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{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
module Numeric.ADDual.Array.Internal where
import Control.Monad (when)
import Control.Monad.Trans.Class (lift)
import Control.Monad.Trans.State.Strict
import Data.IORef
import Data.Proxy
import Data.Typeable
import qualified Data.Vector.Storable as VS
import qualified Data.Vector.Storable.Mutable as VSM
import Foreign.Storable
import GHC.Stack
import GHC.Exts (withDict)
import System.IO.Unsafe
import System.IO (hPutStrLn, stderr)
import Numeric.ADDual.VectorOps
-- TODO: type roles on 's'
debug :: Bool
debug = toEnum 0
-- TODO: full vjp (just some more Traversable mess)
-- TODO: if non-scalar output types are allowed, ensure that all its scalar components are WHNF evaluated before we backpropagate
{-# NOINLINE gradient' #-}
gradient' :: forall a f. (Traversable f, Num a, Storable a, Typeable a)
=> HasCallStack
=> Show a -- TODO: remove
=> (forall s. Taping s a => f (Dual s a) -> Dual s a)
-> f a -> a -> (a, f a)
gradient' f inp topctg = unsafePerformIO $ do
when debug $ hPutStrLn stderr "Preparing input"
let (inp', starti) = runState (traverse (\x -> state (\i -> (Dual x i, i + 1))) inp) 0
-- The tape starts after the input IDs.
taperef <- newIORef (Log starti Start)
when debug $ hPutStrLn stderr "Running function"
let !(Dual result outi) = withDict @(Taping () a) taperef $ f @() inp'
when debug $ hPutStrLn stderr $ "result = " ++ show result ++ "; outi = " ++ show outi
Log _ tape <- readIORef taperef
-- when debug $ do
-- tapestr <- showTape (tapeTail `Snoc` lastChunk)
-- hPutStrLn stderr $ "tape = " ++ tapestr ""
when debug $ hPutStrLn stderr "Backpropagating"
accums <- VSM.new (outi+1)
VSM.write accums outi topctg
let backpropagate i (Cscalar i1 dx i2 dy tape') = do
ctg <- VSM.read accums i
when (i1 /= -1) $ VSM.modify accums (+ ctg*dx) i1
when (i2 /= -1) $ VSM.modify accums (+ ctg*dy) i2
backpropagate (i-1) tape'
backpropagate _ Start = return ()
backpropagate outi tape
when debug $ do
accums' <- VS.freeze accums
hPutStrLn stderr $ "accums = " ++ show accums'
when debug $ hPutStrLn stderr "Reconstructing gradient"
let readDeriv = do i <- get
d <- lift $ VSM.read accums i
put (i+1)
return d
grad <- evalStateT (traverse (\_ -> readDeriv) inp) 0
return (result, grad)
-- | Contribution to a vector-typed value
data VCon a = VCon {-# UNPACK #-} !Int -- ^ the ID of the vector value
{-# UNPACK #-} !(VS.Vector a) -- ^ the cotangent
| VConNothing
deriving (Show)
data Chain a = Cscalar {-# UNPACK #-} !Int !a -- ^ ID == -1 -> no contribution
{-# UNPACK #-} !Int !a -- ^ idem
!(Chain a)
| VCfromList {-# UNPACK #-} !(VS.Vector Int) -- ^ IDs of scalars in the input list
!(Chain a)
| VCtoList {-# UNPACK #-} !Int -- ^ ID of the input vector
{-# UNPACK #-} !Int -- ^ start of the reserved output ID range
{-# UNPACK #-} !Int -- ^ number of reserved output IDs (length of the vector)
!(Chain a)
| VCsum {-# UNPACK #-} !Int -- ^ ID of the input vector
!(Chain a)
| VCreplicate {-# UNPACK #-} !Int -- ^ length of the replicated vector
{-# UNPACK #-} !Int -- ^ ID of the input scalar
!(Chain a)
| Start
deriving (Show)
data Log s a = Log !Int -- ^ next ID to generate
!(Chain a) -- ^ tape
-- | This class does not have any instances defined, on purpose. You'll get one
-- magically when you differentiate.
