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*To*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Subject*: Re: comparison operators and *typos*From*: Paul Schlie <schlie@xxxxxxxxxxx>*Date*: Thu, 30 Jun 2005 20:11:03 -0400*Cc*: <srfi-70@xxxxxxxxxxxxxxxxx>*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <20050630001817.1A6B51B77B4@xxxxxxxxxxxxxxxx>*User-agent*: Microsoft-Entourage/11.1.0.040913

> If we make (/ +1 0.0) ==> #i+1/0, then (/ -1 0.0) ==> #i-1/0. > This choice is arbitrary; ... - which seems very reasonable. > | > Inexact infinities have reciprocals: zero. Their reciprocals > | > are not unique, but that is already the case with IEEE-754 > | > floating-point representations: > ... > Zero is at the center of 0.0's neighborhood. R5RS division by 0.0 > is an error; leaving latitude for SRFI-70's response. - also seems very reasonable, and provide the opportunity to reconsider eliminating IEEE-754's otherwise inconsistent asymmetry, by defining: (/ #i-0/1) => #i-1/0 ; -inf.0 (/ #i+0/1) => #i+1/0 ; +inf.0 thereby truly consistently symmetric with the above: (/ #i-1/0) => #i-0/1 ; -0.0 (/ #i+1/0) => #i+0/1 ; +0.0 > Most neighborhoods mapping through functions project onto adjacent > neighborhoods. But / near 0 is not the only function which does not. > TAN near pi/2 is another example. - and please reconsider this may be consistently symmetrically defined: [where ~ denotes a value being simultaneously positive and negative] (/ #i~0) => #i~1/0 ; ~inf.0 (/ #i~1/0) => #i~0 ; ~0.0 (tan pi/2) => #i~1/0 ; ~inf.0 (abs ~inf.0) => +inf.0 (- (abs ~inf.0) => -inf.0 (abs ~0.0) => +0.0 (- (abs ~0.0)) -0.0 (+ +0.0 -0.0) => ~0.0 Where I believe it's reasonable to redefine the use of IEEE's NAN values to encode these values, as arguably ~inf.0 may be thought of as being NAN, and ~0.0 as being 1/NAN (leaving 0.0 == +0.0)

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