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|
(.module: {#.doc "Pseudo-random number generation (PRNG) algorithms."}
[lux (#- or and list i64 nat int rev char)
[abstract
[functor (#+ Functor)]
[apply (#+ Apply)]
["." monad (#+ do Monad)]
hash]
[data
["." product]
["." maybe]
[number (#+ hex)
["." i64]
["n" nat]
["i" int]
["r" ratio]
["c" complex]
["f" frac]]
["." text (#+ Char) ("#\." monoid)
["." unicode #_
["#" set]]]
[collection
["." list ("#\." fold)]
["." array (#+ Array)]
["." dictionary (#+ Dictionary)]
["." queue (#+ Queue)]
["." set (#+ Set)]
["." stack (#+ Stack)]
["." row (#+ Row)]
[tree
["." finger (#+ Tree)]]]]
[time
["." instant (#+ Instant)]
["." date (#+ Date)]
["." duration (#+ Duration)]
["." month (#+ Month)]
["." day (#+ Day)]]
[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
(Functor Random)
(def: (map f fa)
(function (_ state)
(let [[state' a] (fa state)]
[state' (f a)]))))
(structure: #export apply
(Apply Random)
(def: &functor ..functor)
(def: (apply ff fa)
(function (_ state)
(let [[state' f] (ff state)
[state'' a] (fa state')]
[state'' (f a)]))))
(structure: #export monad
(Monad Random)
(def: &functor ..functor)
(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
[sample gen]
(if (pred sample)
(wrap sample)
(filter pred gen))))
(def: #export (one check random)
(All [a b]
(-> (-> a (Maybe b)) (Random a) (Random b)))
(do ..monad
[sample random]
(case (check sample)
(#.Some output)
(wrap output)
#.None
(one check random))))
(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
[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))])))
(template [<name> <type> <cast>]
[(def: #export <name>
(Random <type>)
(\ ..monad map <cast> ..i64))]
[nat Nat .nat]
[int Int .int]
[rev Rev .rev]
)
(def: #export frac
(Random Frac)
(\ ..monad map (|>> .i64 f.from_bits) ..nat))
(def: #export safe_frac
(Random Frac)
(let [mantissa_range (.int (i64.left_shift 53 1))
mantissa_max (i.frac (dec mantissa_range))]
(\ ..monad map
(|>> (i.% mantissa_range)
i.frac
(f./ mantissa_max))
..int)))
(def: #export (char set)
(-> unicode.Set (Random Char))
(let [[start end] (unicode.range set)
size (n.- start end)
in_range (: (-> Char Char)
(|>> (n.% size) (n.+ start)))]
(|> ..nat
(\ ..monad map in_range)
(..filter (unicode.member? set)))))
(def: #export (text char_gen size)
(-> (Random Char) Nat (Random Text))
(if (n.= 0 size)
(\ ..monad wrap "")
(do ..monad
[x char_gen
xs (text char_gen (dec size))]
(wrap (text\compose (text.from_code x) xs)))))
(template [<name> <set>]
[(def: #export <name>
(-> Nat (Random Text))
(..text (..char <set>)))]
[unicode unicode.character]
[ascii unicode.ascii]
[ascii/alpha unicode.ascii/alpha]
[ascii/alpha_num unicode.ascii/alpha_num]
[ascii/upper_alpha unicode.ascii/upper_alpha]
[ascii/lower_alpha unicode.ascii/lower_alpha]
)
(template [<name> <type> <ctor> <gen>]
[(def: #export <name>
(Random <type>)
(do ..monad
[left <gen>
right <gen>]
(wrap (<ctor> left right))))]
[ratio r.Ratio r.ratio ..nat]
[complex c.Complex c.complex ..safe_frac]
)
(def: #export (and left right)
{#.doc "Sequencing combinator."}
(All [a b] (-> (Random a) (Random b) (Random [a b])))
(do ..monad
[=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}
[? bit]
(if ?
(do !
[=left left]
(wrap (0 #0 =left)))
(do !
[=right right]
(wrap (0 #1 =right))))))
(def: #export (either left right)
{#.doc "Homogeneous alternative combinator."}
(All [a] (-> (Random a) (Random a) (Random a)))
(do ..monad
[? 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}
[some? bit]
(if some?
(do !
[value value_gen]
(wrap (#.Some value)))
(wrap #.None))))
(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
[x value_gen
xs (<name> (dec size) value_gen)]
(wrap (<plus> x xs)))
(\ ..monad wrap <zero>)))]
[list List (.list) #.Cons]
[row Row row.empty row.add]
)
(template [<name> <type> <ctor>]
[(def: #export (<name> size value_gen)
(All [a] (-> Nat (Random a) (Random (<type> a))))
(do ..monad
[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}
[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 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}
[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 wrap (dictionary.new Hash<a>))))
(def: #export instant
(Random Instant)
(\ ..monad map instant.from_millis ..int))
(def: #export date
(Random Date)
(\ ..monad map instant.date ..instant))
(def: #export duration
(Random Duration)
(\ ..monad map duration.from_millis ..int))
(def: #export month
(Random Month)
(let [(^open "\.") ..monad]
(..either (..either (..either (\wrap #month.January)
(..either (\wrap #month.February)
(\wrap #month.March)))
(..either (\wrap #month.April)
(..either (\wrap #month.May)
(\wrap #month.June))))
(..either (..either (\wrap #month.July)
(..either (\wrap #month.August)
(\wrap #month.September)))
(..either (\wrap #month.October)
(..either (\wrap #month.November)
(\wrap #month.December)))))))
(def: #export day
(Random Day)
(let [(^open "\.") ..monad]
(..either (..either (\wrap #day.Sunday)
(..either (\wrap #day.Monday)
(\wrap #day.Tuesday)))
(..either (..either (\wrap #day.Wednesday)
(\wrap #day.Thursday))
(..either (\wrap #day.Friday)
(\wrap #day.Saturday))))))
(def: #export (run prng calc)
(All [a] (-> PRNG (Random a) [PRNG a]))
(calc prng))
(def: #export (prng update return)
(All [a] (-> (-> a a) (-> a I64) (-> a PRNG)))
(function (recur state)
(function (_ _)
[(recur (update state))
(return state)])))
(def: #export (pcg_32 [increase seed])
{#.doc (doc "An implementation of the PCG32 algorithm."
"For more information, please see: http://www.pcg-random.org/")}
(-> [(I64 Any) (I64 Any)] PRNG)
(let [magic 6364136223846793005]
(function (_ _)
[(|> seed .nat (n.* magic) ("lux i64 +" increase) [increase] pcg_32)
(let [rot (|> seed .i64 (i64.logic_right_shift 59))]
(|> seed
(i64.logic_right_shift 18)
(i64.xor seed)
(i64.logic_right_shift 27)
(i64.rotate_right rot)
.i64))])))
(def: #export (xoroshiro_128+ [s0 s1])
{#.doc (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)]))
## https://en.wikipedia.org/wiki/Xorshift#Initialization
## http://xorshift.di.unimi.it/splitmix64.c
(def: #export split_mix_64
{#.doc (doc "An implementation of the SplitMix64 algorithm.")}
(-> Nat PRNG)
(let [twist (: (-> Nat Nat Nat)
(function (_ shift value)
(i64.xor (i64.logic_right_shift shift value) value)))
mix n.*]
(..prng (n.+ (hex "9E,37,79,B9,7F,4A,7C,15"))
(|>> (twist 30)
(mix (hex "BF,58,47,6D,1C,E4,E5,B9"))
(twist 27)
(mix (hex "94,D0,49,BB,13,31,11,EB"))
(twist 31)
.i64))))
|
