Rationale for the proposed standard for a generic package of elementary functions for Ada

Abstract

This paper supplements the "Proposed Standard for a Generic Package of Elementary Functions for Ada," written by the ISO-IEC/JTC1/SC22/WG9 (Ada) Numerics Rapporteur Group. Based on recommendations made jointly by the ACM SIGAda Numerics Working Group and the Ada-Europe Numerics Working Group, the proposed elementary functions standard is the first of several anticipated collateral standards to address the interrelated issues of portability, efficiency, and robustness of numerical software written in Ada. Organized as a series of questions and answers, this supplement outlines the reasoning by which the proposed standard came to acquire certain features and exclude others.

A portable generic elementary function package in Ada and an accurate test suite

“…At present, the proposal is on its way through a hierarchy of committees toward achieving the status of a secondary ISO standard. A detailed rationale of the proposed standard has been written by Dritz [7]. To describe in a self-contained manner our portable implementation of the proposed standard, we summarize its features that concern us the most.…”

“…The calling sequences are Sin(X,Cycle), Cos(X,Cycle), ... , and Arccot(Y,X,Cycle). It will become clear later on why the first 8 functions are not eliminated by assigning suitable default values to the parameter Cycle in the last 8 functions (see also [7]). …”

Rationale for the Proposed Standard for a Generic Package of Primitive Functions for Ada

“…It took considerable effort to describe the primitive function s so that they could be implemented in either IEEE or non-IEEE environments . This issue also had ramification s for the elementary functions standard, resulting in a recent revision of it [10] and in the updating of its rationale document [5] .…”

“…Those imposing the restriction must document it; they can safely use suc h variables, but they must behave in one of several stated ways (i .e ., predictably) if the restriction is violated . (For a detailed discussion of the genesis of this optional restriction and its implications, see the latest revision of [5] . Th e freedom of an implementation to impose the restriction will be revoked in the future if and when Ada-for example , as part of the Ada 9X revision process-acquires additional functionality that allows the declaration of variable s having the precision, but not the range, of a generic formal floating-point type.)…”

Introduction to the proposed standard for the elementary functions in Ada

“…The difference is reflected in the use of subprogram overloading to accommodate tw o versions of the trig functions, one with and one without a CYCLE parameter . (The preceding discussion touches on one of many issues that came up during the development of the standard ; further details can be found in its "rationale" document [3] . ) For similar reasons, the natural-or Napierian-logarithm and logarithms to an arbitrary base are accommodated by a pair of overloaded subprograms for LOG, with and without a BASE parameter, rather than by a singl e subprogram with an optional BASE parameter having a default value .…”