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|
(.module:
[library
[lux "*"
[abstract
[hash {"+" Hash}]
[enum {"+" Enum}]
[interval {"+" Interval}]
[monoid {"+" Monoid}]
[equivalence {"+" Equivalence}]
[codec {"+" Codec}]
[predicate {"+" Predicate}]
["[0]" order {"+" Order}]]
[control
["[0]" maybe]
["[0]" try {"+" Try}]]
[data
[text {"+" Char}]]]]
["[0]" // "_"
["[1][0]" nat]
["[1][0]" i64]])
(def: .public (= reference sample)
(-> Int Int Bit)
("lux i64 =" reference sample))
(def: .public (< reference sample)
(-> Int Int Bit)
("lux i64 <" reference sample))
(def: .public (<= reference sample)
(-> Int Int Bit)
(if ("lux i64 <" reference sample)
#1
("lux i64 =" reference sample)))
(def: .public (> reference sample)
(-> Int Int Bit)
("lux i64 <" sample reference))
(def: .public (>= reference sample)
(-> Int Int Bit)
(if ("lux i64 <" sample reference)
#1
("lux i64 =" reference sample)))
(template [<comparison> <name>]
[(def: .public <name>
(Predicate Int)
(<comparison> +0))]
[..> positive?]
[..< negative?]
[..= zero?]
)
(template [<name> <test> <doc>]
[(def: .public (<name> left right)
(-> Int Int Int)
(if (<test> right left)
left
right))]
[min ..< "Int(eger) minimum."]
[max ..> "Int(eger) maximum."]
)
(template [<name> <op> <doc>]
[(def: .public (<name> param subject)
(-> Int Int Int)
(<op> param subject))]
[+ "lux i64 +" "Int(eger) addition."]
[- "lux i64 -" "Int(eger) substraction."]
[* "lux i64 *" "Int(eger) multiplication."]
[/ "lux i64 /" "Int(eger) division."]
[% "lux i64 %" "Int(eger) remainder."]
)
(def: .public (/% param subject)
(-> Int Int [Int Int])
[(../ param subject)
(..% param subject)])
(def: .public (opposite it)
(-> Int Int)
(..- it +0))
(def: .public (abs it)
(-> Int Int)
(if (..< +0 it)
(..* -1 it)
it))
(def: .public (signum it)
(-> Int Int)
(cond (..= +0 it) +0
(..< +0 it) -1
... else
+1))
... https://rob.conery.io/2018/08/21/mod-and-remainder-are-not-the-same/
(def: .public (mod divisor dividend)
(All (_ m) (-> Int Int Int))
(let [remainder (..% divisor dividend)]
(if (or (and (..< +0 divisor)
(..> +0 remainder))
(and (..> +0 divisor)
(..< +0 remainder)))
(..+ divisor remainder)
remainder)))
(def: .public even?
(-> Int Bit)
(|>> (..% +2) ("lux i64 =" +0)))
(def: .public odd?
(-> Int Bit)
(|>> ..even? not))
... https://en.wikipedia.org/wiki/Greatest_common_divisor
(def: .public (gcd a b)
(-> Int Int Int)
(case b
+0 a
_ (gcd b (..% b a))))
(def: .public (co_prime? a b)
(-> Int Int Bit)
(..= +1 (..gcd a b)))
... https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
(def: .public (extended_gcd a b)
(-> Int Int [[Int Int] Int])
(loop [x +1 x1 +0
y +0 y1 +1
a1 a b1 b]
(case b1
+0 [[x y] a1]
_ (let [q (/ b1 a1)]
(recur x1 (- (* q x1) x)
y1 (- (* q y1) y)
b1 (- (* q b1) a1))))))
... https://en.wikipedia.org/wiki/Least_common_multiple
(def: .public (lcm a b)
(-> Int Int Int)
(case [a b]
(^or [_ +0] [+0 _])
+0
_
(|> a (/ (gcd a b)) (* b))))
(def: .public frac
(-> Int Frac)
(|>> "lux i64 f64"))
(implementation: .public equivalence
(Equivalence Int)
(def: = ..=))
(implementation: .public order
(Order Int)
(def: &equivalence ..equivalence)
(def: < ..<))
(implementation: .public enum
(Enum Int)
(def: &order ..order)
(def: succ ++)
(def: pred --))
... TODO: Find out why the numeric literals fail during JS compilation.
(implementation: .public interval
(Interval Int)
(def: &enum ..enum)
(def: top
... +9,223,372,036,854,775,807
(let [half (//i64.left_shifted 62 +1)]
(+ half
(-- half))))
(def: bottom
... -9,223,372,036,854,775,808
(//i64.left_shifted 63 +1)))
(template [<name> <composite> <identity>]
[(implementation: .public <name>
(Monoid Int)
(def: identity <identity>)
(def: composite <composite>))]
[addition ..+ +0]
[multiplication ..* +1]
[maximum ..max (# ..interval bottom)]
[minimum ..min (# ..interval top)]
)
(def: -sign "-")
(def: +sign "+")
(template [<struct> <codec> <error>]
[(implementation: .public <struct>
(Codec Text Int)
(def: (encoded value)
(if (..< +0 value)
(|> value ++ ..opposite .nat ++ (# <codec> encoded) ("lux text concat" ..-sign))
(|> value .nat (# <codec> encoded) ("lux text concat" ..+sign))))
(def: (decoded repr)
(let [input_size ("lux text size" repr)]
(if (//nat.> 1 input_size)
(case ("lux text clip" 0 1 repr)
(^ (static ..+sign))
(|> repr
("lux text clip" 1 (-- input_size))
(# <codec> decoded)
(# try.functor each .int))
(^ (static ..-sign))
(|> repr
("lux text clip" 1 (-- input_size))
(# <codec> decoded)
(# try.functor each (|>> -- .int ..opposite --)))
_
{try.#Failure <error>})
{try.#Failure <error>}))))]
[binary //nat.binary "Invalid binary syntax for Int: "]
[octal //nat.octal "Invalid octal syntax for Int: "]
[decimal //nat.decimal "Invalid syntax for Int: "]
[hex //nat.hex "Invalid hexadecimal syntax for Int: "]
)
(implementation: .public hash
(Hash Int)
(def: &equivalence ..equivalence)
(def: hash .nat))
(def: .public (right_shifted parameter subject)
(-> Nat Int Int)
(//i64.or (//i64.and //i64.sign subject)
(//i64.right_shifted parameter subject)))
|
