feat(core): add gcd/lcm Semigroup to segment tree

runtime/include/jikka/segment_tree.hpp

@@ -17,8 +17,14 @@ inline int64_t min_int64_t(int64_t a, int64_t b) { return std::min(a, b); }
 
 inline int64_t max_int64_t(int64_t a, int64_t b) { return std::max(a, b); }
 
+inline int64_t gcd_int64_t(int64_t a, int64_t b) { return std::gcd(a, b); }
+
+inline int64_t lcm_int64_t(int64_t a, int64_t b) { return std::lcm(a, b); }
+
 inline int64_t const_zero() { return 0; }
 
+inline int64_t const_one() { return 1; }
+
 inline int64_t const_int64_min() { return INT64_MIN; }
 
 inline int64_t const_int64_max() { return INT64_MAX; }

src/Jikka/CPlusPlus/Convert/FromCore.hs

@@ -68,6 +68,8 @@ runSemigroup = \case
   X.SemigroupIntPlus -> Y.MonoidIntPlus
   X.SemigroupIntMin -> Y.MonoidIntMin
   X.SemigroupIntMax -> Y.MonoidIntMax
+  X.SemigroupIntGcd -> Y.MonoidIntGcd
+  X.SemigroupIntLcm -> Y.MonoidIntLcm
 
 runLiteral :: (MonadAlpha m, MonadError Error m) => Env -> X.Literal -> m Y.Expr
 runLiteral env = \case
@@ -478,6 +480,20 @@ runAppBuiltin env f ts args = wrapError' ("converting builtin " ++ X.formatBuilt
           ],
           Y.Var y
         )
+    X.Gcd1 -> go11' $ \t xs -> do
+      y <- Y.newFreshName Y.LocalNameKind
+      return
+        ( [ Y.Declare t y (Y.DeclareCopy (Y.UnOp Y.Deref (Y.callFunction "std::accumulate" [] [Y.begin xs, Y.end xs, Y.litInt64 0, Y.Lam [(Y.TyAuto, Y.VarName "a"), (Y.TyAuto, Y.VarName "b")] Y.TyAuto [Y.Return $ Y.callFunction "std::gcd" [] [Y.Var $ Y.VarName "a", Y.Var $ Y.VarName "b"]]])))
+          ],
+          Y.Var y
+        )
+    X.Lcm1 -> go11' $ \t xs -> do
+      y <- Y.newFreshName Y.LocalNameKind
+      return
+        ( [ Y.Declare t y (Y.DeclareCopy (Y.UnOp Y.Deref (Y.callFunction "std::accumulate" [] [Y.begin xs, Y.end xs, Y.litInt64 1, Y.Lam [(Y.TyAuto, Y.VarName "a"), (Y.TyAuto, Y.VarName "b")] Y.TyAuto [Y.Return $ Y.callFunction "std::lcm" [] [Y.Var $ Y.VarName "a", Y.Var $ Y.VarName "b"]]])))
+          ],
+          Y.Var y
+        )
     X.All -> go01' $ \xs -> do
       y <- Y.newFreshName Y.LocalNameKind
       return

src/Jikka/CPlusPlus/Format.hs

@@ -189,6 +189,8 @@ formatType = \case
     MonoidIntPlus -> "atcoder::segtree<int64_t, jikka::plus_int64_t, jikka::const_zero>"
     MonoidIntMin -> "atcoder::segtree<int64_t, jikka::min_int64_t, jikka::const_int64_max>"
     MonoidIntMax -> "atcoder::segtree<int64_t, jikka::max_int64_t, jikka::const_int64_min>"
+    MonoidIntGcd -> "atcoder::segtree<int64_t, jikka::gcd_int64_t, jikka::const_zero>"
+    MonoidIntLcm -> "atcoder::segtree<int64_t, jikka::lcm_int64_t, jikka::const_one>"
   TyIntValue n -> show n
 
