{-# LANGUAGE GADTs, EmptyDataDecls, NoMonomorphismRestriction, TypeFamilies, ScopedTypeVariables, FlexibleInstances, RankNTypes, MultiParamTypeClasses, FlexibleContexts, OverloadedStrings, ViewPatterns, RecordWildCards #-}

module Graphics.GPipe.Internal.Expr where

import Prelude hiding ((.), id, (<*))
import Control.Category
import Control.Monad (void, when)
import Control.Monad.Trans.Writer
import Control.Monad.Trans.State
import Control.Monad.Trans.Reader
import Data.Maybe
import Data.Monoid (mconcat, mappend)
import qualified Control.Monad.Trans.Class as T (lift)
import Data.SNMap
import qualified Data.IntMap as Map
import Data.Boolean
import Data.List (intercalate)
import Control.Applicative (liftA, liftA2, liftA3)
import Linear.V4
import Linear.V3
import Linear.V2
import Linear.V1
import Linear.V0
import Linear.Affine
import Linear.Metric
import Linear.Matrix
import Linear.Vector
import Linear.Conjugate
import Data.Foldable (Foldable(toList))
import Data.Int
import Data.Word
import Data.Bits -- (FiniteBits(finiteBitSize))

type NextTempVar = Int
type NextGlobal = Int

data SType = STypeFloat | STypeInt | STypeBool | STypeUInt | STypeDyn String | STypeMat Int Int | STypeVec Int | STypeIVec Int | STypeUVec Int | STypeGenerativeGeometry

stypeName :: SType -> String
stypeName STypeFloat = "float"
stypeName STypeInt = "int"
stypeName STypeBool = "bool"
stypeName STypeUInt = "uint"
stypeName (STypeDyn s) = s
stypeName (STypeMat r c) = "mat" ++ show c ++ 'x' : show r
stypeName (STypeVec n) = "vec" ++ show n
stypeName (STypeIVec n) = "ivec" ++ show n
stypeName (STypeUVec n) = "uvec" ++ show n
stypeName STypeGenerativeGeometry = "bool" -- A generative geometry is inherently a write-only value. The 'bool' type is simply here as a crude workaround (hardly a solution).

stypeSize :: SType -> Int
stypeSize (STypeVec n) = n * 4
stypeSize (STypeIVec n) = n * 4
stypeSize (STypeUVec n) = n * 4
stypeSize _ = 4

-- A functional shader expression.
type ExprM = SNMapReaderT
    [String] -- Cached GLSL source code.
    (StateT
        ExprState -- Shader inputs.
        (WriterT
            String -- Generated GLSL source code.
            (StateT
                NextTempVar -- Next unique variable name.
                IO -- IO to create stable names.
            )
        )
    )

type GlobDeclM = Writer String

data ExprState = ExprState
    {   shaderUsedUniformBlocks :: Map.IntMap (GlobDeclM ())
    ,   shaderUsedSamplers :: Map.IntMap (GlobDeclM ())
    ,   shaderUsedInput :: Map.IntMap -- (For vertex shaders, the value is always undefined and the int is the parameter name, for later shader stages it uses some name local to the transition instead)
        (   GlobDeclM () -- Input declarations for the current shader
        ,   (   ExprM () -- Output assignement required in the previous shader (obviously undefined for the first shader - see comment below.)
            ,   GlobDeclM () -- Output declaration required in the previous shader.
            ) -- Requirements for the previous shader.
        )
    ,   shaderGeometry :: Maybe (GlobDeclM ()) -- Input/ouput layout declarations for current shader (if it is a geometry shader).
    }

data ExprResult = ExprResult
    { finalSource :: String -- Shader source produced.
    , unis        :: [Int] -- Uniforms used in this shader.
    , samps       :: [Int] -- Samplers used in this shader.
    , inps        :: [Int] -- Inputs used in this shader (only varying or uniforms too?).
    , prevDecls   :: GlobDeclM () -- Output declarations required in the previous shader (how it differs from the inputs used?).
    , prevSs      :: ExprM () -- Expression to construct in the previous shader.
    }

{- Rough idea:

    makeDrawcall (sh, shd, _) =
        do  (fsource, funis, fsamps, _, prevDecls1, prevS1) <- runExprM shd sh
            (gsource, gunis, gsamps, _, prevDecls2, prevS2) <- runExprM prevDecls1 prevS1
            (vsource, vunis, vsamps, vinps, _, _) <- runExprM prevDecls2 prevS2
            return $ Drawcall _ _ _ vsource gsource fsource vinps vunis vsamps gunis gsamps funis fsamps _

    A sN expression's leafs are literals and input variables from the previous
    shader (shaders are evaluated here in reverse order). Evaluationg a sN
    expression produces a source and a sN+1 expression to be evaluated in the
    previous shader. This sN+1 expression obtained when evaluating a sN
    expression basically contains the values transformed by the matching arrow
    (ToVertex, ToFragment...). In this regard, the evaluation is the inverse
    arrow with the side effect of outputting the shader source.
-}
runExprM
    :: GlobDeclM () -- output declarations to include in this shader
    -> ExprM () -- expression to construct in this shader (including assignements to the output variables)
    -> IO ExprResult
runExprM d m = do
    (st, body) <- evalStateT (runWriterT (execStateT (runSNMapReaderT m) (ExprState Map.empty Map.empty Map.empty Nothing))) 0
    let (unis, uniDecls) = unzip $ Map.toAscList (shaderUsedUniformBlocks st)
        (samps, sampDecls) = unzip $ Map.toAscList (shaderUsedSamplers st)
        (inps, inpDescs) = unzip $ Map.toAscList (shaderUsedInput st)
        geoDescs = shaderGeometry st
        (inpDecls, prevDesc) = unzip inpDescs
        (sequence_ -> prevSs, sequence_ -> prevDecls) = unzip prevDesc
        decls = do
            d
            when (isJust geoDescs) (fromJust geoDescs)
            sequence_ uniDecls
            sequence_ sampDecls
            sequence_ inpDecls
        finalSource = mconcat
            [ "#version 450\n"
            , execWriter decls
            , "void main() {\n"
            , body
            , "}\n"
            ]
    return ExprResult{..}

--------------------------------------------------------------------------------
-- The section below is just an unused draft.
--------------------------------------------------------------------------------

data ShaderStageInput = ShaderStageInput
    {    -- The output declarations to include in the shader's source.
        outputDeclarations :: GlobDeclM ()
        -- The expression to evaluate as a source using variables to be provided
        -- by a previous shader (or buffer object). The top level of this
        -- expression is expected (how exactly?) to assign a value to the output
        -- variables declared above.
    ,   expression :: ExprM ()
    }

data ShaderStageOutput = ShaderStageOutput
    {   source :: String -- ^ The shader GLSL source to be compiled.
    ,   uniforms :: [Int] -- ^ The uniforms used in this shader.
    ,   samplers :: [Int] -- ^ The samplers used in this shader.
    ,   inputs :: [Int] -- ^ The input variables used in this shader.
    ,   previousDeclarations :: GlobDeclM () -- ^ The output declations to include in the previous shader to provide the needed input variables.
    ,   prevExpression :: ExprM () -- ^ The expression to evaluate in order to produce the previous shader.
    }

evaluateExpression :: [ExprM ()] -> ExprM () -> GlobDeclM () -> IO ShaderStageOutput
evaluateExpression staticExpressions expression requiredOutputDeclarations = do
    ExprResult s u ss is pds pe <- runExprM requiredOutputDeclarations expression
    case staticExpressions of
        (se:ses) -> evaluateExpression ses (pe >> se) pds
        [] -> return $ ShaderStageOutput s u ss is pds pe

--------------------------------------------------------------------------------

newtype S x a = S { unS :: ExprM String }

scalarS :: SType -> ExprM RValue -> S c a
scalarS typ = S . tellAssignment typ

vec2S :: SType -> ExprM RValue -> V2 (S c a)
vec2S typ s =
    let V4 x y _z _w = vec4S typ s
    in  V2 x y
vec3S :: SType -> ExprM RValue -> V3 (S c a)
vec3S typ s =
    let V4 x y z _w = vec4S typ s
    in  V3 x y z
vec4S :: SType -> ExprM RValue -> V4 (S c a)
vec4S typ s =
    let m = tellAssignment typ s
        f p = S $ fmap (++ p) m
    in  V4 (f ".x") (f ".y") (f ".z") (f ".w")

scalarS' :: RValue -> S c a
scalarS' = S . return

vec2S' :: RValue -> V2 (S c a)
vec2S' = vec2S'' . S . return
vec3S' :: RValue -> V3 (S c a)
vec3S' = vec3S'' . S . return
vec4S' :: RValue -> V4 (S c a)
vec4S' = vec4S'' . S . return

vec2S'' :: S c a -> V2 (S c a)
vec2S'' s =
    let V4 x y _z _w = vec4S'' s
    in  V2 x y
vec3S'' :: S c a -> V3 (S c a)
vec3S'' s =
    let V4 x y z _w = vec4S'' s
    in  V3 x y z
vec4S'' :: S c a -> V4 (S c a)
vec4S'' s =
    let f p = S $ fmap (++ ('[': show (p :: Int) ++"]")) (unS s)
    in  V4 (f 0) (f 1) (f 2) (f 3)

-- | Phantom type used as first argument in @'S' 'V' a@ that denotes that the shader value is a vertex value
data V

-- | Phantom type used as first argument in @'S' 'F' a@ that denotes that the shader value is a fragment value
data F

-- | We reuse V for geometry shader, which simplify things and makes sense save the GenerativeGeometry…
type G = V
newtype GenerativeGeometry p a = GenerativeGeometry a

type VFloat = S V Float
type VInt = S V Int
type VWord = S V Word
type VBool = S V Bool

type GGenerativeGeometry p a = S G (GenerativeGeometry p a)

type FFloat = S F Float
type FInt = S F Int
type FWord = S F Word
type FBool = S F Bool

useVInput :: SType -> Int -> ExprM String
useVInput stype i = do
    s <- T.lift get
    T.lift $ put $ s { shaderUsedInput = Map.insert i (gDeclInput, undefined) $ shaderUsedInput s }
    return $ "in" ++ show i
    where
        gDeclInput = do
            tellGlobal "in "
            tellGlobal $ stypeName stype
            tellGlobal " in"
            tellGlobalLn $ show i

useGInput :: String -> SType -> Int -> Int -> ExprM String -> ExprM String
useGInput qual stype i n v = do
    s <- T.lift get
    T.lift $ put $ s { shaderUsedInput = Map.insert n (gDeclIn, (assignOutput, gDeclOut)) $ shaderUsedInput s }
    return $ prefix ++ show n ++ "[" ++ show i ++ "]"
    where
        prefix = "vg"

