module Factory.Math.Power(
square,
squaresFrom,
cube,
cubeRoot,
raiseModulo
) where
square :: Num n => n -> n
square :: n -> n
square n
x = n
x n -> Int -> n
forall a b. (Num a, Integral b) => a -> b -> a
^ (Int
2 :: Int)
{-# INLINE square #-}
cube :: Num n => n -> n
cube :: n -> n
cube = (n -> Int -> n
forall a b. (Num a, Integral b) => a -> b -> a
^ (Int
3 :: Int))
squaresFrom :: (Enum n, Num n)
=> n
-> [(n, n)]
squaresFrom :: n -> [(n, n)]
squaresFrom n
from = ((n, n) -> (n, n)) -> (n, n) -> [(n, n)]
forall a. (a -> a) -> a -> [a]
iterate (\(n
x, n
y) -> (n -> n
forall a. Enum a => a -> a
succ n
x, n -> n
forall a. Enum a => a -> a
succ (n -> n) -> n -> n
forall a b. (a -> b) -> a -> b
$ n
y n -> n -> n
forall a. Num a => a -> a -> a
+ n
2 n -> n -> n
forall a. Num a => a -> a -> a
* n
x)) (n
from, n -> n
forall n. Num n => n -> n
square n
from)
cubeRoot :: Double -> Double
cubeRoot :: Double -> Double
cubeRoot = (Double -> Double -> Double
forall a. Floating a => a -> a -> a
** Double -> Double
forall a. Fractional a => a -> a
recip Double
3)
raiseModulo :: (Integral i, Integral power, Show power)
=> i
-> power
-> i
-> i
raiseModulo :: i -> power -> i -> i
raiseModulo i
_ power
_ i
0 = [Char] -> i
forall a. HasCallStack => [Char] -> a
error [Char]
"Factory.Math.Power.raiseModulo:\tzero modulus."
raiseModulo i
_ power
_ i
1 = i
0
raiseModulo i
_ power
0 i
modulus = i
1 i -> i -> i
forall a. Integral a => a -> a -> a
`mod` i
modulus
raiseModulo i
base power
power i
modulus
| i
base i -> i -> Bool
forall a. Ord a => a -> a -> Bool
< i
0 = (i -> i -> i
forall a. Integral a => a -> a -> a
`mod` i
modulus) (i -> i) -> (i -> i) -> i -> i
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (if power -> Bool
forall a. Integral a => a -> Bool
even power
power then i -> i
forall a. a -> a
id else i -> i
forall n. Num n => n -> n
negate) (i -> i) -> i -> i
forall a b. (a -> b) -> a -> b
$ i -> power -> i -> i
forall i power.
(Integral i, Integral power, Show power) =>
i -> power -> i -> i
raiseModulo (i -> i
forall n. Num n => n -> n
negate i
base) power
power i
modulus
| power
power power -> power -> Bool
forall a. Ord a => a -> a -> Bool
< power
0 = [Char] -> i
forall a. HasCallStack => [Char] -> a
error ([Char] -> i) -> [Char] -> i
forall a b. (a -> b) -> a -> b
$ [Char]
"Factory.Math.Power.raiseModulo:\tnegative power; " [Char] -> [Char] -> [Char]
forall a. [a] -> [a] -> [a]
++ power -> [Char]
forall a. Show a => a -> [Char]
show power
power
| i
first i -> [i] -> Bool
forall (t :: * -> *) a. (Foldable t, Eq a) => a -> t a -> Bool
`elem` [i
0, i
1] = i
first
| Bool
otherwise = power -> i
forall t. Integral t => t -> i
slave power
power
where
first :: i
first = i
base i -> i -> i
forall a. Integral a => a -> a -> a
`mod` i
modulus
slave :: t -> i
slave t
1 = i
first
slave t
e = (i -> i -> i
forall a. Integral a => a -> a -> a
`mod` i
modulus) (i -> i) -> (i -> i) -> i -> i
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (if t
r t -> t -> Bool
forall a. Eq a => a -> a -> Bool
== t
0 then i -> i
forall a. a -> a
id else (i -> i -> i
forall a. Num a => a -> a -> a
* i
base)) (i -> i) -> (i -> i) -> i -> i
forall b c a. (b -> c) -> (a -> b) -> a -> c
. i -> i
forall n. Num n => n -> n
square (i -> i) -> i -> i
forall a b. (a -> b) -> a -> b
$ t -> i
slave t
q where
(t
q, t
r) = t
e t -> t -> (t, t)
forall a. Integral a => a -> a -> (a, a)
`quotRem` t
2