The routine works on one dimension at a time. When supplied with the lower and upper bounds of a rectangular region (box) of input coordinate space, it finds the lowest and highest values taken by a nominated output coordinate within that region. It also returns the input coordinates where these bounding values are attained. It should be used repeatedly to obtain the extent of the bounding box in more than one dimension.
Note that it is permissible for the upper bound to be less than the corresponding lower bound, as the values will simply be swapped before use.
(If the inverse transformation is selected, then references to "input" and "output" coordinates in this description should be transposed. For example, the size of the LBND_IN and UBND_IN arrays should match the number of output coordinates, as given by the Mapping's Nout attribute. Similarly, the COORD_OUT argument, below, should nominate one of the Mapping's input coordinates.)
AST A Library for Handling World Coordinate Systems in Astronomy