{- Copyright (c) 2008, Scott E. Dillard. All rights reserved. -} {-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE NoMonomorphismRestriction #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE TypeSynonymInstances #-} {-# LANGUAGE UndecidableInstances #-} -- | Packed vectors : use these whenever possible. The polymorphic vector type -- is represented at run-time by a linked list of boxed values. Specialized, or -- /packed/ types, store the vector components sequentially in memory, in a -- single boxed value. Definitions for vector operations, given in terms of -- polymorphic vectors, can be (almost) automatically propagated to packed -- types using the functions 'pack' and 'unpack'. The compiler can then -- specialize the definition to the packed type and produce efficient code. -- -- Packed vectors are related to their unpacked representations by way of an -- associated type. An instance of class @'PackedVec' v@ declares that @v@ has -- a packed representation, and the type of that is @'Packed' v@. The packed -- constructors are named @Vec@/NT/ where /N/ is 2, 3 or 4 and /T/ is @I@, @F@ -- or @D@ for @Int@, @Float@ or @Double@. So the expression @Vec3D x y z@ -- constructs a packed 3-vector of Doubles, the type of which is @Packed (Vec3 -- Double)@. The constructor name is also a synonym for the packed type name, -- i.e., @type Vec3D = Packed (Vec3 Double)@, so the packed type acts as if it -- had been declared @data Vec3D = Vec3D x y z@. -- -- 'Storable', 'Num', 'Fractional', 'Fold', 'Map', and 'ZipWith' instances are -- provided for packed vectors, so some operations do not require pack/unpack. -- For example, @'dot'@ does not require pack/unpack because it is defined in -- terms of @'zipWith'@ and @'fold'@. However @'transpose'@, @'det'@, -- @'gaussElim'@ and most others are recursive (i.e., defined in terms of the -- same operation on lower-dimensional vectors), and so you'll still need to -- use pack/unpack with these. This goes for @'multmm'@ as well because it uses -- @'transpose'@. Some functions, like @'multmv'@, do not need their arguments -- to be unpacked, but the result is a polymorphic vector @(:.)@, so you will -- need to pack it again. I admit that this is awkward, and I'm still looking -- for a better way. -- -- There are also instances for 'Access', 'Take', 'Drop', 'Last', 'Head', -- 'Tail' and 'Snoc'. These come in handy for things like quaternions and -- homogenous coordinates. module Data.Vec.Packed where import Prelude hiding (map,foldl,foldr,zipWith,length,head,tail,last, reverse,take,drop) import Data.Vec.Base as V import Data.Vec.Nat import Data.Vec.LinAlg --just for haddock import Data.Word import Data.Int import Foreign import Test.QuickCheck -- | PackedVec class : relates a vector type to its space-optimized -- representation. class PackedVec v where -- | The packed representation of 'v' data Packed v pack :: v -> Packed v unpack :: Packed v -> v --who knows if this even does anything {-# RULES "Vec pack/unpack" forall x. pack (unpack x) = x; "Vec unpack/pack" forall x. unpack (pack x) = x; #-} instance PackedVec (Vec2 Int) where data Packed (Vec2 Int) = Vec2I {-#UNPACK#-} !Int {-#UNPACK#-} !Int pack (a:.b:.()) = Vec2I a b unpack (Vec2I a b) = a:.b:.