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*To*: rrrs-authors@ai.mit.edu*Subject*: non-generic arithmetic*From*: tmb@idiap.ch (Thomas M. Breuel)*Date*: Mon, 1 Jun 92 21:54:46 +0200

=> PROPOSAL Several people (including myself) have in the past asked for a standardization of non-generic arithmetic procedures. Several implementations provide such procedures already, and it would be useful to standardize them by adding them as a non-essential feature to the standard, or at least by agreeing informally to a common naming scheme. => RATIONALE The reasons why people want to use such procedures are two-fold: (1) efficiency (many compilers simply aren't smart enough to optimize the Scheme number system), and (2) a different view of arithmetic (in which, say, there are "real" functions that only take real arguments and return real values and flag errors if they get an argument of the wrong type or cannot represent the result as a real number). => GOALS I think such procedures * should be defined such that applying the procedures to an object of the wrong type (e.g., "(flonum-sin 1)") results in an error (*) * should be "arithmetically safe", i.e., overflows and other arithmetic errors should be detected * should have names that allow people to use them conveniently and regularly in their code => PORTABLE IMPLEMENTATIONS A reasonably portable implementation might define "flonum-+" in terms of type-checks, coercions, and the "+" function. Such an implementation would allow code written in terms of the non-generic primitives to be executed on implementations that do not support non-generic arithmetic. Of course, I would hope that many compilers actually try to do a better job at generating code for such procedures. => NAMING Prefix schemes are commonly used for naming arithmetic operations of the kind proposed here. That is, the name of a non-generic arithmetic function is derived by putting a prefix in front of the name of the corresponding generic function. People would use these operations primarily with fixnums and flonums; hence, the prefixes for those functions should be short: DATATYPE PREFIX fixnum x or i (as in fi[x]num or f[i]xnum) flonum f rational rational integer integer real real complex complex For functions that begin with a non-alphanumeric letter, the prefix is used directly. For other functions, it is separated by a "-" from the name of the corresponding generic procedure. Examples: f+ x* f-sin rational+ rational-quotient complex-sin => STANDARD I'm not sufficiently familiar with a lot of Scheme dialects to make a more concrete proposal, and I'm not well-versed in writing sections for the Scheme standard, so I hope that somebody else can pick this up from here. Of course, some care must be taken to say what is meant by "fixnum" and "flonum" and how that relates to the rest of the number system in Scheme. In particular, it should be made clear that this proposal in no way constitutes a recommendation to implement "fixnum" and "flonum" types, but merely suggests a naming convention if such types are already present in the implementation (as they are, in many implementations). Thomas. (*) I think it is a bad idea to allow implementations not to flag an error for something like "(flonum-sin 1)", since it makes it very difficult to track down unportable constructs on implementations that, say, silently convert the integer 1 to a floating point number. I have encountered such problems frequently when trying to port Lisp code that had type declarations in it that were never actually checked by the implementation that the code was developed on.

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