-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | GHC BigNum library -- -- This package provides the low-level implementation of the standard -- BigNat, Natural and Integer types. @package ghc-bignum @version 1.3 module GHC.Num.Primitives type Bool# = Int# (&&#) :: Bool# -> Bool# -> Bool# infixr 3 &&# (||#) :: Bool# -> Bool# -> Bool# infixr 2 ||# notB# :: Bool# -> Bool# testBitI# :: Int# -> Word# -> Bool# minI# :: Int# -> Int# -> Int# maxI# :: Int# -> Int# -> Int# -- | Branchless signum sgnI# :: Int# -> Int# -- | Branchless abs absI# :: Int# -> Int# -- | Branchless comparison cmpI# :: Int# -> Int# -> Int# -- | Encode (# Int# mantissa, Int# exponent #) into a Double#. -- -- (provided by GHC's RTS) intEncodeDouble# :: Int# -> Int# -> Double# -- | Population count popCntI# :: Int# -> Word# andNot# :: Word# -> Word# -> Word# cmpW# :: Word# -> Word# -> Ordering bitW# :: Int# -> Word# maxW# :: Word# -> Word# -> Word# minW# :: Word# -> Word# -> Word# testBitW# :: Word# -> Word# -> Bool# -- | Safe right shift for Word# shiftRW# :: Word# -> Word# -> Word# -- | Add 3 values together plusWord3# :: Word# -> Word# -> Word# -> (# Word#, Word# #) -- | (h,l) <- a + (hb,lb) plusWord12# :: Word# -> (# Word#, Word# #) -> (# Word#, Word# #) -- | 2-by-1 large division -- -- Requires: b0 /= 0 a1 >= b0 (not required, but if not q1=0) quotRemWord3# :: (# Word#, Word# #) -> Word# -> (# (# Word#, Word# #), Word# #) -- | Return the absolute value of the Int# in a Word# wordFromAbsInt# :: Int# -> Word# -- | Compute base-2 log of Word# -- -- This is internally implemented as count-leading-zeros machine -- instruction. wordLog2# :: Word# -> Word# -- | Logarithm for an arbitrary base wordLogBase# :: Word# -> Word# -> Word# wordSizeInBase# :: Word# -> Word# -> Word# -- | Indicate if the value is a power of two and which one wordIsPowerOf2# :: Word# -> (# (# #) | Word# #) -- | Encode (# Word# mantissa, Int# exponent #) into a Double#. -- -- (provided by GHC's RTS) wordEncodeDouble# :: Word# -> Int# -> Double# -- | Reverse bits in a Word# wordReverseBits# :: Word# -> Word# -- | Reverse bits in the Word32 subwords composing a Word# wordReverseBits32# :: Word# -> Word# -- | Reverse bytes in a Word# wordReverseBytes# :: Word# -> Word# -- | Read a Word from addr in base-256 representation. -- -- @n is the number of bytes to read. -- -- The endianness is selected with the Bool# parameter: write most -- significant byte first (big-endian) if 1# or least -- significant byte first (little-endian) if 0#. wordFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) -- | Read a Word from addr in base-256 little-endian -- representation. -- -- @n is the number of bytes to read. wordFromAddrLE# :: Word# -> Addr# -> State# s -> (# State# s, Word# #) -- | Read a Word from addr in base-256 big-endian -- representation. -- -- @n is the number of bytes to read. wordFromAddrBE# :: Word# -> Addr# -> State# s -> (# State# s, Word# #) -- | Write a Word to addr in base-256 representation and -- return the number of bytes written. -- -- The endianness is selected with the Bool# parameter: write most -- significant byte first (big-endian) if 1# or least -- significant byte first (little-endian) if 0#. wordToAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) -- | Write a Word to addr in base-256 little-endian -- representation and return the number of bytes written. wordToAddrLE# :: Word# -> Addr# -> State# s -> (# State# s, Word# #) -- | Write a Word to addr in base-256 big-endian -- representation and return the number of bytes written. wordToAddrBE# :: Word# -> Addr# -> State# s -> (# State# s, Word# #) -- | Write a full word with little-endian encoding wordWriteAddrLE# :: Word# -> Addr# -> State# s -> State# s -- | Write a full word with little-endian encoding wordWriteAddrBE# :: Word# -> Addr# -> State# s -> State# s -- | Read a Word from ByteArray in base-256 representation. -- -- @n is the number of bytes to read. -- -- The endianness is selected with the Bool# parameter: write most -- significant byte first (big-endian) if 1# or least -- significant byte first (little-endian) if 0#. wordFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> Word# -- | Read a Word from ByteArray in base-256 little-endian -- representation. -- -- @n is the number of bytes to read. wordFromByteArrayLE# :: Word# -> ByteArray# -> Word# -> Word# -- | Read a Word from ByteArray in base-256 big-endian -- representation. -- -- @n is the number of bytes to read. wordFromByteArrayBE# :: Word# -> ByteArray# -> Word# -> Word# -- | Write a Word to MutableByteArray in base-256 -- representation and return the number of bytes written. -- -- The endianness is selected with the Bool# parameter: write most -- significant byte first (big-endian) if 1# or least -- significant byte first (little-endian) if 0#. -- -- The offset is in bytes. wordToMutableByteArray# :: Word# -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) -- | Write a Word to MutableByteArray in base-256 -- little-endian representation and return the number of bytes written. -- -- The offset is in bytes. wordToMutableByteArrayLE# :: Word# -> MutableByteArray# s -> Word# -> State# s -> (# State# s, Word# #) -- | Write a Word to MutableByteArray in base-256 -- big-endian representation and return the number of bytes written. -- -- The offset is in bytes. wordToMutableByteArrayBE# :: Word# -> MutableByteArray# s -> Word# -> State# s -> (# State# s, Word# #) -- | Write a full word with little-endian encoding wordWriteMutableByteArrayLE# :: Word# -> MutableByteArray# s -> Word# -> State# s -> State# s -- | Write a full word with little-endian encoding wordWriteMutableByteArrayBE# :: Word# -> MutableByteArray# s -> Word# -> State# s -> State# s -- | Raise underflowException raiseUnderflow :: a raiseUnderflow_Word# :: (# #) -> Word# -- | Raise divZeroException raiseDivZero :: a raiseDivZero_Word# :: (# #) -> Word# unexpectedValue :: a unexpectedValue_Int# :: (# #) -> Int# unexpectedValue_Word# :: (# #) -> Word# ioWord# :: IO Word -> State# RealWorld -> (# State# RealWorld, Word# #) ioInt# :: IO Int -> State# RealWorld -> (# State# RealWorld, Int# #) ioVoid :: IO a -> State# RealWorld -> State# RealWorld ioBool :: IO Bool -> State# RealWorld -> (# State# RealWorld, Bool# #) module GHC.Num.WordArray -- | Unlifted array of Word type WordArray# = ByteArray# type MutableWordArray# = MutableByteArray# data WordArray WordArray :: WordArray# -> WordArray data MutableWordArray s MutableWordArray :: MutableWordArray# s -> MutableWordArray s -- | Convert limb count into byte