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The Rationale for the section "Fixnums" begins:
Rationale: The operations whose names begin with fixnum implement arithmetic on a quotient ring of the integers ...
No finite quotient ring of the integers is an ordered ring [1](any ordered ring with identity contains an isomorphic copy of the integers, so it is infinite), so the operations that rely on order, namely,
fixnum> fixnum< fixnum>= fixnum<= fixnum-positive? fixnum-negative? fixnum-max fixnum-min don't make sense. I suggest they be removed.Once they *are* removed, then there seems to be no reason to have (now partially) parallel definitions of fixnum-* operations, most of which do *exactly* the same thing as their fx* counterpart.
It would be more helpful identify and list the few fx* and fixnum-* operations that might overflow, and so have different semantics, and specify
Brad [1] An ordered ring satisfies (1) Given a and b, precisely one of a < b, a = b, or a > b is true. (2) Given a < b and any c, a+c < b+c; and if c > 0 then a*c < b*c. (3) x < y and y < z implies x < z.The presumed fixnum-* operations, which claim to operate on a ring, rely on an ordering doesn't satisfy these properties. Without these properties, flow analysis, stated as one of the motivations of this SRFI, of inequalities is useless.