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