count wordsToBytes# :: Int# -> Int# -- | Convert byte count into limb count bytesToWords# :: Int# -> Int# -- | Create a new WordArray# of the given size (*in Word#*) and apply the -- action to it before returning it frozen withNewWordArray# :: Int# -> (MutableWordArray# RealWorld -> State# RealWorld -> State# RealWorld) -> WordArray# -- | Create two new WordArray# of the given sizes (*in Word#*) and apply -- the action to them before returning them frozen withNewWordArray2# :: Int# -> Int# -> (MutableWordArray# RealWorld -> MutableWordArray# RealWorld -> State# RealWorld -> State# RealWorld) -> (# WordArray#, WordArray# #) -- | Create a new WordArray# newWordArray# :: Int# -> State# s -> (# State# s, MutableWordArray# s #) -- | Create a new WordArray# of the given size (*in Word#*), apply the -- action to it, trim its most significant zeroes, then return it frozen withNewWordArrayTrimmed# :: Int# -> (MutableWordArray# RealWorld -> State# RealWorld -> State# RealWorld) -> WordArray# -- | Create two new WordArray# of the given sizes (*in Word#*), apply the -- action to them, trim their most significant zeroes, then return them -- frozen withNewWordArray2Trimmed# :: Int# -> Int# -> (MutableWordArray# RealWorld -> MutableWordArray# RealWorld -> State# RealWorld -> State# RealWorld) -> (# WordArray#, WordArray# #) -- | Create a new WordArray# of the given size (*in Word#*), apply the -- action to it. If the action returns true#, trim its most significant -- zeroes, then return it frozen. Otherwise, return (). withNewWordArrayTrimmedMaybe# :: Int# -> (MutableWordArray# RealWorld -> State# RealWorld -> (# State# RealWorld, Bool# #)) -> (# (# #) | WordArray# #) -- | Create a WordArray# from two Word# -- -- `wordArrayFromWord2# h l where h is the most significant word l is the -- least significant word wordArrayFromWord2# :: Word# -> Word# -> WordArray# -- | Create a WordArray# from one Word# wordArrayFromWord# :: Word# -> WordArray# -- | Word array size wordArraySize# :: WordArray# -> Int# -- | Equality test for WordArray# -- -- Get size in Words mwaSize# :: MutableWordArray# s -> State# s -> (# State# s, Int# #) -- | Get the last Word (must be non empty!) wordArrayLast# :: WordArray# -> Word# -- | Copy Words from a WordArray -- -- Don't do anything if the number of words to copy is <= 0 mwaArrayCopy# :: MutableByteArray# s -> Int# -> WordArray# -> Int# -> Int# -> State# s -> State# s -- | Shrink last words of a WordArray mwaShrink# :: MutableByteArray# s -> Int# -> State# s -> State# s -- | Set size mwaSetSize# :: MutableByteArray# s -> Int# -> State# s -> State# s -- | Copy the WordArray into the MWA and shrink the size of MWA to the one -- of the WordArray mwaInitCopyShrink# :: MutableByteArray# s -> WordArray# -> State# s -> State# s -- | Trim ending zeroes mwaTrimZeroes# :: MutableByteArray# s -> State# s -> State# s -- | Count leading zero Words mwaClz :: MutableWordArray# s -> State# s -> (# State# s, Int# #) -- | Count leading zero Words starting at given position mwaClzAt :: MutableWordArray# s -> Int# -> State# s -> (# State# s, Int# #) -- | Count leading zero Words starting at given position waClzAt :: WordArray# -> Int# -> Int# -- | Compare the most signiciant limbs of a and b. The comparison stops -- (i.e. returns EQ) when there isn't enough lims in a or b to perform -- another comparison. wordArrayCompareMSWords :: WordArray# -> WordArray# -> Ordering -- | Compute MutableWordArray <- WordArray + Word -- -- The MutableWordArray may not be initialized and will be erased anyway. -- -- Input: Size(MutableWordArray) = Size(WordArray) + 1 Output: -- Size(MutableWordArray) = Size(WordArray) [+ 1] mwaInitArrayPlusWord :: MutableWordArray# s -> WordArray# -> Word# -> State# s -> State# s -- | Write the most-significant Word: * if it is 0: shrink the array of 1 -- Word * otherwise: write it mwaWriteOrShrink :: MutableWordArray# s -> Word# -> Int# -> State# s -> State# s -- | Compute the index of the most-significant Word and write it. mwaWriteMostSignificant :: MutableWordArray# s -> Word# -> State# s -> State# s -- | MutableWordArray <- zipWith op wa1 wa2 -- -- Required output: Size(MutableWordArray) = min Size(wa1) Size(wa2) mwaInitArrayBinOp :: MutableWordArray# s -> WordArray# -> WordArray# -> (Word# -> Word# -> Word#) -> State# s -> State# s -- | Write an element of the MutableWordArray mwaWrite# :: MutableWordArray# s -> Int# -> Word# -> State# s -> State# s -- | Fill some part of a MutableWordArray with the given Word# mwaFill# :: MutableWordArray# s -> Word# -> Word# -> Word# -> State# s -> State# s -- | Add Word# inplace (a the specified offset) in the mwa with carry -- propagation. mwaAddInplaceWord# :: MutableWordArray# d -> Int# -> Word# -> State# d -> State# d -- | Sub Word# inplace (at the specified offset) in the mwa with carry -- propagation. -- -- Return False# on underflow mwaSubInplaceWord# :: MutableWordArray# d -> Int# -> Word# -> State# d -> (# State# d, Bool# #) -- | Trim a of k less significant limbs and then compare -- the result with b -- -- "mwa" doesn't need to be trimmed mwaTrimCompare :: Int# -> MutableWordArray# s -> WordArray# -> State# s -> (# State# s, Ordering #) -- | Sub array inplace (at the specified offset) in the mwa with carry -- propagation. -- -- We don't trim the resulting array! -- -- Return False# on underflow. mwaSubInplaceArray :: MutableWordArray# d -> Int# -> WordArray# -> State# d -> (# State# d, Bool# #) -- | Add array inplace (a the specified offset) in the mwa with carry -- propagation. -- -- Upper bound of the result mutable aray is not checked against -- overflow. mwaAddInplaceArray :: MutableWordArray# d -> Int# -> WordArray# -> State# d -> State# d -- | Sub array inplace (at the specified offset) in the mwa with carry -- propagation. -- -- We don't trim the resulting array! -- -- Return False# on underflow. mwaSubInplaceMutableArray :: MutableWordArray# d -> Int# -> MutableWordArray# d -> State# d -> (# State# d, Bool# #) -- | Sub an array inplace and then trim zeroes -- -- Don't check overflow. The caller must ensure that a>=b mwaSubInplaceArrayTrim :: MutableWordArray# d -> Int# -> WordArray# -> State# d -> State# d -- | Read an indexed Word in the MutableWordArray. If the index is -- out-of-bound, return zero. mwaReadOrZero :: MutableWordArray# s -> Int# -> State# s -> (# State# s, Word# #) mwaRead# :: MutableWordArray# s -> Int# -> State# s -> (# State# s, Word# #) -- | Selected backend -- -- We need this module in addition to GHC.Num.Backend to avoid module -- loops with Check backend. module