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*To*: gls@think.com*Subject*: Numbers and Pork Rinds*From*: Luddy Harrison <harrison@s45.csrd.uiuc.edu>*Date*: Fri, 25 Aug 89 10:30:39 PDT*Cc*: bawden.pa@xerox.com, rrrs-authors@mc.lcs.mit.edu*In-Reply-To*: Guy Steele's message of Thu, 24 Aug 89 12:28:42 EDT <8908241628.AA00798@verdi.think.com>

>Hey, all you out there: does anyone else care? Has anyone's mind been >changed as a result of our discussion? Yes. I have but a minor comment to make. Alan, the inexactness you attribute to floating point numbers is not a property of the representation itself, but rather its interpretation (as a projection of the space of real values). I, knowing the algebra of a floating point implementation, may certainly write down an "exact" computation in terms of floating point values. For example: (+ 2.0 3.0). Knowing that by 2.0 and 3.0 I mean exactly 2 and 3, and knowing the floating point unit of my machine, I know that the 5.0 that results will be an "exact" result. By the same token, I may write down an "inexact" computation in terms of integers. For example, let H be a procedure that heuristically evaluates a chess position and returns an integer representing the goodness of the position. I interpret H's return value as an interval, a distribution, around the "real" goodness of the board. Now, when I write (max (H board-1) (H board-2)), I don't expect max to understand that its arguments are grossly lacking in precision. Neither would I expect it to do so if H returned a floating point value. It is my job to determine the MEANING of the representations I ask the computer to manipulate; I want only for the computer to act predicatably upon the representations. Predictably, in the case of floating point values, has traditionally meant that the computer behaves as though the values were exact. -Luddy Harrison

**Follow-Ups**:**Numbers and Pork Rinds***From:*Alan Bawden <bawden@arisia.xerox.com>

**References**:**Numbers and Pork Rinds***From:*Guy Steele <gls@think.com>

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