        -- Output assignement in the previous shader
        assignOutput = do
            val <- v
            let name = prefix ++ show n
            tellAssignment' name val

        -- Output declaration in the previous shader.
        gDeclOut = do
            tellGlobal $ qual ++ " out "
            tellGlobal $ stypeName stype
            tellGlobal $ ' ':prefix
            tellGlobalLn $ show n

        -- Input declaration in the current shader.
        gDeclIn = do
            tellGlobal $ qual ++ " in "
            tellGlobal $ stypeName stype
            tellGlobal $ ' ':prefix
            tellGlobal $ show n
            tellGlobalLn $ "[]"

useFInputFromG :: String -> SType -> Int -> ExprM String -> ExprM String
useFInputFromG qual stype i v = do
    s <- T.lift get
    val :: Int <- read <$> v
    T.lift $ put $ s { shaderUsedInput = Map.insert i (gDecl val (qual ++ " in "), (return (), gDecl val (qual ++ " out "))) $ shaderUsedInput s }
    return $ prefix ++ show val
    where
        prefix = "vgf"

        gDecl val s = do
            tellGlobal s
            tellGlobal $ stypeName stype
            tellGlobal $ ' ':prefix
            tellGlobalLn $ show val

useFInput :: String -> String -> SType -> Int -> ExprM String -> ExprM String
useFInput qual prefix stype i v = do
    s <- T.lift get
    T.lift $ put $ s { shaderUsedInput = Map.insert i (gDecl (qual ++ " in "), (assignOutput, gDecl (qual ++ " out "))) $ shaderUsedInput s }
    return $ prefix ++ show i
    where
        assignOutput = do
            val <- v
            let name = prefix ++ show i
            tellAssignment' name val

        gDecl s = do
            tellGlobal s
            tellGlobal $ stypeName stype
            tellGlobal $ ' ':prefix
            tellGlobalLn $ show i

declareGeometryLayout :: String -> String -> Int -> ExprM ()
declareGeometryLayout inputPrimitive outputPrimitive maxVertices = T.lift $ modify $ \ s -> s { shaderGeometry = Just gDeclBlock }
    where
        gDeclBlock = do
            tellGlobalLn $ "layout(" ++ inputPrimitive ++ ") in"
            tellGlobalLn $ "layout(" ++ outputPrimitive ++ ", max_vertices = " ++ show maxVertices ++ ") out"

useUniform :: GlobDeclM () -> Int -> Int -> ExprM String
useUniform decls blockI offset = do
    T.lift $ modify $ \ s -> s { shaderUsedUniformBlocks = Map.insert blockI gDeclUniformBlock $ shaderUsedUniformBlocks s }
    return $ 'u':show blockI ++ '.':'u': show offset -- "u8.u4"
    where
        gDeclUniformBlock = do
            let blockStr = show blockI
            tellGlobal "layout(std140) uniform uBlock"
            tellGlobal blockStr
            tellGlobal " {\n"
            decls
            tellGlobal "} u"
            tellGlobalLn blockStr

useSampler :: String -> String -> Int -> ExprM String
useSampler prefix str name = do
    T.lift $ modify $ \ s -> s { shaderUsedSamplers = Map.insert name gDeclSampler $ shaderUsedSamplers s }
    return $ 's':show name
    where
        gDeclSampler = do
            tellGlobal "uniform "
            tellGlobal prefix
            tellGlobal "sampler"
            tellGlobal str
            tellGlobal " s"
            tellGlobalLn $ show name

getNext :: Monad m => StateT Int m Int
getNext = do
    s <- get
    put $ s + 1
    return s

type RValue = String

tellAssignment :: SType -> ExprM RValue -> ExprM String
tellAssignment typ m = fmap head . memoizeM $ do
    val <- m
    var <- T.lift $ T.lift $ T.lift getNext
    let name = 't' : show var
    T.lift $ T.lift $ tell (stypeName typ ++ " ")
    tellAssignment' name val
    return [name]

tellAssignment' :: String -> RValue -> ExprM ()
tellAssignment' name string = T.lift $ T.lift $ tell $ mconcat [name, " = ", string, ";\n"]

discard :: FBool -> ExprM ()
discard (S m) = do
    b <- m
    when (b /= "true") $ T.lift $ T.lift $ tell $ mconcat ["if (!(", b, ")) discard;\n"]

--
tellGlobalLn :: String -> GlobDeclM ()
tellGlobalLn string = tell $ string `mappend` ";\n"
--
tellGlobal :: String -> GlobDeclM ()
tellGlobal = tell

-----------------------

-- | An opaque type
data ShaderBase a x where
    ShaderBaseFloat :: S x Float -> ShaderBase (S x Float) x
    ShaderBaseInt :: S x Int -> ShaderBase (S x Int) x
    ShaderBaseWord :: S x Word -> ShaderBase (S x Word) x
    ShaderBaseBool :: S x Bool -> ShaderBase (S x Bool) x
    ShaderBaseUnit :: ShaderBase () x
    ShaderBaseProd :: ShaderBase a x -> ShaderBase b x -> ShaderBase (a,b) x
    ShaderBaseGenerativeGeometry :: S x (GenerativeGeometry p a) -> ShaderBase (S x (GenerativeGeometry p a)) x

shaderbaseDeclare :: ShaderBase a x -> WriterT [String] ExprM (ShaderBase a x)
shaderbaseAssign :: ShaderBase a x -> StateT [String] ExprM ()
shaderbaseReturn :: ShaderBase a x -> ReaderT (ExprM [String]) (State Int) (ShaderBase a x)

shaderbaseDeclare (ShaderBaseFloat _) = ShaderBaseFloat <$> shaderbaseDeclareDef STypeFloat
shaderbaseDeclare (ShaderBaseInt _) = ShaderBaseInt <$> shaderbaseDeclareDef STypeInt
shaderbaseDeclare (ShaderBaseWord _) = ShaderBaseWord <$> shaderbaseDeclareDef STypeUInt
shaderbaseDeclare (ShaderBaseBool _) = ShaderBaseBool <$> shaderbaseDeclareDef STypeBool
shaderbaseDeclare ShaderBaseUnit = return ShaderBaseUnit
shaderbaseDeclare (ShaderBaseProd a b) = do
    a' <- shaderbaseDeclare a
    b' <- shaderbaseDeclare b
    return $ ShaderBaseProd a' b'
shaderbaseDeclare (ShaderBaseGenerativeGeometry _) = ShaderBaseGenerativeGeometry <$> shaderbaseDeclareDef STypeGenerativeGeometry

shaderbaseAssign (ShaderBaseFloat a) = shaderbaseAssignDef a
shaderbaseAssign (ShaderBaseInt a) = shaderbaseAssignDef a
shaderbaseAssign (ShaderBaseWord a) = shaderbaseAssignDef a
shaderbaseAssign (ShaderBaseBool a) = shaderbaseAssignDef a
shaderbaseAssign ShaderBaseUnit = return ()
shaderbaseAssign (ShaderBaseProd a b) = do
    shaderbaseAssign a
    shaderbaseAssign b
shaderbaseAssign (ShaderBaseGenerativeGeometry a) = shaderbaseAssignDef a

shaderbaseReturn (ShaderBaseFloat _) = ShaderBaseFloat <$> shaderbaseReturnDef
shaderbaseReturn (ShaderBaseInt _) = ShaderBaseInt <$> shaderbaseReturnDef
shaderbaseReturn (ShaderBaseWord _) = ShaderBaseWord <$> shaderbaseReturnDef
shaderbaseReturn (ShaderBaseBool _) = ShaderBaseBool <$> shaderbaseReturnDef
shaderbaseReturn ShaderBaseUnit = return ShaderBaseUnit
shaderbaseReturn (ShaderBaseProd a b) = do
    a' <- shaderbaseReturn a
    b' <- shaderbaseReturn b
    return $ ShaderBaseProd a' b'
shaderbaseReturn (ShaderBaseGenerativeGeometry _) = ShaderBaseGenerativeGeometry <$> shaderbaseReturnDef

shaderbaseDeclareDef :: SType -> WriterT [String] ExprM (S x a)
shaderbaseDeclareDef styp = do
    var <- T.lift $ T.lift $ T.lift $ T.lift getNext
    let root = 't' : show var
    T.lift $ T.lift $ T.lift $ tell $ mconcat [stypeName styp, ' ':root, ";\n"]
    tell [root]
    return $ S $ return root

shaderbaseAssignDef :: (S x a) -> StateT [String] ExprM ()
shaderbaseAssignDef (S shaderM) = do
    ul <- T.lift shaderM
    xs <- get
    put $ tail xs
    T.lift $ tellAssignment' (head xs) ul
    return ()

shaderbaseReturnDef :: ReaderT (ExprM [String]) (State Int) (S x a)
shaderbaseReturnDef = do
    i <- T.lift getNext
    m <- ask
    return $ S $ fmap (!!i) m