GHC.Num.Backend.Selected -- | ghc-bignum backend name backendName :: [Char] -- | Type representing a GMP Limb type GmpLimb = Word type GmpLimb# = Word# -- | Count of GmpLimbs, must be positive (unless specified -- otherwise). type GmpSize = Int type GmpSize# = Int# narrowGmpSize# :: Int# -> Int# narrowCInt# :: Int# -> Int# bignat_compare :: WordArray# -> WordArray# -> Int# c_mpn_cmp :: ByteArray# -> ByteArray# -> GmpSize# -> Int# bignat_add :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_add :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO GmpLimb bignat_add_word :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> State# RealWorld c_mpn_add_1 :: MutableByteArray# s -> ByteArray# -> GmpSize# -> GmpLimb# -> IO GmpLimb bignat_sub :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> (# State# RealWorld, Bool# #) c_mpn_sub :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO GmpLimb bignat_sub_word :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> (# State# RealWorld, Bool# #) c_mpn_sub_1 :: MutableByteArray# s -> ByteArray# -> GmpSize# -> GmpLimb# -> IO GmpLimb bignat_mul :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_mul :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO GmpLimb bignat_mul_word :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> State# RealWorld c_mpn_mul_1 :: MutableByteArray# s -> ByteArray# -> GmpSize# -> GmpLimb# -> IO GmpLimb bignat_popcount :: WordArray# -> Word# c_mpn_popcount :: ByteArray# -> GmpSize# -> Word# bignat_shiftl :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> State# RealWorld c_mpn_lshift :: MutableByteArray# s -> ByteArray# -> GmpSize# -> Word# -> IO GmpLimb bignat_shiftr :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> State# RealWorld c_mpn_rshift :: MutableByteArray# s -> ByteArray# -> GmpSize# -> Word# -> IO GmpLimb bignat_or :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_ior_n :: MutableByteArray# s -> ByteArray# -> ByteArray# -> GmpSize# -> IO () bignat_xor :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_xor_n :: MutableByteArray# s -> ByteArray# -> ByteArray# -> GmpSize# -> IO () bignat_and :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_and_n :: MutableByteArray# s -> ByteArray# -> ByteArray# -> GmpSize# -> IO () bignat_and_not :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_andn_n :: MutableByteArray# s -> ByteArray# -> ByteArray# -> GmpSize# -> IO () bignat_quotrem :: MutableWordArray# RealWorld -> MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_tdiv_qr :: MutableByteArray# s -> MutableByteArray# s -> GmpSize# -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO () bignat_quot :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_tdiv_q :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO () bignat_rem :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_tdiv_r :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO () bignat_quotrem_word :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> (# State# RealWorld, Word# #) c_mpn_divrem_1 :: MutableByteArray# s -> GmpSize# -> ByteArray# -> GmpSize# -> GmpLimb# -> IO GmpLimb bignat_quot_word :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> State# RealWorld bignat_rem_word :: WordArray# -> Word# -> Word# c_mpn_mod_1 :: ByteArray# -> GmpSize# -> GmpLimb# -> GmpLimb# bignat_gcd :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld c_mpn_gcd# :: MutableByteArray# s -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO GmpSize bignat_gcd_word :: WordArray# -> Word# -> Word# c_mpn_gcd_1# :: ByteArray# -> GmpSize# -> GmpLimb# -> GmpLimb# bignat_gcd_word_word :: Word# -> Word# -> Word# integer_gmp_gcd_word :: GmpLimb# -> GmpLimb# -> GmpLimb# bignat_encode_double :: WordArray# -> Int# -> Double# c_mpn_get_d :: ByteArray# -> GmpSize# -> Int# -> Double# bignat_shiftr_neg :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> State# RealWorld c_mpn_rshift_2c :: MutableByteArray# s -> ByteArray# -> GmpSize# -> Word# -> IO GmpLimb bignat_powmod_word :: WordArray# -> WordArray# -> Word# -> Word# integer_gmp_powm1# :: ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> GmpLimb# -> GmpLimb# bignat_powmod_words :: Word# -> Word# -> Word# -> Word# integer_gmp_powm_word :: GmpLimb# -> GmpLimb# -> GmpLimb# -> GmpLimb# bignat_powmod :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld sbignat_powmod :: MutableWordArray# RealWorld -> Int# -> WordArray# -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld integer_powmod :: Integer -> Natural -> Natural -> Natural integer_gmp_powm# :: MutableByteArray# RealWorld -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO GmpSize integer_gcde :: Integer -> Integer -> (# Integer, Integer, Integer #) integer_gmp_gcdext# :: MutableByteArray# s -> Addr# -> MutableByteArray# s -> Addr# -> MutableByteArray# s -> Addr# -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO () integer_recip_mod :: Integer -> Natural -> (# Natural | () #) -- | Return 0 for invalid inputs sbignat_recip_mod :: Int# -> BigNat# -> BigNat# -> BigNat# integer_gmp_invert# :: MutableByteArray# RealWorld -> ByteArray# -> GmpSize# -> ByteArray# -> GmpSize# -> IO GmpSize -- | Selected backend module GHC.Num.Backend -- | Multi-precision natural module GHC.Num.BigNat -- | A BigNat -- -- Represented as an array of limbs (Word#) stored in little-endian order -- (Word# themselves use machine order). -- -- Invariant (canonical representation): higher Word# is non-zero. -- -- As a consequence, zero is represented with a WordArray# whose size is -- 0. type BigNat# = WordArray# -- | A lifted BigNat -- -- Represented as an array of limbs (Word#) stored in little-endian order -- (Word# themselves use machine order). -- -- Invariant (canonical representation): higher Word# is non-zero. -- -- As a consequence, zero is represented with a WordArray# whose size is -- 0. data BigNat BN# :: BigNat# -> BigNat [unBigNat] :: BigNat -> BigNat# -- | Check that the BigNat is valid bigNatCheck# :: BigNat# -> Bool# -- | Check that the BigNat is valid bigNatCheck :: BigNat# -> Bool -- | Number of words in the BigNat bigNatSize :: BigNat# -> Word -- | Number of words in the BigNat bigNatSize# :: BigNat# -> Int# bigNatZero :: BigNat bigNatOne :: BigNat -- | BigNat Zero bigNatZero# :: (# #) -> BigNat# -- | BigNat one bigNatOne# :: (# #) -> BigNat# raiseDivZero_BigNat :: (# #) -> BigNat# -- | Indicate if a bigNat is zero bigNatIsZero :: BigNat# -> Bool -- | Indicate if a bigNat is zero bigNatIsZero# :: BigNat# -> Bool# -- | Indicate if a bigNat is one bigNatIsOne :: BigNat# -> Bool -- | Indicate if a bigNat is one bigNatIsOne# :: BigNat# -> Bool# -- | Indicate if a bigNat is two bigNatIsTwo :: BigNat# -> Bool -- | Indicate if a bigNat is two bigNatIsTwo# :: BigNat# -> Bool# -- | Indicate if the value is a power of two and which one bigNatIsPowerOf2# :: BigNat# -> (# (# #) | Word# #) -- | Return the Word# at the given index bigNatIndex# :: BigNat# -> Int# -> Word# -- | Return the Word# at the given index bigNatIndex :: BigNat# -> Int# -> Word -- | Create a BigNat from a Word bigNatFromWord :: Word -> BigNat# -- | Create a BigNat from a Word bigNatFromWord# :: Word# -> BigNat# -- | Convert a list of non-zero Words (most-significant first) into a -- BigNat bigNatFromWordList :: [Word] -> BigNat# -- | Convert a list of non-zero Words (most-significant first) into a -- BigNat bigNatFromWordList# :: [Word] -> WordArray# -- | Return the absolute value of the Int# in a BigNat bigNatFromAbsInt# :: Int# -> BigNat# -- | Convert a list of non-zero Words (most-significant first) into a -- BigNat. Don't remove most-significant zero words bigNatFromWordListUnsafe :: [Word] -> BigNat# -- | Convert a BigNat into a list of non-zero Words (most-significant -- first) bigNatToWordList :: BigNat# -> [Word] -- | Convert two Word# (most-significant first) into a BigNat bigNatFromWord2# :: Word# -> Word# -> BigNat# -- | Convert a BigNat into a Word# bigNatToWord# :: BigNat# -> Word# -- | Convert a BigNat into a Word# if it fits bigNatToWordMaybe# :: BigNat# -> (# (# #) | Word# #) -- | Convert a BigNat into a Word bigNatToWord :: BigNat# -> Word -- | Convert a BigNat into a Int# bigNatToInt# :: BigNat# -> Int# -- | Convert a BigNat into a Int bigNatToInt :: BigNat# -> Int -- | Convert a Word64# into a BigNat on 64-bit architectures bigNatFromWord64# :: Word64# -> BigNat# -- | Convert a BigNat into a Word64# on 64-bit architectures bigNatToWord64# :: BigNat# -> Word64# -- | Encode (# BigNat mantissa, Int# exponent #) into a Double# bigNatEncodeDouble# :: BigNat# -> Int# -> Double# -- | Test if a BigNat is greater than a Word bigNatGtWord# :: BigNat# -> Word# -> Bool# -- | Test if a BigNat is equal to a Word bigNatEqWord# :: BigNat# -> Word# -> Bool# -- | Test if a BigNat is greater than a Word bigNatGtWord :: BigNat# -> Word -> Bool -- | Test if a BigNat is lower than or equal to a Word bigNatLeWord# :: BigNat# -> Word# -> Bool# -- | Test if a BigNat is lower than or equal to a Word bigNatLeWord :: BigNat# -> Word -> Bool -- | Equality test for BigNat bigNatEq# :: BigNat# -> BigNat# -> Bool# -- | Equality test for BigNat bigNatEq :: BigNat# -> BigNat# -> Bool -- | Inequality test for BigNat bigNatNe# :: BigNat# -> BigNat# -> Bool# -- | Equality test for BigNat bigNatNe :: BigNat# -> BigNat# -> Bool -- | Compare a BigNat and a Word# bigNatCompareWord# :: BigNat# -> Word# -> Ordering -- | Compare a BigNat and a Word bigNatCompareWord :: BigNat# -> Word -> Ordering -- | Compare two BigNat bigNatCompare :: BigNat# -> BigNat# -> Ordering -- | Predicate: a < b bigNatLt# :: BigNat# -> BigNat# -> Bool# -- | Predicate: a < b bigNatLt :: BigNat# -> BigNat# -> Bool -- | Predicate: a <= b bigNatLe# :: BigNat# -> BigNat# -> Bool# -- | Predicate: a <= b bigNatLe :: BigNat# -> BigNat# -> Bool -- | Predicate: a > b bigNatGt# :: BigNat# -> BigNat# -> Bool# -- | Predicate: a > b bigNatGt :: BigNat# -> BigNat# -> Bool -- | Predicate: a >= b bigNatGe# :: BigNat# -> BigNat# -> Bool# -- | Predicate: a >= b bigNatGe :: BigNat# -> BigNat# -> Bool -- | Add a bigNat and a Word# bigNatAddWord# :: BigNat# -> Word# -> BigNat# -- | Add a bigNat and a Word bigNatAddWord :: BigNat# -> Word -> BigNat# -- | Add two bigNats bigNatAdd :: BigNat# -> BigNat# -> BigNat# -- | Multiply a BigNat by a Word# bigNatMulWord# :: BigNat# -> Word# -> BigNat# -- | Multiply a BigNAt by a Word bigNatMulWord :: BigNat# -> Word -> BigNat# -- | Square a BigNat bigNatSqr :: BigNat# -> BigNat# -- | Multiplication (classical algorithm) bigNatMul :: BigNat# -> BigNat# -> BigNat# -- | Subtract a Word# from a BigNat -- -- The BigNat must be bigger than the Word#. bigNatSubWordUnsafe# :: BigNat# -> Word# -> BigNat# -- | Subtract a Word# from a BigNat -- -- The BigNat must be bigger than the Word#. bigNatSubWordUnsafe :: BigNat# -> Word -> BigNat# -- | Subtract a Word# from a BigNat bigNatSubWord# :: BigNat# -> Word# -> (# (# #) | BigNat# #) -- | Subtract two BigNat (don't check if a >= b) bigNatSubUnsafe :: BigNat# -> BigNat# -> BigNat# -- | Subtract two BigNat bigNatSub :: BigNat# -> BigNat# -> (# (# #) | BigNat# #) -- | Divide a BigNat by a Word, return the quotient -- -- Require: b /= 0 bigNatQuotWord# :: BigNat# -> Word# -> BigNat# -- | Divide a BigNat by a Word, return the quotient -- -- Require: b /= 0 bigNatQuotWord :: BigNat# -> Word -> BigNat# -- | Divide a BigNat by a Word, return the remainder -- -- Require: b /= 0 bigNatRemWord# :: BigNat# -> Word# -> Word# -- | Divide a BigNat by a Word, return the remainder -- -- Require: b /= 0 bigNatRemWord :: BigNat# -> Word -> Word -- | QuotRem a BigNat by a Word -- -- Require: b /= 0 bigNatQuotRemWord# :: BigNat# -> Word# -> (# BigNat#, Word# #) -- | BigNat division returning (quotient,remainder) bigNatQuotRem# :: BigNat# -> BigNat# -> (# BigNat#, BigNat# #) -- | BigNat division returning quotient bigNatQuot :: BigNat# -> BigNat# -> BigNat# -- | BigNat division returning remainder bigNatRem :: BigNat# -> BigNat# -> BigNat# -- | Greatest common divisor between two Word# gcdWord# :: Word# -> Word# -> Word# -- | Greatest common divisor between two Word gcdWord :: Word -> Word -> Word -- | Greatest common divisor between two Int# -- -- Warning: result may become negative if (at least) one argument -- is minBound gcdInt# :: Int# -> Int# -> Int# -- | Greatest common divisor between two Int -- -- Warning: result may become negative if (at least) one argument -- is minBound gcdInt :: Int -> Int -> Int -- | Greatest common divisor bigNatGcd :: BigNat# -> BigNat# -> BigNat# -- | Greatest common divisor bigNatGcdWord# :: BigNat# -> Word# -> Word# -- | Least common multiple bigNatLcm :: BigNat# -> BigNat# -> BigNat# -- | Least common multiple with a Word# bigNatLcmWord# :: BigNat# -> Word# -> BigNat# -- | Least common multiple between two Word# bigNatLcmWordWord# :: Word# -> Word# -> BigNat# -- | Bitwise OR bigNatOr :: BigNat# -> BigNat# -> BigNat# -- | Bitwise OR with Word# bigNatOrWord# :: BigNat# -> Word# -> BigNat# -- | Bitwise AND bigNatAnd :: BigNat# -> BigNat# -> BigNat# -- | Bitwise ANDNOT bigNatAndNot :: BigNat# -> BigNat# -> BigNat# -- | Bitwise AND with