-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Natural number arithmetic
--   
@package arithmetic
@version 1.0


module Arithmetic.Random
randomWidth :: Int -> Random -> Natural
randomOdd :: Int -> Random -> Natural
randomCoprime :: Int -> Random -> (Natural, Natural)
uniformInteger :: Integer -> Random -> Integer
randomCoprimeInteger :: Int -> Random -> (Integer, Integer)


module Arithmetic.Modular
multiplyExponential :: (a -> a -> a) -> a -> a -> Natural -> a
functionPower :: (a -> a) -> Natural -> a -> a
normalize :: Natural -> Natural -> Natural
add :: Natural -> Natural -> Natural -> Natural
negate :: Natural -> Natural -> Natural
subtract :: Natural -> Natural -> Natural -> Natural
multiply :: Natural -> Natural -> Natural -> Natural
square :: Natural -> Natural -> Natural
exp :: Natural -> Natural -> Natural -> Natural
exp2 :: Natural -> Natural -> Natural -> Natural


module Arithmetic.Montgomery
data Parameters
Parameters :: Natural -> Natural -> Natural -> Natural -> Natural -> Natural -> Natural -> Parameters
nParameters :: Parameters -> Natural
wParameters :: Parameters -> Natural
sParameters :: Parameters -> Natural
kParameters :: Parameters -> Natural
rParameters :: Parameters -> Natural
r2Parameters :: Parameters -> Natural
zParameters :: Parameters -> Natural
data Montgomery
Montgomery :: Parameters -> Natural -> Montgomery
pMontgomery :: Montgomery -> Parameters
nMontgomery :: Montgomery -> Natural
align :: Natural -> Natural -> Natural
customParameters :: Natural -> Natural -> Parameters
alignedParameters :: Natural -> Natural -> Parameters
standardParameters :: Natural -> Parameters
normalize :: Parameters -> Natural -> Montgomery
normalize1 :: Parameters -> Natural -> Montgomery
reduce :: Parameters -> Natural -> Natural
toNatural :: Montgomery -> Natural
fromNatural :: Parameters -> Natural -> Montgomery
zero :: Parameters -> Montgomery
one :: Parameters -> Montgomery
two :: Parameters -> Montgomery
add :: Montgomery -> Montgomery -> Montgomery
double :: Montgomery -> Montgomery
negate :: Montgomery -> Montgomery
subtract :: Montgomery -> Montgomery -> Montgomery
multiply :: Montgomery -> Montgomery -> Montgomery
square :: Montgomery -> Montgomery
exp :: Montgomery -> Natural -> Montgomery
exp2 :: Montgomery -> Natural -> Montgomery
modexp :: Natural -> Natural -> Natural -> Natural
modexp2 :: Natural -> Natural -> Natural -> Natural
instance Show Parameters
instance Show Montgomery


module Arithmetic.Prime
factorTwos :: Natural -> (Int, Natural)
millerRabinWitness :: Natural -> Natural -> Bool
millerRabin :: Int -> Natural -> Random -> Bool
isPrime :: Natural -> Random -> Bool
previousPrime :: Natural -> Random -> Natural
randomPrime :: Int -> Random -> Natural