1 files changed, 290 insertions, 0 deletions
diff --git a/src/AST/Sparse.hs b/src/AST/Sparse.hs
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+++ b/src/AST/Sparse.hs
@@ -0,0 +1,290 @@
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE ImpredicativeTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE RankNTypes #-}
+
+{-# OPTIONS_GHC -fmax-pmcheck-models=80 #-}
+module AST.Sparse (module AST.Sparse, module AST.Sparse.Types) where
+
+import Data.Type.Equality
+
+import AST
+import AST.Sparse.Types
+import Data (SBool(..))
+
+
+sparsePlus :: SMTy t -> Sparse t t' -> Ex env t' -> Ex env t' -> Ex env t'
+sparsePlus _ SpAbsent e1 e2 = use e1 $ use e2 $ ENil ext
+sparsePlus t sp e1 e2 | Just Refl <- isDense t sp = EPlus ext t e1 e2
+sparsePlus t (SpSparse sp) e1 e2 = sparsePlus (SMTMaybe t) (SpMaybe sp) e1 e2  -- heh
+sparsePlus (SMTPair t1 t2) (SpPair sp1 sp2) e1 e2 =
+  eunPair e1 $ \w1 e1a e1b ->
+  eunPair (weakenExpr w1 e2) $ \w2 e2a e2b ->
+    EPair ext (sparsePlus t1 sp1 (weakenExpr w2 e1a) e2a)
+              (sparsePlus t2 sp2 (weakenExpr w2 e1b) e2b)
+sparsePlus (SMTLEither t1 t2) (SpLEither sp1 sp2) e1 e2 =
+  elet e2 $
+    elcase (weakenExpr WSink e1)
+      (evar IZ)
+      (elcase (evar (IS IZ))
+        (ELInl ext (applySparse sp2 (fromSMTy t2)) (evar IZ))
+        (ELInl ext (applySparse sp2 (fromSMTy t2)) (sparsePlus t1 sp1 (evar (IS IZ)) (evar IZ)))
+        (EError ext (fromSMTy (applySparse (SpLEither sp1 sp2) (SMTLEither t1 t2))) "splus ll+lr"))
+      (elcase (evar (IS IZ))
+        (ELInr ext (applySparse sp1 (fromSMTy t1)) (evar IZ))
+        (EError ext (fromSMTy (applySparse (SpLEither sp1 sp2) (SMTLEither t1 t2))) "splus lr+ll")
+        (ELInr ext (applySparse sp1 (fromSMTy t1)) (sparsePlus t2 sp2 (evar (IS IZ)) (evar IZ))))
+sparsePlus (SMTMaybe t) (SpMaybe sp) e1 e2 =
+  elet e2 $
+    emaybe (weakenExpr WSink e1)
+      (evar IZ)
+      (emaybe (evar (IS IZ))
+        (EJust ext (evar IZ))
+        (EJust ext (sparsePlus t sp (evar (IS IZ)) (evar IZ))))
+sparsePlus (SMTArr _ t) (SpArr sp) e1 e2 = ezipWith (sparsePlus t sp (evar (IS IZ)) (evar IZ)) e1 e2
+sparsePlus t@SMTScal{} SpScal e1 e2 = EPlus ext t e1 e2
+
+
+cheapZero :: SMTy t -> Maybe (forall env. Ex env t)
+cheapZero SMTNil = Just (ENil ext)
+cheapZero (SMTPair t1 t2)
+  | Just e1 <- cheapZero t1
+  , Just e2 <- cheapZero t2
+  = Just (EPair ext e1 e2)
+  | otherwise
+  = Nothing
+cheapZero (SMTLEither t1 t2) = Just (ELNil ext (fromSMTy t1) (fromSMTy t2))
+cheapZero (SMTMaybe t) = Just (ENothing ext (fromSMTy t))
+cheapZero SMTArr{} = Nothing
+cheapZero (SMTScal t) = case t of
+  STI32 -> Just (EConst ext t 0)
+  STI64 -> Just (EConst ext t 0)
+  STF32 -> Just (EConst ext t 0.0)
+  STF64 -> Just (EConst ext t 0.0)
+
+
+data Injection sp a b where
+  -- | 'Inj' is purposefully also allowed when @sp@ is @False@ so that
+  -- 'sparsePlusS' can provide injections even if the caller doesn't require
+  -- them. This simplifies the sparsePlusS code.
