module Data.NumInstances.Tuple () where
lift2 :: (a->u) -> (b->v) -> (a,b) -> (u,v)
lift2 f g (a,b) = (f a, g b)
instance (Num a, Num b) => Num (a,b) where
fromInteger n = (fromInteger n, fromInteger n)
(a,b) + (a',b') = (a+a',b+b')
(a,b) (a',b') = (aa',bb')
(a,b) * (a',b') = (a*a',b*b')
negate = lift2 negate negate
abs = lift2 abs abs
signum = lift2 signum signum
instance (Fractional a, Fractional b) => Fractional (a,b) where
fromRational x = (fromRational x, fromRational x)
recip = lift2 recip recip
instance (Floating a, Floating b) => Floating (a,b) where
pi = (pi,pi)
exp = lift2 exp exp
log = lift2 log log
sqrt = lift2 sqrt sqrt
sin = lift2 sin sin
cos = lift2 cos cos
sinh = lift2 sinh sinh
cosh = lift2 cosh cosh
asin = lift2 asin asin
acos = lift2 acos acos
atan = lift2 atan atan
asinh = lift2 asinh asinh
acosh = lift2 acosh acosh
atanh = lift2 atanh atanh
instance (Num a, Num b, Num c) => Num (a,b,c) where
fromInteger n = (fromInteger n, fromInteger n, fromInteger n)
(a,b,c) + (a',b',c') = (a+a',b+b',c+c')
(a,b,c) (a',b',c') = (aa',bb',cc')
(a,b,c) * (a',b',c') = (a*a',b*b',c*c')
negate = lift3 negate negate negate
abs = lift3 abs abs abs
signum = lift3 signum signum signum
instance (Fractional a, Fractional b, Fractional c)
=> Fractional (a,b,c) where
fromRational x = (fromRational x, fromRational x, fromRational x)
recip = lift3 recip recip recip
lift3 :: (a->u) -> (b->v) -> (c->w) -> (a,b,c) -> (u,v,w)
lift3 f g h (a,b,c) = (f a, g b, h c)
instance (Floating a, Floating b, Floating c)
=> Floating (a,b,c) where
pi = (pi,pi,pi)
exp = lift3 exp exp exp
log = lift3 log log log
sqrt = lift3 sqrt sqrt sqrt
sin = lift3 sin sin sin
cos = lift3 cos cos cos
sinh = lift3 sinh sinh sinh
cosh = lift3 cosh cosh cosh
asin = lift3 asin asin asin
acos = lift3 acos acos acos
atan = lift3 atan atan atan
asinh = lift3 asinh asinh asinh
acosh = lift3 acosh acosh acosh
atanh = lift3 atanh atanh atanh
lift4 :: (a->u) -> (b->v) -> (c->w) -> (d->x)
-> (a,b,c,d) -> (u,v,w,x)
lift4 f g h k (a,b,c,d) = (f a, g b, h c, k d)
instance (Num a, Num b, Num c, Num d) => Num (a,b,c,d) where
fromInteger n = (fromInteger n, fromInteger n, fromInteger n, fromInteger n)
(a,b,c,d) + (a',b',c',d') = (a+a',b+b',c+c',d+d')
(a,b,c,d) (a',b',c',d') = (aa',bb',cc',dd')
(a,b,c,d) * (a',b',c',d') = (a*a',b*b',c*c',d*d')
negate = lift4 negate negate negate negate
abs = lift4 abs abs abs abs
signum = lift4 signum signum signum signum
instance (Fractional a, Fractional b, Fractional c, Fractional d)
=> Fractional (a,b,c,d) where
fromRational x = (fromRational x, fromRational x, fromRational x, fromRational x)
recip = lift4 recip recip recip recip
instance (Floating a, Floating b, Floating c, Floating d)
=> Floating (a,b,c,d) where
pi = (pi,pi,pi,pi)
exp = lift4 exp exp exp exp
log = lift4 log log log log
sqrt = lift4 sqrt sqrt sqrt sqrt
sin = lift4 sin sin sin sin
cos = lift4 cos cos cos cos
sinh = lift4 sinh sinh sinh sinh
cosh = lift4 cosh cosh cosh cosh
asin = lift4 asin asin asin asin
acos = lift4 acos acos acos acos
atan = lift4 atan atan atan atan
asinh = lift4 asinh asinh asinh asinh
acosh = lift4 acosh acosh acosh acosh
atanh = lift4 atanh atanh atanh atanh