Variable length data formats

The purpose of this paper is to discuss a number of variable length floating point and integer formats and to give the various advantages and disadvantages of their use. Often it is known in advance that a given integer will not exceed a certain magnitude or that a particular floating point number is accurate to only 'n' places of accuracy. Faced with this, it is good engineering to choose variable length floating point and integer formats which require the least amount of hardware or the minimum amount of software or which have some other dominant advantage. The formats discussed have the advantage that length change algorithms are invariant with respect to data types (unsigned, signed, floating point, integers, and complex numbers). The STARAN associative array processor, which uses a completely variable fixed point and floating point formats, is described.