The Fortress Language Specification - CiteSeerX

25.1.11 opr (self,other: Q):Boolean
The comparison operators < , ≤ , = , ≥ , and > allow any rational value to be compared numerically to any other
rational value.
For types Q ∗ and Q # , the rational values are totally ordered except for 0/0 , which is unordered with respect to
all other rational values; moreover, for compatibility with floating-point arithmetic, 0/0 is unordered with respect to
itself, and therefore these five comparison operators always return false if either argument is 0/0 . The value −∞ is
less than any finite rational value, and +∞ is greater than any finite rational value.
For ≠ see Section 26.1.4.
25.1.16 opr CMP(self,other: Q): TotalComparison
25.1.17 opr CMP(self,other: Q # ):Comparison
The CMP operator compares the arguments and returns one of the four values LessThan, EqualTo, GreaterThan,
and Unordered. If the argument types are such that the result cannot be Unordered, then the result has type
TotalComparison rather than simply Comparison.
25.1.18 opr MAX(self,other: Q): Q
25.1.19 opr MIN(self,other: Q): Q
25.1.20 opr MAXNUM(self,other: Q): Q
25.1.21 opr MINNUM(self,other: Q): Q
The operators MAX and MAXNUM return whichever argument is larger in the total order defined by < , ≤ , = , ≥ , > ,
and CMP , and the operators MIN and MINNUM return whichever argument is smaller. (For all four, if the arguments
are equal, then the result equals that same value.)
For type Q # , MAXNUM and MINNUM differ from MAX and MIN in their treatment of 0/0 : if one argument is 0/0 and
the other is not, then MAX or MIN returns 0/0 but MAXNUM or MINNUM returns the argument that is not 0/0 .
25.1.22 opr |self| : Q ≥
The absolute value operator |. . .| returns the negative of this rational number if the argument is less than zero, and
otherwise returns the argument.
For type Q # , the absolute value of 0/0 is 0/0 .
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