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-- |
-- Module: Math.NumberTheory.Moduli.Class
-- Copyright: (c) 2017 Andrew Lelechenko
-- Licence: MIT
-- Maintainer: Andrew Lelechenko <andrew.lelechenko@gmail.com>
--
-- Safe modular arithmetic with modulo on type level.
--
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
module Math.NumberTheory.Moduli.Class
( -- * Known modulo
Mod
, getVal
, getNatVal
, getMod
, getNatMod
, invertMod
, powMod
, (^%)
-- * Multiplicative group
, MultMod
, multElement
, isMultElement
, invertGroup
-- * Unknown modulo
, SomeMod(..)
, modulo
, invertSomeMod
, powSomeMod
-- * Re-exported from GHC.TypeNats.Compat
, KnownNat
) where
import Data.Mod
import GHC.Natural
import GHC.TypeNats (KnownNat, natVal)
import Math.NumberTheory.Moduli.Multiplicative
import Math.NumberTheory.Moduli.SomeMod
-- | Linking type and value levels: extract modulo @m@ as a value.
getMod :: KnownNat m => Mod m -> Integer
getMod = toInteger . natVal
{-# INLINE getMod #-}
-- | Linking type and value levels: extract modulo @m@ as a value.
getNatMod :: KnownNat m => Mod m -> Natural
getNatMod = natVal
{-# INLINE getNatMod #-}
-- | The canonical representative of the residue class, always between 0 and m-1 inclusively.
getVal :: Mod m -> Integer
getVal = toInteger . unMod
{-# INLINE getVal #-}
-- | The canonical representative of the residue class, always between 0 and m-1 inclusively.
getNatVal :: Mod m -> Natural
getNatVal = unMod
{-# INLINE getNatVal #-}
-- | Synonym of '(^%)'.
powMod :: (KnownNat m, Integral a) => Mod m -> a -> Mod m
powMod = (^%)
{-# INLINE powMod #-}
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