{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE UnboxedSums #-}

{-# OPTIONS_HADDOCK not-home #-}

-- | Compatibility module for pre ghc-bignum code.
module GHC.Internal.Natural
   ( Natural (NatS#, NatJ#)
   , B.BigNat (..)
   , mkNatural
   , isValidNatural
     -- * Arithmetic
   , plusNatural
   , minusNatural
   , minusNaturalMaybe
   , timesNatural
   , negateNatural
   , signumNatural
   , quotRemNatural
   , quotNatural
   , remNatural
   , gcdNatural
   , lcmNatural
     -- * Bits
   , andNatural
   , orNatural
   , xorNatural
   , bitNatural
   , testBitNatural
   , popCountNatural
   , shiftLNatural
   , shiftRNatural
     -- * Conversions
   , naturalToInteger
   , naturalToWord
   , naturalToWordMaybe
   , wordToNatural
   , wordToNatural#
   , naturalFromInteger
     -- * Modular arithmetic
   , powModNatural
   )
where

import GHC.Prim
import GHC.Types
import GHC.Internal.Maybe
import GHC.Num.Natural (Natural)
import GHC.Num.Integer (Integer)
import qualified GHC.Num.BigNat  as B
import qualified GHC.Num.Natural as N
import qualified GHC.Num.Integer as I

{-# COMPLETE NatS#, NatJ# #-}

pattern NatS# :: Word# -> Natural
pattern $mNatS# :: forall {r}. Natural -> (Word# -> r) -> ((# #) -> r) -> r
$bNatS# :: Word# -> Natural
NatS# w = N.NS w

pattern NatJ# :: B.BigNat -> Natural
pattern $mNatJ# :: forall {r}. Natural -> (BigNat -> r) -> ((# #) -> r) -> r
$bNatJ# :: BigNat -> Natural
NatJ# b <- N.NB (B.BN# -> b)
   where
      NatJ# BigNat
b = ByteArray# -> Natural
N.NB (BigNat -> ByteArray#
B.unBigNat BigNat
b)

int2Word :: Int -> Word
int2Word :: Int -> Word
int2Word (I# Int#
i) = Word# -> Word
W# (Int# -> Word#
int2Word# Int#
i)

word2Int :: Word -> Int
word2Int :: Word -> Int
word2Int (W# Word#
w) = Int# -> Int
I# (Word# -> Int#
word2Int# Word#
w)

-- | Construct 'Natural' value from list of 'Word's.
mkNatural :: [Word] -> Natural
mkNatural :: [Word] -> Natural
mkNatural = [Word] -> Natural
N.naturalFromWordList

-- | Test whether all internal invariants are satisfied by 'Natural' value
--
-- This operation is mostly useful for test-suites and/or code which
-- constructs 'Integer' values directly.
--
-- @since base-4.8.0.0
isValidNatural :: Natural -> Bool
isValidNatural :: Natural -> Bool
isValidNatural = Natural -> Bool
N.naturalCheck

-- | 'Natural' Addition
plusNatural :: Natural -> Natural -> Natural
plusNatural :: Natural -> Natural -> Natural
plusNatural = Natural -> Natural -> Natural
N.naturalAdd

-- | 'Natural' subtraction. May @'GHC.Internal.Control.Exception.throw'
-- 'Control.Exception.Underflow'@.
minusNatural :: Natural -> Natural -> Natural
minusNatural :: Natural -> Natural -> Natural
minusNatural = Natural -> Natural -> Natural
N.naturalSubThrow

-- | 'Natural' subtraction. Returns 'Nothing's for non-positive results.
--
-- @since base-4.8.0.0
minusNaturalMaybe :: Natural -> Natural -> Maybe Natural
minusNaturalMaybe :: Natural -> Natural -> Maybe Natural
minusNaturalMaybe Natural
x Natural
y = case Natural -> Natural -> (# (# #) | Natural #)
N.naturalSub Natural
x Natural
y of
   (# (# #) |   #) -> Maybe Natural
forall a. Maybe a
Nothing
   (#       | Natural
n #) -> Natural -> Maybe Natural
forall a. a -> Maybe a
Just Natural
n

-- | 'Natural' multiplication
timesNatural :: Natural -> Natural -> Natural
timesNatural :: Natural -> Natural -> Natural
timesNatural = Natural -> Natural -> Natural
N.naturalMul

negateNatural :: Natural -> Natural
negateNatural :: Natural -> Natural
negateNatural = Natural -> Natural
N.naturalNegate

signumNatural :: Natural -> Natural
signumNatural :: Natural -> Natural
signumNatural = Natural -> Natural
N.naturalSignum

quotRemNatural :: Natural -> Natural -> (Natural, Natural)
quotRemNatural :: Natural -> Natural -> (Natural, Natural)
quotRemNatural = Natural -> Natural -> (Natural, Natural)
N.naturalQuotRem

remNatural :: Natural -> Natural -> Natural
remNatural :: Natural -> Natural -> Natural
remNatural = Natural -> Natural -> Natural
N.naturalRem

quotNatural :: Natural -> Natural -> Natural
quotNatural :: Natural -> Natural -> Natural
quotNatural = Natural -> Natural -> Natural
N.naturalQuot

