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|
(;module: {#;doc "Pseudo-random number generation (PRNG) algorithms."}
[lux #- list]
(lux (control ["F" functor]
["A" applicative]
["M" monad #+ do Monad]
hash)
(data [bit]
[text "Text/" Monoid<Text>]
text/format
[product]
[maybe]
[number]
(number ["r" ratio]
["c" complex])
(coll [list "List/" Fold<List>]
["a" array]
["D" dict]
["Q" queue]
["S" set]
["ST" stack]
["V" vector]))
))
(type: #export #rec PRNG
{#;doc "An abstract way to represent any PRNG."}
(-> Unit [PRNG Nat]))
(type: #export (Random a)
{#;doc "A producer of random values based on a PRNG."}
(-> PRNG [PRNG a]))
(struct: #export _ (F;Functor Random)
(def: (map f fa)
(function [state]
(let [[state' a] (fa state)]
[state' (f a)]))))
(struct: #export _ (A;Applicative Random)
(def: functor Functor<Random>)
(def: (wrap a)
(function [state]
[state a]))
(def: (apply ff fa)
(function [state]
(let [[state' f] (ff state)
[state'' a] (fa state')]
[state'' (f a)]))))
(struct: #export _ (Monad Random)
(def: applicative Applicative<Random>)
(def: (join ffa)
(function [state]
(let [[state' fa] (ffa state)]
(fa state')))))
(def: #export nat
(Random Nat)
(function [prng]
(let [[prng left] (prng [])
[prng right] (prng [])]
[prng (n.+ (bit;shift-left +32 left)
right)])))
(def: #export int
(Random Int)
(function [prng]
(let [[prng left] (prng [])
[prng right] (prng [])]
[prng (nat-to-int (n.+ (bit;shift-left +32 left)
right))])))
(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;shift-right (n.- n +64) output)])))
(def: #export frac
(Random Frac)
(do Monad<Random>
[left (bits +26)
right (bits +27)]
(wrap (|> right
(n.+ (bit;shift-left +27 left))
nat-to-int
int-to-frac
(f./ (|> +1 (bit;shift-left +53) nat-to-int int-to-frac))))))
(def: #export deg
(Random Deg)
(:: Monad<Random> map frac-to-deg frac))
(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)))))
(def: #export (text size)
(-> Nat (Random Text))
(text' nat 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 (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 (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]
[vector V;Vector V;empty V;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 a;Array a;from-list]
[queue Q;Queue Q;from-list]
[stack ST;Stack (List/fold ST;push ST;empty)]
)
(def: #export (set Hash<a> size value-gen)
(All [a] (-> (Hash a) Nat (Random a) (Random (S;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+ (S;add x xs)]]
(if (n.= size (S;size xs+))
(wrap xs+)
(recur [])))))
(:: Monad<Random> wrap (S;new Hash<a>))))
(def: #export (dict Hash<a> size key-gen value-gen)
(All [k v] (-> (Hash k) Nat (Random k) (Random v) (Random (D;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+ (D;put k v kv)]]
(if (n.= size (D;size kv+))
(wrap kv+)
(recur [])))))
(:: Monad<Random> wrap (D;new Hash<a>))))
(def: #export (run prng calc)
(All [a] (-> PRNG (Random a) [PRNG a]))
(calc prng))
## PCG32 http://www.pcg-random.org/
## Based on this Java implementation: https://github.com/alexeyr/pcg-java
(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;shift-right +18) (bit;xor seed) (bit;shift-right +27))
rot (|> seed (bit;shift-right +59))]
[(pcg-32 [inc seed']) (bit;rotate-right rot xor-shifted)]
)))
## Xoroshiro128+ http://xoroshiro.di.unimi.it/
(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;shift-left +14 s01)))
s1' (bit;rotate-left +36 s01)]
[(xoroshiro-128+ [s0' s1']) result])
))
(def: (swap from to vec)
(All [a] (-> Nat Nat (V;Vector a) (V;Vector a)))
(|> vec
(V;put to (maybe;assume (V;nth from vec)))
(V;put from (maybe;assume (V;nth to vec)))))
(def: #export (shuffle seed vector)
{#;doc "Shuffle a vector randomly based on a seed value."}
(All [a] (-> Nat (V;Vector a) (V;Vector a)))
(let [_size (V;size vector)
_shuffle (M;fold Monad<Random>
(function [idx vec]
(do Monad<Random>
[rand nat]
(wrap (swap idx (n.% _size rand) vec))))
vector
(list;n.range +0 (n.dec _size)))]
(|> _shuffle
(run (pcg-32 [+123 seed]))
product;right)))
|
