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*Subject*: Re: arithmetic issues*From*: bear <bear@xxxxxxxxx>*Date*: Fri, 21 Oct 2005 20:55:03 -0700 (PDT)*Cc*: srfi-77@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-77@xxxxxxxxxxxxxxxxx*In-reply-to*: <20051022023936.F0AAC1B77BB@xxxxxxxxxxxxxxxxxxxxx>*References*: <20051021145326.816C11B77BB@xxxxxxxxxxxxxxxxxxxxx> <20051021155906.GC16464@NYCMJCOWA2> <20051022023936.F0AAC1B77BB@xxxxxxxxxxxxxxxxxxxxx>

It's been an interesting discussion. I started with a some well-defined prejudices and several barely-connected ideas, and I've been refining them - discovering what I think is the "right thing" - by agreeing and disagreeing with points people have made. First of all, I want to say explicitly that I agree with the idea that Scheme (or any good lisp) ought to express algorithms, not hardware implementation. So I reject the idea that anything in numerics should depend on a particular representation, IEEE sanctioned or not. But that doesn't mean we have infinite memory available to run programs on, and there is a vital purpose to serve (a necessary feature) in knowing how much computation to expend and space to allocate for a particular operation or a particular result. I was surprised by (and agree completely with) the suggestion that there should be multiple different functions for addition (and other functions) depending on what behaviors you want; is it more important to preserve exactness given exact arguments, or more important to produce a result of a known and finite size? Should the size depend on the size of the arguments, or the degree to which the arguments' precision is known, or just be equal to some constant? Would you prefer modular arithmetic with some user-definable modulus that happens to be ridiculously fast if the user chooses 2^32? etc... These are all different functions. We should probably give them names and standard semantics and build specialized math libraries around them. We can even implement these math libraries in portable R5RS scheme code (assuming the existence of bignums of course) noting drily that the implementor can of course provide a much faster solution on most current architectures. This was like a light going on; it's just plain obvious in retrospect. Bear

**Follow-Ups**:**Re: arithmetic issues***From:*Thomas Bushnell BSG

**References**:**arithmetic issues***From:*Aubrey Jaffer

**Re: arithmetic issues***From:*John.Cowan

**Re: arithmetic issues***From:*Aubrey Jaffer

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