Word# bigNatAndWord# :: BigNat# -> Word# -> BigNat# -- | Bitwise ANDNOT with Word# bigNatAndNotWord# :: BigNat# -> Word# -> BigNat# -- | Bitwise AND with Int# bigNatAndInt# :: BigNat# -> Int# -> BigNat# -- | Bitwise XOR bigNatXor :: BigNat# -> BigNat# -> BigNat# -- | Bitwise XOR with Word# bigNatXorWord# :: BigNat# -> Word# -> BigNat# -- | PopCount for BigNat bigNatPopCount :: BigNat# -> Word -- | PopCount for BigNat bigNatPopCount# :: BigNat# -> Word# -- | Bit shift right bigNatShiftR# :: BigNat# -> Word# -> BigNat# -- | Bit shift right (two's complement) bigNatShiftRNeg# :: BigNat# -> Word# -> BigNat# -- | Bit shift right bigNatShiftR :: BigNat# -> Word -> BigNat# -- | Bit shift left bigNatShiftL :: BigNat# -> Word -> BigNat# -- | Bit shift left bigNatShiftL# :: BigNat# -> Word# -> BigNat# -- | BigNat bit test bigNatTestBit# :: BigNat# -> Word# -> Bool# -- | BigNat bit test bigNatTestBit :: BigNat# -> Word -> Bool -- | Return a BigNat whose bit i is the only one set. -- -- Specialized version of `bigNatShiftL (bigNatFromWord# 1##)` bigNatBit# :: Word# -> BigNat# -- | Return a BigNat whose bit i is the only one set. -- -- Specialized version of `bigNatShiftL (bigNatFromWord# 1##)` bigNatBit :: Word -> BigNat# -- | BigNat clear bit bigNatClearBit# :: BigNat# -> Word# -> BigNat# -- | BigNat set bit bigNatSetBit# :: BigNat# -> Word# -> BigNat# -- | Reverse the given bit bigNatComplementBit# :: BigNat# -> Word# -> BigNat# -- | Base 2 logarithm bigNatLog2# :: BigNat# -> Word# -- | Base 2 logarithm bigNatLog2 :: BigNat# -> Word -- | Logarithm for an arbitrary base bigNatLogBase# :: BigNat# -> BigNat# -> Word# -- | Logarithm for an arbitrary base bigNatLogBase :: BigNat# -> BigNat# -> Word -- | Logarithm for an arbitrary base bigNatLogBaseWord# :: Word# -> BigNat# -> Word# -- | Logarithm for an arbitrary base bigNatLogBaseWord :: Word -> BigNat# -> Word -- | Compute the number of digits of the BigNat in the given base. -- -- base must be > 1 bigNatSizeInBase# :: Word# -> BigNat# -> Word# -- | Compute the number of digits of the BigNat in the given base. -- -- base must be > 1 bigNatSizeInBase :: Word -> BigNat# -> Word powModWord# :: Word# -> Word# -> Word# -> Word# -- | "bigNatPowModWord# b e m" -- computes base b raised to exponent e -- modulo m. bigNatPowModWord# :: BigNat# -> BigNat# -> Word# -> Word# -- | "bigNatPowMod b e m" computes -- base b raised to exponent e modulo -- m. bigNatPowMod :: BigNat# -> BigNat# -> BigNat# -> BigNat# -- | Return count of trailing zero bits -- -- Return 0 for zero BigNat bigNatCtz# :: BigNat# -> Word# -- | Return count of trailing zero bits -- -- Return 0 for zero BigNat bigNatCtz :: BigNat# -> Word -- | Return count of trailing zero words -- -- Return 0 for zero BigNat bigNatCtzWord# :: BigNat# -> Word# -- | Return count of trailing zero words -- -- Return 0 for zero BigNat bigNatCtzWord :: BigNat# -> Word -- | Write a BigNat in base-256 little-endian representation and return the -- number of bytes written. -- -- Use "bigNatSizeInBase 256# i" to compute the -- exact number of bytes written in advance. In case of i == -- 0, the function will write and report zero bytes written. bigNatToAddrLE# :: BigNat# -> Addr# -> State# s -> (# State# s, Word# #) -- | Write a BigNat in base-256 big-endian representation and return the -- number of bytes written. -- -- Use "bigNatSizeInBase 256# i" to compute the -- exact number of bytes written in advance. In case of i == -- 0, the function will write and report zero bytes written. bigNatToAddrBE# :: BigNat# -> Addr# -> State# s -> (# State# s, Word# #) -- | Write a BigNat in base-256 representation and return the number of -- bytes written. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Use "bigNatSizeInBase 256# i" to compute the -- exact number of bytes written in advance. In case of i == -- 0, the function will write and report zero bytes written. bigNatToAddr# :: BigNat# -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) -- | Write a BigNat in base-256 representation and return the number of -- bytes written. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Use "bigNatSizeInBase 256# i" to compute the -- exact number of bytes written in advance. In case of i == -- 0, the function will write and report zero bytes written. bigNatToAddr :: BigNat# -> Addr# -> Bool# -> IO Word -- | Read a BigNat in base-256 little-endian representation from an Addr#. -- -- The size is given in bytes. -- -- Higher limbs equal to 0 are automatically trimmed. bigNatFromAddrLE# :: Word# -> Addr# -> State# s -> (# State# s, BigNat# #) -- | Read a BigNat in base-256 big-endian representation from an Addr#. -- -- The size is given in bytes. -- -- Null higher limbs are automatically trimmed. bigNatFromAddrBE# :: Word# -> Addr# -> State# s -> (# State# s, BigNat# #) -- | Read a BigNat in base-256 representation from an Addr#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimmed. bigNatFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, BigNat# #) -- | Write a BigNat in base-256 little-endian representation and return the -- number of bytes written. -- -- Use "bigNatSizeInBase 256# i" to compute the -- exact number of bytes written in advance. In case of i == -- 0, the function will write and report zero bytes written. bigNatToMutableByteArrayLE# :: BigNat# -> MutableByteArray# s -> Word# -> State# s -> (# State# s, Word# #) -- | Write a BigNat in base-256 big-endian representation and return the -- number of bytes written. -- -- Use "bigNatSizeInBase 256# i" to compute the -- exact number of bytes written in advance. In case of i == -- 0, the function will write and report zero bytes written. bigNatToMutableByteArrayBE# :: BigNat# -> MutableByteArray# s -> Word# -> State# s -> (# State# s, Word# #) -- | Write a BigNat in base-256 representation and return the number of -- bytes written. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Use "bigNatSizeInBase 256# i" to compute the -- exact number of bytes written in advance. In case of i == -- 0, the function will write and report zero bytes written. bigNatToMutableByteArray# :: BigNat# -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) -- | Read a BigNat in base-256 little-endian representation from a -- ByteArray#. -- -- The size is given in bytes. -- -- Null higher limbs are automatically trimmed. bigNatFromByteArrayLE# :: Word# -> ByteArray# -> Word# -> State# s -> (# State# s, BigNat# #) -- | Read a BigNat in base-256 big-endian representation from a ByteArray#. -- -- The size is given in bytes. -- -- Null higher limbs are automatically trimmed. bigNatFromByteArrayBE# :: Word# -> ByteArray# -> Word# -> State# s -> (# State# s, BigNat# #) -- | Read a BigNat in base-256 representation from a ByteArray#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimmed. bigNatFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, BigNat# #) -- | Create a BigNat# from a WordArray# containing n limbs in -- least-significant-first order. -- -- If possible WordArray#, will be used directly (i.e. shared -- without cloning the WordArray# into a newly allocated -- one) bigNatFromWordArray# :: WordArray# -> Word# -> BigNat# -- | Create a BigNat from a WordArray# containing n limbs in -- least-significant-first order. -- -- If possible WordArray#, will be used directly (i.e. shared -- without cloning the WordArray# into a newly allocated -- one) bigNatFromWordArray :: WordArray# -> Word# -> BigNat instance GHC.Classes.Eq GHC.Num.BigNat.BigNat instance GHC.Classes.Ord GHC.Num.BigNat.BigNat module GHC.Num.Natural -- | Natural number -- -- Invariant: numbers <= 0xffffffffffffffff use the NS -- constructor data Natural NS :: Word# -> Natural NB :: ByteArray# -> Natural -- | Check Natural invariants naturalCheck# :: Natural -> Bool# -- | Check Natural invariants naturalCheck :: Natural -> Bool -- | Zero Natural naturalZero :: Natural -- | One Natural naturalOne :: Natural -- | Test Zero Natural naturalIsZero :: Natural -> Bool -- | Test One Natural naturalIsOne :: Natural -> Bool -- | Indicate if the value is a power of two and which one naturalIsPowerOf2# :: Natural -> (# (# #) | Word# #) -- | Create a Natural from a BigNat# (respect the invariants) naturalFromBigNat# :: BigNat# -> Natural -- | Convert a Natural into a BigNat# naturalToBigNat# :: Natural -> BigNat# -- | Create a Natural from a Word# naturalFromWord# :: Word# -> Natural -- | Convert two Word# (most-significant first) into a Natural naturalFromWord2# :: Word# -> Word# -> Natural -- | Create a Natural from a Word naturalFromWord :: Word -> Natural -- | Convert the lower bits of a Natural into a Word# naturalToWord# :: Natural -> Word# -- | Convert the lower bits of a Natural into a Word naturalToWord :: Natural -> Word -- | Convert a Natural into a Word# clamping to (maxBound :: Word#). naturalToWordClamp# :: Natural -> Word# -- | Convert a Natural into a Word# clamping to (maxBound :: Word). naturalToWordClamp :: Natural -> Word -- | Try downcasting Natural to Word value. Returns -- (##) if value doesn't fit in Word. naturalToWordMaybe# :: Natural -> (# (# #) | Word# #) -- | Create a Natural from a list of Word naturalFromWordList :: [Word] -> Natural -- | Write a Natural in base-256 representation and return the number of -- bytes written. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. naturalToMutableByteArray# :: Natural -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) -- | Read a Natural in base-256 representation from a ByteArray#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimed. naturalFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Natural #) -- | Encode (# Natural mantissa, Int# exponent #) into a Double# naturalEncodeDouble# :: Natural -> Int# -> Double# -- | Encode (# Natural mantissa, Int# exponent #) into a Float# -- -- TODO: Not sure if it's worth to write Float optimized versions -- here naturalEncodeFloat# :: Natural -> Int# -> Float# -- | Write a Natural to addr in base-256 -- representation and return the number of bytes written. -- -- The endianness is selected with the Bool# parameter: write most -- significant byte first (big-endian) if 1# or least -- significant byte first (little-endian) if 0#. naturalToAddr# :: Natural -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) -- | Write a Natural to addr in base-256 -- representation and return the number of bytes written. -- -- The endianness is selected with the Bool# parameter: write most -- significant byte first (big-endian) if 1# or least -- significant byte first (little-endian) if 0#. naturalToAddr :: Natural -> Addr# -> Bool# -> IO Word -- | Read a Natural in base-256 representation from an Addr#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimed. naturalFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Natural #) -- | Read a Natural in base-256 representation from an Addr#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimed. naturalFromAddr :: Word# -> Addr# -> Bool# -> IO Natural -- | Equality test for Natural naturalEq# :: Natural -> Natural -> Bool# -- | Equality test for Natural naturalEq :: Natural -> Natural -> Bool -- | Inequality test for Natural naturalNe# :: Natural -> Natural -> Bool# -- | Inequality test for Natural naturalNe :: Natural -> Natural -> Bool -- | Greater or equal test for Natural naturalGe# :: Natural -> Natural -> Bool# -- | Greater or equal test for Natural naturalGe :: Natural -> Natural -> Bool -- | Lower or equal test for Natural naturalLe# :: Natural -> Natural -> Bool# -- | Lower or equal test for Natural naturalLe :: Natural -> Natural -> Bool -- | Greater test for Natural naturalGt# :: Natural -> Natural -> Bool# -- | Greater test for Natural naturalGt :: Natural -> Natural -> Bool -- | Lower test for Natural naturalLt# :: Natural -> Natural -> Bool# -- | Lower test for Natural naturalLt :: Natural -> Natural -> Bool -- | Compare two Natural naturalCompare :: Natural -> Natural -> Ordering -- | PopCount for Natural naturalPopCount# :: Natural -> Word# -- | PopCount for Natural naturalPopCount :: Natural -> Word -- | Right shift for Natural naturalShiftR# :: Natural -> Word# -> Natural -- | Right shift for Natural naturalShiftR :: Natural -> Word -> Natural -- | Left shift naturalShiftL# :: Natural -> Word# -> Natural -- | Left shift naturalShiftL :: Natural -> Word -> Natural naturalAnd :: Natural -> Natural -> Natural naturalAndNot :: Natural -> Natural -> Natural naturalOr :: Natural -> Natural -> Natural naturalXor :: Natural -> Natural -> Natural naturalTestBit# :: Natural -> Word# -> Bool# naturalTestBit :: Natural -> Word -> Bool naturalBit# :: Word# -> Natural naturalBit :: Word -> Natural naturalSetBit# :: Natural -> Word# -> Natural naturalSetBit :: Natural -> Word -> Natural naturalClearBit# :: Natural -> Word# -> Natural naturalClearBit :: Natural -> Word -> Natural naturalComplementBit# :: Natural -> Word# -> Natural naturalComplementBit :: Natural -> Word -> Natural -- | Add two naturals naturalAdd :: Natural -> Natural -> Natural -- | Sub two naturals naturalSub :: Natural -> Natural -> (# (# #) | Natural #) -- | Sub two naturals -- -- Throw an Underflow exception