-*     the "init" flag is set, it also initialises the contents of a virtual
-*     function table for a PcdMap at the start of the memory passed via the
-*     "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory in which the PcdMap is to be initialised.
-*        This must be of sufficient size to accommodate the PcdMap data
-*        (sizeof(PcdMap)) plus any data used by the derived class. If a value
-*        of NULL is given, this function will allocate the memory itself using
-*        the "size" parameter to determine its size.
-*     size
-*        The amount of memory used by the PcdMap (plus derived class data).
-*        This will be used to allocate memory if a value of NULL is given for
-*        the "mem" parameter. This value is also stored in the PcdMap
-*        structure, so a valid value must be supplied even if not required for
-*        allocating memory.
-*     init
-*        A logical flag indicating if the PcdMap's virtual function table is
-*        to be initialised. If this value is non-zero, the virtual function
-*        table will be initialised by this function.
-*     vtab
-*        Pointer to the start of the virtual function table to be associated
-*        with the new PcdMap.
-*     name
-*        Pointer to a constant null-terminated character string which contains
-*        the name of the class to which the new object belongs (it is this
-*        pointer value that will subsequently be returned by the astGetClass
-*        method).
-*     disco
-*        Distortion coefficient.
-*     pcdcen
-*        Distortion centre.
-
-*  Returned Value:
-*     A pointer to the new PcdMap.
-
-*  Notes:
-*     -  A null pointer will be returned if this function is invoked with the
-*     global error status set, or if it should fail for any reason.
-*-
-*/
-
-/* Local Variables: */
-   AstPcdMap *new;              /* Pointer to new PcdMap */
-
-/* Check the global status. */
-   if ( !astOK ) return NULL;
-
-/* If necessary, initialise the virtual function table. */
-   if ( init ) astInitPcdMapVtab( vtab, name );
-
-/* Initialise. */
-   new = NULL;
-
-/* Initialise a Mapping structure (the parent class) as the first component
-   within the PcdMap structure, allocating memory if necessary. Specify that
-   the Mapping should be defined in both the forward and inverse directions. */
-   new = (AstPcdMap *) astInitMapping( mem, size, 0,
-                                       (AstMappingVtab *) vtab, name,
-                                       2, 2, 1, 1 );
-
-   if ( astOK ) {
-
-/* Initialise the PcdMap data. */
-/* ---------------------------- */
-/* Store the shift and scale for each axis. */
-      new->pcdcen[0] = pcdcen[0];
-      new->pcdcen[1] = pcdcen[1];
-      new->disco = disco;
-
-/* If an error occurred, clean up by deleting the new PcdMap. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return a pointer to the new PcdMap. */
-   return new;
-}
-
-AstPcdMap *astLoadPcdMap_( void *mem, size_t size,
-                           AstPcdMapVtab *vtab, const char *name,
-                           AstChannel *channel, int *status ) {
-/*
-*+
-*  Name:
-*     astLoadPcdMap
-
-*  Purpose:
-*     Load a PcdMap.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "pcdmap.h"
-*     AstPcdMap *astLoadPcdMap( void *mem, size_t size,
-*                               AstPcdMapVtab *vtab, const char *name,
-*                               AstChannel *channel )
-
-*  Class Membership:
-*     PcdMap loader.
-
-*  Description:
-*     This function is provided to load a new PcdMap using data read
-*     from a Channel. It first loads the data used by the parent class
-*     (which allocates memory if necessary) and then initialises a
-*     PcdMap structure in this memory, using data read from the input
-*     Channel.
-*
-*     If the "init" flag is set, it also initialises the contents of a
-*     virtual function table for a PcdMap at the start of the memory
-*     passed via the "vtab" parameter.
-
-
-*  Parameters:
-*     mem
-*        A pointer to the memory into which the PcdMap is to be
-*        loaded.  This must be of sufficient size to accommodate the
-*        PcdMap data (sizeof(PcdMap)) plus any data used by derived
-*        classes. If a value of NULL is given, this function will
-*        allocate the memory itself using the "size" parameter to
-*        determine its size.
