Delta compressed Storage Form

In this form of storage, the values stored internally within an NDF's array component are a compressed form of the external values of interest to application code. Delta form provides a lossless compression scheme designed for arrays of integers in which there is at least one pixel axis along which the array value changes only slowly. It uses two methods to achieve compression:

• Differences between adjacent data values are stored, rather than the full data values themselves. For many forms of astronomical data, the differences between adjacent data values have a much smaller range than the data values themselves. This means that they can be represented in fewer bits. For instance, if the data values are _INTEGER, then the differences between adjacent values may fit into the range of a _WORD (-32767 to +32767) or even a _BYTE (-127 to +127). This use of a shorter data type usually provides the majority of the compression. However, it is not necessary for all differences to be small - if the difference between two adjacent data values is too large for the compressed data type, the second of the two data values will be stored explicitly using the full data type of the original uncompressed data. Obviously, the more values that need to be stored in full in this way, the lower will be the compression.

  In the above description, the term ``adjacent'' means ``adjacent along a specified pixel axis''. The pixel axis along which differences are taken is referred to as the ``compression axis''. It may be specified explicitly by the calling application when NDF_ZDELT is called, or it may be left unspecified in which case NDF_ZDELT will choose the axis that gives the best compression.

• If the uncompressed array contains runs of more than three identical values along the compression axis, then the run of identical values is replaced by a single value (stored in full, not as a difference) and a repetition count.

Support for delta arrays is currently limited, since it is anticipated that they will only be of interest as an archive format. The following details should be noted:

1. Delta arrays are ``read-only''. An error will be reported if an attempt is made to map a delta array for WRITE or UPDATE access. When mapped for READ access, the pointer returned by NDF_MAP provides access to the original uncompressed data values.

2. The result of copying a delta array (for instance, using NDF_PROP, etc.) will be an equivalent simple array.

3. Delta arrays cannot be created directly. To create an NDF with delta compressed arrays, first create an NDF with simple arrays, and then copy it using NDF_ZDELT. The output NDF created by NDF_ZDELT is a copy of the input NDF, but stored with delta storage form.

4. Delta form can only be used to store integer data values, but NDFs with floating point data values may be compressed indirectly, by first storing the floating point values in a scaled NDF, and then using NDF_ZDELT to create a delta compressed copy of the scaled NDF. Note, the scaled NDF must use an integer data type to store the internal (i.e. scaled) values. The use of the scaled NDF means that the compression is not lossless, since some information will have been lost in scaling the floating point values into integers.

5. The NDF_GTDLT routine will return details of the compression applied to a delta compressed NDF array component.

6. Delta arrays cannot have complex data types. An error will be reported if an attempt is made to to import an HDS structure describing a complex delta array.

7. When applied to a delta array, the NDF_TYPE and NDF_FTYPE routines return information about the data type of the original uncompressed data values.