() {-# INLINE pack #-} {-# INLINE unpack #-} instance PackedVec (Vec3 Int) where data Packed (Vec3 Int) = Vec3I {-#UNPACK#-} !Int {-#UNPACK#-} !Int {-#UNPACK#-} !Int pack (a:.b:.c:.()) = Vec3I a b c; unpack (Vec3I a b c) = a:.b:.c:.(); {-# INLINE pack #-} {-# INLINE unpack #-} instance PackedVec (Vec4 Int) where data Packed (Vec4 Int) = Vec4I {-#UNPACK#-} !Int {-#UNPACK#-} !Int {-#UNPACK#-} !Int {-#UNPACK#-} !Int pack (a:.b:.c:.d:.()) = Vec4I a b c d unpack (Vec4I a b c d) = a:.b:.c:.d:.() {-# INLINE pack #-} {-# INLINE unpack #-} type Vec2I = Packed (Vec2 Int) type Vec3I = Packed (Vec3 Int) type Vec4I = Packed (Vec4 Int) instance PackedVec (Vec2 Float) where data Packed (Vec2 Float) = Vec2F {-#UNPACK#-} !Float {-#UNPACK#-} !Float pack (a:.b:.()) = Vec2F a b unpack (Vec2F a b) = a:.b:.() {-# INLINE pack #-} {-# INLINE unpack #-} instance PackedVec (Vec3 Float) where data Packed (Vec3 Float) = Vec3F {-#UNPACK#-} !Float {-#UNPACK#-} !Float {-#UNPACK#-} !Float pack (a:.b:.c:.()) = Vec3F a b c; unpack (Vec3F a b c) = a:.b:.c:.(); {-# INLINE pack #-} {-# INLINE unpack #-} instance PackedVec (Vec4 Float) where data Packed (Vec4 Float) = Vec4F {-#UNPACK#-} !Float {-#UNPACK#-} !Float {-#UNPACK#-} !Float {-#UNPACK#-} !Float pack (a:.b:.c:.d:.()) = Vec4F a b c d unpack (Vec4F a b c d) = a:.b:.c:.d:.() {-# INLINE pack #-} {-# INLINE unpack #-} type Vec2F = Packed (Vec2 Float) type Vec3F = Packed (Vec3 Float) type Vec4F = Packed (Vec4 Float) instance PackedVec (Vec2 Double) where data Packed (Vec2 Double) = Vec2D {-#UNPACK#-} !Double {-#UNPACK#-} !Double pack (a:.b:.()) = Vec2D a b unpack (Vec2D a b) = a:.b:.() {-# INLINE pack #-} {-# INLINE unpack #-} instance PackedVec (Vec3 Double) where data Packed (Vec3 Double) = Vec3D {-#UNPACK#-} !Double {-#UNPACK#-} !Double {-#UNPACK#-} !Double pack (a:.b:.c:.()) = Vec3D a b c; unpack (Vec3D a b c) = a:.b:.c:.(); {-# INLINE pack #-} {-# INLINE unpack #-} instance PackedVec (Vec4 Double) where data Packed (Vec4 Double) = Vec4D {-#UNPACK#-} !Double {-#UNPACK#-} !Double {-#UNPACK#-} !Double {-#UNPACK#-} !Double pack (a:.b:.c:.d:.()) = Vec4D a b c d unpack (Vec4D a b c d) = a:.b:.c:.d:.() {-# INLINE pack #-} {-# INLINE unpack #-} type Vec2D = Packed (Vec2 Double) type Vec3D = Packed (Vec3 Double) type Vec4D = Packed (Vec4 Double) type Mat22D = Vec2 (Vec2D) type Mat23D = Vec2 (Vec3D) type Mat24D = Vec2 (Vec4D) type Mat33D = Vec3 (Vec3D) type Mat34D = Vec3 (Vec4D) type Mat44D = Vec4 (Vec4D) -- | Construct a semi-packed matrix, one whose rows are packed. packMat :: (Map row (Packed row) mat packedMat, PackedVec row) => mat -> packedMat packMat = map pack unpackMat :: (Map (Packed row) row packedMat mat, PackedVec row) => packedMat -> mat unpackMat = map unpack instance (Eq v, PackedVec v) => Eq (Packed v) where u == v = unpack u == unpack v u /= v = unpack u /= unpack v {-# INLINE (==) #-} {-# INLINE (/=) #-} instance (Ord v, PackedVec v) => Ord (Packed v) where compare u v = compare (unpack u) (unpack v) {-# INLINE compare #-} instance (Show v, PackedVec v) => Show (Packed v) where show v = show (unpack v) instance (Map a b u v, PackedVec u, PackedVec v) => Map a b (Packed u) (Packed v) where map f = pack . map f . unpack {-# INLINE map #-} instance (Fold v a, PackedVec v) => Fold (Packed v) a where fold f = fold f . unpack foldl f z = foldl f z . unpack foldr f z = foldr f z . unpack {-# INLINE fold #-} {-# INLINE foldl #-} {-# INLINE foldr #-} instance (ZipWith a b c u v w, PackedVec u, PackedVec v, PackedVec w) => ZipWith a b c (Packed u) (Packed v) (Packed w) where zipWith f u v = pack $ zipWith f (unpack u) (unpack v) {-# INLINE zipWith #-} instance (Num v, PackedVec v) => Num (Packed v) where (+) u v = pack (unpack u + unpack v) (-) u v = pack (unpack u - unpack v) (*) u v = pack (unpack u * unpack v) abs u = pack (abs (unpack u)) signum u = pack (signum (unpack u)) fromInteger i = pack (fromInteger i) {-# INLINE (+) #-} {-# INLINE (-) #-} {-# INLINE (*) #-} {-# INLINE abs #-} {-# INLINE signum #-} {-# INLINE fromInteger #-} instance (Fractional v, PackedVec v) => Fractional (Packed v) where (/) u v = pack (unpack u / unpack v) recip u = pack (recip (unpack u)) fromRational r = pack (fromRational r) {-# INLINE (/) #-} {-# INLINE recip #-} {-# INLINE fromRational #-} instance (Storable v, PackedVec v) => Storable (Packed v) where sizeOf _ = sizeOf (undefined::v) alignment _ = alignment (undefined::v) peek p = peek (castPtr p) >>= \v -> return (pack v) peekByteOff p o = peek (p`plusPtr`o) peekElemOff p i = peek (p`plusPtr`(i*sizeOf(undefined::v))) poke p v = poke (castPtr p) (unpack v) pokeByteOff p o x = poke (p`plusPtr`o) x pokeElemOff p i x = poke (p`plusPtr`(i*sizeOf(undefined::v))) x {-# INLINE sizeOf #-} {-# INLINE alignment #-} {-# INLINE peek #-} {-# INLINE peekByteOff #-} {-# INLINE peekElemOff #-} {-# INLINE poke #-} {-# INLINE pokeByteOff #-} {-# INLINE pokeElemOff #-} instance (Arbitrary v, PackedVec v) => Arbitrary (Packed v) where arbitrary = arbitrary >>= return . pack coarbitrary v = coarbitrary (unpack v) instance (Length v n, PackedVec v) => Length (Packed v) n where length v = length (unpack v) {-# INLINE length #-} instance (Head v h, PackedVec v) => Head (Packed v) h where head v = head (unpack v) {-# INLINE head #-} instance (Tail v t, PackedVec v, PackedVec t) => Tail (Packed v) (Packed t) where tail v = pack (tail (unpack v)) {-# INLINE tail #-} instance (Last v l, PackedVec v) => Last (Packed v) l where last v = last (unpack v) {-# INLINE last #-} instance (Snoc v a v', PackedVec v, PackedVec v') => Snoc (Packed v) a (Packed v') where snoc v a = pack (snoc (unpack v) a) {-# INLINE snoc #-} instance (Reverse' () v v', PackedVec v, PackedVec v') => Reverse' () (Packed v) (Packed v') where reverse' _ v = pack (reverse (unpack v)) {-# INLINE reverse' #-} instance (Take (Succ n) v v', PackedVec v, PackedVec v') => Take (Succ n) (Packed v) (Packed v') where take n v = pack (take n (unpack v)) {-# INLINE take #-} instance (Drop n v v', PackedVec v, PackedVec v') => Drop n (Packed v) (Packed v') where drop n v = pack (drop n (unpack v)) {-# INLINE drop #-} instance (Access n a v, PackedVec v) => Access n a (Packed v) where get n v = get n (unpack v) set n a v = pack (set n a (unpack v)) {-# INLINE get #-} {-# INLINE set #-} instance (VecList a v, PackedVec v) => VecList a (Packed v) where fromList = pack . fromList getElem i = getElem i . unpack setElem i a = pack . setElem i a . unpack {-# INLINE setElem #-} {-# INLINE getElem #-} {-# INLINE fromList #-}