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{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
module Numeric.ADDual.Array.Internal where
import Control.Monad (when)
import Control.Monad.Trans.State.Strict
import Data.Foldable (toList)
import Data.IORef
import Data.List (foldl')
import qualified Data.IntMap.Strict as IM
import Data.Proxy
import qualified Data.Vector.Storable as VS
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)
=> HasCallStack
=> Show a -- TODO: remove
=> (forall s. Taping s a => f (VDual s a) -> Dual s a)
-> f (VS.Vector a) -> a -> (a, f (VS.Vector a))
gradient' f inp topctg = unsafePerformIO $ do
when debug $ hPutStrLn stderr "Preparing input"
let (inp', starti) = runState (traverse (\x -> state (\i -> (VDual x i, i + 1))) inp) 0
inpSizes = VS.fromListN starti (map VS.length (toList inp))
-- 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"
let (outaccS, outaccV) = backpropagate (IM.singleton outi topctg) IM.empty 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
let d = IM.findWithDefault (VS.replicate (inpSizes VS.! i) 0) i outaccV
put (i+1)
return d
let grad = evalState (traverse (\_ -> readDeriv) inp) 0
return (result, grad)
backpropagate :: (Num a, Storable a)
=> IM.IntMap a -> IM.IntMap (VS.Vector a) -> Int -> Chain a -> (IM.IntMap a, IM.IntMap (VS.Vector a))
backpropagate accS accV i (Cscalar i1 dx i2 dy tape) =
case IM.lookup i accS of
Nothing -> backpropagate accS accV (i-1) tape
Just ctg ->
let accS1 | i1 /= -1 = IM.insertWith (+) i1 (ctg*dx) accS
| otherwise = accS
accS2 | i2 /= -1 = IM.insertWith (+) i2 (ctg*dy) accS1
| otherwise = accS1
in backpropagate accS2 accV (i-1) tape
backpropagate accS accV i (VCfromList is tape) =
case IM.lookup i accV of
Nothing -> backpropagate accS accV (i-1) tape
Just ctg ->
let accS1 | VS.length ctg == VS.length is =
foldl' (\accS' idx -> IM.insertWith (+) (is VS.! idx) (ctg VS.! idx) accS') accS [0 .. VS.length ctg - 1]
| otherwise = error "Numeric.ADDual.Array: wrong cotangent length to vfromList"
in backpropagate accS1 accV (i-1) tape
backpropagate accS accV i (VCtoList j len tape) =
case IM.lookupGE (i - len) accS of
Just (smallid, _) | smallid < i ->
let ctg = VS.fromListN len [IM.findWithDefault 0 (i - len + idx) accS | idx <- [0 .. len-1]]
accV1 = IM.insertWith (VS.zipWith (+)) j ctg accV
in backpropagate accS accV1 (i - 1 - len) tape
_ -> backpropagate accS accV (i - 1 - len) tape
backpropagate accS accV i (VCsum j len tape) =
case IM.lookup i accS of
Nothing -> backpropagate accS accV (i-1) tape
Just ctg ->
let accV1 = IM.alter (\case Nothing -> Just (VS.replicate len ctg)
Just d -> Just (VS.map (+ ctg) d))
j accV
in backpropagate accS accV1 (i - 1 - len) tape
backpropagate accS accV i (VCreplicate j len tape) =
case IM.lookup i accV of
Nothing -> backpropagate accS accV (i-1) tape
Just ctg ->
let accS1 = IM.insertWith (+) j (fromIntegral len * VS.sum ctg) accS
in backpropagate accS1 accV (i - 1 - len) tape
backpropagate accS accV _ Start = (accS, accV)
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 -- ^ number of reserved output IDs (length of the vector)
!(Chain a)
| VCsum {-# UNPACK #-} !Int -- ^ ID of the input vector
{-# UNPACK #-} !Int -- ^ length of the vector
!(Chain a)
| VCreplicate {-# UNPACK #-} !Int -- ^ ID of the input scalar
{-# UNPACK #-} !Int -- ^ length of the replicated vector
!(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) =
let starti = allocTapeToListUnsafe (Proxy @a) (Proxy @s) i (VS.length v)
in zipWith Dual (VS.toList v) [starti..]
vreplicate n (Dual x i) = mkVDual (VS.replicate n x) (VCreplicate i n)
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 (VS.length v)))
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)
{-# NOINLINE allocTapeToListUnsafe #-}
allocTapeToListUnsafe :: forall a s proxy. Taping s a => proxy a -> proxy s -> Int -> Int -> Int
allocTapeToListUnsafe _ _ vecid len =
unsafePerformIO $
atomicModifyIORef' (getTape @s @a) $ \(Log i tape) ->
(Log (i + len + 1) (VCtoList vecid len tape), i)
|
