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precision, accuracy, and floating conversion (GJC's comment)

GJC's view that a floating point number x means an interval
[x-epsilon,x+epsilon]  for some unknown epsilon, is not
treated kindly in most of the current thinking about floating
point arithmetic.  To be consistent here, you should also propose
that in combining floating point numbers, the SHORTEST precision
should be used, because that would indicate that the answer is 
particularly uncertain.

As for GJC's example, if I understand it, you want a floating point
number so you can return (the float (* 1/2 ...))  or (* (the float 1/2) ...)