-- | Constraint for types that may pass in and out of shader control structures. Define your own instances in terms of others and make sure to
--   make toBase as lazy as possible.
class ShaderType a x where
    -- | A base type that this type can convert into. Use the 'ShaderBaseType' function on an existing instance of 'ShaderType' to define this in your instance.
    type ShaderBaseType a
    -- | Convert this type to the shader base type. Make sure this is as lazy as possible (e.g. use tilde (@~@) on each pattern match).
    toBase :: x -> a -> ShaderBase (ShaderBaseType a) x
    -- | Convert back from the shader base type to this type.
    fromBase :: x -> ShaderBase (ShaderBaseType a) x -> a

instance ShaderType (S x Float) x where
    type ShaderBaseType (S x Float) = (S x Float)
    toBase _ = ShaderBaseFloat
    fromBase _ (ShaderBaseFloat a) = a

instance ShaderType (S x Int) x where
    type ShaderBaseType (S x Int) = (S x Int)
    toBase _ = ShaderBaseInt
    fromBase _ (ShaderBaseInt a) = a

instance ShaderType (S x Word) x where
    type ShaderBaseType (S x Word) = (S x Word)
    toBase _ = ShaderBaseWord
    fromBase _ (ShaderBaseWord a) = a

instance ShaderType (S x Bool) x where
    type ShaderBaseType (S x Bool) = (S x Bool)
    toBase _ = ShaderBaseBool
    fromBase _ (ShaderBaseBool a) = a

instance ShaderType () x where
    type ShaderBaseType () = ()
    toBase _ _ = ShaderBaseUnit
    fromBase _ ShaderBaseUnit = ()

instance ShaderType (S x (GenerativeGeometry p a)) x where
    type ShaderBaseType (S x (GenerativeGeometry p a)) = (S x (GenerativeGeometry p a))
    toBase _ = ShaderBaseGenerativeGeometry
    fromBase _ (ShaderBaseGenerativeGeometry a) = a

instance ShaderType a x => ShaderType (V0 a) x where
    type ShaderBaseType (V0 a) = ()
    toBase _ V0 = ShaderBaseUnit
    fromBase _ ShaderBaseUnit = V0
instance ShaderType a x => ShaderType (V1 a) x where
    type ShaderBaseType (V1 a) = ShaderBaseType a
    toBase x ~(V1 a) = toBase x a
    fromBase x a = V1 (fromBase x a)
instance ShaderType a x => ShaderType (V2 a) x where
    type ShaderBaseType (V2 a) = (ShaderBaseType a, ShaderBaseType a)
    toBase x ~(V2 a b) = ShaderBaseProd (toBase x a) (toBase x b)
    fromBase x (ShaderBaseProd a b) = V2 (fromBase x a) (fromBase x b)
instance ShaderType a x => ShaderType (V3 a) x where
    type ShaderBaseType (V3 a) = (ShaderBaseType a, (ShaderBaseType a, ShaderBaseType a))
    toBase x ~(V3 a b c) = ShaderBaseProd (toBase x a) (ShaderBaseProd (toBase x b) (toBase x c))
    fromBase x (ShaderBaseProd a (ShaderBaseProd b c)) = V3 (fromBase x a) (fromBase x b) (fromBase x c)
instance ShaderType a x => ShaderType (V4 a) x where
    type ShaderBaseType (V4 a) = (ShaderBaseType a, (ShaderBaseType a, (ShaderBaseType a, ShaderBaseType a)))
    toBase x ~(V4 a b c d) = ShaderBaseProd (toBase x a) (ShaderBaseProd (toBase x b) (ShaderBaseProd (toBase x c) (toBase x d)))
    fromBase x (ShaderBaseProd a (ShaderBaseProd b (ShaderBaseProd c d))) = V4 (fromBase x a) (fromBase x b) (fromBase x c) (fromBase x d)

instance (ShaderType a x, ShaderType b x) => ShaderType (a,b) x where
    type ShaderBaseType (a,b) = (ShaderBaseType a, ShaderBaseType b)
    toBase x ~(a,b) = ShaderBaseProd (toBase x a) (toBase x b)
    fromBase x (ShaderBaseProd a b) = (fromBase x a, fromBase x b)
instance (ShaderType a x, ShaderType b x, ShaderType c x) => ShaderType (a,b,c) x where
    type ShaderBaseType (a,b,c) = (ShaderBaseType a, (ShaderBaseType b, ShaderBaseType c))
    toBase x ~(a,b,c) = ShaderBaseProd (toBase x a) (ShaderBaseProd (toBase x b) (toBase x c))
    fromBase x (ShaderBaseProd a (ShaderBaseProd b c)) = (fromBase x a, fromBase x b, fromBase x c)
instance (ShaderType a x, ShaderType b x, ShaderType c x, ShaderType d x) => ShaderType (a,b,c,d) x where
    type ShaderBaseType (a,b,c,d) = (ShaderBaseType a, (ShaderBaseType b, (ShaderBaseType c, ShaderBaseType d)))
    toBase x ~(a,b,c,d) = ShaderBaseProd (toBase x a) (ShaderBaseProd (toBase x b) (ShaderBaseProd (toBase x c) (toBase x d)))
    fromBase x (ShaderBaseProd a (ShaderBaseProd b (ShaderBaseProd c d))) = (fromBase x a, fromBase x b, fromBase x c, fromBase x d)
instance (ShaderType a x, ShaderType b x, ShaderType c x, ShaderType d x, ShaderType e x) => ShaderType (a,b,c,d,e) x where
    type ShaderBaseType (a,b,c,d,e) = (ShaderBaseType a, (ShaderBaseType b, (ShaderBaseType c, (ShaderBaseType d, ShaderBaseType e))))
    toBase x ~(a,b,c,d,e) = ShaderBaseProd (toBase x a) (ShaderBaseProd (toBase x b) (ShaderBaseProd (toBase x c) (ShaderBaseProd (toBase x d) (toBase x e))))
    fromBase x (ShaderBaseProd a (ShaderBaseProd b (ShaderBaseProd c (ShaderBaseProd d e)))) = (fromBase x a, fromBase x b, fromBase x c, fromBase x d, fromBase x e)
instance (ShaderType a x, ShaderType b x, ShaderType c x, ShaderType d x, ShaderType e x, ShaderType f x) => ShaderType (a,b,c,d,e,f) x where
    type ShaderBaseType (a,b,c,d,e,f) = (ShaderBaseType a, (ShaderBaseType b, (ShaderBaseType c, (ShaderBaseType d, (ShaderBaseType e, ShaderBaseType f)))))
    toBase x ~(a,b,c,d,e,f) = ShaderBaseProd (toBase x a) (ShaderBaseProd (toBase x b) (ShaderBaseProd (toBase x c) (ShaderBaseProd (toBase x d) (ShaderBaseProd (toBase x e) (toBase x f)))))
    fromBase x (ShaderBaseProd a (ShaderBaseProd b (ShaderBaseProd c (ShaderBaseProd d (ShaderBaseProd e f))))) = (fromBase x a, fromBase x b, fromBase x c, fromBase x d, fromBase x e, fromBase x f)
instance (ShaderType a x, ShaderType b x, ShaderType c x, ShaderType d x, ShaderType e x, ShaderType f x, ShaderType g x) => ShaderType (a,b,c,d,e,f,g) x where
    type ShaderBaseType (a,b,c,d,e,f,g) = (ShaderBaseType a, (ShaderBaseType b, (ShaderBaseType c, (ShaderBaseType d, (ShaderBaseType e, (ShaderBaseType f, ShaderBaseType g))))))
    toBase x ~(a,b,c,d,e,f,g) = ShaderBaseProd (toBase x a) (ShaderBaseProd (toBase x b) (ShaderBaseProd (toBase x c) (ShaderBaseProd (toBase x d) (ShaderBaseProd (toBase x e) (ShaderBaseProd (toBase x f) (toBase x g))))))
    fromBase x (ShaderBaseProd a (ShaderBaseProd b (ShaderBaseProd c (ShaderBaseProd d (ShaderBaseProd e (ShaderBaseProd f g)))))) = (fromBase x a, fromBase x b, fromBase x c, fromBase x d, fromBase x e, fromBase x f, fromBase x g)

-- | Works just like 'ifB', return second argument if first is 'true' otherwise return third argument.
--
-- The difference from 'ifB' is that it in most cases generate more efficient code when @a@ is a compound type (e.g. a tuple or a vector).
-- For simple types such as @S x Float@, @ifThenElse' == ifB@.
ifThenElse' :: forall a x. (ShaderType a x) => S x Bool -> a -> a -> a
ifThenElse' b t e = ifThenElse b (const t) (const e) ()

-- | @ifThenElse c f g x@ will return @f x@ if @c@ evaluates to 'true' or @g x@ otherwise.
--
--   In most cases functionally equivalent to 'ifThenElse'' but
--   usually generate smaller shader code since the last argument is not inlined into the two branches, which also would affect implicit derivates (e.g. 'dFdx', 'dFdy' or sampling using @SampleAuto@)
ifThenElse :: forall a b x. (ShaderType a x, ShaderType b x) => S x Bool -> (a -> b) -> (a -> b) -> a -> b
ifThenElse c t e i = fromBase x $ ifThenElse_ c (toBase x . t . fromBase x) (toBase x . e . fromBase x) (toBase x i)
    where
        x = undefined :: x
        ifThenElse_
            :: S x Bool
            -> (ShaderBase (ShaderBaseType a) x -> ShaderBase (ShaderBaseType b) x)
            -> (ShaderBase (ShaderBaseType a) x -> ShaderBase (ShaderBaseType b) x)
            -> ShaderBase (ShaderBaseType a) x -> ShaderBase (ShaderBaseType b) x
        ifThenElse_ bool thn els a =
            let ifM :: ExprM [String]
                ifM = memoizeM $ do
                    boolStr <- unS bool
                    (lifted, aDecls) <- runWriterT $ shaderbaseDeclare (toBase x (errShaderType :: a))
                    void $ evalStateT (shaderbaseAssign a) aDecls
                    decls <- execWriterT $ shaderbaseDeclare (toBase x (errShaderType :: b))
                    tellIf boolStr
                    scopedM $ void $ evalStateT (shaderbaseAssign $ thn lifted) decls
                    T.lift $ T.lift $ tell "} else {\n"
                    scopedM $ void $ evalStateT (shaderbaseAssign $ els lifted) decls
                    T.lift $ T.lift $ tell "}\n"
                    return decls
            in  evalState (runReaderT (shaderbaseReturn (toBase x (errShaderType :: b))) ifM) 0

