diff options
Diffstat (limited to '')
| -rw-r--r-- | stdlib/test/test/lux/math/modular.lux | 146 | ||||
| -rw-r--r-- | stdlib/test/tests.lux | 2 |
2 files changed, 147 insertions, 1 deletions
diff --git a/stdlib/test/test/lux/math/modular.lux b/stdlib/test/test/lux/math/modular.lux new file mode 100644 index 000000000..76d56cbc2 --- /dev/null +++ b/stdlib/test/test/lux/math/modular.lux @@ -0,0 +1,146 @@ +(.module: + lux + (lux (control [monad #+ do]) + (data [product] + [bool "bool/" Eq<Bool>] + ["e" error] + text/format) + (math ["r" random] + ["/" modular]) + (lang [type "type/" Eq<Type>])) + lux/test) + +(def: %3 (/.modulus 3)) +(def: Mod3 Type (type-of %3)) + +(def: modulusR + (r.Random Int) + (|> r.int + (:: r.Monad<Random> map (i/% 1000)) + (r.filter (|>> (i/= 0) not)))) + +(def: valueR + (r.Random Int) + (|> r.int (:: r.Monad<Random> map (i/% 1000)))) + +(def: (modR modulus) + (All [m] (-> (/.Modulus m) (r.Random [Int (/.Mod m)]))) + (do r.Monad<Random> + [raw valueR] + (wrap [raw (/.mod modulus raw)]))) + +(def: value + (All [m] (-> (/.Mod m) Int)) + (|>> /.un-mod product.left)) + +(def: (comparison m/? i/?) + (All [m] + (-> (-> (/.Mod m) (/.Mod m) Bool) + (-> Int Int Bool) + (-> (/.Mod m) (/.Mod m) Bool))) + (function [param subject] + (bool/= (m/? param subject) + (i/? (value param) + (value subject))))) + +(def: (arithmetic modulus m/! i/!) + (All [m] + (-> (/.Modulus m) + (-> (/.Mod m) (/.Mod m) (/.Mod m)) + (-> Int Int Int) + (-> (/.Mod m) (/.Mod m) Bool))) + (function [param subject] + (|> (i/! (value param) + (value subject)) + (/.mod modulus) + (/.m/= (m/! param subject))))) + +(context: "Modular arithmetic." + (<| (times +100) + (do @ + [_normalM modulusR + _alternativeM (|> modulusR (r.filter (|>> (i/= _normalM) not))) + #let [normalM (|> _normalM /.from-int e.assume) + alternativeM (|> _alternativeM /.from-int e.assume)] + [_param param] (modR normalM) + [_subject subject] (modR normalM) + #let [copyM (|> normalM /.to-int /.from-int e.assume)]] + ($_ seq + (test "Every modulus has a unique type, even if the numeric value is the same as another." + (and (type/= (type-of normalM) + (type-of normalM)) + (not (type/= (type-of normalM) + (type-of alternativeM))) + (not (type/= (type-of normalM) + (type-of copyM))))) + + (test "Can extract the original integer from the modulus." + (i/= _normalM + (/.to-int normalM))) + + (test "Can compare mod'ed values." + (and (/.m/= subject subject) + ((comparison /.m/= i/=) param subject) + ((comparison /.m/< i/<) param subject) + ((comparison /.m/<= i/<=) param subject) + ((comparison /.m/> i/>) param subject) + ((comparison /.m/>= i/>=) param subject))) + + (test "Mod'ed values are ordered." + (and (bool/= (/.m/< param subject) + (not (/.m/>= param subject))) + (bool/= (/.m/> param subject) + (not (/.m/<= param subject))) + (bool/= (/.m/= param subject) + (not (or (/.m/< param subject) + (/.m/> param subject)))))) + + (test "Can do arithmetic." + (and ((arithmetic normalM /.m/+ i/+) param subject) + ((arithmetic normalM /.m/- i/-) param subject) + ((arithmetic normalM /.m/* i/*) param subject))) + + (test "Can sometimes find multiplicative inverse." + (case (/.inverse subject) + (#.Some subject^-1) + (|> subject + (/.m/* subject^-1) + (/.m/= (/.mod normalM 1))) + + #.None + true)) + + (test "Can encode/decode to text." + (let [(^open "mod/") (/.Codec<Text,Mod> normalM)] + (case (|> subject mod/encode mod/decode) + (#e.Success output) + (/.m/= subject output) + + (#e.Error error) + false))) + + (test "Can equalize 2 moduli if they are equal." + (case (/.equalize (/.mod normalM _subject) + (/.mod copyM _param)) + (#e.Success paramC) + (/.m/= param paramC) + + (#e.Error error) + false)) + + (test "Cannot equalize 2 moduli if they are the different." + (case (/.equalize (/.mod normalM _subject) + (/.mod alternativeM _param)) + (#e.Success paramA) + false + + (#e.Error error) + true)) + + (test "All numbers are congruent to themselves." + (/.congruent? normalM _subject _subject)) + + (test "If 2 numbers are congruent under a modulus, then they must also be equal under the same modulus." + (bool/= (/.congruent? normalM _param _subject) + (/.m/= param subject))) + )))) diff --git a/stdlib/test/tests.lux b/stdlib/test/tests.lux index 899582b54..1742334d8 100644 --- a/stdlib/test/tests.lux +++ b/stdlib/test/tests.lux @@ -56,6 +56,7 @@ ["_." regex])) ["_." math] (math ["_." random] + ["_." modular] (logic ["_." continuous] ["_." fuzzy])) (macro ["_." code] @@ -82,7 +83,6 @@ [html] [css]) (coll (tree ["tree_." parser]))) - (math [random]) [macro] (macro (poly [json])) (type [unit]) |