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(.module: {#.doc "Pseudo-random number generation (PRNG) algorithms."}
[lux #- list]
(lux (control [functor #+ Functor]
[apply #+ Apply]
[monad #+ do Monad]
hash)
(data [bit]
[text "text/" Monoid<Text>]
[product]
[maybe]
[number #+ hex]
(number ["r" ratio]
["c" complex])
(coll [list "list/" Fold<List>]
[array]
(dictionary ["dict" unordered #+ Dict])
[queue #+ Queue]
(set ["set" unordered #+ Set])
[stack #+ Stack]
[sequence #+ Sequence]))
))
(type: #export #rec PRNG
{#.doc "An abstract way to represent any PRNG."}
(-> Top [PRNG Nat]))
(type: #export (Random a)
{#.doc "A producer of random values based on a PRNG."}
(-> PRNG [PRNG a]))
(struct: #export _ (Functor Random)
(def: (map f fa)
(function (_ state)
(let [[state' a] (fa state)]
[state' (f a)]))))
(struct: #export _ (Apply Random)
(def: functor Functor<Random>)
(def: (apply ff fa)
(function (_ state)
(let [[state' f] (ff state)
[state'' a] (fa state')]
[state'' (f a)]))))
(struct: #export _ (Monad Random)
(def: functor Functor<Random>)
(def: (wrap a)
(function (_ state)
[state a]))
(def: (join ffa)
(function (_ state)
(let [[state' fa] (ffa state)]
(fa state')))))
(def: #export (filter pred gen)
{#.doc "Retries the generator until the output satisfies a predicate."}
(All [a] (-> (-> a Bool) (Random a) (Random a)))
(do Monad<Random>
[sample gen]
(if (pred sample)
(wrap sample)
(filter pred gen))))
(def: #export nat
(Random Nat)
(function (_ prng)
(let [[prng left] (prng [])
[prng right] (prng [])]
[prng (n/+ (bit.left-shift +32 left)
right)])))
(def: #export int
(Random Int)
(:: Monad<Random> map nat-to-int nat))
(def: #export bool
(Random Bool)
(function (_ prng)
(let [[prng output] (prng [])]
[prng (|> output (bit.and +1) (n/= +1))])))
(def: (bits n)
(-> Nat (Random Nat))
(function (_ prng)
(let [[prng output] (prng [])]
[prng (bit.logical-right-shift (n/- n +64) output)])))
(def: #export frac
(Random Frac)
(do Monad<Random>
[left (bits +26)
right (bits +27)]
(wrap (|> right
(n/+ (bit.left-shift +27 left))
nat-to-int
int-to-frac
(f// (|> +1 (bit.left-shift +53) nat-to-int int-to-frac))))))
(def: #export deg
(Random Deg)
(:: Monad<Random> map (|>> (:! Deg)) nat))
(def: #export (text' char-gen size)
(-> (Random Nat) Nat (Random Text))
(if (n/= +0 size)
(:: Monad<Random> wrap "")
(do Monad<Random>
[x char-gen
xs (text' char-gen (n/dec size))]
(wrap (text/compose (text.from-code x) xs)))))
(type: Char-Range [Nat Nat])
(do-template [<name> <from> <to>]
[(def: <name> Char-Range [(hex <from>) (hex <to>)])]
[Thaana "+0780" "+07BF"]
[Khmer-Symbols "+19E0" "+19FF"]
[Phonetic-Extensions "+1D00" "+1D7F"]
[Hangul-Syllables "+AC00" "+D7AF"]
[Cypriot-Syllabary "+10800" "+1083F"]
[Tai-Xuan-Jing-Symbols "+1D300" "+1D35F"]
[Mathematical-Alphanumeric-Symbols "+1D400" "+1D7FF"]
[CJK-Unified-Ideographs-Extension-B "+20000" "+2A6DF"]
[CJK-Compatibility-Ideographs-Supplement "+2F800" "+2FA1F"]
)
(def: (within? [from to] char)
(-> Char-Range Nat Bool)
(and (n/>= from char) (n/<= to char)))
(def: unicode-ceiling (n/inc (product.right CJK-Compatibility-Ideographs-Supplement)))
(def: #export unicode