-- | @ifThen c f x@ will return @f x@ if @c@ evaluates to 'true' or @x@ otherwise.
--
--   In most cases functionally equivalent to 'ifThenElse'' but
--   usually generate smaller shader code since the last argument is not inlined into the two branches, which also would affect implicit derivates (e.g. 'dFdx', 'dFdy' or sampling using @SampleAuto@)
ifThen :: forall a x. (ShaderType a x) => S x Bool -> (a -> a) -> a -> a
ifThen c t i = fromBase x $ ifThen_ c (toBase x . t . fromBase x) (toBase x i)
    where
        x = undefined :: x
        ifThen_ :: S x Bool -> (ShaderBase (ShaderBaseType a) x -> ShaderBase (ShaderBaseType a) x) -> ShaderBase (ShaderBaseType a) x -> ShaderBase (ShaderBaseType a) x
        ifThen_ bool thn a =
            let ifM = memoizeM $ do
                    boolStr <- unS bool
                    (lifted, decls) <- runWriterT $ shaderbaseDeclare (toBase x (errShaderType :: a))
                    void $ evalStateT (shaderbaseAssign a) decls
                    tellIf boolStr
                    scopedM $ void $ evalStateT (shaderbaseAssign $ thn lifted) decls
                    T.lift $ T.lift $ tell "}\n"
                    return decls
            in  evalState (runReaderT (shaderbaseReturn (toBase x (errShaderType :: a))) ifM) 0

tellIf :: RValue -> ExprM ()
tellIf boolStr = T.lift $ T.lift $ tell $ mconcat ["if(", boolStr, "){\n" ]

-- | @while f g x@ will iteratively transform @x@ with @g@ as long as @f@ generates 'true'.
while :: forall a x. (ShaderType a x) => (a -> S x Bool) -> (a -> a) -> a -> a
while c f i = fromBase x $ while_ (c . fromBase x) (toBase x . f . fromBase x) (toBase x i)
    where
        x = undefined :: x
        while_ :: (ShaderBase (ShaderBaseType a) x -> S x Bool) -> (ShaderBase (ShaderBaseType a) x -> ShaderBase (ShaderBaseType a) x) -> ShaderBase (ShaderBaseType a) x -> ShaderBase (ShaderBaseType a) x
        while_ bool loopF a =
            let whileM = memoizeM $ do
                    (lifted, decls) <- runWriterT $ shaderbaseDeclare (toBase x (errShaderType :: a))
                    void $ evalStateT (shaderbaseAssign a) decls
                    boolDecl <- tellAssignment STypeBool (unS $ bool a)
                    T.lift $ T.lift $ tell $ mconcat ["while(", boolDecl, "){\n" ]
                    let looped = loopF lifted
                    scopedM $ do
                        void $ evalStateT (shaderbaseAssign looped) decls
                        loopedBoolStr <- unS $ bool looped
                        tellAssignment' boolDecl loopedBoolStr
                    T.lift $ T.lift $ tell "}\n"
                    return decls
            in  evalState (runReaderT (shaderbaseReturn (toBase x (errShaderType :: a))) whileM) 0

errShaderType = error "toBase in an instance of ShaderType is not lazy enough! Make sure you use tilde (~) for each pattern match on a data constructor."

--------------------------------------------------------------------------------------------------------------------------------


bin :: SType -> String -> S c x -> S c y -> S c z
bin typ o (S a) (S b) = S $ tellAssignment typ $ do a' <- a
                                                    b' <- b
                                                    return $ '(' : a' ++ o ++ b' ++ ")"

fun1 :: SType -> String -> S c x -> S c y
fun1 typ f (S a) = S $ tellAssignment typ $ do a' <- a
                                               return $ f ++ '(' : a' ++ ")"

fun2 :: SType -> String -> S c x -> S c y -> S c z
fun2 typ f (S a) (S b) = S $ tellAssignment typ $ do a' <- a
                                                     b' <- b
                                                     return $ f ++ '(' : a' ++ ',' : b' ++ ")"

fun3 :: SType -> String -> S c x -> S c y -> S c z -> S c w
fun3 typ f (S a) (S b) (S c) = S $ tellAssignment typ $ do a' <- a
                                                           b' <- b
                                                           c' <- c
                                                           return $ f ++ '(' : a' ++ ',' : b' ++ ',' : c' ++")"

fun4 :: SType -> String -> S c x -> S c y -> S c z -> S c w -> S c r
fun4 typ f (S a) (S b) (S c) (S d) = S $ tellAssignment typ $ do a' <- a
                                                                 b' <- b
                                                                 c' <- c
                                                                 d' <- d
                                                                 return $ f ++ '(' : a' ++ ',' : b' ++ ',' : c' ++ ',' : d' ++")"

postop :: SType -> String -> S c x -> S c y
postop typ f (S a) = S $ tellAssignment typ $ do a' <- a
                                                 return $ '(' : a' ++ f ++ ")"

preop :: SType -> String -> S c x -> S c y
preop typ f (S a) = S $ tellAssignment typ $ do a' <- a
                                                return $ '(' : f ++ a' ++ ")"

binf :: String -> S c x -> S c y -> S c Float
binf = bin STypeFloat
fun1f :: String -> S c x -> S c Float
fun1f = fun1 STypeFloat
fun2f :: String -> S c x -> S c y -> S c Float
fun2f = fun2 STypeFloat
fun3f :: String -> S c x -> S c y -> S c z -> S c Float
fun3f = fun3 STypeFloat
preopf :: String -> S c x -> S c Float
preopf = preop STypeFloat
postopf :: String -> S c x -> S c Float
postopf = postop STypeFloat

bini :: String -> S c x -> S c y -> S c Int
bini = bin STypeInt
fun1i :: String -> S c x -> S c Int
fun1i = fun1 STypeInt
preopi :: String -> S c x -> S c Int
preopi = preop STypeInt

binu :: String -> S c x -> S c y -> S c Word
binu = bin STypeUInt
fun1u :: String -> S c x -> S c Word
fun1u = fun1 STypeUInt
preopu :: String -> S c x -> S c Word
preopu = preop STypeUInt

instance Num (S a Float) where
    (+) = binf "+"
    (-) = binf "-"
    abs = fun1f "abs"
    signum = fun1f "sign"
    (*) = binf "*"
    fromInteger = S . return . show
    negate = preopf "-"

instance Num (S a Int) where
    (+) = bini "+"
    (-) = bini "-"
    abs = fun1i "abs"
    signum = fun1i "sign"
    (*) = bini "*"
    fromInteger = S . return . show
    negate = preopi "-"

instance Num (S a Word) where
    (+) = binu "+"
    (-) = binu "-"
    abs = fun1u "abs"
    signum = fun1u "sign"
    (*) = binu "*"
    fromInteger x = S $ return $ show x ++ "u"
    negate = preopu "-"

instance Fractional (S a Float) where
  (/)          = binf "/"
  fromRational = S . return . ("float(" ++) . (++ ")") . show . (`asTypeOf` (undefined :: Float)) . fromRational

class Integral' a where
    div' :: a -> a -> a
    mod' :: a -> a -> a

instance Integral' Int where
    div' = div
    mod' = mod
instance Integral' Int32 where
    div' = div
    mod' = mod
instance Integral' Int16 where
    div' = div
    mod' = mod
instance Integral' Int8 where
    div' = div
    mod' = mod
instance Integral' Word where
    div' = div
    mod' = mod
instance Integral' Word32 where
    div' = div
    mod' = mod
instance Integral' Word16 where
    div' = div
    mod' = mod
instance Integral' Word8 where
    div' = div
    mod' = mod
instance Integral' (S a Int) where
    div' = bini "/"
    mod' = bini "%"
instance Integral' (S a Word) where
    div' = binu "/"
    mod' = binu "%"
instance Integral' a => Integral' (V0 a) where
    div' = liftA2 div'
    mod' = liftA2 mod'
instance Integral' a => Integral' (V1 a) where
    div' = liftA2 div'
    mod' = liftA2 mod'
instance Integral' a => Integral' (V2 a) where
    div' = liftA2 div'
    mod' = liftA2 mod'
instance Integral' a => Integral' (V3 a) where
    div' = liftA2 div'
    mod' = liftA2 mod'
instance Integral' a => Integral' (V4 a) where
    div' = liftA2 div'
    mod' = liftA2 mod'

class Bits' a where
    and' :: a -> a -> a
    or' :: a -> a -> a
    xor' :: a -> a -> a
    complement' :: a -> a
    shiftL' :: a -> a -> a
    shiftR' :: a -> a -> a
    bitSize' :: a -> Int

instance Bits' (S a Int) where
    and' = bini "&"
    or' = bini "|"
    xor' = bini "^"
    complement' = fun1i "~"
    shiftL' = bini "<<"
    shiftR' = bini ">>"
    bitSize' = pure (finiteBitSize (undefined :: Int))
instance Bits' (S a Word) where
    and' = binu "&"
    or' = binu "|"
    xor' = binu "^"
    complement' = fun1u "~"
    shiftL' = binu "<<"
    shiftR' = binu ">>"
    bitSize' = pure (finiteBitSize (undefined :: Word))

instance Floating (S a Float) where
  pi    = S $ return $ show (pi :: Float)
  sqrt  = fun1f "sqrt"
  exp   = fun1f "exp"
  log   = fun1f "log"
  (**)  = fun2f "pow"
  sin   = fun1f "sin"
  cos   = fun1f "cos"
  tan   = fun1f "tan"
  asin  = fun1f "asin"
  acos  = fun1f "acos"
  atan  = fun1f "atan"
  sinh  = fun1f "sinh"
  cosh  = fun1f "cosh"
  asinh = fun1f "asinh"
  atanh = fun1f "atanh"
  acosh = fun1f "acosh"

instance Boolean (S a Bool) where
  true = S $ return "true"
  false = S $ return "false"
  notB  = preop STypeBool "!"
  (&&*) = bin STypeBool "&&"
  (||*) = bin STypeBool "||"

type instance BooleanOf (S a x) = S a Bool

instance Eq x => EqB (S a x) where
  (==*) = bin STypeBool "=="
  (/=*) = bin STypeBool "!="

instance Ord x => OrdB (S a x) where
  (<*) = bin STypeBool "<"
  (<=*) = bin STypeBool "<="
  (>=*) = bin STypeBool ">="
  (>*) = bin STypeBool ">"

instance IfB (S a Float) where ifB = ifThenElse'
instance IfB (S a Int) where ifB = ifThenElse'
instance IfB (S a Word) where ifB = ifThenElse'
instance IfB (S a Bool) where ifB = ifThenElse'
instance IfB (S a (GenerativeGeometry p b)) where ifB = ifThenElse'

instance Conjugate (S a Float)
instance Conjugate (S a Int)
instance Conjugate (S a Word)
instance TrivialConjugate  (S a Float)
instance TrivialConjugate  (S a Int)
instance TrivialConjugate  (S a Word)

