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fun die str = (
print (str ^ "\n");
raise Overflow
)
local fun loop (big: IntInf.int, small: IntInf.int): IntInf.int =
if small = 0
then big
else loop (small,
IntInf.rem (big, small))
in fun gcd (x: IntInf.int, y: IntInf.int): IntInf.int =
let val x = IntInf.abs x
val y = IntInf.abs y
val (x, y) = if x >= y
then (x, y)
else (y, x)
in loop (x, y)
end
end
fun reduce (num: IntInf.int, den: IntInf.int) : IntInf.int * IntInf.int =
let val g = gcd (num, den)
val gs = if den >= 0
then g
else ~ g
in if gs = 1
then (num, den)
else let val rnum = IntInf.quot (num, gs)
val badn = IntInf.rem (num, gs)
val rden = IntInf.quot (den, gs)
val badd = IntInf.rem (den, gs)
in if badn <> 0
orelse num <> rnum * gs
orelse badd <> 0
orelse den <> rden * gs
then die ("Bad: num " ^ (IntInf.toString num)
^ ", den " ^ (IntInf.toString den)
^ ", gcds " ^ (IntInf.toString gs)
^ ", rnum " ^ (IntInf.toString rnum)
^ ", rden " ^ (IntInf.toString rden)
^ ", badn " ^ (IntInf.toString badn)
^ ", badd " ^ (IntInf.toString badd))
else ();
(rnum, rden)
end
end
fun addrecip (xxx: int, (num: IntInf.int, den: IntInf.int))
: IntInf.int * IntInf.int =
let val xxx = IntInf.fromInt xxx
val xnum = xxx * num + den
val xden = xxx * den
in reduce (xnum, xden)
end
fun printRat (num: IntInf.int, den: IntInf.int): unit =
print (IntInf.toString num ^ "/" ^ IntInf.toString den ^ "\n")
fun spin (limit: int): IntInf.int * IntInf.int =
let fun loop (n: int, res: IntInf.int * IntInf.int)
: IntInf.int * IntInf.int =
if n = limit
then res
else loop (n + 1,
addrecip (n, res))
in if limit <= 0
then die "Bad limit"
else loop (1, (0, 1))
end
val (n, d) = spin 3000
val _ = printRat (n, d)
val _ = printRat (reduce (n * d * n, d * d * n))
val _ = printRat (reduce (n + 1, d + 1))
val _ = printRat (reduce (n * (d + 1) + d * (n + 1), d * (d + 1)))
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