Why You Cannot (Yet) Write an "Interval Arithmetic" Library in Common Lisp ... or: Hammering Some Sense into :ieee-floating-point

"Interval Arithmetic" (IA) appears to be a useful numerical tool to have at hand in several applications.  Alas, the current IA descriptions and proposed standards are always formulated in terms of the IEEE-754 standard, and the status of IEEE-754 compliance of most Common Lisp (CL) implementations is not up to par.

A solution would be for CL implementations to adhere to the Language Independent Arithmetic (LIA) IEC standard, which includes IEEE-754.

While the LIA standard provides a set of proposed bindings for CL, the format and depth of the specification documents is not readily usable by a CL programmer, should an implementation decide to comply with the provisions.  Moreover, much latitude is left to each implementation to provide the LIA "environmental" setup.

It would be most beneficial if more precision were agreed upon by the CL community about how to provide LIA compliance in the implementations.  In that case, a new set of documentation or manuals in the style of the HyperSpec could be provided, for the benefit of the CL programmer.

The goal of this paper is to foster a discussion within the CL community to converge on a complete specification for LIA compliance. The paper discusses some of the issues that must be resolved to reach that goal, e.g., error handling and full specification of mathematical functions behavior.