+  Inj :: (forall e. Ex e a -> Ex e b) -> Injection sp a b
+  Noinj :: Injection False a b
+
+withInj :: Injection sp a b -> ((forall e. Ex e a -> Ex e b) -> (forall e'. Ex e' a' -> Ex e' b')) -> Injection sp a' b'
+withInj (Inj f) k = Inj (k f)
+withInj Noinj _ = Noinj
+
+withInj2 :: Injection sp a1 b1 -> Injection sp a2 b2
+         -> ((forall e. Ex e a1 -> Ex e b1)
+             -> (forall e. Ex e a2 -> Ex e b2)
+             -> (forall e'. Ex e' a' -> Ex e' b'))
+         -> Injection sp a' b'
+withInj2 (Inj f) (Inj g) k = Inj (k f g)
+withInj2 Noinj _ _ = Noinj
+withInj2 _ Noinj _ = Noinj
+
+use :: Ex env a -> Ex env b -> Ex env b
+use a b = elet a $ weakenExpr WSink b
+
+-- | This function produces quadratically-sized code in the presence of nested
+-- dynamic sparsity. TODO can this be improved?
+sparsePlusS
+  :: SBool inj1 -> SBool inj2
+  -> SMTy t -> Sparse t t1 -> Sparse t t2
+  -> (forall t3. Sparse t t3
+              -> Injection inj1 t1 t3  -- only available if first injection is requested (second argument may be absent)
+              -> Injection inj2 t2 t3  -- only available if second injection is requested (first argument may be absent)
+              -> (forall e. Ex e t1 -> Ex e t2 -> Ex e t3)
+              -> r)
+  -> r
+-- nil override (but don't destroy effects!)
+sparsePlusS _ _ SMTNil _ _ k =
+  k SpAbsent (Inj $ \a -> use a $ ENil ext) (Inj $ \b -> use b $ ENil ext) (\a b -> use a $ use b $ ENil ext)
+
+-- simplifications
+sparsePlusS req1 req2 t (SpSparse SpAbsent) sp2 k =
+  sparsePlusS req1 req2 t SpAbsent sp2 $ \sp3 minj1 minj2 plus ->
+    k sp3 (withInj minj1 $ \inj1 -> \a -> use a $ inj1 (ENil ext)) minj2 (\a b -> use a $ plus (ENil ext) b)
+sparsePlusS req1 req2 t sp1 (SpSparse SpAbsent) k =
+  sparsePlusS req1 req2 t sp1 SpAbsent $ \sp3 minj1 minj2 plus ->
+    k sp3 minj1 (withInj minj2 $ \inj2 -> \b -> use b $ inj2 (ENil ext)) (\a b -> use b $ plus a (ENil ext))
+
+sparsePlusS req1 req2 t (SpSparse (SpSparse sp1)) sp2 k =
+  let ta = applySparse sp1 (fromSMTy t) in
+  sparsePlusS req1 req2 t (SpSparse sp1) sp2 $ \sp3 minj1 minj2 plus ->
+    k sp3
+      (withInj minj1 $ \inj1 -> \a -> inj1 (emaybe a (ENothing ext ta) (EVar ext (STMaybe ta) IZ)))
+      minj2
+      (\a b -> plus (emaybe a (ENothing ext ta) (EVar ext (STMaybe ta) IZ)) b)
+sparsePlusS req1 req2 t sp1 (SpSparse (SpSparse sp2)) k =
+  let tb = applySparse sp2 (fromSMTy t) in
+  sparsePlusS req1 req2 t sp1 (SpSparse sp2) $ \sp3 minj1 minj2 plus ->
+    k sp3
+      minj1
+      (withInj minj2 $ \inj2 -> \b -> inj2 (emaybe b (ENothing ext tb) (EVar ext (STMaybe tb) IZ)))
+      (\a b -> plus a (emaybe b (ENothing ext tb) (EVar ext (STMaybe tb) IZ)))
+