 formatLiteral :: Literal -> Code

src/Jikka/CPlusPlus/Language/Expr.hs

@@ -41,6 +41,8 @@ data Monoid'
   = MonoidIntPlus
   | MonoidIntMin
   | MonoidIntMax
+  | MonoidIntGcd
+  | MonoidIntLcm
   deriving (Eq, Ord, Show, Read)
 
 data Literal

src/Jikka/Core/Convert/CumulativeSum.hs

@@ -59,6 +59,14 @@ rule = RewriteRule $ \_ -> \case
     Just <$> cumulativeMax (Min2' t) t (Just a0) a n
   Min1' t (Map' _ _ (Lam x _ (At' _ a (Var x'))) (Range1' n)) | x' == x && x `isUnusedVar` a -> do
     Just <$> cumulativeMax (Min2' t) t Nothing a n
+  Lcm1' t (Cons' _ a0 (Map' _ _ (Lam x _ (At' _ a (Var x'))) (Range1' n))) | x' == x && x `isUnusedVar` a -> do
+    Just <$> cumulativeMax Lcm' t (Just a0) a n
+  Lcm1' t (Map' _ _ (Lam x _ (At' _ a (Var x'))) (Range1' n)) | x' == x && x `isUnusedVar` a -> do
+    Just <$> cumulativeMax Lcm' t Nothing a n
+  Gcd1' t (Cons' _ a0 (Map' _ _ (Lam x _ (At' _ a (Var x'))) (Range1' n))) | x' == x && x `isUnusedVar` a -> do
+    Just <$> cumulativeMax Gcd' t (Just a0) a n
+  Gcd1' t (Map' _ _ (Lam x _ (At' _ a (Var x'))) (Range1' n)) | x' == x && x `isUnusedVar` a -> do
+    Just <$> cumulativeMax Gcd' t Nothing a n
   _ -> return Nothing
 
 runProgram :: (MonadAlpha m, MonadError Error m) => Program -> m Program

src/Jikka/Core/Convert/SegmentTree.hs

@@ -74,13 +74,17 @@ builtinToSemigroup builtin ts = case (builtin, ts) of
   (Plus, []) -> Just SemigroupIntPlus
   (Min2, [IntTy]) -> Just SemigroupIntMin
   (Max2, [IntTy]) -> Just SemigroupIntMax
+  (Gcd, []) -> Just SemigroupIntGcd
+  (Lcm, []) -> Just SemigroupIntLcm
   _ -> Nothing
 
 semigroupToBuiltin :: Semigroup' -> (Builtin, [Type])
 semigroupToBuiltin = \case
   SemigroupIntPlus -> (Plus, [])
   SemigroupIntMin -> (Min2, [IntTy])
   SemigroupIntMax -> (Max2, [IntTy])
+  SemigroupIntGcd -> (Gcd, [])
+  SemigroupIntLcm -> (Lcm, [])
 
 unCumulativeSum :: Expr -> Expr -> Maybe (Semigroup', Expr)
 unCumulativeSum a = \case

src/Jikka/Core/Convert/SpecializeFoldl.hs

@@ -50,6 +50,12 @@ rule = simpleRewriteRule $ \case
     -- Max1
     Min2' _ (Var x2') e | x2' == x2 && x2 `isUnusedVar` e -> Just $ Min1' t2 (Cons' t2 init (Map' t1 t2 (Lam x1 t1 e) xs))
     Min2' _ e (Var x2') | x2' == x2 && x2 `isUnusedVar` e -> Just $ Min1' t2 (Cons' t2 init (Map' t1 t2 (Lam x1 t1 e) xs))
+    -- Lcm1
+    Lcm' (Var x2') e | x2' == x2 && x2 `isUnusedVar` e -> Just $ Lcm1' t2 (Cons' t2 init (Map' t1 t2 (Lam x1 t1 e) xs))
+    Lcm' e (Var x2') | x2' == x2 && x2 `isUnusedVar` e -> Just $ Lcm1' t2 (Cons' t2 init (Map' t1 t2 (Lam x1 t1 e) xs))
+    -- Gcd1
+    Gcd' (Var x2') e | x2' == x2 && x2 `isUnusedVar` e -> Just $ Gcd1' t2 (Cons' t2 init (Map' t1 t2 (Lam x1 t1 e) xs))
+    Gcd' e (Var x2') | x2' == x2 && x2 `isUnusedVar` e -> Just $ Gcd1' t2 (Cons' t2 init (Map' t1 t2 (Lam x1 t1 e) xs))
     -- others
     _ -> Nothing
   -- The outer floor-mod is required because foldl for empty lists returns values without modulo.