-*     size
-*        The amount of memory used by the PcdMap (plus derived class
-*        data).  This will be used to allocate memory if a value of
-*        NULL is given for the "mem" parameter. This value is also
-*        stored in the PcdMap structure, so a valid value must be
-*        supplied even if not required for allocating memory.
-*
-*        If the "vtab" parameter is NULL, the "size" value is ignored
-*        and sizeof(AstPcdMap) is used instead.
-*     vtab
-*        Pointer to the start of the virtual function table to be
-*        associated with the new PcdMap. If this is NULL, a pointer
-*        to the (static) virtual function table for the PcdMap class
-*        is used instead.
-*     name
-*        Pointer to a constant null-terminated character string which
-*        contains the name of the class to which the new object
-*        belongs (it is this pointer value that will subsequently be
-*        returned by the astGetClass method).
-*
-*        If the "vtab" parameter is NULL, the "name" value is ignored
-*        and a pointer to the string "PcdMap" is used instead.
-
-*  Returned Value:
-*     A pointer to the new PcdMap.
-
-*  Notes:
-*     - A null pointer will be returned if this function is invoked
-*     with the global error status set, or if it should fail for any
-*     reason.
-*-
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstPcdMap *new;              /* Pointer to the new PcdMap */
-
-/* Initialise. */
-   new = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return new;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(channel);
-
-/* If a NULL virtual function table has been supplied, then this is
-   the first loader to be invoked for this PcdMap. In this case the
-   PcdMap belongs to this class, so supply appropriate values to be
-   passed to the parent class loader (and its parent, etc.). */
-   if ( !vtab ) {
-      size = sizeof( AstPcdMap );
-      vtab = &class_vtab;
-      name = "PcdMap";
-
-/* If required, initialise the virtual function table for this class. */
-      if ( !class_init ) {
-         astInitPcdMapVtab( vtab, name );
-         class_init = 1;
-      }
-   }
-
-/* Invoke the parent class loader to load data for all the ancestral
-   classes of the current one, returning a pointer to the resulting
-   partly-built PcdMap. */
-   new = astLoadMapping( mem, size, (AstMappingVtab *) vtab, name,
-                         channel );
-
-   if ( astOK ) {
-
-/* Read input data. */
-/* ================ */
-/* Request the input Channel to read all the input data appropriate to
-   this class into the internal "values list". */
-      astReadClassData( channel, "PcdMap" );
-
-/* Now read each individual data item from this list and use it to
-   initialise the appropriate instance variable(s) for this class. */
-
-/* In the case of attributes, we first read the "raw" input value,
-   supplying the "unset" value as the default. If a "set" value is
-   obtained, we then use the appropriate (private) Set... member
-   function to validate and set the value properly. */
-
-/* PcdCen(0). */
-/* ---------- */
-      new->pcdcen[0] = astReadDouble( channel, "pcdcn0", AST__BAD );
-      if ( TestPcdCen( new, 0, status ) ) SetPcdCen( new, 0, new->pcdcen[0], status );
-
-/* PcdCen(1). */
-/* ---------- */
-      new->pcdcen[1] = astReadDouble( channel, "pcdcn1", AST__BAD );
-      if ( TestPcdCen( new, 1, status ) ) SetPcdCen( new, 1, new->pcdcen[1], status );
-
-/* Disco. */
-/* ------ */
-      new->disco = astReadDouble( channel, "disco", AST__BAD );
-      if ( TestDisco( new, status ) ) SetDisco( new, new->disco, status );
-
-/* If an error occurred, clean up by deleting the new PcdMap. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return the new PcdMap pointer. */
-   return new;
-}
-
-/* Virtual function interfaces. */
-/* ============================ */
-/* These provide the external interface to the virtual functions defined by
-   this class. Each simply checks the global error status and then locates and
-   executes the appropriate member function, using the function pointer stored
-   in the object's virtual function table (this pointer is located using the
-   astMEMBER macro defined in "object.h").
-
-   Note that the member function may not be the one defined here, as it may
-   have been over-ridden by a derived class. However, it should still have the
-   same interface. */
-
-
-
-
-