+sparsePlusS req1 req2 t (SpSparse (SpLEither sp1a sp1b)) sp2 k =
+  let STLEither ta tb = applySparse (SpLEither sp1a sp1b) (fromSMTy t) in
+  sparsePlusS req1 req2 t (SpLEither sp1a sp1b) sp2 $ \sp3 minj1 minj2 plus ->
+    k sp3
+      (withInj minj1 $ \inj1 -> \a -> inj1 (emaybe a (ELNil ext ta tb) (EVar ext (STLEither ta tb) IZ)))
+      minj2
+      (\a b -> plus (emaybe a (ELNil ext ta tb) (EVar ext (STLEither ta tb) IZ)) b)
+sparsePlusS req1 req2 t sp1 (SpSparse (SpLEither sp2a sp2b)) k =
+  let STLEither ta tb = applySparse (SpLEither sp2a sp2b) (fromSMTy t) in
+  sparsePlusS req1 req2 t sp1 (SpLEither sp2a sp2b) $ \sp3 minj1 minj2 plus ->
+    k sp3
+      minj1
+      (withInj minj2 $ \inj2 -> \b -> inj2 (emaybe b (ELNil ext ta tb) (EVar ext (STLEither ta tb) IZ)))
+      (\a b -> plus a (emaybe b (ELNil ext ta tb) (EVar ext (STLEither ta tb) IZ)))
+
+sparsePlusS req1 req2 t (SpSparse (SpMaybe sp1)) sp2 k =
+  let STMaybe ta = applySparse (SpMaybe sp1) (fromSMTy t) in
+  sparsePlusS req1 req2 t (SpMaybe sp1) sp2 $ \sp3 minj1 minj2 plus ->
+    k sp3
+      (withInj minj1 $ \inj1 -> \a -> inj1 (emaybe a (ENothing ext ta) (evar IZ)))
+      minj2
+      (\a b -> plus (emaybe a (ENothing ext ta) (EVar ext (STMaybe ta) IZ)) b)
+sparsePlusS req1 req2 t sp1 (SpSparse (SpMaybe sp2)) k =
+  let STMaybe tb = applySparse (SpMaybe sp2) (fromSMTy t) in
+  sparsePlusS req1 req2 t sp1 (SpMaybe sp2) $ \sp3 minj1 minj2 plus ->
+    k sp3
+      minj1
+      (withInj minj2 $ \inj2 -> \b -> inj2 (emaybe b (ENothing ext tb) (evar IZ)))
+      (\a b -> plus a (emaybe b (ENothing ext tb) (EVar ext (STMaybe tb) IZ)))
+sparsePlusS req1 req2 t (SpMaybe (SpSparse sp1)) sp2 k = sparsePlusS req1 req2 t (SpSparse (SpMaybe sp1)) sp2 k
+sparsePlusS req1 req2 t sp1 (SpMaybe (SpSparse sp2)) k = sparsePlusS req1 req2 t sp1 (SpSparse (SpMaybe sp2)) k
+
+-- TODO: sparse of Just is just Maybe
+
+-- dense plus
+sparsePlusS _ _ t sp1 sp2 k
+  | Just Refl <- isDense t sp1
+  , Just Refl <- isDense t sp2
+  = k (spDense t) (Inj id) (Inj id) (\a b -> EPlus ext t a b)
+
+-- handle absents
+sparsePlusS SF _ _ SpAbsent sp2 k = k sp2 Noinj (Inj id) (\a b -> use a $ b)
+sparsePlusS ST _ t SpAbsent sp2 k
+  | Just zero2 <- cheapZero (applySparse sp2 t) =
+      k sp2 (Inj $ \a -> use a $ zero2) (Inj id) (\a b -> use a $ b)
+  | otherwise =
+      k (SpSparse sp2) (Inj $ \a -> use a $ ENothing ext (applySparse sp2 (fromSMTy t))) (Inj $ EJust ext) (\a b -> use a $ EJust ext b)
+
+sparsePlusS _ SF _ sp1 SpAbsent k = k sp1 (Inj id) Noinj (\a b -> use b $ a)
+sparsePlusS _ ST t sp1 SpAbsent k
+  | Just zero1 <- cheapZero (applySparse sp1 t) =
+      k sp1 (Inj id) (Inj $ \b -> use b $ zero1) (\a b -> use b $ a)
