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|
(.require
[library
[lux (.except or and list i64 nat int rev char only)
[abstract
[hash (.only Hash)]
[functor (.only Functor)]
[apply (.only Apply)]
["[0]" monad (.only Monad do)]]
[data
["[0]" text (.use "[1]#[0]" monoid)
[char (.only Char)]
["[0]" unicode
["[1]" set]]]
[collection
["[0]" list (.use "[1]#[0]" mix)]
["[0]" array (.only Array)]
["[0]" dictionary (.only Dictionary)]
["[0]" queue (.only Queue)]
["[0]" set (.only Set)]
["[0]" stack (.only Stack)]
["[0]" sequence (.only Sequence)]
[tree
["[0]" finger (.only Tree)]]]]
[math
[number (.only hex)
["n" nat]
["i" int]
["f" frac]
["r" ratio]
["c" complex]
["[0]" i64]]]
[meta
[type
[refinement (.only Refiner Refined)]]]
[world
["[0]" time (.only Time)
["[0]" instant (.only Instant)]
["[0]" date (.only Date)]
["[0]" duration (.only Duration)]
["[0]" month (.only Month)]
["[0]" day (.only Day)]]]]])
(type .public PRNG
(Rec PRNG
(-> Any [PRNG I64])))
(type .public (Random a)
(-> PRNG [PRNG a]))
(def .public functor
(Functor Random)
(implementation
(def (each f fa)
(function (_ state)
(let [[state' a] (fa state)]
[state' (f a)])))))
(def .public apply
(Apply Random)
(implementation
(def functor ..functor)
(def (on fa ff)
(function (_ state)
(let [[state' f] (ff state)
[state'' a] (fa state')]
[state'' (f a)])))))
(def .public monad
(Monad Random)
(implementation
(def functor ..functor)
(def (in a)
(function (_ state)
[state a]))
(def (conjoint ffa)
(function (_ state)
(let [[state' fa] (ffa state)]
(fa state'))))))
(def .public (only pred gen)
(All (_ a) (-> (-> a Bit) (Random a) (Random a)))
(do ..monad
[sample gen]
(if (pred sample)
(in sample)
(only pred gen))))
(def .public (one check random)
(All (_ a b)
(-> (-> a (Maybe b)) (Random a) (Random b)))
(do ..monad
[sample random]
(when (check sample)
{.#Some output}
(in output)
{.#None}
(one check random))))
(def .public (refined refiner gen)
(All (_ t r) (-> (Refiner t r) (Random t) (Random (Refined t r))))
(do ..monad
[sample gen]
(when (refiner sample)
{.#Some refined}
(in refined)
{.#None}
(refined refiner gen))))
(def .public bit
(Random Bit)
(function (_ prng)
(let [[prng output] (prng [])]
[prng (|> output (i64.and 1) (n.= 1))])))
(def .public i64
(Random I64)
(function (_ prng)
(let [[prng left] (prng [])
[prng right] (prng [])]
[prng (|> left
(i64.left_shifted 32)
(.i64_+# right))])))
(with_template [<name> <type> <cast>]
[(def .public <name>
(Random <type>)
(at ..functor each (|>> <cast>) ..i64))]
[nat Nat .nat]
[int Int .int]
[rev Rev .rev]
)
(def .public frac
(Random Frac)
(at ..functor each (|>> .i64 f.of_bits) ..nat))
(def .public safe_frac
(Random Frac)
(let [mantissa_range (.int (i64.left_shifted 53 1))
mantissa_max (i.frac (-- mantissa_range))]
(at ..functor each
(|>> (i.% mantissa_range)
i.frac
(f./ mantissa_max))
..int)))
(def .public (char set)
(-> unicode.Set (Random Char))
(let [start (unicode.start set)
end (unicode.end set)
size (n.- start end)
in_range (is (-> Char Char)
(|>> (n.% size) (n.+ start)))]
(|> ..nat
(at ..functor each in_range)
(..only (unicode.member? set)))))
(def .public (text char_gen size)
(-> (Random Char) Nat (Random Text))
(if (n.= 0 size)
(at ..monad in "")
(do ..monad
[x char_gen
xs (text char_gen (-- size))]
(in (text#composite (text.of_char x) xs)))))
(with_template [<name> <set>]
[(def .public <name>
(-> Nat (Random Text))
(..text (..char <set>)))]
[unicode unicode.character]
[ascii unicode.ascii]
[alphabetic unicode.alphabetic]
[alpha_numeric unicode.alpha_numeric]
[numeric unicode.numeric]
[upper_cased unicode.upper_case]
[lower_cased unicode.lower_case]
)
(with_template [<name> <type> <ctor> <gen>]
[(def .public <name>
(Random <type>)
(do ..monad
[left <gen>
right <gen>]
(in (<ctor> left right))))]
[ratio r.Ratio r.ratio ..nat]
[complex c.Complex c.complex ..safe_frac]
)
(def .public (and left right)
(All (_ a b) (-> (Random a) (Random b) (Random [a b])))
(function (_ prng)
(let [[prng left] (left prng)
[prng right] (right prng)]
[prng [left right]])))
(def .public (or left right)
(All (_ a b) (-> (Random a) (Random b) (Random (Or a b))))
(function (_ prng)
(let [[prng ?] (..bit prng)]
(if ?
