Arithmetic/Rational: Difference between revisions
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→{{header|Rust}}: Add Rust example |
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candidate Num.(to_int !sum) (if Num.(!sum = 1) then "perfect!" else "") |
candidate Num.(to_int !sum) (if Num.(!sum = 1) then "perfect!" else "") |
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done</lang> |
done</lang> |
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It might be implemented like this: |
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A type for rational numbers might be implemented like this: |
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[insert implementation here] |
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First define the interface, hiding implementation details: |
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<lang ocaml>(* interface *) |
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module type RATIO = |
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sig |
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type t |
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(* construct *) |
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val frac : int -> int -> t |
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val from_int : int -> t |
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(* integer test *) |
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val is_int : t -> bool |
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(* output *) |
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val to_string : t -> string |
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(* arithmetic *) |
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val cmp : t -> t -> int |
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val ( +/ ) : t -> t -> t |
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val ( -/ ) : t -> t -> t |
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val ( */ ) : t -> t -> t |
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val ( // ) : t -> t -> t |
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end</lang> |
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then implement the module: |
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<lang ocaml>(* implementation conforming to signature *) |
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module Frac : RATIO = |
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struct |
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open Big_int |
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type t = { num : big_int; den : big_int } |
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(* short aliases for big_int values and functions *) |
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let zero, one = zero_big_int, unit_big_int |
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let big, to_int, eq = big_int_of_int, int_of_big_int, eq_big_int |
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let (+~), (-~), ( *~) = add_big_int, sub_big_int, mult_big_int |
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(* helper function *) |
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let rec norm ({num=n;den=d} as k) = |
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if lt_big_int d zero then |
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norm {num=minus_big_int n;den=minus_big_int d} |
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else |
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let rec hcf a b = |
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let q,r = quomod_big_int a b in |
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if eq r zero then b else hcf b r in |
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let f = hcf n d in |
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if eq f one then k else |
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let div = div_big_int in |
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{ num=div n f; den = div d f } (* inefficient *) |
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(* public functions *) |
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let frac a b = norm { num=big a; den=big b } |
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let from_int a = norm { num=big a; den=one } |
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let is_int {num=n; den=d} = |
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eq d one || |
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eq (mod_big_int n d) zero |
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let to_string ({num=n; den=d} as r) = |
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let r1 = norm r in |
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let str = string_of_big_int in |
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if is_int r1 then |
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str (r1.num) |
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else |
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str (r1.num) ^ "/" ^ str (r1.den) |
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let cmp a b = |
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let a1 = norm a and b1 = norm b in |
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compare_big_int (a1.num*~b1.den) (b1.num*~a1.den) |
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let ( */ ) {num=n1; den=d1} {num=n2; den=d2} = |
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norm { num = n1*~n2; den = d1*~d2 } |
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let ( // ) {num=n1; den=d1} {num=n2; den=d2} = |
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norm { num = n1*~d2; den = d1*~n2 } |
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let ( +/ ) {num=n1; den=d1} {num=n2; den=d2} = |
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norm { num = n1*~d2 +~ n2*~d1; den = d1*~d2 } |
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let ( -/ ) {num=n1; den=d1} {num=n2; den=d2} = |
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norm { num = n1*~d2 -~ n2*~d1; den = d1*~d2 } |
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end</lang> |
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Finally the use type defined by the module to perform the perfect number calculation: |
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<lang ocaml>(* use the module to calculate perfect numbers *) |
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let () = |
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for i = 2 to 1 lsl 19 do |
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let sum = ref (Frac.frac 1 i) in |
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for factor = 2 to truncate (sqrt (float i)) do |
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if i mod factor = 0 then |
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Frac.( |
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sum := !sum +/ frac 1 factor +/ frac 1 (i / factor) |
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) |
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done; |
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if Frac.is_int !sum then |
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Printf.printf "Sum of reciprocal factors of %d = %s exactly %s\n%!" |
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i (Frac.to_string !sum) (if Frac.to_string !sum = "1" then "perfect!" else "") |
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done</lang> |
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which produces this output: |
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Sum of reciprocal factors of 6 = 1 exactly perfect! |
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Sum of reciprocal factors of 28 = 1 exactly perfect! |
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Sum of reciprocal factors of 120 = 2 exactly |
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Sum of reciprocal factors of 496 = 1 exactly perfect! |
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Sum of reciprocal factors of 672 = 2 exactly |
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Sum of reciprocal factors of 8128 = 1 exactly perfect! |
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Sum of reciprocal factors of 30240 = 3 exactly |
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Sum of reciprocal factors of 32760 = 3 exactly |
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Sum of reciprocal factors of 523776 = 2 exactly |
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=={{header|ooRexx}}== |
=={{header|ooRexx}}== |