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|
(.module: {#.doc "Pseudo-random number generation (PRNG) algorithms."}
[lux (#- or and list i64 nat int rev char)
[control
[functor (#+ Functor)]
[apply (#+ Apply)]
["." monad (#+ do Monad)]
hash]
[data
["." product]
["." maybe]
["." number (#+ hex)
["." i64]
["r" ratio]
["c" complex]]
["." text ("text/." Monoid<Text>)
["." unicode (#+ Char Segment)]]
[collection
["." list ("list/." Fold<List>)]
["." array]
["." dictionary (#+ Dictionary)]
["." queue (#+ Queue)]
["." set (#+ Set)]
["." stack (#+ Stack)]
["." row (#+ Row)]
[tree
["." finger (#+ Tree)]]]]
[type
[refinement (#+ Refiner Refined)]]
])
(type: #export #rec PRNG
{#.doc "An abstract way to represent any PRNG."}
(-> Any [PRNG I64]))
(type: #export (Random a)
{#.doc "A producer of random values based on a PRNG."}
(-> PRNG [PRNG a]))
(structure: #export _ (Functor Random)
(def: (map f fa)
(function (_ state)
(let [[state' a] (fa state)]
[state' (f a)]))))
(structure: #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)]))))
(structure: #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 Bit) (Random a) (Random a)))
(do Monad<Random>
[sample gen]
(if (pred sample)
(wrap sample)
(filter pred gen))))
(def: #export (refine refiner gen)
{#.doc "Retries the generator until the output can be refined."}
(All [t r] (-> (Refiner t r) (Random t) (Random (Refined t r))))
(do Monad<Random>
[sample gen]
(case (refiner sample)
(#.Some refined)
(wrap refined)
#.None
(refine refiner gen))))
(def: #export bit
(Random Bit)
(function (_ prng)
(let [[prng output] (prng [])]
[prng (|> output (i64.and +1) (n/= +1))])))
(def: #export i64
(Random I64)
(function (_ prng)
(let [[prng left] (prng [])
[prng right] (prng [])]
[prng (|> left
(i64.left-shift +32)
("lux i64 +" right))])))
(def: #export nat
(Random Nat)
(:: Monad<Random> map .nat ..i64))
(def: #export int
(Random Int)
(:: Monad<Random> map .int ..i64))
(def: #export rev
(Random Rev)
(:: Monad<Random> map .rev ..i64))
(def: #export frac
(Random Frac)
(:: Monad<Random> map number.bits-to-frac nat))
(def: #export (char set)
(-> unicode.Set (Random Char))
(let [summary (finger.tag set)
start (unicode.start summary)
size (unicode.size summary)
in-range (: (-> Char Char)
(|>> (n/% size) (n/+ start)))]
(|> nat
(:: Monad<Random> map in-range)
(..filter (function (_ char)
(finger.found? (function (_ segment)
(unicode.within? segment char))
set))))))
(def: #export (text char-gen size)
(-> (Random Char) Nat (Random Text))
(if (n/= +0 size)
(:: Monad<Random> wrap "")
(do Monad<Random>
[x char-gen
xs (text char-gen (dec size))]
(wrap (text/compose (text.from-code x) xs)))))
(def: #export unicode
(-> Nat (Random Text))
(text (char unicode.full)))
(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 (and 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 (or left right)
{#.doc "Heterogeneous alternative combinator."}
(All [a b] (-> (Random a) (Random b) (Random (| a b))))
(do Monad<Random>
[? bit]
(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>
[? bit]
(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? bit]
(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> (dec size) value-gen)]
(wrap (<plus> x xs)))
(:: Monad<Random> wrap <zero>)))]
[list List (.list) #.Cons]
[row Row row.empty row.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> (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 (dictionary Hash<a> size key-gen value-gen)
(All [k v] (-> (Hash k) Nat (Random k) (Random v) (Random (Dictionary k v))))
(if (n/> +0 size)
(do Monad<Random>
[kv (dictionary Hash<a> (dec size) key-gen value-gen)]
(loop [_ []]
(do @
[k key-gen
v value-gen
#let [kv+ (dictionary.put k v kv)]]
(if (n/= size (dictionary.size kv+))
(wrap kv+)
(recur [])))))
(:: Monad<Random> wrap (dictionary.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/"}
(-> [(I64 Any) (I64 Any)] PRNG)
(function (_ _)
[(|> seed .nat (n/* pcg-32-magic-mult) ("lux i64 +" inc) [inc] pcg-32)
(let [rot (|> seed .i64 (i64.logical-right-shift +59))]
(|> seed
(i64.logical-right-shift +18)
(i64.xor seed)
(i64.logical-right-shift +27)
(i64.rotate-right rot)
.i64))]))
(def: #export (xoroshiro-128+ [s0 s1])
{#.doc "An implementation of the Xoroshiro128+ algorithm.
For more information, please see: http://xoroshiro.di.unimi.it/"}
(-> [(I64 Any) (I64 Any)] PRNG)
(function (_ _)
[(let [s01 (i64.xor s0 s1)]
(xoroshiro-128+ [(|> s0
(i64.rotate-left +55)
(i64.xor s01)
(i64.xor (i64.left-shift +14 s01)))
(i64.rotate-left +36 s01)]))
("lux i64 +" s0 s1)]))
(def: (swap from to vec)
(All [a] (-> Nat Nat (Row a) (Row a)))
(|> vec
(row.put to (maybe.assume (row.nth from vec)))
(row.put from (maybe.assume (row.nth to vec)))))
(def: #export (shuffle seed row)
{#.doc "Shuffle a row randomly based on a seed value."}
(All [a] (-> Nat (Row a) (Row a)))
(let [_size (row.size row)
_shuffle (monad.fold Monad<Random>
(function (_ idx vec)
(do Monad<Random>
[rand nat]
(wrap (swap idx (n/% _size rand) vec))))
row
(list.n/range +0 (dec _size)))]
(|> _shuffle
(run (pcg-32 [+123 seed]))
product.right)))
|