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*To*: <srfi-77@xxxxxxxxxxxxxxxxx>*Subject*: Re: arithmetic issues*From*: Paul Schlie <schlie@xxxxxxxxxxx>*Date*: Wed, 18 Jan 2006 22:25:47 -0500*Delivered-to*: srfi-77@xxxxxxxxxxxxxxxxx*Thread-index*: AcYcqAm7SFGmuoibEdqC6wADk1ictA==*Thread-topic*: arithmetic issues*User-agent*: Microsoft-Entourage/11.2.1.051004

As a potential hybrid alternative (being a believer that all numeric types beyond some "reasonable" minimally useful fixnum precision should be enabled though optionally, although possibly typically, supported libraries); might it be acceptable to consider modeling fixnums after flonums whose operations are arguably closed over their domain bounded by infinites; thereby some minimally required fixnum precision domain may be similarly bounded by infinites and thereby closed over arithmetic operations? Thereby hypothetically to keep things real simple, it may even be considered reasonable to bound fixnums by a sign-less Inf (i.e. NaN); effectively enabling basic balanced fixnums to be defined as: NaN -(2^(P-1)-1) 0 +(2^(P-1)-1) NaN [where NaN is effectively = -2^(P-1), i.e. the pattern 10...] Thereby any overflow may be relatively easily detected, and trapped to return NaN, which in turn closes all subsequent operations to corresponding return NaN. Where then precision required beyond (for the sake of argument P=16) and more efficient modulo and/or greater precision fixnum data types may be enabled through either virtual or literal libraries, as would be the support for extended exact and inexact data types and their correspondingly overloaded operators? Where further for the sake of argument, as I personally dislike the proposed use of typed functions (i.e. fl+ etc.); I'd much prefer that simple default semantics be defined for mixed data type operations. For example something along the line of "operations will be performed in the declared order at the precision of the most precise operand"; and enable the precision of the operation to be generically explicitly controlled by enabling either the operator and/or operands to be cast to an alternate explicit type, i.e.: (+ 1/4 2.5) :: (+ 1/4 (<exact> 2.5)) :: (+ 1/4 5/2) => 11/4 <exact> ; as <exact> is most precise. ((<float> +) 1/4 2.5) :: (+ (<float> 1/4) (<float> 2.5)) :: (+ 0.25 2.5) => 2.75 <float> ; as both operands were effectively cast to <float>. (+ (<fixed> 1/4) 2.5) :: (+ 0 2.5) => 2.5 <float> ; as <float> is most precise. ((<fixed> +) 1/4 2.5) :: (+ (<fixed> 1/4) (<fixed> 2.5)) :: (+ 0 2) => 2 <fixed> ; as both operands were effectively cast to <fixed>.

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