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*To*: bear <bear@xxxxxxxxx>*Subject*: Re: Wrapping up SRFI-70*From*: Paul Schlie <schlie@xxxxxxxxxxx>*Date*: Wed, 17 Aug 2005 22:08:57 -0400*Cc*: Aubrey Jaffer <agj@xxxxxxxxxxxx>, <srfi-70@xxxxxxxxxxxxxxxxx>*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*User-agent*: Microsoft-Entourage/11.1.0.040913

> From: bear <bear@xxxxxxxxx> > On Wed, 17 Aug 2005, Paul Schlie wrote: >> ... >> therefore in representations where they >> are not distinguishable, it would seem that it may then be correspondingly >> appropriate to presume values represented as infinites are over/under- >> flowed values, thereby implying that any value other than an exact >> infinity multiplied by an exact 0 is 0, and correspondingly implying >> that only 0/0 and/or any value who's absolute value is greater than 1 >> divided by, or who's absolute value is less than 1 multiplied by, an >> infinity are considered NaN's [aka 0/0] (as otherwise the resulting value >> will be known to be within the value ranges designated for infinites >> and/or their reciprocals, and represented as such)? > > Okay, I had to reread that three times, but if I understand > you correctly, I think I agree. I've been awake too long > maybe and I'm having trouble thinking around corners. In attempt to more clearly depict the above: (additive inverse axis) | * -sInf | * -s0.0 | * +s0.0 | * +sInf => sInf | => s0.0 | => s0.0 | => sInf --------|---------|---------|-------- (multiplicative Infinities) -Inf -1 -0.0 0 +0.0 +1 +Inf ==|=====|====|====|====|====|=====|== (multiplicative inverse axis) -0.0 -1 -Inf Inf +Inf +1 +0.0 --------|---------|---------|-------- (multiplicative NaN's) * sInf | * s0.0 | * s0.0 | * sInf => NaN | => NaN | => NaN | => NaN i.e: for x!=Inf: (* x 0) => 0, (/ x Inf) => 0 ; true zero for x!=0: (* x Inf) => Inf, (/ x 0) => Inf ; true infinity for x<=-1: (* x -Inf) => +Inf, (/ x -0.0) => +Inf ; +infinity/overflow (* x +Inf) => -Inf, (/ x +0.0) => -Inf ; -infinity/overflow for -1<=x<0: (* x -0.0) => +0.0, (/ x -Inf) => +0.0 ; +zero/underflow (* x +0.0) => -0.0, (/ x +Inf) => -0.0 ; -zero/underflow for 0<x<=+1: (* x +0.0) => +0.0, (/ x +Inf) => +0.0 ; +zero/underflow (* x -0.0) => -0.0, (/ x -Inf) => -0.0 ; -zero/underflow for +1<=x: (* x +Inf) => +Inf, (/ x +0.0) => +Inf ; +infinity/overflow (* x -Inf) => -Inf, (/ x -0.0) => -Inf ; -infinity/overflow otherwise for any other value of x above, => NaN

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