(Random Nat)
(|> ..nat
(:: Monad<Random> map (n/% unicode-ceiling))
(..filter (function (_ raw)
## From "Basic Latin" to "Syriac"
(or (n/<= (hex "+074F") raw)
(within? Thaana raw)
## From "Devanagari" to "Ethiopic"
(and (n/>= (hex "+0900") raw)
(n/<= (hex "+137F") raw))
## From "Cherokee" to "Mongolian"
(and (n/>= (hex "+13A0") raw)
(n/<= (hex "+18AF") raw))
## From "Limbu" to "Tai Le"
(and (n/>= (hex "+1900") raw)
(n/<= (hex "+197F") raw))
(within? Khmer-Symbols raw)
(within? Phonetic-Extensions raw)
## From "Latin Extended Additional" to "Miscellaneous Symbols and Arrows"
(and (n/>= (hex "+1E00") raw)
(n/<= (hex "+2BFF") raw))
## From "CJK Radicals Supplement" to "Kangxi Radicals"
(and (n/>= (hex "+2E80") raw)
(n/<= (hex "+2FDF") raw))
## From "Ideographic Description Characters" to "Bopomofo Extended"
(and (n/>= (hex "+2FF0") raw)
(n/<= (hex "+31BF") raw))
## From "Katakana Phonetic Extensions" to "CJK Unified Ideographs"
(and (n/>= (hex "+31F0") raw)
(n/<= (hex "+9FAF") raw))
## From "Yi Syllables" to "Yi Radicals"
(and (n/>= (hex "+A000") raw)
(n/<= (hex "+A4CF") raw))
(within? Hangul-Syllables raw)
## From "CJK Compatibility Ideographs" to "Arabic Presentation Forms-A"
(and (n/>= (hex "+F900") raw)
(n/<= (hex "+FDFF") raw))
## From "Combining Half Marks" to "Halfwidth and Fullwidth Forms"
(and (n/>= (hex "+FE20") raw)
(n/<= (hex "+FFEF") raw))
## From "Linear B Syllabary" to "Aegean Numbers"
(and (n/>= (hex "+10000") raw)
(n/<= (hex "+1013F") raw))
## From "Old Italic" to "Osmanya"
(and (n/>= (hex "+10300") raw)
(n/<= (hex "+104AF") raw))
(within? Cypriot-Syllabary raw)
## From "Byzantine Musical Symbols" to "Musical Symbols"
(and (n/>= (hex "+1D000") raw)
(n/<= (hex "+1D1FF") raw))
(within? Tai-Xuan-Jing-Symbols raw)
(within? Mathematical-Alphanumeric-Symbols raw)
(within? CJK-Unified-Ideographs-Extension-B raw)
(within? CJK-Compatibility-Ideographs-Supplement raw)
)))))
(def: #export (text size)
(-> Nat (Random Text))
(text' unicode size))
(do-template [<name> <type> <ctor> <gen>]
[(def: #export <name>
(Random <type>)
(do Monad<Random>
[left <gen>
right <gen>]
(wrap (<ctor> left right))))]
[ratio r.Ratio r.ratio nat]
[complex c.Complex c.complex frac]
)
(def: #export (seq left right)
{#.doc "Sequencing combinator."}
(All [a b] (-> (Random a) (Random b) (Random [a b])))
(do Monad<Random>
[=left left
=right right]
(wrap [=left =right])))
(def: #export (alt left right)
{#.doc "Heterogeneous alternative combinator."}
(All [a b] (-> (Random a) (Random b) (Random (| a b))))
(do Monad<Random>
[? bool]
(if ?
(do @
[=left left]
(wrap (+0 =left)))
(do @
[=right right]
(wrap (+1 =right))))))
(def: #export (either left right)
{#.doc "Homogeneous alternative combinator."}
(All [a] (-> (Random a) (Random a) (Random a)))
(do Monad<Random>
[? bool]
(if ?
left
right)))
(def: #export (rec gen)
{#.doc "A combinator for producing recursive random generators."}
(All [a] (-> (-> (Random a) (Random a)) (Random a)))
(function (_ state)
(let [gen' (gen (rec gen))]
(gen' state))))
(def: #export (maybe value-gen)
(All [a] (-> (Random a) (Random (Maybe a))))
(do Monad<Random>
[some? bool]
(if some?