class Taping s a where
getTape :: IORef (Log s a)
data Dual s a = Dual !a
{-# UNPACK #-} !Int -- ^ -1 if this is a constant
instance Eq a => Eq (Dual s a) where
Dual x _ == Dual y _ = x == y
instance Ord a => Ord (Dual s a) where
compare (Dual x _) (Dual y _) = compare x y
instance (Num a, Taping s a) => Num (Dual s a) where
Dual x i1 + Dual y i2 = mkDual (x + y) i1 1 i2 1
Dual x i1 - Dual y i2 = mkDual (x - y) i1 1 i2 (-1)
Dual x i1 * Dual y i2 = mkDual (x * y) i1 y i2 x
negate (Dual x i1) = mkDual (negate x) i1 (-1) (-1) 0
abs (Dual x i1) = mkDual (abs x) i1 (x * signum x) (-1) 0
signum (Dual x _) = Dual (signum x) (-1)
fromInteger n = Dual (fromInteger n) (-1)
instance (Fractional a, Taping s a) => Fractional (Dual s a) where
Dual x i1 / Dual y i2 = mkDual (x / y) i1 (recip y) i2 (-x/(y*y))
recip (Dual x i1) = mkDual (recip x) i1 (-1/(x*x)) (-1) 0
fromRational r = Dual (fromRational r) (-1)
instance (Floating a, Taping s a) => Floating (Dual s a) where
pi = Dual pi (-1)
exp (Dual x i1) = mkDual (exp x) i1 (exp x) (-1) 0
log (Dual x i1) = mkDual (log x) i1 (recip x) (-1) 0
sqrt (Dual x i1) = mkDual (sqrt x) i1 (recip (2*sqrt x)) (-1) 0
-- d/dx (x ^ y) = d/dx (e ^ (y ln x)) = e ^ (y ln x) * d/dx (y ln x) = e ^ (y ln x) * y/x
-- d/dy (x ^ y) = d/dy (e ^ (y ln x)) = e ^ (y ln x) * d/dy (y ln x) = e ^ (y ln x) * ln x
Dual x i1 ** Dual y i2 =
let z = x ** y
in mkDual z i1 (z * y/x) i2 (z * log x)
logBase = undefined ; sin = undefined ; cos = undefined ; tan = undefined
asin = undefined ; acos = undefined ; atan = undefined ; sinh = undefined
cosh = undefined ; tanh = undefined ; asinh = undefined ; acosh = undefined
atanh = undefined
constant :: a -> Dual s a
constant x = Dual x (-1)
mkDual :: forall a s. Taping s a => a -> Int -> a -> Int -> a -> Dual s a
mkDual res i1 dx i2 dy = Dual res (writeTapeUnsafe (Proxy @s) (Cscalar i1 dx i2 dy))
data VDual s a = VDual !(VS.Vector a)
{-# UNPACK #-} !Int -- ^ -1 if this is a constant vector
instance (Storable a, Taping s a) => VectorOps (VDual s a) where
type VectorOpsScalar (VDual s a) = Dual s a
vfromListN n l =
let (xs, is) = unzip [(x, i) | Dual x i <- l]
in mkVDual (VS.fromListN n xs) (VCfromList (VS.fromListN n is))
vfromList l =
let (xs, is) = unzip [(x, i) | Dual x i <- l]
in mkVDual (VS.fromList xs) (VCfromList (VS.fromList is))
vtoList (VDual v i) = _
vreplicate n (Dual x i) = mkVDual (VS.replicate n x) (VCreplicate n i)
instance (Storable a, Num a, Taping s a) => VectorOpsNum (VDual s a) where
vsum (VDual v i) = Dual (VS.sum v) (writeTapeUnsafe @a (Proxy @s) (VCsum i))
vconstant :: VS.Vector a -> VDual s a
vconstant v = VDual v (-1)
mkVDual :: forall a s. Taping s a => VS.Vector a -> (Chain a -> Chain a) -> VDual s a
mkVDual res f = VDual res (writeTapeUnsafe (Proxy @s) f)
{-# NOINLINE writeTapeUnsafe #-}
writeTapeUnsafe :: forall a s proxy. Taping s a
=> proxy s -> (Chain a -> Chain a) -> Int
writeTapeUnsafe _ f =
unsafePerformIO $
atomicModifyIORef' (getTape @s) $ \(Log i tape) ->
(Log (i + 1) (f tape), i)
|
