blob: 8287d5a0b605d8ce8e635bb01e9a3d10a0abd7ba (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
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
|