src/Jikka/Core/Format.hs

@@ -133,6 +133,8 @@ formatSemigroup = \case
   SemigroupIntPlus -> "int.plus"
   SemigroupIntMin -> "int.min"
   SemigroupIntMax -> "int.max"
+  SemigroupIntGcd -> "int.gcd"
+  SemigroupIntLcm -> "int.lcm"
 
 data Builtin'
   = Fun String
@@ -217,6 +219,8 @@ analyzeBuiltin = \case
   Max1 -> Fun "max"
   ArgMin -> Fun "argmin"
   ArgMax -> Fun "argmax"
+  Gcd1 -> Fun "gcd"
+  Lcm1 -> Fun "lcm"
   All -> Fun "all"
   Any -> Fun "any"
   Sorted -> Fun "sort"

src/Jikka/Core/Language/BuiltinPatterns.hs

@@ -147,6 +147,10 @@ pattern ArgMin' t e = AppBuiltin11 ArgMin t e
 
 pattern ArgMax' t e = AppBuiltin11 ArgMax t e
 
+pattern Gcd1' t e = AppBuiltin11 Gcd1 t e
+
+pattern Lcm1' t e = AppBuiltin11 Lcm1 t e
+
 pattern All' e = AppBuiltin1 All e
 
 pattern Any' e = AppBuiltin1 Any e

src/Jikka/Core/Language/Expr.hs

@@ -66,6 +66,8 @@ data Semigroup'
   = SemigroupIntPlus
   | SemigroupIntMin
   | SemigroupIntMax
+  | SemigroupIntGcd
+  | SemigroupIntLcm
   deriving (Eq, Ord, Show, Read, Data, Typeable)
 
 -- | TODO: What is the difference between `Literal` and `Builtin`?
@@ -210,6 +212,10 @@ data Builtin
     ArgMin
   | -- | \(: \forall \alpha. \list(\alpha) \to \int\)
     ArgMax
+  | -- | \(: \list(\int) \to \int\)
+    Gcd1
+  | -- | \(: \list(\int) \to \int\)
+    Lcm1
   | -- | \(: \list(\bool) \to \bool\)
     All
   | -- | \(: \list(\bool) \to \bool\)

src/Jikka/Core/Language/TypeCheck.hs

@@ -96,6 +96,8 @@ builtinToType builtin ts =
         Max1 -> go1 $ \t -> FunLTy t
         ArgMin -> go1 $ \t -> FunTy (ListTy t) IntTy
         ArgMax -> go1 $ \t -> FunTy (ListTy t) IntTy
+        Gcd1 -> go0 $ FunLTy IntTy
+        Lcm1 -> go0 $ FunLTy IntTy
         All -> go0 $ FunLTy BoolTy
         Any -> go0 $ FunLTy BoolTy
         Sorted -> go1 $ \t -> Fun1STy (ListTy t)
@@ -131,6 +133,8 @@ semigroupToType = \case
   SemigroupIntPlus -> IntTy
   SemigroupIntMin -> IntTy
   SemigroupIntMax -> IntTy
+  SemigroupIntGcd -> IntTy
+  SemigroupIntLcm -> IntTy
 
 literalToType :: MonadError Error m => Literal -> m Type
 literalToType = \case