+  | otherwise =
+      k (SpSparse sp1) (Inj $ EJust ext) (Inj $ \b -> use b $ ENothing ext (applySparse sp1 (fromSMTy t))) (\a b -> use b $ EJust ext a)
+
+-- double sparse yields sparse
+sparsePlusS _ _ t (SpSparse sp1) (SpSparse sp2) k =
+  sparsePlusS ST ST t sp1 sp2 $ \sp3 (Inj inj1) (Inj inj2) plus ->
+    k (SpSparse sp3)
+      (Inj $ \a -> emaybe a (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj1 (evar IZ))))
+      (Inj $ \b -> emaybe b (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj2 (evar IZ))))
+      (\a b ->
+        elet b $
+          emaybe (weakenExpr WSink a)
+            (emaybe (evar IZ)
+              (ENothing ext (applySparse sp3 (fromSMTy t)))
+              (EJust ext (inj2 (evar IZ))))
+            (emaybe (evar (IS IZ))
+              (EJust ext (inj1 (evar IZ)))
+              (EJust ext (plus (evar (IS IZ)) (evar IZ)))))
+
+-- single sparse can yield non-sparse if the other argument is always present
+sparsePlusS SF _ t (SpSparse sp1) sp2 k =
+  sparsePlusS SF ST t sp1 sp2 $ \sp3 _ (Inj inj2) plus ->
+    k sp3 Noinj (Inj inj2)
+      (\a b ->
+        elet b $
+          emaybe (weakenExpr WSink a)
+            (inj2 (evar IZ))
+            (plus (evar IZ) (evar (IS IZ))))
+sparsePlusS ST _ t (SpSparse sp1) sp2 k =
+  sparsePlusS ST ST t sp1 sp2 $ \sp3 (Inj inj1) (Inj inj2) plus ->
+    k (SpSparse sp3)
+      (Inj $ \a -> emaybe a (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj1 (evar IZ))))
+      (Inj $ \b -> EJust ext (inj2 b))
+      (\a b ->
+        elet b $
+          emaybe (weakenExpr WSink a)
+            (EJust ext (inj2 (evar IZ)))
+            (EJust ext (plus (evar IZ) (evar (IS IZ)))))
+sparsePlusS req1 req2 t sp1 (SpSparse sp2) k =
+  sparsePlusS req2 req1 t (SpSparse sp2) sp1 $ \sp3 inj1 inj2 plus ->
+    k sp3 inj2 inj1 (flip plus)
+
+-- products
+sparsePlusS req1 req2 (SMTPair ta tb) (SpPair sp1a sp1b) (SpPair sp2a sp2b) k =
+  sparsePlusS req1 req2 ta sp1a sp2a $ \sp3a minj13a minj23a plusa ->
+  sparsePlusS req1 req2 tb sp1b sp2b $ \sp3b minj13b minj23b plusb ->
+    k (SpPair sp3a sp3b)
+      (withInj2 minj13a minj13b $ \inj13a inj13b ->
+        \x1 -> eunPair x1 $ \_ x1a x1b -> EPair ext (inj13a x1a) (inj13b x1b))
+      (withInj2 minj23a minj23b $ \inj23a inj23b ->
+        \x2 -> eunPair x2 $ \_ x2a x2b -> EPair ext (inj23a x2a) (inj23b x2b))
+      (\x1 x2 ->
+        eunPair x1 $ \w1 x1a x1b ->
+        eunPair (weakenExpr w1 x2) $ \w2 x2a x2b ->
+          EPair ext (plusa (weakenExpr w2 x1a) x2a) (plusb (weakenExpr w2 x1b) x2b))
+
+-- coproducts
+sparsePlusS _ _ (SMTLEither ta tb) (SpLEither sp1a sp1b) (SpLEither sp2a sp2b) k =
+  sparsePlusS ST ST ta sp1a sp2a $ \(sp3a :: Sparse _t3 t3a) (Inj inj13a) (Inj inj23a) plusa ->
