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*To*: will@xxxxxxxxxxx*Subject*: Re: numerical conditioning MAGNITUDE and /*From*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Date*: Wed, 21 Jun 2006 20:47:26 -0400 (EDT)*Cc*: srfi-77@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-77@xxxxxxxxxxxxxxxxx*In-reply-to*: <E1Ft6iN-0001YC-W0@xxxxxxxxxxxxxxxxx> (message from William D Clinger on Wed, 21 Jun 2006 13:42:08 -0400)*References*: <E1Ft6iN-0001YC-W0@xxxxxxxxxxxxxxxxx>

| From: William D Clinger <will@xxxxxxxxxxx> | Date: Wed, 21 Jun 2006 13:42:08 -0400 | | Aubrey Jaffer wrote: | > The correct versions are unlikely to be much slower than naive | > ones; correct-/ is perhaps faster. So the arguments for | > implementing these procedures incorrectly are weak. | | I haven't heard any arguments at all for implementing | those procedures incorrectly. I got ahead of myself. (where is that strawman!) | On the other hand, it often happens that people fail | to distinguish between arguments for incorrectness | and arguments against attempting to require correctness. | | We often see this in the political and legal arenas. | If you oppose a constitutional amendment to make | flag-burning a capital offense, someone will say you | want people to burn flags. Requiring MAGNITUDE and / to work over their full ranges is good because it provides more portability between implementations. Objections I can think of are: * the full-range implementation might run more slowly; * implementations should be free to restrict the range of arithmetic functions; and * that MAGNITUDE and / should work over their full ranges is too obvious to state in a specification. How would such a constraint be expressed? The tangent function proved a counterexample to general statements about the output range of functions. But specifics seem workable: The procedure MAGNITUDE returns a finite real nonnegative number for every argument whose (mathematical) magnitude is less than the most-positive-finite-flonum in the implementation. The procedure / applied to z1 and z2 returns a finite number when (/ (magnitude z1) (magnitude z2)) is less than the most-positive-finite-flonum in the implementation. Both of these constraints are compatible with both polar and rectangular representations of complex numbers.

**References**:**Re: numerical conditioning MAGNITUDE and /***From:*William D Clinger

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