| Abstract: | The specification of a truly portable implementation independent programming language requires that digital arithmetic be specified in an implementation independent manner. Variable length storage is proposed for digital numbers. Linked storage and linked overflow storage are proposed so as to enable the use of variable length numbers. It is suggested that significant digit arithmetic be used for single numbers and interval arithmetic be used for interval pairs. The question is put to numerical mathematicians to specify the decision rules to be used in deciding on the number of digits to be retained when computing in either the significant digit mode or in the interval mode. The question is also raised as to what other arithmetic modes should be provided for. The speculation is offered not for the purposes of suggesting useful hardware design techniques but rather to indicate feasibility of some design. If the implementation independent arithmetic is considered feasible, then language designers can design a language freed from present hardware restrictions. |
