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*To*: Common-Lisp @ SU-AI*Subject*: gaussian rationals, transcendental functions, etc.*From*: Alan Bawden <ALAN @ MIT-MC>*Date*: Sun, 05 Jun 1983 22:58:00 -0000

Date: 5 Jun 83 11:13:57 PDT (Sun) From: fateman%UCBKIM at Berkeley (Richard Fateman) Frankly, complex arithmetic should not be designed by a consensus of Lisp hackers. The difference between mathematical theory and computation is perhaps not clear to Alan, but there is a difference between thinking mathematically and computationally. I believe I have now argued this point from both mathematical and computational standpoints, and have demonstrated how to fit the two together acceptably. I'll not continue to argue the issue. If a degree in mathematics and several years experience as a "Lisp hacker" don't qualify me to have an intelligent opinion on this subject in fateman's eyes, so be it. If anyone else would like to say something new on the subject... The issue raised by Fahlman about needing a rule that says that that putting in a real gets you a real answer if possible, is dealt with by specifying appropriate ranges for the transcendental functions. In the laser manual, GLS has already suggested ranges that have this property. (This is nothing new really, mathematicians have always chosen the principle values of such functions to satisfy Fahlman's rule.) Let me reiterate what I said yesterday: the only new behavior exhibited by that handful of transcendental functions, when given a pure real argument, would be the generation of a complex number in some cases, rather than an error. BTW, I accidentally excluded the EXPT function from my list of transcendental functions that have "questionable" (from a user-interface, or "computational" viewpoint) regions in the real part of their domains. So make that 7 functions with the "problem". The suggestion that numbers like #C(3/4 3.14159) be eliminated has a certain appeal. Would the proposal extend to eliminating numbers like #C(1.0S0 1.0L0)? Eliminating such mixed floating types might frowned upon by the masters of floating point, although I can also imagine that converting this to #C(1.0L0 1.0L0), (that is, converting to the maximum of the two precisions), would be acceptable to them.

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