-- | This class provides the GPU functions either not found in Prelude's numerical classes, or that has wrong types.
--   Instances are also provided for normal 'Float's and 'Double's.
class Floating a => Real' a where
  rsqrt :: a -> a
  exp2 :: a -> a
  log2 :: a -> a
  floor' :: a -> a
  ceiling' :: a -> a
  fract' :: a -> a
  mod'' :: a -> a -> a
  mix :: a -> a -> a-> a
  atan2' :: a -> a -> a

  rsqrt = (1/) . sqrt
  exp2 = (2**)
  log2 = logBase 2
  mix x y a = x*(1-a)+y*a
  fract' x = x - floor' x
  mod'' x y = x - y* floor' (x/y)
  floor' x = -ceiling' (-x)
  ceiling' x = -floor' (-x)

  {-# MINIMAL (floor' | ceiling') , atan2' #-}

instance Real' Float where
  floor' = fromIntegral . floor
  ceiling' = fromIntegral . ceiling
  atan2' = atan2

instance Real' Double where
  floor' = fromIntegral . floor
  ceiling' = fromIntegral . ceiling
  atan2' = atan2

instance Real' (S x Float) where
  rsqrt = fun1f "inversesqrt"
  exp2 = fun1f "exp2"
  log2 = fun1f "log2"
  floor' = fun1f "floor"
  ceiling' = fun1f "ceil"
  fract' = fun1f "fract"
  mod'' = fun2f "mod"
  mix = fun3f "mix"
  atan2' = fun2f "atan"

instance (Real' a) => Real' (V0 a) where
  rsqrt = liftA rsqrt
  exp2 = liftA exp2
  log2 = liftA log2
  floor' = liftA floor'
  ceiling' = liftA ceiling'
  fract' = liftA fract'
  mod'' = liftA2 mod''
  mix = liftA3 mix
  atan2' = liftA2 atan2'
instance (Real' a) => Real' (V1 a) where
  rsqrt = liftA rsqrt
  exp2 = liftA exp2
  log2 = liftA log2
  floor' = liftA floor'
  ceiling' = liftA ceiling'
  fract' = liftA fract'
  mod'' = liftA2 mod''
  mix = liftA3 mix
  atan2' = liftA2 atan2'
instance (Real' a) => Real' (V2 a) where
  rsqrt = liftA rsqrt
  exp2 = liftA exp2
  log2 = liftA log2
  floor' = liftA floor'
  ceiling' = liftA ceiling'
  fract' = liftA fract'
  mod'' = liftA2 mod''
  mix = liftA3 mix
  atan2' = liftA2 atan2'
instance (Real' a) => Real' (V3 a) where
  rsqrt = liftA rsqrt
  exp2 = liftA exp2
  log2 = liftA log2
  floor' = liftA floor'
  ceiling' = liftA ceiling'
  fract' = liftA fract'
  mod'' = liftA2 mod''
  mix = liftA3 mix
  atan2' = liftA2 atan2'
instance (Real' a) => Real' (V4 a) where
  rsqrt = liftA rsqrt
  exp2 = liftA exp2
  log2 = liftA log2
  floor' = liftA floor'
  ceiling' = liftA ceiling'
  fract' = liftA fract'
  mod'' = liftA2 mod''
  mix = liftA3 mix
  atan2' = liftA2 atan2'

-- | This class provides various order comparing functions
class (IfB a, OrdB a, Floating a) => FloatingOrd a where
  clamp :: a -> a -> a -> a
  saturate :: a -> a
  step :: a -> a -> a
  smoothstep :: a -> a -> a -> a
  clamp x a = minB (maxB x a)
  saturate x = clamp x 0 1
  step a x = ifB (x <* a) 0 1
  smoothstep a b x = let t = saturate ((x-a) / (b-a)) in t*t*(3-2*t)

instance FloatingOrd Float
instance FloatingOrd Double
instance FloatingOrd (S x Float) where
  clamp = fun3f "clamp"
  step = fun2f "step"
  smoothstep = fun3f "smoothstep"

-- | Provides a common way to convert numeric types to integer and floating point representations.
class Convert a where
    type ConvertFloat a
    type ConvertInt a
    type ConvertWord a
    -- | Convert to a floating point number.
    toFloat :: a -> ConvertFloat a
    -- | Convert to an integral number, using truncation if necessary.
    toInt :: a -> ConvertInt a
    -- | Convert to an unsigned integral number, using truncation if necessary.
    toWord :: a -> ConvertWord a

instance Convert Float where
    type ConvertFloat Float = Float
    type ConvertInt Float = Int
    type ConvertWord Float = Word
    toFloat = id
    toInt = truncate
    toWord = truncate
instance Convert Int where
    type ConvertFloat Int = Float
    type ConvertInt Int = Int
    type ConvertWord Int = Word
    toFloat = fromIntegral
    toInt = id
    toWord = fromIntegral
instance Convert Word where
    type ConvertFloat Word = Float
    type ConvertInt Word = Int
    type ConvertWord Word = Word
    toFloat = fromIntegral
    toInt = fromIntegral
    toWord = id
instance Convert (S x Float) where
    type ConvertFloat (S x Float) = S x Float
    type ConvertInt (S x Float) = S x Int
    type ConvertWord (S x Float) = S x Word
    toFloat = id
    toInt = fun1i "int"
    toWord = fun1u "uint"
instance Convert (S x Int) where
    type ConvertFloat (S x Int) = S x Float
    type ConvertInt (S x Int) = S x Int
    type ConvertWord (S x Int) = S x Word
    toFloat = fun1f "float"
    toInt = id
    toWord = fun1u "uint"
instance Convert (S x Word) where
    type ConvertFloat (S x Word) = S x Float
    type ConvertInt (S x Word) = S x Int
    type ConvertWord (S x Word) = S x Word
    toFloat = fun1f "float"
    toInt = fun1i "int"
    toWord = id

-- | The derivative in x using local differencing of the rasterized value.
dFdx :: FFloat -> FFloat
-- | The derivative in y using local differencing of the rasterized value.
dFdy :: FFloat -> FFloat
-- | The sum of the absolute derivative in x and y using local differencing of the rasterized value.
fwidth :: FFloat -> FFloat
dFdx = fun1f "dFdx"
dFdy = fun1f "dFdy"
fwidth = fun1f "fwidth"

---------------------------------
fromV f s v = S $ do params <- mapM (unS . f) $ toList v
                     return $ s ++ '(' : intercalate "," params ++ ")"

fromVec4 :: V4 (S x Float) -> S x (V4 Float)
fromVec4 = fromV id "vec4"
fromVec3 :: V3 (S x Float) -> S x (V3 Float)
fromVec3 = fromV id "vec3"
fromVec2 :: V2 (S x Float) -> S x (V2 Float)
fromVec2 = fromV id "vec2"

-- FromMat will transpose to keep inner vectors packed
fromMat22 :: V2 (V2 (S x Float)) -> S x (V2 (V2 Float))
fromMat22 = fromV fromVec2 "mat2x2"
fromMat23 :: V2 (V3 (S x Float)) -> S x (V2 (V3 Float))
fromMat23 = fromV fromVec3 "mat2x3"
fromMat24 :: V2 (V4 (S x Float)) -> S x (V2 (V4 Float))
fromMat24 = fromV fromVec4 "mat2x4"

fromMat32 :: V3 (V2 (S x Float)) -> S x (V3 (V2 Float))
fromMat32 = fromV fromVec2 "mat3x2"
fromMat33 :: V3 (V3 (S x Float)) -> S x (V3 (V3 Float))
fromMat33 = fromV fromVec3 "mat3x3"
fromMat34 :: V3 (V4 (S x Float)) -> S x (V3 (V4 Float))
fromMat34 = fromV fromVec4 "mat3x4"

fromMat42 :: V4 (V2 (S x Float)) -> S x (V4 (V2 Float))
fromMat42 = fromV fromVec2 "mat4x2"
fromMat43 :: V4 (V3 (S x Float)) -> S x (V4 (V3 Float))
fromMat43 = fromV fromVec3 "mat4x3"
fromMat44 :: V4 (V4 (S x Float)) -> S x (V4 (V4 Float))
fromMat44 = fromV fromVec4 "mat4x4"

mulToV4 a b = vec4S'' $ bin (STypeVec 4) "*" a b
mulToV3 a b = vec3S'' $ bin (STypeVec 3) "*" a b
mulToV2 a b = vec2S'' $ bin (STypeVec 2) "*" a b

mulToM (r,x) (c,y) a b = fmap y $ x $ bin (STypeMat c r) "*" a b

d2 = (2,vec2S'')
d3 = (3,vec3S'')
d4 = (4,vec4S'')

unV1 :: V1 t -> t
unV1 (V1 x) = x

outerToM (r,x) (c,y) a b = fmap y $ x $ fun2 (STypeMat c r) "outerProduct" a b

------------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------------------
-------------------------------------------------- Rewrite rules for linear types --------------------------------------------------
------------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------------------

{-# RULES "norm/length4" norm = length4 #-}
{-# RULES "norm/length3" norm = length3 #-}
{-# RULES "norm/length2" norm = length2 #-}
length4 :: V4 (S x Float) -> S x Float
length4 = fun1f "length" . fromVec4
length3 :: V3 (S x Float) -> S x Float
length3 = fun1f "length" . fromVec3
length2 :: V2 (S x Float) -> S x Float
length2 = fun1f "length" . fromVec2

{-# RULES "signorm/normalize4" signorm = normalize4 #-}
{-# RULES "signorm/normalize3" signorm = normalize3 #-}
{-# RULES "signorm/normalize2" signorm = normalize2 #-}
normalize4 :: V4 (S x Float) -> V4 (S x Float)
normalize4 = vec4S'' . fun1 (STypeVec 4) "normalize" . fromVec4
normalize3 :: V3 (S x Float) -> V3 (S x Float)
normalize3 = vec3S'' . fun1 (STypeVec 3) "normalize" . fromVec3
normalize2 :: V2 (S x Float) -> V2 (S x Float)
normalize2 = vec2S'' . fun1 (STypeVec 2) "normalize" . fromVec2

