ADD mathy stuff

This commit is contained in:
Nathan Dwarshuis 2023-03-27 23:55:53 -04:00
parent 2a38b52fc4
commit ab70012642
3 changed files with 345 additions and 15 deletions

147
dhall/Decimal.dhall Normal file
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@ -0,0 +1,147 @@
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 }

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@ -4,6 +4,10 @@ let List/map =
let T = ./Types.dhall let T = ./Types.dhall
let D = ./Decimal.dhall
let M = ./math.dhall
let nullSplit = let nullSplit =
\(a : T.SplitAcnt) -> \(a : T.SplitAcnt) ->
\(c : T.SplitCur) -> \(c : T.SplitCur) ->
@ -112,19 +116,6 @@ let part1_ =
\(a : T.SplitAcnt) -> \(a : T.SplitAcnt) ->
partN c a "" ([] : List PartSplit) partN c a "" ([] : List PartSplit)
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 addDay = let addDay =
\(x : T.GregorianM) -> \(x : T.GregorianM) ->
\(d : Natural) -> \(d : Natural) ->
@ -170,8 +161,6 @@ in { nullSplit
, partN , partN
, part1 , part1
, part1_ , part1_
, d
, d_
, addDay , addDay
, comma = 44 , comma = 44
, tab = 9 , tab = 9
@ -186,3 +175,5 @@ in { nullSplit
, PartSplit , PartSplit
} }
/\ T /\ T
/\ D
/\ M

192
dhall/math.dhall Normal file
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@ -0,0 +1,192 @@
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 foldWhile
: forall (n : Natural) ->
forall (res : Type) ->
forall (succ : res -> Optional res) ->
forall (zero : res) ->
res
= \(n : Natural) ->
\(R : Type) ->
\(succ : R -> Optional R) ->
\(zero : R) ->
let Acc
: Type
= { current : R, done : Bool }
let update
: Acc -> Acc
= \(acc : Acc) ->
if acc.done
then acc
else merge
{ Some = \(r : R) -> acc // { current = r }
, None = acc // { done = True }
}
(succ acc.current)
let init
: Acc
= { current = zero, done = False }
let result
: Acc
= Natural/fold n Acc update init
in result.current
let DivRes = \(a : Type) -> { remainder : a, quotiant : a }
let QED = assert : True === True
let downwardSteps =
\(x : Natural) ->
\(y : Natural) ->
let initAcc
: DivRes Natural
= { remainder = x, quotiant = 0 }
let updateAcc
: DivRes Natural -> Optional (DivRes Natural)
= \(acc : DivRes Natural) ->
if Nat.lessThan acc.remainder y
then None (DivRes Natural)
else Some
{ remainder = Natural/subtract y acc.remainder
, quotiant = acc.quotiant + 1
}
in foldWhile (x + 1) (DivRes Natural) updateAcc initAcc
let Natural/quotRemUnsafe
: forall (a : Natural) -> Natural -> DivRes Natural
= \(x : Natural) -> \(y : Natural) -> downwardSteps y x
let Natural/quotRem
: forall (a : Natural) ->
Nat.isZero a == False === True ->
Natural ->
DivRes Natural
= \(x : Natural) ->
\(_ : Nat.isZero x == False === True) ->
\(y : Natural) ->
Natural/quotRemUnsafe x y
let Natural/div
: forall (a : Natural) ->
Nat.isZero a == False === True ->
Natural ->
Natural
= \(x : Natural) ->
\(a : Nat.isZero x == False === True) ->
\(y : Natural) ->
(Natural/quotRem x a y).quotiant
let d1 = assert : Natural/div 1 QED 1 === 1
let d2 = assert : Natural/div 2 QED 1 === 0
let d3 = assert : Natural/div 2 QED 5 === 2
let Natural/rem
: forall (a : Natural) ->
Nat.isZero a == False === True ->
Natural ->
Natural
= \(x : Natural) ->
\(a : Nat.isZero x == False === True) ->
\(y : Natural) ->
(Natural/quotRem x a y).remainder
let r1 = assert : Natural/rem 2 QED 4 === 0
let r2 = assert : Natural/rem 2 QED 5 === 1
let Natural/pow
: Natural -> Natural -> Natural
= \(b : Natural) ->
\(p : Natural) ->
Natural/fold p Natural (\(x : Natural) -> x * b) 1
let p1 = assert : Natural/pow 10 1 === 10
let p2 = assert : Natural/pow 10 3 === 1000
let p3 = assert : Natural/pow 10 0 === 1
let Integer/quotRemUnsafe
: Natural -> Integer -> DivRes Integer
= \(x : Natural) ->
\(y : Integer) ->
if Int.equal y +0
then { quotiant = +0, remainder = +0 }
else let sign = if Int.positive y then +1 else -1
let toInt = \(x : Natural) -> Int.multiply sign (Nat.toInteger x)
let res = Natural/quotRemUnsafe x (Int.abs y)
in { quotiant = toInt res.quotiant
, remainder = toInt res.remainder
}
let Integer/quotRem
: forall (a : Natural) ->
Nat.isZero a == False === True ->
Integer ->
DivRes Integer
= \(x : Natural) ->
\(_ : Nat.isZero x == False === True) ->
\(y : Integer) ->
Integer/quotRemUnsafe x y
let Integer/div
: forall (a : Natural) ->
Nat.isZero a == False === True ->
Integer ->
Integer
= \(x : Natural) ->
\(a : Nat.isZero x == False === True) ->
\(y : Integer) ->
(Integer/quotRem x a y).quotiant
let id1 = assert : Integer/div 1 QED +3 === +3
let id2 = assert : Integer/div 1 QED -3 === -3
let id3 = assert : Integer/div 2 QED -7 === -3
let Integer/rem
: forall (a : Natural) ->
Nat.isZero a == False === True ->
Integer ->
Integer
= \(x : Natural) ->
\(a : Nat.isZero x == False === True) ->
\(y : Integer) ->
(Integer/quotRem x a y).remainder
let ir1 = assert : Integer/rem 1 QED +3 === +0
let ir2 = assert : Integer/rem 1 QED -3 === -0
let ir3 = assert : Integer/rem 2 QED -7 === -1
in { QED
, DivRes
, Natural/div
, Natural/rem
, Natural/quotRem
, Natural/quotRemUnsafe
, Natural/pow
, Integer/quotRem
, Integer/quotRemUnsafe
, Integer/div
, Integer/rem
}