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IEEE 754 floating-point arithmetic is not completely ordered



In IEEE 754 floating-point arithmetic, if x is NaN then none of x < y, 
x=y, or x>y is true for any y (not even x=x).  How do you propose to 
implement compare-real?  You say sign(x-y) is computed, but this may 
not have a consistent definition if x or y is a NaN.

You give an example involving PLT 208 and coercion of an exact real 
part to inexact because of an inexact imaginary part.  You might note 
that other Scheme implementations may not require or implement this 
coercion.

Brad Lucier