{-# RULES "distanceA/dist4" distanceA = dist4 #-}
{-# RULES "distanceA/dist3" distanceA = dist3 #-}
{-# RULES "distanceA/dist2" distanceA = dist2 #-}
{-# RULES "distance/dist4" distance = dist4 #-}
{-# RULES "distance/dist3" distance = dist3 #-}
{-# RULES "distance/dist2" distance = dist2 #-}
dist4 :: V4 (S x Float) -> V4 (S x Float) -> S x Float
dist4 a b = fun2f "distance" (fromVec4 a) (fromVec4 b)
dist3 :: V3 (S x Float) -> V3 (S x Float) -> S x Float
dist3 a b = fun2f "distance" (fromVec3 a) (fromVec3 b)
dist2 :: V2 (S x Float) -> V2 (S x Float) -> S x Float
dist2 a b = fun2f "distance" (fromVec2 a) (fromVec2 b)


{-# RULES "cross/S" cross = crossS #-}
crossS :: V3 (S x Float) -> V3 (S x Float) -> V3 (S x Float)
crossS a b = vec3S'' $ fun2 (STypeVec 3) "cross" (fromVec3 a) (fromVec3 b)

{-# RULES "minB/S" minB = minS #-}
{-# RULES "maxB/S" maxB = maxS #-}
minS :: S x Float -> S x Float -> S x Float
minS = fun2f "min"
maxS :: S x Float -> S x Float -> S x Float
maxS = fun2f "max"

--------------------------------------------------------------

-- Matrix*Matrix, Vector*Matrix, Matrix*Vextor and outer Vector*Vector multiplications have operands in flipped order since glsl is column major
-- inner products are not flipped since why bother :)

-- Also, special verions when explicit V1 matrices are used (so eg 4 version of each dot function: v*v, v*m, m*v, m*m )

-- No rules for scalar products with vectors or matrices (eg scalar * matrix), we hope the glsl compiler will manage to optimize that...

{-# RULES "mul_12_21vv" dot = mul_12_21vv #-}
{-# RULES "mul_13_31vv" dot = mul_13_31vv #-}
{-# RULES "mul_14_41vv" dot = mul_14_41vv #-}
mul_12_21vv :: V2 (S x Float) -> V2 (S x Float) -> S x Float
mul_12_21vv a b = fun2f "dot" (fromVec2 a) (fromVec2 b)
mul_13_31vv :: V3 (S x Float) -> V3 (S x Float) -> S x Float
mul_13_31vv a b = fun2f "dot" (fromVec3 a) (fromVec3 b)
mul_14_41vv :: V4 (S x Float) -> V4 (S x Float) -> S x Float
mul_14_41vv a b = fun2f "dot" (fromVec4 a) (fromVec4 b)

{-# RULES "mul_12_21vm" (*!) = mul_12_21vm #-}
{-# RULES "mul_13_31vm" (*!) = mul_13_31vm #-}
{-# RULES "mul_14_41vm" (*!) = mul_14_41vm #-}
mul_12_21vm :: V2 (S x Float) -> V2 (V1 (S x Float)) -> V1 (S x Float)
mul_12_21vm a b = V1 $ fun2f "dot" (fromVec2 a) (fromVec2 $ fmap unV1 b)
mul_13_31vm :: V3 (S x Float) -> V3 (V1 (S x Float)) -> V1 (S x Float)
mul_13_31vm a b = V1 $ fun2f "dot" (fromVec3 a) (fromVec3 $ fmap unV1 b)
mul_14_41vm :: V4 (S x Float) -> V4 (V1 (S x Float)) -> V1 (S x Float)
mul_14_41vm a b = V1 $ fun2f "dot" (fromVec4 a) (fromVec4 $ fmap unV1 b)

{-# RULES "mul_12_21mv" (!*) = mul_12_21mv #-}
{-# RULES "mul_13_31mv" (!*) = mul_13_31mv #-}
{-# RULES "mul_14_41mv" (!*) = mul_14_41mv #-}
mul_12_21mv :: V1 (V2 (S x Float)) -> V2 (S x Float) -> V1 (S x Float)
mul_12_21mv a b = V1 $ fun2f "dot" (fromVec2 $ unV1 a) (fromVec2 b)
mul_13_31mv :: V1 (V3 (S x Float)) -> V3 (S x Float) -> V1 (S x Float)
mul_13_31mv a b = V1 $ fun2f "dot" (fromVec3 $ unV1 a) (fromVec3 b)
mul_14_41mv :: V1 (V4 (S x Float)) -> V4 (S x Float) -> V1 (S x Float)
mul_14_41mv a b = V1 $ fun2f "dot" (fromVec4 $ unV1 a) (fromVec4 b)

{-# RULES "mul_12_21mm" (!*!) = mul_12_21mm #-}
{-# RULES "mul_13_31mm" (!*!) = mul_13_31mm #-}
{-# RULES "mul_14_41mm" (!*!) = mul_14_41mm #-}
mul_12_21mm :: V1 (V2 (S x Float)) -> V2 (V1 (S x Float)) -> V1 (V1 (S x Float))
mul_12_21mm a b = V1 $ V1 $ fun2f "dot" (fromVec2 $ unV1 a) (fromVec2 $ fmap unV1 b)
mul_13_31mm :: V1 (V3 (S x Float)) -> V3 (V1 (S x Float)) -> V1 (V1 (S x Float))
mul_13_31mm a b = V1 $ V1 $ fun2f "dot" (fromVec3 $ unV1 a) (fromVec3 $ fmap unV1 b)
mul_14_41mm :: V1 (V4 (S x Float)) -> V4 (V1 (S x Float)) -> V1 (V1 (S x Float))
mul_14_41mm a b = V1 $ V1 $ fun2f "dot" (fromVec4 $ unV1 a) (fromVec4 $ fmap unV1 b)


{-# RULES "mul_21_12" outer = mul_21_12 #-}
{-# RULES "mul_21_13" outer = mul_21_13 #-}
{-# RULES "mul_21_14" outer = mul_21_14 #-}
{-# RULES "mul_31_12" outer = mul_31_12 #-}
{-# RULES "mul_31_13" outer = mul_31_13 #-}
{-# RULES "mul_31_14" outer = mul_31_14 #-}
{-# RULES "mul_41_12" outer = mul_41_12 #-}
{-# RULES "mul_41_13" outer = mul_41_13 #-}
{-# RULES "mul_41_14" outer = mul_41_14 #-}
mul_21_12 :: V2 (S x Float) -> V2 (S x Float) -> V2 (V2 (S x Float))
mul_21_12 a b = outerToM d2 d2 (fromVec2 b) (fromVec2 a)
mul_21_13 :: V2 (S x Float) -> V3 (S x Float) -> V2 (V3 (S x Float))
mul_21_13 a b = outerToM d2 d3 (fromVec3 b) (fromVec2 a)
mul_21_14 :: V2 (S x Float) -> V4 (S x Float) -> V2 (V4 (S x Float))
mul_21_14 a b = outerToM d2 d4 (fromVec4 b) (fromVec2 a)
mul_31_12 :: V3 (S x Float) -> V2 (S x Float) -> V3 (V2 (S x Float))
mul_31_12 a b = outerToM d3 d2 (fromVec2 b) (fromVec3 a)
mul_31_13 :: V3 (S x Float) -> V3 (S x Float) -> V3 (V3 (S x Float))
mul_31_13 a b = outerToM d3 d3 (fromVec3 b) (fromVec3 a)
mul_31_14 :: V3 (S x Float) -> V4 (S x Float) -> V3 (V4 (S x Float))
mul_31_14 a b = outerToM d3 d4 (fromVec4 b) (fromVec3 a)
mul_41_12 :: V4 (S x Float) -> V2 (S x Float) -> V4 (V2 (S x Float))
mul_41_12 a b = outerToM d4 d2 (fromVec2 b) (fromVec4 a)
mul_41_13 :: V4 (S x Float) -> V3 (S x Float) -> V4 (V3 (S x Float))
mul_41_13 a b = outerToM d4 d3 (fromVec3 b) (fromVec4 a)
mul_41_14 :: V4 (S x Float) -> V4 (S x Float) -> V4 (V4 (S x Float))
mul_41_14 a b = outerToM d4 d4 (fromVec4 b) (fromVec4 a)
{-# RULES "mul_21_12m" (!*!) = mul_21_12m #-}
{-# RULES "mul_21_13m" (!*!) = mul_21_13m #-}
{-# RULES "mul_21_14m" (!*!) = mul_21_14m #-}
{-# RULES "mul_31_12m" (!*!) = mul_31_12m #-}
{-# RULES "mul_31_13m" (!*!) = mul_31_13m #-}
{-# RULES "mul_31_14m" (!*!) = mul_31_14m #-}
{-# RULES "mul_41_12m" (!*!) = mul_41_12m #-}
{-# RULES "mul_41_13m" (!*!) = mul_41_13m #-}
{-# RULES "mul_41_14m" (!*!) = mul_41_14m #-}
mul_21_12m :: V2 (V1 (S x Float)) -> V1 (V2 (S x Float)) -> V2 (V2 (S x Float))
mul_21_12m a b = outerToM d2 d2 (fromVec2 $ unV1 b) (fromVec2 $ fmap unV1 a)
mul_21_13m :: V2 (V1 (S x Float)) -> V1 (V3 (S x Float)) -> V2 (V3 (S x Float))
mul_21_13m a b = outerToM d2 d3 (fromVec3 $ unV1 b) (fromVec2 $ fmap unV1 a)
mul_21_14m :: V2 (V1 (S x Float)) -> V1 (V4 (S x Float)) -> V2 (V4 (S x Float))
mul_21_14m a b = outerToM d2 d4 (fromVec4 $ unV1 b) (fromVec2 $ fmap unV1 a)
mul_31_12m :: V3 (V1 (S x Float)) -> V1 (V2 (S x Float)) -> V3 (V2 (S x Float))
mul_31_12m a b = outerToM d3 d2 (fromVec2 $ unV1 b) (fromVec3 $ fmap unV1 a)
mul_31_13m :: V3 (V1 (S x Float)) -> V1 (V3 (S x Float)) -> V3 (V3 (S x Float))
mul_31_13m a b = outerToM d3 d3 (fromVec3 $ unV1 b) (fromVec3 $ fmap unV1 a)
mul_31_14m :: V3 (V1 (S x Float)) -> V1 (V4 (S x Float)) -> V3 (V4 (S x Float))
mul_31_14m a b = outerToM d3 d4 (fromVec4 $ unV1 b) (fromVec3 $ fmap unV1 a)
mul_41_12m :: V4 (V1 (S x Float)) -> V1 (V2 (S x Float)) -> V4 (V2 (S x Float))
mul_41_12m a b = outerToM d4 d2 (fromVec2 $ unV1 b) (fromVec4 $ fmap unV1 a)
mul_41_13m :: V4 (V1 (S x Float)) -> V1 (V3 (S x Float)) -> V4 (V3 (S x Float))
mul_41_13m a b = outerToM d4 d3 (fromVec3 $ unV1 b) (fromVec4 $ fmap unV1 a)
mul_41_14m :: V4 (V1 (S x Float)) -> V1 (V4 (S x Float)) -> V4 (V4 (S x Float))
mul_41_14m a b = outerToM d4 d4 (fromVec4 $ unV1 b) (fromVec4 $ fmap unV1 a)


