giles
7ca5bfbb70
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Defines:
type frac = { num : int; den : int }
let rec gcd a b = if b = 0 then a else gcd b (a mod b)
let make n d = (* canonicalise: gcd-reduce and
force den > 0 *)
let add x y = make (x.num * y.den + y.num * x.den) (x.den * y.den)
let mul x y = make (x.num * y.num) (x.den * y.den)
Test:
let r = add (make 1 2) (make 1 3) in (* 5/6 *)
let s = mul (make 2 3) (make 3 4) in (* 1/2 *)
let t = add r s in (* 5/6 + 1/2 = 4/3 *)
t.num + t.den (* = 7 *)
Exercises records, recursive gcd, mod, abs, integer division (the
truncate-toward-zero semantics from iter 94 are essential here —
make would diverge from real OCaml's behaviour with float division).
28 baseline programs total.
21 lines
459 B
OCaml
21 lines
459 B
OCaml
type frac = { num : int; den : int }
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let rec gcd a b = if b = 0 then a else gcd b (a mod b)
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let make n d =
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let g = gcd (abs n) (abs d) in
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if d < 0 then { num = -n / g; den = -d / g }
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else { num = n / g; den = d / g }
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let add x y =
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make (x.num * y.den + y.num * x.den) (x.den * y.den)
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let mul x y = make (x.num * y.num) (x.den * y.den)
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;;
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let r = add (make 1 2) (make 1 3) in
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let s = mul (make 2 3) (make 3 4) in
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let t = add r s in
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t.num + t.den
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