builtin cleaning

1 files changed, 66 insertions, 0 deletions

diff --git a/src/Builtin.hs b/src/Builtin.hs
new file mode 100644
index 0000000..8287d5a
--- /dev/null
+++ b/src/Builtin.hs
@@ -0,0 +1,66 @@
+module Builtin where
+
+
+builtinAdd :: Expr -> Expr -> Maybe Expr
+
+builtinAdd (Rational a)    (Rational b)    = Just $ Rational (a + b)
+builtinAdd (Rational a)    (Imaginary b)   = Just $ Complex a b
+builtinAdd (Rational a)    (Complex br bi) = Just $ Complex (br + a) bi
+
+builtinAdd (Imaginary a)   (Imaginary b)   = Just $ Imaginary (a + b)
+builtinAdd (Imaginary a)   (Rational b)    = Just $ Complex b a
+builtinAdd (Imaginary a)   (Complex br bi) = Just $ Complex br (a + bi)
+
+builtinAdd (Complex ar ai) (Complex br bi) = Just $ Complex (ar + br) (ai + bi)
+builtinAdd (Complex ar ai) (Rational b)    = Just $ Complex (ar + b) ai
+builtinAdd (Complex ar ai) (Imaginary b)   = Just $ Complex ar (ai + b)
+
+builtinAdd _ _ = Nothing
+
+
+builtinSub :: Expr -> Expr -> Maybe Expr
+builtinSub a b = a `builtinAdd` ((Rational (-1)) `builtinMul` b)
+builtinSub _ _ = Nothing
+
+
+-- could be derived from addition
+builtinMul :: Expr -> Expr -> Maybe Expr
+builtinMul (Rational a) (Rational b)    = Just $ Ratinal (a * b)
+builtinMul (Rational a) (Imaginary b)   = Just $ Imaginary (a * b)
+builtinMul (Rational a) (Complex br bi) = Just $ Complex (a * br) (a * bi)
+
+builtinMul (Imaginary a) (Imaginary b)   = Just $ Imaginary (a * b)
+builtinMul (Imaginary a) (Rational b)    = Just $ Complex b a
+builtinMul (Imaginary a) (Complex br bi) = Just $ Complex (a * br) (a * bi)
+
+builtinMul _ _ = Nothing
+
+
+builtinDiv :: Expr -> Expr -> Maybe Expr
+builtinDiv _ (Rational 0)  = Nothing
+builtinDiv _ (Imaginary 0) = Nothing
+builtinDiv _ (Complex 0 0) = Nothing
+builtinDiv a b = Just $ a `builtinMul` (b `builtinExp` (Rational -1))
+builtinDiv _ _ = Nothing
+
+
+builtinMod :: Expr -> Expr -> Maybe Expr
+builtinMod _ _ = Nothing
+
+
+-- could be derived from multiplication
+builtinExp :: Expr -> Expr -> Maybe Expr
+builtinExp (Rational a)  (Rational b) = Just $ Rational (a ** b)
+
+builtinExp (Imaginary a) (Rational b)
+  | b < 0     = Just $ (Rational 1) `builtinDiv` ((Imaginary a) `builtinExp` (Rational b)
+  | b == 0    = Just $ Rational a
+  | b == 1    = Just $ Imaginary a
+  | b == 2    = Just $ Rational (-a)
+  | b == 3    = Just $ Imaginary (-a)
+  | otherwise = Imaginary a `builtinExp` (Rational (b - 4))
+
+builtinExp _ _ = Nothing
+
+builtinDot :: Expr -> Expr -> Maybe Expr
+_ **? _ = Nothing