(do @
[value value-gen]
(wrap (#.Some value)))
(wrap #.None))))
(do-template [<name> <type> <zero> <plus>]
[(def: #export (<name> size value-gen)
(All [a] (-> Nat (Random a) (Random (<type> a))))
(if (n/> +0 size)
(do Monad<Random>
[x value-gen
xs (<name> (n/dec size) value-gen)]
(wrap (<plus> x xs)))
(:: Monad<Random> wrap <zero>)))]
[list List (.list) #.Cons]
[sequence Sequence sequence.empty sequence.add]
)
(do-template [<name> <type> <ctor>]
[(def: #export (<name> size value-gen)
(All [a] (-> Nat (Random a) (Random (<type> a))))
(do Monad<Random>
[values (list size value-gen)]
(wrap (|> values <ctor>))))]
[array Array array.from-list]
[queue Queue queue.from-list]
[stack Stack (list/fold stack.push stack.empty)]
)
(def: #export (set Hash<a> size value-gen)
(All [a] (-> (Hash a) Nat (Random a) (Random (Set a))))
(if (n/> +0 size)
(do Monad<Random>
[xs (set Hash<a> (n/dec size) value-gen)]
(loop [_ []]
(do @
[x value-gen
#let [xs+ (set.add x xs)]]
(if (n/= size (set.size xs+))
(wrap xs+)
(recur [])))))
(:: Monad<Random> wrap (set.new Hash<a>))))
(def: #export (dict Hash<a> size key-gen value-gen)
(All [k v] (-> (Hash k) Nat (Random k) (Random v) (Random (Dict k v))))
(if (n/> +0 size)
(do Monad<Random>
[kv (dict Hash<a> (n/dec size) key-gen value-gen)]
(loop [_ []]
(do @
[k key-gen
v value-gen
#let [kv+ (dict.put k v kv)]]
(if (n/= size (dict.size kv+))
(wrap kv+)
(recur [])))))
(:: Monad<Random> wrap (dict.new Hash<a>))))
(def: #export (run prng calc)
(All [a] (-> PRNG (Random a) [PRNG a]))
(calc prng))
(def: pcg-32-magic-mult Nat +6364136223846793005)
(def: #export (pcg-32 [inc seed])
{#.doc "An implementation of the PCG32 algorithm.
For more information, please see: http://www.pcg-random.org/"}
(-> [Nat Nat] PRNG)
(function (_ _)
(let [seed' (|> seed (n/* pcg-32-magic-mult) (n/+ inc))
xor-shifted (|> seed (bit.logical-right-shift +18) (bit.xor seed) (bit.logical-right-shift +27))
rot (|> seed (bit.logical-right-shift +59))]
[(pcg-32 [inc seed']) (bit.rotate-right rot xor-shifted)]
)))
(def: #export (xoroshiro-128+ [s0 s1])
{#.doc "An implementation of the Xoroshiro128+ algorithm.
For more information, please see: http://xoroshiro.di.unimi.it/"}
(-> [Nat Nat] PRNG)
(function (_ _)
(let [result (n/+ s0 s1)
s01 (bit.xor s0 s1)
s0' (|> (bit.rotate-left +55 s0)
(bit.xor s01)
(bit.xor (bit.left-shift +14 s01)))
s1' (bit.rotate-left +36 s01)]
[(xoroshiro-128+ [s0' s1']) result])
))
(def: (swap from to vec)
(All [a] (-> Nat Nat (Sequence a) (Sequence a)))
(|> vec
(sequence.put to (maybe.assume (sequence.nth from vec)))
(sequence.put from (maybe.assume (sequence.nth to vec)))))
(def: #export (shuffle seed sequence)
{#.doc "Shuffle a sequence randomly based on a seed value."}
(All [a] (-> Nat (Sequence a) (Sequence a)))
(let [_size (sequence.size sequence)
_shuffle (monad.fold Monad<Random>
(function (_ idx vec)
(do Monad<Random>
[rand nat]
(wrap (swap idx (n/% _size rand) vec))))
sequence
(list.n/range +0 (n/dec _size)))]
(|> _shuffle
(run (pcg-32 [+123 seed]))
product.right)))
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