+  sparsePlusS ST ST tb sp1b sp2b $ \(sp3b :: Sparse _t3' t3b) (Inj inj13b) (Inj inj23b) plusb ->
+    let nil :: Ex e (TLEither t3a t3b) ; nil = ELNil ext (applySparse sp3a (fromSMTy ta)) (applySparse sp3b (fromSMTy tb))
+        inl :: Ex e t3a -> Ex e (TLEither t3a t3b) ; inl = ELInl ext (applySparse sp3b (fromSMTy tb))
+        inr :: Ex e t3b -> Ex e (TLEither t3a t3b) ; inr = ELInr ext (applySparse sp3a (fromSMTy ta))
+    in
+    k (SpLEither sp3a sp3b)
+      (Inj $ \x1 -> elcase x1 nil (inl (inj13a (evar IZ))) (inr (inj13b (evar IZ))))
+      (Inj $ \x2 -> elcase x2 nil (inl (inj23a (evar IZ))) (inr (inj23b (evar IZ))))
+      (\x1 x2 ->
+        elet x2 $
+          elcase (weakenExpr WSink x1)
+            (elcase (evar IZ)
+              nil
+              (inl (inj23a (evar IZ)))
+              (inr (inj23b (evar IZ))))
+            (elcase (evar (IS IZ))
+              (inl (inj13a (evar IZ)))
+              (inl (plusa (evar (IS IZ)) (evar IZ)))
+              (EError ext (applySparse (SpLEither sp3a sp3b) (fromSMTy (SMTLEither ta tb))) "plusS ll+lr"))
+            (elcase (evar (IS IZ))
+              (inr (inj13b (evar IZ)))
+              (EError ext (applySparse (SpLEither sp3a sp3b) (fromSMTy (SMTLEither ta tb))) "plusS lr+ll")
+              (inr (plusb (evar (IS IZ)) (evar IZ)))))
+
+-- maybe
+sparsePlusS _ _ (SMTMaybe t) (SpMaybe sp1) (SpMaybe sp2) k =
+  sparsePlusS ST ST t sp1 sp2 $ \sp3 (Inj inj1) (Inj inj2) plus ->
+    k (SpMaybe sp3)
+      (Inj $ \a -> emaybe a (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj1 (evar IZ))))
+      (Inj $ \b -> emaybe b (ENothing ext (applySparse sp3 (fromSMTy t))) (EJust ext (inj2 (evar IZ))))
+      (\a b ->
+        elet b $
+          emaybe (weakenExpr WSink a)
+            (emaybe (evar IZ)
+              (ENothing ext (applySparse sp3 (fromSMTy t)))
+              (EJust ext (inj2 (evar IZ))))
+            (emaybe (evar (IS IZ))
+              (EJust ext (inj1 (evar IZ)))
+              (EJust ext (plus (evar (IS IZ)) (evar IZ)))))
+
+-- dense array cotangents simply recurse
+sparsePlusS req1 req2 (SMTArr _ t) (SpArr sp1) (SpArr sp2) k =
+  sparsePlusS req1 req2 t sp1 sp2 $ \sp3 minj1 minj2 plus ->
+    k (SpArr sp3)
+      (withInj minj1 $ \inj1 -> emap (inj1 (EVar ext (applySparse sp1 (fromSMTy t)) IZ)))
+      (withInj minj2 $ \inj2 -> emap (inj2 (EVar ext (applySparse sp2 (fromSMTy t)) IZ)))
+      (ezipWith (plus (EVar ext (applySparse sp1 (fromSMTy t)) (IS IZ))
+                      (EVar ext (applySparse sp2 (fromSMTy t)) IZ)))
+
+-- scalars
+sparsePlusS _ _ (SMTScal t) SpScal SpScal k = k SpScal (Inj id) (Inj id) (EPlus ext (SMTScal t))