(let [[prng left] (left prng)]
[prng {0 #0 left}])
(let [[prng right] (right prng)]
[prng {0 #1 right}])))))
(def .public (either left right)
(All (_ a) (-> (Random a) (Random a) (Random a)))
(function (_ prng)
(let [[prng ?] (..bit prng)]
(if ?
(left prng)
(right prng)))))
(def .public (rec gen)
(All (_ a) (-> (-> (Random a) (Random a)) (Random a)))
(function (_ state)
(let [gen' (gen (rec gen))]
(gen' state))))
(def .public (maybe value_gen)
(All (_ a) (-> (Random a) (Random (Maybe a))))
(do [! ..monad]
[some? bit]
(if some?
(do !
[value value_gen]
(in {.#Some value}))
(in {.#None}))))
(def .public (list size value_gen)
(All (_ a) (-> Nat (Random a) (Random (List a))))
(if (n.> 0 size)
(do ..monad
[x value_gen
xs (list (-- size) value_gen)]
(in {.#Item x xs}))
(at ..monad in (.list))))
(def .public (sequence size value_gen)
(All (_ a) (-> Nat (Random a) (Random (Sequence a))))
(if (n.> 0 size)
(do ..monad
[x value_gen
xs (sequence (-- size) value_gen)]
(in (sequence.suffix x xs)))
(at ..monad in sequence.empty)))
(with_template [<name> <type> <ctor>]
[(def .public (<name> size value_gen)
(All (_ a) (-> Nat (Random a) (Random (<type> a))))
(do ..monad
[values (list size value_gen)]
(in (|> values <ctor>))))]
[array Array array.of_list]
[queue Queue queue.of_list]
[stack Stack (list#mix stack.top stack.empty)]
)
(def .public (set hash size value_gen)
(All (_ a) (-> (Hash a) Nat (Random a) (Random (Set a))))
(if (n.> 0 size)
(do [! ..monad]
[xs (set hash (-- size) value_gen)]
(loop (again [_ []])
(do !
[x value_gen
.let [xs+ (set.has x xs)]]
(if (n.= size (set.size xs+))
(in xs+)
(again [])))))
(at ..monad in (set.empty hash))))
(def .public (dictionary hash 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 (-- size) key_gen value_gen)]
(loop (again [_ []])
(do !
[k key_gen
v value_gen
.let [kv+ (dictionary.has k v kv)]]
(if (n.= size (dictionary.size kv+))
(in kv+)
(again [])))))
(at ..monad in (dictionary.empty hash))))
(def .public instant
(Random Instant)
(at ..functor each instant.of_millis ..int))
(def .public date
(Random Date)
(at ..functor each instant.date ..instant))
(def .public time
(Random Time)
(at ..functor each instant.time ..instant))
(def .public duration
(Random Duration)
(at ..functor each duration.of_millis ..int))
(def .public month
(Random Month)
(let [(open "_#[0]") ..monad]
(..either (..either (..either (_#in {month.#January})
(..either (_#in {month.#February})
(_#in {month.#March})))
(..either (_#in {month.#April})
(..either (_#in {month.#May})
(_#in {month.#June}))))
(..either (..either (_#in {month.#July})
(..either (_#in {month.#August})
(_#in {month.#September})))
(..either (_#in {month.#October})
(..either (_#in {month.#November})
(_#in {month.#December})))))))
(def .public day
(Random Day)
(let [(open "_#[0]") ..monad]
(..either (..either (_#in {day.#Sunday})
(..either (_#in {day.#Monday})
(_#in {day.#Tuesday})))
(..either (..either (_#in {day.#Wednesday})
(_#in {day.#Thursday}))
(..either (_#in {day.#Friday})
(_#in {day.#Saturday}))))))
(def .public (result prng calc)
(All (_ a) (-> PRNG (Random a) [PRNG a]))
(calc prng))
(def .public (prng update return)
(All (_ a) (-> (-> a a) (-> a I64) (-> a PRNG)))
(function (again state)
(function (_ _)
[(again (update state))
(return state)])))
(def .public (pcg_32 [increase seed])
(-> [(I64 Any) (I64 Any)] PRNG)
(let [magic 6364136223846793005]
(function (_ _)
[(|> seed .nat (n.* magic) (.i64_+# increase) [increase] pcg_32)
(let [rot (|> seed .nat (i64.right_shifted 59))]
(|> seed
(i64.right_shifted 18)
(i64.xor seed)
(i64.right_shifted 27)
(i64.right_rotated rot)
.i64))])))
(def .public (xoroshiro_128+ [s0 s1])
(-> [(I64 Any) (I64 Any)] PRNG)
(function (_ _)
[(let [s01 (i64.xor s0 s1)]
(xoroshiro_128+ [(|> s0
(i64.left_rotated 55)
(i64.xor s01)
(i64.xor (i64.left_shifted 14 s01)))
(i64.left_rotated 36 s01)]))
(.i64_+# s0 s1)]))
... https://en.wikipedia.org/wiki/Xorshift#Initialization
... http://xorshift.di.unimi.it/splitmix64.c
(def .public split_mix_64
(-> Nat PRNG)
(let [twist (is (-> Nat Nat Nat)
(function (_ shift value)
(i64.xor (i64.right_shifted 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))))
|