if x < y naturalSubThrow :: Natural -> Natural -> Natural -- | Sub two naturals -- -- Unsafe: don't check that x >= y Undefined results if it happens naturalSubUnsafe :: Natural -> Natural -> Natural -- | Multiplication naturalMul :: Natural -> Natural -> Natural -- | Square a Natural naturalSqr :: Natural -> Natural -- | Signum for Natural naturalSignum :: Natural -> Natural -- | Negate for Natural naturalNegate :: Natural -> Natural -- | Return division quotient and remainder -- -- Division by zero is handled by BigNat naturalQuotRem# :: Natural -> Natural -> (# Natural, Natural #) -- | Return division quotient and remainder naturalQuotRem :: Natural -> Natural -> (Natural, Natural) -- | Return division quotient naturalQuot :: Natural -> Natural -> Natural -- | Return division remainder naturalRem :: Natural -> Natural -> Natural -- | Compute greatest common divisor. naturalGcd :: Natural -> Natural -> Natural -- | Compute least common multiple. naturalLcm :: Natural -> Natural -> Natural -- | Base 2 logarithm naturalLog2# :: Natural -> Word# -- | Base 2 logarithm naturalLog2 :: Natural -> Word -- | Logarithm for an arbitrary base naturalLogBaseWord# :: Word# -> Natural -> Word# -- | Logarithm for an arbitrary base naturalLogBaseWord :: Word -> Natural -> Word -- | Logarithm for an arbitrary base naturalLogBase# :: Natural -> Natural -> Word# -- | Logarithm for an arbitrary base naturalLogBase :: Natural -> Natural -> Word -- | "naturalPowMod b e m" computes -- base b raised to exponent e modulo -- m. naturalPowMod :: Natural -> Natural -> Natural -> Natural -- | Compute the number of digits of the Natural in the given base. -- -- base must be > 1 naturalSizeInBase# :: Word# -> Natural -> Word# instance GHC.Classes.Eq GHC.Num.Natural.Natural instance GHC.Classes.Ord GHC.Num.Natural.Natural -- | The Integer type. module GHC.Num.Integer -- | Arbitrary precision integers. In contrast with fixed-size integral -- types such as Int, the Integer type represents the -- entire infinite range of integers. -- -- Integers are stored in a kind of sign-magnitude form, hence do not -- expect two's complement form when using bit operations. -- -- If the value is small (i.e., fits into an Int), the IS -- constructor is used. Otherwise IP and IN constructors -- are used to store a BigNat representing the positive or the -- negative value magnitude, respectively. -- -- Invariant: IP and IN are used iff the value does not fit -- in IS. data Integer -- | iff value in [minBound::Int, maxBound::Int] -- range IS :: Int# -> Integer -- | iff value in ]maxBound::Int, +inf[ range IP :: ByteArray# -> Integer -- | iff value in ]-inf, minBound::Int[ range IN :: ByteArray# -> Integer -- | Check Integer invariants integerCheck :: Integer -> Bool -- | Check Integer invariants integerCheck# :: Integer -> Bool# -- | Integer Zero integerZero :: Integer -- | Integer One integerOne :: Integer -- | Create an Integer from an Int# integerFromInt# :: Int# -> Integer -- | Create an Integer from an Int integerFromInt :: Int -> Integer -- | Truncates Integer to least-significant Int# integerToInt# :: Integer -> Int# -- | Truncates Integer to least-significant Int# integerToInt :: Integer -> Int -- | Create a positive Integer from a BigNat integerFromBigNat# :: BigNat# -> Integer -- | Create a negative Integer from a BigNat integerFromBigNatNeg# :: BigNat# -> Integer -- | Create an Integer from a sign-bit and a BigNat integerFromBigNatSign# :: Int# -> BigNat# -> Integer -- | Convert an Integer into a sign-bit and a BigNat integerToBigNatSign# :: Integer -> (# Int#, BigNat# #) -- | Convert an Integer into a BigNat. -- -- Return 0 for negative Integers. integerToBigNatClamp# :: Integer -> BigNat# -- | Convert a Word# into an Integer integerFromWord# :: Word# -> Integer -- | Convert a Word into an Integer integerFromWord :: Word -> Integer -- | Create a negative Integer with the given Word magnitude integerFromWordNeg# :: Word# -> Integer -- | Create an Integer from a sign and a Word magnitude integerFromWordSign# :: Int# -> Word# -> Integer -- | Truncate an Integer into a Word integerToWord# :: Integer -> Word# -- | Truncate an Integer into a Word integerToWord :: Integer -> Word -- | Convert a Natural into an Integer integerFromNatural :: Natural -> Integer -- | Convert an Integer into a Natural -- -- Return 0 for negative Integers. integerToNaturalClamp :: Integer -> Natural -- | Convert an Integer into a Natural -- -- Return absolute value integerToNatural :: Integer -> Natural -- | Convert an Integer into a Natural -- -- Throw an Underflow exception if input is negative. integerToNaturalThrow :: Integer -> Natural -- | Convert an Int64# into an Integer integerFromInt64# :: Int64# -> Integer -- | Convert a Word64# into an Integer integerFromWord64# :: Word64# -> Integer -- | Convert an Integer into an Int64# integerToInt64# :: Integer -> Int64# -- | Convert an Integer into a Word64# integerToWord64# :: Integer -> Word64# -- | Decode a Double# into (# Integer mantissa, Int# exponent #) integerDecodeDouble# :: Double# -> (# Integer, Int# #) -- | Encode (# Integer mantissa, Int# exponent #) into a Double# integerEncodeDouble# :: Integer -> Int# -> Double# -- | Encode (Integer mantissa, Int exponent) into a Double integerEncodeDouble :: Integer -> Int -> Double -- | Encode (# Integer mantissa, Int# exponent #) into a Float# -- -- TODO: Not sure if it's worth to write Float optimized versions -- here integerEncodeFloat# :: Integer -> Int# -> Float# -- | Write an Integer (without sign) to addr in -- base-256 representation and return the number of bytes written. -- -- The endianness is selected with the Bool# parameter: write most -- significant byte first (big-endian) if 1# or least -- significant byte first (little-endian) if 0#. integerToAddr# :: Integer -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) -- | Write an Integer (without sign) to addr in -- base-256 representation and return the number of bytes written. -- -- The endianness is selected with the Bool# parameter: write most -- significant byte first (big-endian) if 1# or least -- significant byte first (little-endian) if 0#. integerToAddr :: Integer -> Addr# -> Bool# -> IO Word -- | Read an Integer (without sign) in base-256 representation from -- an Addr#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimed. integerFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Integer #) -- | Read an Integer (without sign) in base-256 representation from -- an Addr#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimed. integerFromAddr :: Word# -> Addr# -> Bool# -> IO Integer -- | Convert a list of Word into an Integer integerFromWordList :: Bool -> [Word] -> Integer -- | Write an Integer (without sign) in base-256 representation and -- return the number of bytes written. