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1 | (* Copyright (C) 2009 Matthew Fluet. |
2 | * Copyright (C) 1999-2006 Henry Cejtin, Matthew Fluet, Suresh | |
3 | * Jagannathan, and Stephen Weeks. | |
4 | * | |
5 | * MLton is released under a BSD-style license. | |
6 | * See the file MLton-LICENSE for details. | |
7 | *) | |
8 | ||
9 | functor Integer (S: INTEGER_STRUCTS): INTEGER = | |
10 | struct | |
11 | ||
12 | open S | |
13 | ||
14 | structure In = In0 | |
15 | ||
16 | structure Int = | |
17 | struct | |
18 | open S | |
19 | ||
20 | type t = int | |
21 | ||
22 | val zero = fromInt 0 | |
23 | ||
24 | val layout = Layout.str o toString | |
25 | ||
26 | val equals = op = | |
27 | end | |
28 | ||
29 | structure R = | |
30 | OrderedRing (structure R = | |
31 | RingWithIdentity (structure R = Ring (Int) | |
32 | open R S | |
33 | val one = fromInt 1) | |
34 | open R S | |
35 | val {compare, ...} = | |
36 | Relation.lessEqual {< = op <, equals = equals}) | |
37 | open R S | |
38 | ||
39 | exception Input | |
40 | fun input i = (In.ignoreSpaces i | |
41 | ; (case fromString (In.inputToSpace i) of | |
42 | NONE => raise Input | |
43 | | SOME n => n)) | |
44 | ||
45 | structure I = EuclideanRing (open R S | |
46 | val metric = toIntInf o abs | |
47 | val monics = Stream.infinite (two, fn n => n + one) | |
48 | val unitEquivalent = abs) | |
49 | open I | |
50 | ||
51 | fun isEven n = isZero (n mod two) | |
52 | ||
53 | val isOdd = not o isEven | |
54 | ||
55 | fun toCommaString n = | |
56 | let | |
57 | fun loop (chars, accum) = | |
58 | let | |
59 | fun done () = implode (rev chars @ accum) | |
60 | in | |
61 | case chars of | |
62 | x1 :: x2 :: x3 :: chars => | |
63 | (case chars of | |
64 | [] => done () | |
65 | | [#"~"] => done () | |
66 | | _ => loop (chars, #"," :: x3 :: x2 :: x1 :: accum)) | |
67 | | _ => done () | |
68 | end | |
69 | in loop (rev (explode (toString n)), []) | |
70 | end | |
71 | ||
72 | fun choose (n, k) = | |
73 | let val k = max (k, n - k) | |
74 | in prodFromTo {from = add1 k, to = n, term = fn i => i} | |
75 | div factorial (n - k) | |
76 | end | |
77 | ||
78 | fun output (n, out) = Out.output (out, toString n) | |
79 | ||
80 | fun largest (i, f) = | |
81 | let | |
82 | fun loop (n: t) = | |
83 | if f n | |
84 | then n | |
85 | else loop (sub1 n) | |
86 | in | |
87 | loop i | |
88 | end | |
89 | ||
90 | fun smallest (i, f) = | |
91 | let | |
92 | fun loop (n: t) = | |
93 | if f n | |
94 | then n | |
95 | else loop (add1 n) | |
96 | in loop i | |
97 | end | |
98 | ||
99 | fun least (start: t, stop: t, f: int -> bool): int option = | |
100 | let | |
101 | fun loop (i: t) = | |
102 | if i >= stop | |
103 | then NONE | |
104 | else if f i | |
105 | then SOME i | |
106 | else loop (i + one) | |
107 | in loop start | |
108 | end | |
109 | ||
110 | fun 'a fold (start: t, stop: t, a: 'a, f: int * 'a -> 'a): 'a = | |
111 | let | |
112 | val _ = Assert.assert ("Integer.fold", fn () => start <= stop + one) | |
113 | fun loop (i: t, a: 'a): 'a = | |
114 | if i >= stop | |
115 | then a | |
116 | else loop (i + one, f (i, a)) | |
117 | in loop (start, a) | |
118 | end | |
119 | ||
120 | fun forall (start: t, stop: t, f: int -> bool): bool = | |
121 | Exn.withEscape | |
122 | (fn escape => (fold (start, stop, (), fn (i, ()) => | |
123 | if f i then () else escape false) | |
124 | ; true)) | |
125 | ||
126 | fun exists (start, stop, f) = not (forall (start, stop, not o f)) | |
127 | ||
128 | fun 'a foldDown (start: t, stop: t, a: 'a, f: int * 'a -> 'a): 'a = | |
129 | let | |
130 | val _ = Assert.assert ("Integer.foldDown", fn () => start <= stop + one) | |
131 | fun loop (i: t, a: 'a) = | |
132 | if i < start | |
133 | then a | |
134 | else loop (sub1 i, f (i, a)) | |
135 | in loop (sub1 stop, a) | |
136 | end | |
137 | ||
138 | fun map (start: t, stop: t, f: t -> 'a): 'a list = | |
139 | foldDown (start, stop, [], fn (i, l) => f i :: l) | |
140 | ||
141 | fun for (start: t, stop: t, f: t -> unit): unit = | |
142 | fold (start, stop, (), f o #1) | |
143 | ||
144 | fun forDown (start: t, stop: t, f: t -> unit): unit = | |
145 | foldDown (start, stop, (), f o #1) | |
146 | ||
147 | fun scan (radix, reader) = Int.scan radix reader | |
148 | ||
149 | fun format (i, r) = fmt r i | |
150 | ||
151 | end |