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|
## Copyright (c) Eduardo Julian. All rights reserved.
## This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.
## If a copy of the MPL was not distributed with this file,
## You can obtain one at http://mozilla.org/MPL/2.0/.
(;module:
[lux #- list]
(lux (control functor
applicative
monad
hash)
(data [bit]
[char]
[text "Text/" Monoid<Text>]
text/format
[product]
[number]
(struct [list "List/" Fold<List>]
["A" array]
["D" dict]
["Q" queue]
["S" set]
["ST" stack]
["V" vector]))
(math ["r" ratio]
["c" complex])))
## [Exports]
(type: #export #rec PRNG
(-> Unit [PRNG Nat]))
(type: #export (Random a)
(-> PRNG [PRNG a]))
(struct: #export _ (Functor Random)
(def: (map f fa)
(lambda [state]
(let [[state' a] (fa state)]
[state' (f a)]))))
(struct: #export _ (Applicative Random)
(def: functor Functor<Random>)
(def: (wrap a)
(lambda [state]
[state a]))
(def: (apply ff fa)
(lambda [state]
(let [[state' f] (ff state)
[state'' a] (fa state')]
[state'' (f a)]))))
(struct: #export _ (Monad Random)
(def: applicative Applicative<Random>)
(def: (join ffa)
(lambda [state]
(let [[state' fa] (ffa state)]
(fa state')))))
(def: #export nat
(Random Nat)
(lambda [prng]
(let [[prng left] (prng [])
[prng right] (prng [])]
[prng (++ (bit;<< +32 left)
right)])))
(def: #export int
(Random Int)
(lambda [prng]
(let [[prng left] (prng [])
[prng right] (prng [])]
[prng (nat-to-int (++ (bit;<< +32 left)
right))])))
(def: #export bool
(Random Bool)
(lambda [prng]
(let [[prng output] (prng [])]
[prng (|> output (bit;& +1) (=+ +1))])))
(def: (bits n)
(-> Nat (Random Nat))
(lambda [prng]
(let [[prng output] (prng [])]
[prng (bit;>>> (-+ n +64) output)])))
(def: #export real
(Random Real)
(do Monad<Random>
[left (bits +26)
right (bits +27)]
(wrap (|> right
(++ (bit;<< +27 left))
nat-to-int
int-to-real
(/. (|> +1 (bit;<< +53) nat-to-int int-to-real))))))
(def: #export frac
(Random Frac)
(:: Monad<Random> map real-to-frac real))
(def: #export char
(Random Char)
(do Monad<Random>
[base nat]
(wrap (char;char base))))
(def: #export (text' char-gen size)
(-> (Random Char) Nat (Random Text))
(if (=+ +0 size)
(:: Monad<Random> wrap "")
(do Monad<Random>
[x char-gen
xs (text' char-gen (dec+ size))]
(wrap (Text/append (char;as-text x) xs)))))
(def: #export (text size)
(-> Nat (Random Text))
(text' char 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 int]
[complex c;Complex c;complex real]
)
(def: #export (seq left right)
(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)
(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)
(All [a] (-> (Random a) (Random a) (Random a)))
(do Monad<Random>
[? bool]
(if ?
left
right)))
(def: #export (rec gen)
(All [a] (-> (-> (Random a) (Random a)) (Random a)))
(lambda [state]
(let [gen' (gen (rec gen))]
(gen' state))))
(def: #export (filter pred gen)
(All [a] (-> (-> a Bool) (Random a) (Random a)))
(do Monad<Random>
[sample gen]
(if (pred sample)
(wrap sample)
(filter pred gen))))
(do-template [<name> <type> <zero> <plus>]
[(def: #export (<name> size value-gen)
(All [a] (-> Nat (Random a) (Random (<type> a))))
(if (>+ +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]
[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 a/Hash size value-gen)
(All [a] (-> (Hash a) Nat (Random a) (Random (S;Set a))))
(if (>+ +0 size)
(do Monad<Random>
[xs (set a/Hash (dec+ size) value-gen)]
(loop [_ []]
(do @
[x value-gen
#let [xs+ (S;add x xs)]]
(if (=+ size (S;size xs+))
(wrap xs+)
(recur [])))))
(:: Monad<Random> wrap (S;new a/Hash))))
(def: #export (dict a/Hash size key-gen value-gen)
(All [k v] (-> (Hash k) Nat (Random k) (Random v) (Random (D;Dict k v))))
(if (>+ +0 size)
(do Monad<Random>
[kv (dict a/Hash (dec+ size) key-gen value-gen)]
(loop [_ []]
(do @
[k key-gen
v value-gen
#let [kv+ (D;put k v kv)]]
(if (=+ size (D;size kv+))
(wrap kv+)
(recur [])))))
(:: Monad<Random> wrap (D;new a/Hash))))
(def: #export (run prng calc)
(All [a] (-> PRNG (Random a) [PRNG a]))
(calc prng))
## [PRNGs]
## 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])
(-> [Nat Nat] PRNG)
(lambda [_]
(let [seed' (|> seed (*+ pcg-32-magic-mult) (++ inc))
xor-shifted (|> seed (bit;>>> +18) (bit;^ seed) (bit;>>> +27))
rot (|> seed (bit;>>> +59))]
[(pcg-32 [inc seed']) (bit;rotate-right rot xor-shifted)]
)))
## Xoroshiro128+ http://xoroshiro.di.unimi.it/
(def: #export (xoroshiro-128+ [s0 s1])
(-> [Nat Nat] PRNG)
(lambda [_]
(let [result (++ s0 s1)
s01 (bit;^ s0 s1)
s0' (|> (bit;rotate-left +55 s0)
(bit;^ s01)
(bit;^ (bit;<< +14 s01)))
s1' (bit;rotate-left +36 s01)]
[(xoroshiro-128+ [s0' s1']) result])
))
## [Values]
(def: (swap from to vec)
(All [a] (-> Nat Nat (V;Vector a) (V;Vector a)))
(V;put to (default (undefined)
(V;at from vec))
vec))
(def: #export (shuffle seed vector)
(All [a] (-> Nat (V;Vector a) (V;Vector a)))
(let [_size (V;size vector)
_shuffle (foldM Monad<Random>
(lambda [idx vec]
(do Monad<Random>
[rand nat]
(wrap (swap idx (%+ _size rand) vec))))
vector
(list;range+ +0 (dec+ _size)))]
(|> _shuffle
(run (pcg-32 [+123 seed]))
product;right)))
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