-- | Compute greatest common divisor.
gcdNatural :: Natural -> Natural -> Natural
gcdNatural :: Natural -> Natural -> Natural
gcdNatural = Natural -> Natural -> Natural
N.naturalGcd

-- | Compute least common multiple.
lcmNatural :: Natural -> Natural -> Natural
lcmNatural :: Natural -> Natural -> Natural
lcmNatural = Natural -> Natural -> Natural
N.naturalLcm

andNatural :: Natural -> Natural -> Natural
andNatural :: Natural -> Natural -> Natural
andNatural = Natural -> Natural -> Natural
N.naturalAnd

orNatural :: Natural -> Natural -> Natural
orNatural :: Natural -> Natural -> Natural
orNatural = Natural -> Natural -> Natural
N.naturalOr

xorNatural :: Natural -> Natural -> Natural
xorNatural :: Natural -> Natural -> Natural
xorNatural = Natural -> Natural -> Natural
N.naturalXor

bitNatural :: Int# -> Natural
bitNatural :: Int# -> Natural
bitNatural Int#
i = Word# -> Natural
N.naturalBit# (Int# -> Word#
int2Word# Int#
i)

testBitNatural :: Natural -> Int -> Bool
testBitNatural :: Natural -> Int -> Bool
testBitNatural Natural
n Int
i = Natural -> Word -> Bool
N.naturalTestBit Natural
n (Int -> Word
int2Word Int
i)

popCountNatural :: Natural -> Int
popCountNatural :: Natural -> Int
popCountNatural Natural
n = Word -> Int
word2Int (Natural -> Word
N.naturalPopCount Natural
n)

shiftLNatural :: Natural -> Int -> Natural
shiftLNatural :: Natural -> Int -> Natural
shiftLNatural Natural
n Int
i = Natural -> Word -> Natural
N.naturalShiftL Natural
n (Int -> Word
int2Word  Int
i)

shiftRNatural :: Natural -> Int -> Natural
shiftRNatural :: Natural -> Int -> Natural
shiftRNatural Natural
n Int
i = Natural -> Word -> Natural
N.naturalShiftR Natural
n (Int -> Word
int2Word Int
i)

-- | @since base-4.12.0.0
naturalToInteger :: Natural -> Integer
naturalToInteger :: Natural -> Integer
naturalToInteger = Natural -> Integer
I.integerFromNatural

naturalToWord :: Natural -> Word
naturalToWord :: Natural -> Word
naturalToWord = Natural -> Word
N.naturalToWord

-- | @since base-4.10.0.0
naturalFromInteger :: Integer -> Natural
naturalFromInteger :: Integer -> Natural
naturalFromInteger = Integer -> Natural
I.integerToNatural

-- | Construct 'Natural' from 'Word' value.
--
-- @since base-4.8.0.0
wordToNatural :: Word -> Natural
wordToNatural :: Word -> Natural
wordToNatural = Word -> Natural
N.naturalFromWord

-- | Try downcasting 'Natural' to 'Word' value.
-- Returns 'Nothing' if value doesn't fit in 'Word'.
--
-- @since base-4.8.0.0
naturalToWordMaybe :: Natural -> Maybe Word
naturalToWordMaybe :: Natural -> Maybe Word
naturalToWordMaybe Natural
n = case Natural -> (# (# #) | Word# #)
N.naturalToWordMaybe# Natural
n of
   (#       | Word#
w #) -> Word -> Maybe Word
forall a. a -> Maybe a
Just (Word# -> Word
W# Word#
w)
   (# (# #) |   #) -> Maybe Word
forall a. Maybe a
Nothing

wordToNatural# :: Word -> Natural
wordToNatural# :: Word -> Natural
wordToNatural# = Word -> Natural
N.naturalFromWord

-- | \"@'powModNatural' /b/ /e/ /m/@\" computes base @/b/@ raised to
-- exponent @/e/@ modulo @/m/@.
--
-- @since base-4.8.0.0
powModNatural :: Natural -> Natural -> Natural -> Natural
powModNatural :: Natural -> Natural -> Natural -> Natural
powModNatural = Natural -> Natural -> Natural -> Natural
N.naturalPowMod