module Complex where

data Repr = Normal | Polar

data Complex :: Repr -> Type where
  Complex :: forall r . Float -> Float -> Complex r

repr :: forall r . Complex r -> Repr
repr @r _ = r

normal :: Float -> Float -> Complex Normal
normal a b = Complex a b

polar :: Float -> Float -> Complex Polar
polar a b = Complex a b

-- TODO: Write tests that checks if the derived type is the same as the given
cabs :: forall r . Complex r -> Float
cabs @'Normal (Complex a b)    = sqrt (a*a + b*b)
cabs @'Polar  (Complex r _phi) = r

toPolar :: Complex Normal -> Complex Polar
toPolar (Complex x y) =
       if x >  0.0             then polar r (atan (y / x))
  else if x <  0.0 && y >= 0.0 then polar r (atan (y / x) + pi)
  else if x <  0.0 && y <  0.0 then polar r (atan (y / x) - pi)
  else if x == 0.0 && y >= 0.0 then polar r ( pi / 2.0)
  else if x == 0.0 && y <  0.0 then polar r (-pi / 2.0)
  else undefined -- x == 0.0 && y == 0.0
  where
    r = sqrt (x*x + y*y)

{- TODO:
       if x >  0.0             then polar r (arctan (y / x))
       if x <  0.0 && y >= 0.0 then polar r (arctan (y / x) + pi)
!Failed complex
  "./testdata/accept/complex.lc" (line 32, column 10):
  unexpected reserved word "if"
  expecting lowercase ident or uppercase ident
-}
{- TODO:
!Failed complex
  can't find: error in "./testdata/accept/complex.lc" (line 33, column 9):
    else (error "indeterminate polar complex number")
          ^^^^^
-}
{-
toPolar (Complex x y)
  | x > 0.0 && y >= 0.0 = polar r 0
  | x > 0.0 && y <  0.0 = polar r 0
  where
    r = sqrt (x*x + y*y)
!Failed complex
  "./testdata/accept/complex.lc" (line 26, column 4):
  unexpected reserved operator "|"
  expecting symbols
-}
{-
toPolar c@(Complex a b) = undefined
!Crashed mandel
  ../src/LambdaCube/Compiler/Infer.hs:(1162,1)-(1164,98): Non-exhaustive patterns in function addLams'
-}

toNormal :: Complex Polar -> Complex Normal
toNormal (Complex r phi) = Complex (r * cos phi) (r * sin phi)

{-
convert :: forall r0 . forall r1 . Complex r0 -> Complex r1
convert @'Normal @'Normal c = c
convert @'Polar  @'Polar  c = c
convert @'Normal @'Polar  c = toPolar c
convert @'Polar  @'Normal c = toNormal c
!Failed mandel
  checkMetas lam: \(a : V0~Polar) (b : Normal~V1) (c : 'Num ('MatVecElem 'Float)) (d : 'Num ('MatVecElem
  'Float)) (e : Polar~V4) (f : Normal~V5) (g : V6~Normal) {h:'Repr} (i : h~V8) (j : 'Complex V9) ->
  'ReprCase (\'Repr -> 'Complex V11) ('ReprCase (\'Repr -> 'Complex V11) (labend j) (labend (toPolar j))
  h) ('ReprCase (\'Repr -> 'Complex Normal) (labend (toNormal c d j)) (labend j) h) V10
-}

{-
convert :: forall r0 . forall r1 . Complex r0 -> Complex r1
convert @'Normal @'Normal = id
convert @'Polar  @'Polar  = id
convert @'Normal @'Polar  = toPolar
convert @'Polar  @'Normal = toNormal
!Failed mandel
  type error: can not unify
  Polar
  with
  Normal

  in "./testdata/accept/mandel.lc" (line 51, column 27):
  convert @'Normal @'Polar  = toPolar
                            ^^^^^^^
-}

{- ISSUE: Which is expected, which is found???
crepr :: forall r . Complex r -> r
crepr @r (Complex _ _) = r

!Failed mandel
  type error: can not unify
  Type
  with
  'Repr

r should have type X, but it has Y
-}

-- ISSUE: It compiles
it_should_fail (Complex r _ _ _ _) = r

add :: forall r0 . forall r1 . Complex r0 -> Complex r1 -> Complex r0
add @'Normal @'Normal (Complex a b) (Complex c d) = Complex (a + c) (b + d)

{-
add @'Polar  @'Polar  c0 c1 = toPolar (add (toNormal c0) (toNormal c1))
!Failed mandel
  checkMetas lam: \(a : Polar~V0) (b : 'Num ('MatVecElem 'Float)) (c : 'Num ('MatVecElem 'Float))
  {d:'Repr} (e : Polar~d) (f : V5~Polar) (g : 'Complex V6) (h : 'Complex d) -> 'ReprCase (\'Repr ->
  'Complex Polar) ('ReprCase (\'Repr -> 'Complex Polar) ('ComplexCase (\'Repr 'Complex k -> 'Complex
  Polar) (\{m:'Repr} n:'Float o:'Float -> 'ComplexCase (\'Repr 'Complex p -> 'Complex Polar) (\{r:'Repr}
  s:'Float t:'Float -> labend (Complex Polar (PrimAdd 'Float V19 n s) (PrimAdd 'Float V18 o t))) d h) V8
  g) (labend (undefined ('Complex Polar))) d) ('ReprCase (\'Repr -> 'Complex Polar) (labend (undefined
  ('Complex Polar))) (labend (toPolar (V9 Normal Normal (toNormal V11 V10 g) (toNormal b c h)))) d) V8
-}

mul :: forall r0 r1 . Complex r0 -> Complex r1 -> Complex r0
mul @'Normal @'Normal (Complex a b) (Complex c d) = Complex (a*c - b*d) (b*c + a*d)

{- TODO: The hidden parameters should not be shown... or a configuration level...
{a : 'Num ('MatVecElem 'Float)} -> {b : 'Num ('MatVecElem 'Float)} -> {c : 'Num ('MatVecElem 'Float)} ->
{d : 'Num ('MatVecElem 'Float)} -> {e : 'Num ('MatVecElem 'Float)} -> {f : 'Num ('MatVecElem 'Float)} ->
'Complex Normal -> 'Complex Normal -> 'Complex Normal
-}

s :: Complex r -> Complex r
s c = (mul c c) `add` c

-- ISSUE: More application consumes lot of memory
s4 c = s (s (s (s c)))

iter = s4

mandel c = cabs (iter c) < 2.0

{- PROPOSAL:
main should be called screenOut
main :: Output
main = ...
-}