# Section 8.12.2.1:
CARD

evenly_divides( other : SAME ) : BOOL is -- This predicate returns true if and only if self is an exact divisor -- of other. return (other % self) = zero end ; is_prime_to( other : SAME ) : BOOL is -- This predicate returns true if and only if self is relatively prime -- to other. return gcd(other) = 1 end ; middle( first, second : SAME ) : SAME pre true post ((self > first) and (first > second) and (result = first)) or ((self < first) and (self > second) and (result = self)) or (result = second) is -- This routine returns the result of min(second) being applied to -- max(first). extended_gcd( other : SAME, out self_factor, out i_factor : SAME ) : SAME pre true post ((result % self) = 0) and ((result % other) = 0) and (((self_factor * self) + (i_factor * other)) = result) is -- This routine returns the result of applying the extended Euclidean -- algorithm (Geddes et al, p36) to self and other. The three parts of -- the return value `g', `g1', and `g2' are such that `g' is the greatest -- common divisor of self and other and `g1 * self + g2 * other = g'. aelt! : BOOL is -- This iter is effectively a predicate which yields true or false -- depending upon whether the indicated bit of self was set or not. binary!( once limit : SAME ) : SAME pre limit >= one post (result >= one) and (result <= limit) is -- This iter yields successive doublings of the initial value (1) up to -- the given limit.

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