pwncash/dhall/Decimal.dhall

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2023-03-27 23:55:53 -04:00
let Nat =
https://prelude.dhall-lang.org/v21.1.0/Natural/package.dhall
sha256:ee9ed2b28a417ed4e9a0c284801b928bf91b3fbdc1a68616347678c1821f1ddf
let Int =
https://prelude.dhall-lang.org/v21.1.0/Integer/package.dhall
sha256:d1a572ca3a764781496847e4921d7d9a881c18ffcfac6ae28d0e5299066938a0
let T = ./Types.dhall
let M = ./math.dhall
let dec =
\(s : Bool) ->
\(w : Natural) ->
\(d : Natural) ->
\(p : Natural) ->
{ whole = w, decimal = d, precision = p, sign = s } : T.Decimal
let dec2 = \(s : Bool) -> \(w : Natural) -> \(d : Natural) -> dec s w d 2
let d = dec2 True
let d_ = dec2 False
let Decimal/toNatural =
\(a : T.Decimal) ->
let p = M.Natural/pow 10 a.precision in a.whole * p + a.decimal
let Decimal/toInteger =
\(x : T.Decimal) ->
let n = Nat.toInteger (Decimal/toNatural x)
in if x.sign == True then n else Int.negate n
let Decimal/add
: T.Decimal -> T.Decimal -> T.Decimal
= \(a : T.Decimal) ->
\(b : T.Decimal) ->
let final_precision = Nat.max a.precision b.precision
let to_int =
\(z : T.Decimal) ->
Decimal/toInteger
( z
// { precision = final_precision
, decimal =
z.decimal
* M.Natural/pow
10
(Nat.subtract z.precision final_precision)
}
)
let x = to_int a
let y = to_int b
let p = M.Natural/pow 10 final_precision
let res = M.Integer/quotRemUnsafe p (Int.add x y)
in dec
(Int.positive res.quotiant)
(Int.abs res.quotiant)
(Int.abs res.remainder)
final_precision
let test =
assert : Decimal/add (dec True 1 0 0) (dec True 1 0 0) === dec True 2 0 0
let test =
assert
: Decimal/add (dec True 1 5 1) (dec False 2 0 0) === dec False 0 5 1
let Decimal/multiply
: T.Decimal -> T.Decimal -> T.Decimal
= \(a : T.Decimal) ->
\(b : T.Decimal) ->
let x = Decimal/toNatural a
let y = Decimal/toNatural b
let p = a.precision + b.precision
let res = M.Natural/quotRemUnsafe (M.Natural/pow 10 p) (x * y)
in dec (a.sign == b.sign) res.quotiant res.remainder p
let test =
assert
: Decimal/multiply (dec True 1 0 1) (dec True 0 0 0) === dec True 0 0 1
let test =
assert
: Decimal/multiply (dec True 1 0 1) (dec True 1 0 0) === dec True 1 0 1
let test =
assert
: Decimal/multiply (dec True 1 4 1) (dec False 2 0 2)
=== dec False 2 800 3
let Decimal/round
: Natural -> T.Decimal -> T.Decimal
= \(p : Natural) ->
\(a : T.Decimal) ->
if Nat.equal a.precision p
then a
else if Nat.greaterThan p a.precision
then a
// { precision = p
, decimal =
a.decimal * M.Natural/pow 10 (Nat.subtract a.precision p)
}
else let subp = M.Natural/pow 10 (Nat.subtract (p + 1) a.precision)
let subRes =
M.Natural/quotRem
10
M.QED
(M.Natural/quotRemUnsafe subp a.decimal).quotiant
in if Nat.lessThan subRes.remainder 5
then a // { precision = p, decimal = subRes.quotiant }
else let dec = subRes.quotiant + 1
in if Nat.equal dec (M.Natural/pow 10 p)
then a
// { whole = a.whole + 1
, decimal = 0
, precision = p
}
else a // { decimal = dec, precision = p }
let test = assert : Decimal/round 2 (dec True 0 49 2) === dec True 0 49 2
let test = assert : Decimal/round 1 (dec True 0 49 2) === dec True 0 5 1
let test = assert : Decimal/round 0 (dec True 0 49 2) === dec True 0 0 0
let test =
assert
: Decimal/round 3 (dec True 0 49 2) === Decimal/round 3 (dec True 0 490 3)
let test = assert : Decimal/round 1 (dec True 0 95 2) === dec True 1 0 1
in { dec, dec2, d, d_, Decimal/add, Decimal/multiply, Decimal/round }