{-# RULES "mul_12_22" (*!) = mul_12_22 #-}
{-# RULES "mul_13_32" (*!) = mul_13_32 #-}
{-# RULES "mul_14_42" (*!) = mul_14_42 #-}
{-# RULES "mul_12_23" (*!) = mul_12_23 #-}
{-# RULES "mul_13_33" (*!) = mul_13_33 #-}
{-# RULES "mul_14_43" (*!) = mul_14_43 #-}
{-# RULES "mul_12_24" (*!) = mul_12_24 #-}
{-# RULES "mul_13_34" (*!) = mul_13_34 #-}
{-# RULES "mul_14_44" (*!) = mul_14_44 #-}
mul_12_22 :: V2 (S x Float) -> V2 (V2 (S x Float)) -> V2 (S x Float)
mul_12_22 v m = mulToV2 (fromMat22 m) (fromVec2 v)
mul_13_32 :: V3 (S x Float) -> V3 (V2 (S x Float)) -> V2 (S x Float)
mul_13_32 v m = mulToV2 (fromMat32 m) (fromVec3 v)
mul_14_42 :: V4 (S x Float) -> V4 (V2 (S x Float)) -> V2 (S x Float)
mul_14_42 v m = mulToV2 (fromMat42 m) (fromVec4 v)
mul_12_23 :: V2 (S x Float) -> V2 (V3 (S x Float)) -> V3 (S x Float)
mul_12_23 v m = mulToV3 (fromMat23 m) (fromVec2 v)
mul_13_33 :: V3 (S x Float) -> V3 (V3 (S x Float)) -> V3 (S x Float)
mul_13_33 v m = mulToV3 (fromMat33 m) (fromVec3 v)
mul_14_43 :: V4 (S x Float) -> V4 (V3 (S x Float)) -> V3 (S x Float)
mul_14_43 v m = mulToV3 (fromMat43 m) (fromVec4 v)
mul_12_24 :: V2 (S x Float) -> V2 (V4 (S x Float)) -> V4 (S x Float)
mul_12_24 v m = mulToV4 (fromMat24 m) (fromVec2 v)
mul_13_34 :: V3 (S x Float) -> V3 (V4 (S x Float)) -> V4 (S x Float)
mul_13_34 v m = mulToV4 (fromMat34 m) (fromVec3 v)
mul_14_44 :: V4 (S x Float) -> V4 (V4 (S x Float)) -> V4 (S x Float)
mul_14_44 v m = mulToV4 (fromMat44 m) (fromVec4 v)

{-# RULES "mul_12_22m" (!*!) = mul_12_22m #-}
{-# RULES "mul_13_32m" (!*!) = mul_13_32m #-}
{-# RULES "mul_14_42m" (!*!) = mul_14_42m #-}
{-# RULES "mul_12_23m" (!*!) = mul_12_23m #-}
{-# RULES "mul_13_33m" (!*!) = mul_13_33m #-}
{-# RULES "mul_14_43m" (!*!) = mul_14_43m #-}
{-# RULES "mul_12_24m" (!*!) = mul_12_24m #-}
{-# RULES "mul_13_34m" (!*!) = mul_13_34m #-}
{-# RULES "mul_14_44m" (!*!) = mul_14_44m #-}
mul_12_22m :: V1 (V2 (S x Float)) -> V2 (V2 (S x Float)) -> V1 (V2 (S x Float))
mul_12_22m v m = V1 $ mulToV2 (fromMat22 m) (fromVec2 $ unV1 v)
mul_13_32m :: V1 (V3 (S x Float)) -> V3 (V2 (S x Float)) -> V1 (V2 (S x Float))
mul_13_32m v m = V1 $ mulToV2 (fromMat32 m) (fromVec3 $ unV1 v)
mul_14_42m :: V1 (V4 (S x Float)) -> V4 (V2 (S x Float)) -> V1 (V2 (S x Float))
mul_14_42m v m = V1 $ mulToV2 (fromMat42 m) (fromVec4 $ unV1 v)
mul_12_23m :: V1 (V2 (S x Float)) -> V2 (V3 (S x Float)) -> V1 (V3 (S x Float))
mul_12_23m v m = V1 $ mulToV3 (fromMat23 m) (fromVec2 $ unV1 v)
mul_13_33m :: V1 (V3 (S x Float)) -> V3 (V3 (S x Float)) -> V1 (V3 (S x Float))
mul_13_33m v m = V1 $ mulToV3 (fromMat33 m) (fromVec3 $ unV1 v)
mul_14_43m :: V1 (V4 (S x Float)) -> V4 (V3 (S x Float)) -> V1 (V3 (S x Float))
mul_14_43m v m = V1 $ mulToV3 (fromMat43 m) (fromVec4 $ unV1 v)
mul_12_24m :: V1 (V2 (S x Float)) -> V2 (V4 (S x Float)) -> V1 (V4 (S x Float))
mul_12_24m v m = V1 $ mulToV4 (fromMat24 m) (fromVec2 $ unV1 v)
mul_13_34m :: V1 (V3 (S x Float)) -> V3 (V4 (S x Float)) -> V1 (V4 (S x Float))
mul_13_34m v m = V1 $ mulToV4 (fromMat34 m) (fromVec3 $ unV1 v)
mul_14_44m :: V1 (V4 (S x Float)) -> V4 (V4 (S x Float)) -> V1 (V4 (S x Float))
mul_14_44m v m = V1 $ mulToV4 (fromMat44 m) (fromVec4 $ unV1 v)

{-# RULES "mul_22_21" (!*) = mul_22_21 #-}
{-# RULES "mul_23_31" (!*) = mul_23_31 #-}
{-# RULES "mul_24_41" (!*) = mul_24_41 #-}
{-# RULES "mul_32_21" (!*) = mul_32_21 #-}
{-# RULES "mul_33_31" (!*) = mul_33_31 #-}
{-# RULES "mul_34_41" (!*) = mul_34_41 #-}
{-# RULES "mul_42_21" (!*) = mul_42_21 #-}
{-# RULES "mul_43_31" (!*) = mul_43_31 #-}
{-# RULES "mul_44_41" (!*) = mul_44_41 #-}
mul_22_21 :: V2 (V2 (S x Float)) -> V2 (S x Float) -> V2 (S x Float)
mul_22_21 m v = mulToV2 (fromVec2 v) (fromMat22 m)
mul_23_31 :: V2 (V3 (S x Float)) -> V3 (S x Float) -> V2 (S x Float)
mul_23_31 m v = mulToV2 (fromVec3 v) (fromMat23 m)
mul_24_41 :: V2 (V4 (S x Float)) -> V4 (S x Float) -> V2 (S x Float)
mul_24_41 m v = mulToV2 (fromVec4 v) (fromMat24 m)
mul_32_21 :: V3 (V2 (S x Float)) -> V2 (S x Float) -> V3 (S x Float)
mul_32_21 m v = mulToV3 (fromVec2 v) (fromMat32 m)
mul_33_31 :: V3 (V3 (S x Float)) -> V3 (S x Float) -> V3 (S x Float)
mul_33_31 m v = mulToV3 (fromVec3 v) (fromMat33 m)
mul_34_41 :: V3 (V4 (S x Float)) -> V4 (S x Float) -> V3 (S x Float)
mul_34_41 m v = mulToV3 (fromVec4 v) (fromMat34 m)
mul_42_21 :: V4 (V2 (S x Float)) -> V2 (S x Float) -> V4 (S x Float)
mul_42_21 m v = mulToV4 (fromVec2 v) (fromMat42 m)
mul_43_31 :: V4 (V3 (S x Float)) -> V3 (S x Float) -> V4 (S x Float)
mul_43_31 m v = mulToV4 (fromVec3 v) (fromMat43 m)
mul_44_41 :: V4 (V4 (S x Float)) -> V4 (S x Float) -> V4 (S x Float)
mul_44_41 m v = mulToV4 (fromVec4 v) (fromMat44 m)

