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*To*: Michael Sperber <sperber@xxxxxxxxxxxxxxxxxxxxxxxxxxx>*Subject*: Re: arithmetic issues*From*: bear <bear@xxxxxxxxx>*Date*: Thu, 17 Nov 2005 09:34:30 -0800 (PST)*Cc*: Thomas Bushnell BSG <tb@xxxxxxxxxx>, srfi-77@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-77@xxxxxxxxxxxxxxxxx*In-reply-to*: <y9lzmo3gs2u.fsf@xxxxxxxxxxxxxxxxxxxxxxxxxxx>*References*: <20051021145326.816C11B77BB@xxxxxxxxxxxxxxxxxxxxx> <20051021155906.GC16464@NYCMJCOWA2> <20051022023936.F0AAC1B77BB@xxxxxxxxxxxxxxxxxxxxx> <Pine.LNX.4.58.0510211945090.11738@xxxxxxxxxxxxxx> <87mzl1v5ha.fsf@xxxxxxxxxxxxxxxxx> <y9lzmo3gs2u.fsf@xxxxxxxxxxxxxxxxxxxxxxxxxxx>

On Thu, 17 Nov 2005, Michael Sperber wrote: > >Thomas Bushnell BSG <tb@xxxxxxxxxx> writes: > >> bear <bear@xxxxxxxxx> writes: >> >>> 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 [...] >> >> Yay! A convert! :) > >Now, this reads like you're agreeing with the approach of SRFI 77, if >not with all the details of its realization. Is that a correct >interpretation of what you two wrote? On my part, I think so.... what the programmer wants when he uses a mathematical operator is often not what he gets if the numbers are exact or inexact in a configuration unexpected to him, and specifying the operation directly is better than lying about the exactness of the results. I think of it in terms of principles: 1) I firmly believe that *relying* on numbers being inexact or *relying* on some value being not exactly representable is an error. This is because exactness is good; representations that can represent a larger or more useful subset of the numbers exactly are useful; and whenever an exact result is mathematically true no one should be constrained against returning the result exactly. 2) I firmly believe that converting numbers to inexact explicitly in order to gain access to fast mathematical operations that run in finite memory is something we shouldn't have to do. In the first place, exactness is good and this is throwing it away for the sake of a side effect on further computation. In the second place it may happen that the "side effect" we want, if we have vocabulary to specify it directly, may in many cases be had without the loss of that information. It may be that for most inputs, the fast operations do not encounter a roundoff error, and in that case returning exact results would be a bonus. 3) I firmly believe that even when results are known to be inexact, it should be the programmer's choice when and how to reduce their precision. If I have something that's 300 bits accurate but known to be inexact starting in the 301st bit, the language semantics should not force me to jump through hoops and convert to exact in order to access operations that preserve the known precision. This is even worse than the above case, because it's actively introducing *wrong* information for the sake of a side effect, and had we the ability to specify the effect directly, we could preserve the correct information through the operation. 4) I think that the simplest way to solve a whole lot of semantic nonsense is for there to be a one-to-one correspondence between exact and inexact numbers. But if there's a range conflict, I believe that the inexact numbers should *always* have the greater dynamic range. "number too large/small to be exactly represented" is valid, where "number too large/small to be inexactly represented, but we can represent it exactly" is just silly and invites lying about the exactness of operands and results. Bear

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

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

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

**Re: arithmetic issues***From:*bear

**Re: arithmetic issues***From:*Thomas Bushnell BSG

**Re: arithmetic issues***From:*Michael Sperber

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