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|
(;module: {#;doc "Rational arithmetic."}
lux
(lux [math]
(control eq
[ord]
number
codec
monad)
(data [number "n/" Number<Nat> Codec<Text,Nat>]
[text "Text/" Monoid<Text>]
text/format
error
[product])
[compiler]
(macro [ast]
["s" syntax #+ syntax: Syntax])))
(type: #export Ratio
{#numerator Nat
#denominator Nat})
(def: #hidden (normalize (^slots [#numerator #denominator]))
(-> Ratio Ratio)
(let [common (math;gcd numerator denominator)]
{#numerator (n./ common numerator)
#denominator (n./ common denominator)}))
(def: #export (q.* param input)
(-> Ratio Ratio Ratio)
(normalize [(n.* (get@ #numerator param)
(get@ #numerator input))
(n.* (get@ #denominator param)
(get@ #denominator input))]))
(def: #export (q./ param input)
(-> Ratio Ratio Ratio)
(normalize [(n.* (get@ #denominator param)
(get@ #numerator input))
(n.* (get@ #numerator param)
(get@ #denominator input))]))
(def: #export (q.+ param input)
(-> Ratio Ratio Ratio)
(normalize [(n.+ (n.* (get@ #denominator input)
(get@ #numerator param))
(n.* (get@ #denominator param)
(get@ #numerator input)))
(n.* (get@ #denominator param)
(get@ #denominator input))]))
(def: #export (q.- param input)
(-> Ratio Ratio Ratio)
(normalize [(n.- (n.* (get@ #denominator input)
(get@ #numerator param))
(n.* (get@ #denominator param)
(get@ #numerator input)))
(n.* (get@ #denominator param)
(get@ #denominator input))]))
(def: #export (q.% param input)
(-> Ratio Ratio Ratio)
(let [quot (n./ (n.* (get@ #denominator input)
(get@ #numerator param))
(n.* (get@ #denominator param)
(get@ #numerator input)))]
(q.- (update@ #numerator (n.* quot) param)
input)))
(def: #export (q.= param input)
(-> Ratio Ratio Bool)
(and (n.= (get@ #numerator param)
(get@ #numerator input))
(n.= (get@ #denominator param)
(get@ #denominator input))))
(do-template [<name> <op>]
[(def: #export (<name> param input)
(-> Ratio Ratio Bool)
(and (<op> (n.* (get@ #denominator input)
(get@ #numerator param))
(n.* (get@ #denominator param)
(get@ #numerator input)))))]
[q.< n.<]
[q.<= n.<=]
[q.> n.>]
[q.>= n.>=]
)
(do-template [<name> <comp>]
[(def: #export (<name> left right)
(-> Ratio Ratio Ratio)
(if (<comp> left right)
right
left))]
[q.min q.<]
[q.max q.>]
)
(struct: #export _ (Eq Ratio)
(def: = q.=))
(struct: #export _ (ord;Ord Ratio)
(def: eq Eq<Ratio>)
(def: < q.<)
(def: <= q.<=)
(def: > q.>)
(def: >= q.>=))
(struct: #export _ (Number Ratio)
(def: ord Ord<Ratio>)
(def: + q.+)
(def: - q.-)
(def: * q.*)
(def: / q./)
(def: % q.%)
(def: (negate (^slots [#numerator #denominator]))
{#numerator denominator
#denominator numerator})
(def: abs id)
(def: (signum x)
{#numerator +1
#denominator +1}))
(def: separator Text ":")
(def: part-encode
(-> Nat Text)
(|>. n/encode (text;split +1) (default (undefined)) product;right))
(def: part-decode
(-> Text (Error Nat))
(|>. (format "+") n/decode))
(struct: #export _ (Codec Text Ratio)
(def: (encode (^slots [#numerator #denominator]))
($_ Text/append (part-encode numerator) separator (part-encode denominator)))
(def: (decode input)
(case (text;split-with separator input)
(#;Some [num denom])
(do Monad<Error>
[numerator (part-decode num)
denominator (part-decode denom)]
(wrap (normalize {#numerator numerator
#denominator denominator})))
#;None
(#;Left (Text/append "Invalid syntax for ratio: " input)))))
(syntax: #export (ratio numerator [?denominator (s;opt s;any)])
{#;doc (doc "Rational literals."
(ratio numerator denominator)
"The denominator can be omitted if it's 1."
(ratio numerator))}
(wrap (list (` (normalize {#;;numerator (~ numerator)
#;;denominator (~ (default (' +1)
?denominator))})))))
|