{-# RULES "mul_22_21m" (!*!) = mul_22_21m #-}
{-# RULES "mul_23_31m" (!*!) = mul_23_31m #-}
{-# RULES "mul_24_41m" (!*!) = mul_24_41m #-}
{-# RULES "mul_32_21m" (!*!) = mul_32_21m #-}
{-# RULES "mul_33_31m" (!*!) = mul_33_31m #-}
{-# RULES "mul_34_41m" (!*!) = mul_34_41m #-}
{-# RULES "mul_42_21m" (!*!) = mul_42_21m #-}
{-# RULES "mul_43_31m" (!*!) = mul_43_31m #-}
{-# RULES "mul_44_41m" (!*!) = mul_44_41m #-}
mul_22_21m :: V2 (V2 (S x Float)) -> V2 (V1 (S x Float)) -> V2 (V1 (S x Float))
mul_22_21m m v = V1 <$> mulToV2 (fromVec2 $ fmap unV1 v) (fromMat22 m)
mul_23_31m :: V2 (V3 (S x Float)) -> V3 (V1 (S x Float)) -> V2 (V1 (S x Float))
mul_23_31m m v = V1 <$> mulToV2 (fromVec3 $ fmap unV1 v) (fromMat23 m)
mul_24_41m :: V2 (V4 (S x Float)) -> V4 (V1 (S x Float)) -> V2 (V1 (S x Float))
mul_24_41m m v = V1 <$> mulToV2 (fromVec4 $ fmap unV1 v) (fromMat24 m)
mul_32_21m :: V3 (V2 (S x Float)) -> V2 (V1 (S x Float)) -> V3 (V1 (S x Float))
mul_32_21m m v = V1 <$> mulToV3 (fromVec2 $ fmap unV1 v) (fromMat32 m)
mul_33_31m :: V3 (V3 (S x Float)) -> V3 (V1 (S x Float)) -> V3 (V1 (S x Float))
mul_33_31m m v = V1 <$> mulToV3 (fromVec3 $ fmap unV1 v) (fromMat33 m)
mul_34_41m :: V3 (V4 (S x Float)) -> V4 (V1 (S x Float)) -> V3 (V1 (S x Float))
mul_34_41m m v = V1 <$> mulToV3 (fromVec4 $ fmap unV1 v) (fromMat34 m)
mul_42_21m :: V4 (V2 (S x Float)) -> V2 (V1 (S x Float)) -> V4 (V1 (S x Float))
mul_42_21m m v = V1 <$> mulToV4 (fromVec2 $ fmap unV1 v) (fromMat42 m)
mul_43_31m :: V4 (V3 (S x Float)) -> V3 (V1 (S x Float)) -> V4 (V1 (S x Float))
mul_43_31m m v = V1 <$> mulToV4 (fromVec3 $ fmap unV1 v) (fromMat43 m)
mul_44_41m :: V4 (V4 (S x Float)) -> V4 (V1 (S x Float)) -> V4 (V1 (S x Float))
mul_44_41m m v = V1 <$> mulToV4 (fromVec4 $ fmap unV1 v) (fromMat44 m)
-----------------------

{-# RULES "mul_22_22" (!*!) = mul_22_22 #-}
{-# RULES "mul_23_32" (!*!) = mul_23_32 #-}
{-# RULES "mul_24_42" (!*!) = mul_24_42 #-}
{-# RULES "mul_22_23" (!*!) = mul_22_23 #-}
{-# RULES "mul_23_33" (!*!) = mul_23_33 #-}
{-# RULES "mul_24_43" (!*!) = mul_24_43 #-}
{-# RULES "mul_22_24" (!*!) = mul_22_24 #-}
{-# RULES "mul_23_34" (!*!) = mul_23_34 #-}
{-# RULES "mul_24_44" (!*!) = mul_24_44 #-}
mul_22_22 :: V2 (V2 (S x Float)) -> V2 (V2 (S x Float)) -> V2 (V2 (S x Float))
mul_22_22 a b = mulToM d2 d2 (fromMat22 b) (fromMat22 a)
mul_23_32 :: V2 (V3 (S x Float)) -> V3 (V2 (S x Float)) -> V2 (V2 (S x Float))
mul_23_32 a b = mulToM d2 d2 (fromMat32 b) (fromMat23 a)
mul_24_42 :: V2 (V4 (S x Float)) -> V4 (V2 (S x Float)) -> V2 (V2 (S x Float))
mul_24_42 a b = mulToM d2 d2 (fromMat42 b) (fromMat24 a)
mul_22_23 :: V2 (V2 (S x Float)) -> V2 (V3 (S x Float)) -> V2 (V3 (S x Float))
mul_22_23 a b = mulToM d2 d3 (fromMat23 b) (fromMat22 a)
mul_23_33 :: V2 (V3 (S x Float)) -> V3 (V3 (S x Float)) -> V2 (V3 (S x Float))
mul_23_33 a b = mulToM d2 d3 (fromMat33 b) (fromMat23 a)
mul_24_43 :: V2 (V4 (S x Float)) -> V4 (V3 (S x Float)) -> V2 (V3 (S x Float))
mul_24_43 a b = mulToM d2 d3 (fromMat43 b) (fromMat24 a)
mul_22_24 :: V2 (V2 (S x Float)) -> V2 (V4 (S x Float)) -> V2 (V4 (S x Float))
mul_22_24 a b = mulToM d2 d4 (fromMat24 b) (fromMat22 a)
mul_23_34 :: V2 (V3 (S x Float)) -> V3 (V4 (S x Float)) -> V2 (V4 (S x Float))
mul_23_34 a b = mulToM d2 d4 (fromMat34 b) (fromMat23 a)
mul_24_44 :: V2 (V4 (S x Float)) -> V4 (V4 (S x Float)) -> V2 (V4 (S x Float))
mul_24_44 a b = mulToM d2 d4 (fromMat44 b) (fromMat24 a)


{-# RULES "mul_32_22" (!*!) = mul_32_22 #-}
{-# RULES "mul_33_32" (!*!) = mul_33_32 #-}
{-# RULES "mul_34_42" (!*!) = mul_34_42 #-}
{-# RULES "mul_32_23" (!*!) = mul_32_23 #-}
{-# RULES "mul_33_33" (!*!) = mul_33_33 #-}
{-# RULES "mul_34_43" (!*!) = mul_34_43 #-}
{-# RULES "mul_32_24" (!*!) = mul_32_24 #-}
{-# RULES "mul_33_34" (!*!) = mul_33_34 #-}
{-# RULES "mul_34_44" (!*!) = mul_34_44 #-}
mul_32_22 :: V3 (V2 (S x Float)) -> V2 (V2 (S x Float)) -> V3 (V2 (S x Float))
mul_32_22 a b = mulToM d3 d2 (fromMat22 b) (fromMat32 a)
mul_33_32 :: V3 (V3 (S x Float)) -> V3 (V2 (S x Float)) -> V3 (V2 (S x Float))
mul_33_32 a b = mulToM d3 d2 (fromMat32 b) (fromMat33 a)
mul_34_42 :: V3 (V4 (S x Float)) -> V4 (V2 (S x Float)) -> V3 (V2 (S x Float))
mul_34_42 a b = mulToM d3 d2 (fromMat42 b) (fromMat34 a)
mul_32_23 :: V3 (V2 (S x Float)) -> V2 (V3 (S x Float)) -> V3 (V3 (S x Float))
mul_32_23 a b = mulToM d3 d3 (fromMat23 b) (fromMat32 a)
mul_33_33 :: V3 (V3 (S x Float)) -> V3 (V3 (S x Float)) -> V3 (V3 (S x Float))
mul_33_33 a b = mulToM d3 d3 (fromMat33 b) (fromMat33 a)
mul_34_43 :: V3 (V4 (S x Float)) -> V4 (V3 (S x Float)) -> V3 (V3 (S x Float))
mul_34_43 a b = mulToM d3 d3 (fromMat43 b) (fromMat34 a)
mul_32_24 :: V3 (V2 (S x Float)) -> V2 (V4 (S x Float)) -> V3 (V4 (S x Float))
mul_32_24 a b = mulToM d3 d4 (fromMat24 b) (fromMat32 a)
mul_33_34 :: V3 (V3 (S x Float)) -> V3 (V4 (S x Float)) -> V3 (V4 (S x Float))
mul_33_34 a b = mulToM d3 d4 (fromMat34 b) (fromMat33 a)
mul_34_44 :: V3 (V4 (S x Float)) -> V4 (V4 (S x Float)) -> V3 (V4 (S x Float))
mul_34_44 a b = mulToM d3 d4 (fromMat44 b) (fromMat34 a)


{-# RULES "mul_42_22" (!*!) = mul_42_22 #-}
{-# RULES "mul_43_32" (!*!) = mul_43_32 #-}
{-# RULES "mul_44_42" (!*!) = mul_44_42 #-}
{-# RULES "mul_42_23" (!*!) = mul_42_23 #-}
{-# RULES "mul_43_33" (!*!) = mul_43_33 #-}
{-# RULES "mul_44_43" (!*!) = mul_44_43 #-}
{-# RULES "mul_42_24" (!*!) = mul_42_24 #-}
{-# RULES "mul_43_34" (!*!) = mul_43_34 #-}
{-# RULES "mul_44_44" (!*!) = mul_44_44 #-}
mul_42_22 :: V4 (V2 (S x Float)) -> V2 (V2 (S x Float)) -> V4 (V2 (S x Float))
mul_42_22 a b = mulToM d4 d2 (fromMat22 b) (fromMat42 a)
mul_43_32 :: V4 (V3 (S x Float)) -> V3 (V2 (S x Float)) -> V4 (V2 (S x Float))
mul_43_32 a b = mulToM d4 d2 (fromMat32 b) (fromMat43 a)
mul_44_42 :: V4 (V4 (S x Float)) -> V4 (V2 (S x Float)) -> V4 (V2 (S x Float))
mul_44_42 a b = mulToM d4 d2 (fromMat42 b) (fromMat44 a)
mul_42_23 :: V4 (V2 (S x Float)) -> V2 (V3 (S x Float)) -> V4 (V3 (S x Float))
mul_42_23 a b = mulToM d4 d3 (fromMat23 b) (fromMat42 a)
mul_43_33 :: V4 (V3 (S x Float)) -> V3 (V3 (S x Float)) -> V4 (V3 (S x Float))
mul_43_33 a b = mulToM d4 d3 (fromMat33 b) (fromMat43 a)
mul_44_43 :: V4 (V4 (S x Float)) -> V4 (V3 (S x Float)) -> V4 (V3 (S x Float))
mul_44_43 a b = mulToM d4 d3 (fromMat43 b) (fromMat44 a)
mul_42_24 :: V4 (V2 (S x Float)) -> V2 (V4 (S x Float)) -> V4 (V4 (S x Float))
mul_42_24 a b = mulToM d4 d4 (fromMat24 b) (fromMat42 a)
mul_43_34 :: V4 (V3 (S x Float)) -> V3 (V4 (S x Float)) -> V4 (V4 (S x Float))
mul_43_34 a b = mulToM d4 d4 (fromMat34 b) (fromMat43 a)
mul_44_44 :: V4 (V4 (S x Float)) -> V4 (V4 (S x Float)) -> V4 (V4 (S x Float))
mul_44_44 a b = mulToM d4 d4 (fromMat44 b) (fromMat44 a)