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This page is part of the web mail archives of SRFI 73 from before July 7th, 2015. The new archives for SRFI 73 contain all messages, not just those from before July 7th, 2015.

*To*: schlie@xxxxxxxxxxx*Subject*: Re: comparison operators and *typos*From*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Date*: Mon, 27 Jun 2005 13:53:19 -0400 (EDT)*Cc*: srfi-73@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-73@xxxxxxxxxxxxxxxxx*In-reply-to*: <BEE514F8.A9E5%schlie@xxxxxxxxxxx> (message from Paul Schlie on Mon, 27 Jun 2005 02:29:12 -0400)*References*: <BEE514F8.A9E5%schlie@xxxxxxxxxxx>

| Date: Mon, 27 Jun 2005 02:29:12 -0400 | From: Paul Schlie <schlie@xxxxxxxxxxx> | | I wonder if the following may represent a reasonable balance between | existing assumptions/practice/code and the benefits of a virtually | bounded reciprocal real number system: | | 1/0 == inf ; exact sign-less 0 and corresponding reciprocal. | 1/0.0 == inf.0 ; inexact sign-less 0.0 and corresponding reciprocal. | 1/-0 == -inf ; exact signed 0, and corresponding reciprocal. | 1/-0.0 == -inf.0 ; inexact signed 0, and corresponding reciprocal. | 1/+0 == +inf ; exact signed 0, and corresponding reciprocal. | 1/+0.0 == +inf.0 ; inexact signed 0, and corresponding reciprocal. | | (where sign-less infinities ~ nan's as their sign is ambiguous) | | And realize I've taken liberties designating values without decimal points | as being exact, but only did so to enable their symbolic designation if | desired to preserve the correspondence between exact and inexact | designations. (as if -0 is considered exact, then so presumably must -1/0) | | Thereby one could define that an unsigned 0 compares = to signed 0's to | preserve existing code practices which typically compare a value against | a sign-less 0. i.e.: | | (= 0 0.0 -0 -0.0) => #t | (= 0 0.0 +0 +0.0) => #t | | (= -0 -0.0 +0 +0.0) => #f The `=' you propose is not transitive, which is a requirement of R5RS. | While preserving the ability to define a relative relationship between | the respective 0 values: | | (< 1/-0 -0 +0 1/+0) => #t | | (<= 1/-0 1/-0.0 -0 -0.0 0 +0 +0.0 1/+0 1/+0.0) => #t | | (= 1/0 1/0.0) => #t ; essentially nan's | (= 1/0 1/+0) => #f ; as inf (aka nan) != +inf | | Correspondingly, it seems desirable, although apparently contentious: | | 1/0 == inf :: 1/inf == 0 :: 0/0 == 1/1 == inf/inf == 1 Are you saying that (/ 0 0) ==> 1 or that (= 0/0 1)? Mathematical division by 0 is undefined; if you return 1, then code receiving that value can't detect that a boundary case occured. | and (although most likely more relevant to SRFI 70): | | x^y == 1 | | As lim{|x|==|y|->0} x^y :: lim{|x|==|y|->0} (exp (* x (log y))) = 1 | | As it seems that the expression should converge to 1 about the | limit of 0; as although it may be argued that the (log 0) -> -inf, | it does so at an exponentially slower rate than it's operand, | therefore: lim{|x|==|y|->0} (* x (log y)) = 0, and lim{|x|==|y|->0} | (exp (* x (log y))) = (exp 0) = 1; and although it can argued that | it depends on it's operands trajectories and rates, I see no valid | argument to assume that it's operands will not approach that limit | at equivalent rates from equidistances, That would mean that the program was computing some variety of x^x. Lets look at some real examples. FreeSnell is a program which computes optical properties of multilayer thin-film coatings. It has three occurrences of EXPT. opticolr.scm:152: (let ((thk (* (expt ratio-thk (/ (+ -1 ydx) (+ -1 cnt-thk))) opticolr.scm:173: (let ((thk (* (expt ratio-thk (/ (+ -1 ydx) (+ -1 cnt-thk))) opticompute.scm:131: (let ((winc (expt (/ wmax wmin) (/ (+ -1 samples))))) | which will also typically yield the most useful result, and tend | not to introduce otherwise useless value discontinuities and/or | ambiguities. (expt 0 0) ==> 1 is one of the possibilities for SRFI-70. | Where I understand that all inf's are not strictly equivalent, but when | expressed as inexact values it seems more ideal to consider +-inf.0 to | be equivalent to the bounds of the inexact representation number system, | thereby +-inf.0 are simply treated as the greatest, and +-0.0 the smallest | representable inexact value; as +-1/0 and +-0 may be considered abstractions | of exact infinite precision values if desired. | | However as it's not strictly compatible with many existing floating point | implementations, efficiency may be a problem? (but do like it's simplifying | symmetry). | |

**References**:**Re: comparison operators and *typos***From:*Paul Schlie

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