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. integerToMutableByteArray# :: Integer -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) -- | Write an Integer (without sign) in base-256 representation and -- return the number of bytes written. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. integerToMutableByteArray :: Integer -> MutableByteArray# RealWorld -> Word# -> Bool# -> IO Word -- | Read an Integer (without sign) in base-256 representation from -- a ByteArray#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimed. integerFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Integer #) -- | Read an Integer (without sign) in base-256 representation from -- a ByteArray#. -- -- The size is given in bytes. -- -- The endianness is selected with the Bool# parameter: most significant -- byte first (big-endian) if 1# or least significant byte first -- (little-endian) if 0#. -- -- Null higher limbs are automatically trimed. integerFromByteArray :: Word# -> ByteArray# -> Word# -> Bool# -> Integer -- | Negative predicate integerIsNegative# :: Integer -> Bool# -- | Negative predicate integerIsNegative :: Integer -> Bool -- | Zero predicate integerIsZero :: Integer -> Bool -- | One predicate integerIsOne :: Integer -> Bool -- | Not-equal predicate. integerNe :: Integer -> Integer -> Bool -- | Equal predicate. integerEq :: Integer -> Integer -> Bool -- | Lower-or-equal predicate. integerLe :: Integer -> Integer -> Bool -- | Lower predicate. integerLt :: Integer -> Integer -> Bool -- | Greater predicate. integerGt :: Integer -> Integer -> Bool -- | Greater-or-equal predicate. integerGe :: Integer -> Integer -> Bool -- | Equal predicate. integerEq# :: Integer -> Integer -> Bool# -- | Not-equal predicate. integerNe# :: Integer -> Integer -> Bool# -- | Greater predicate. integerGt# :: Integer -> Integer -> Bool# -- | Lower-or-equal predicate. integerLe# :: Integer -> Integer -> Bool# -- | Lower predicate. integerLt# :: Integer -> Integer -> Bool# -- | Greater-or-equal predicate. integerGe# :: Integer -> Integer -> Bool# -- | Compare two Integer integerCompare :: Integer -> Integer -> Ordering -- | Subtract one Integer from another. integerSub :: Integer -> Integer -> Integer -- | Add two Integers integerAdd :: Integer -> Integer -> Integer -- | Multiply two Integers integerMul :: Integer -> Integer -> Integer -- | Negate Integer. -- -- One edge-case issue to take into account is that Int's range is not -- symmetric around 0. I.e. minBound+maxBound = -1 -- -- IP is used iff n > maxBound::Int IN is used iff n < -- minBound::Int integerNegate :: Integer -> Integer -- | Compute absolute value of an Integer integerAbs :: Integer -> Integer -- | Return -1, 0, and 1 depending on whether -- argument is negative, zero, or positive, respectively integerSignum :: Integer -> Integer -- | Return -1#, 0#, and 1# depending on whether -- argument is negative, zero, or positive, respectively integerSignum# :: Integer -> Int# -- | Simultaneous integerQuot and integerRem. -- -- Divisor must be non-zero otherwise the GHC runtime will terminate with -- a division-by-zero fault. integerQuotRem# :: Integer -> Integer -> (# Integer, Integer #) -- | Simultaneous integerQuot and integerRem. -- -- Divisor must be non-zero otherwise the GHC runtime will terminate with -- a division-by-zero fault. integerQuotRem :: Integer -> Integer -> (Integer, Integer) integerQuot :: Integer -> Integer -> Integer integerRem :: Integer -> Integer -> Integer -- | Simultaneous integerDiv and integerMod. -- -- Divisor must be non-zero otherwise the GHC runtime will terminate with -- a division-by-zero fault. integerDivMod# :: Integer -> Integer -> (# Integer, Integer #) -- | Simultaneous integerDiv and integerMod. -- -- Divisor must be non-zero otherwise the GHC runtime will terminate with -- a division-by-zero fault. integerDivMod :: Integer -> Integer -> (Integer, Integer) integerDiv :: Integer -> Integer -> Integer integerMod :: Integer -> Integer -> Integer -- | Compute greatest common divisor. integerGcd :: Integer -> Integer -> Integer -- | Compute least common multiple. integerLcm :: Integer -> Integer -> Integer -- | Square a Integer integerSqr :: Integer -> Integer -- | Base 2 logarithm (floor) -- -- For numbers <= 0, return 0 integerLog2# :: Integer -> Word# -- | Base 2 logarithm (floor) -- -- For numbers <= 0, return 0 integerLog2 :: Integer -> Word -- | Logarithm (floor) for an arbitrary base -- -- For numbers <= 0, return 0 integerLogBaseWord# :: Word# -> Integer -> Word# -- | Logarithm (floor) for an arbitrary base -- -- For numbers <= 0, return 0 integerLogBaseWord :: Word -> Integer -> Word -- | Logarithm (floor) for an arbitrary base -- -- For numbers <= 0, return 0 integerLogBase# :: Integer -> Integer -> Word# -- | Logarithm (floor) for an arbitrary base -- -- For numbers <= 0, return 0 integerLogBase :: Integer -> Integer -> Word -- | Indicate if the value is a power of two and which one integerIsPowerOf2# :: Integer -> (# (# #) | Word# #) -- | Get the extended GCD of two integers. -- -- `integerGcde# a b` returns (# g,x,y #) where * ax + by = g = |gcd a b| integerGcde# :: Integer -> Integer -> (# Integer, Integer, Integer #) -- | Get the extended GCD of two integers. -- -- `integerGcde a b` returns (g,x,y) where * ax + by = g = |gcd a b| integerGcde :: Integer -> Integer -> (Integer, Integer, Integer) -- | Computes the modular inverse. -- -- integerRecipMod# x m behaves as follows: -- -- -- -- NB. Successful evaluation returns a value of the form (# n | -- #); failure is indicated by returning (# | () #). integerRecipMod# :: Integer -> Natural -> (# Natural | () #) -- | Computes the modular exponentiation. -- -- integerPowMod# b e m behaves as follows: -- -- -- -- NB. Successful evaluation returns a value of the form (# n | -- #); failure is indicated by returning (# | () #). integerPowMod# :: Integer -> Integer -> Natural -> (# Natural | () #) -- | Count number of set bits. For negative arguments returns the negated -- population count of the absolute value. integerPopCount# :: Integer -> Int# -- | Positive Integer for which only n-th bit is set integerBit# :: Word# -> Integer -- | Integer for which only n-th bit is set integerBit :: Word -> Integer -- | Test if n-th bit is set. -- -- Fake 2's complement for negative values (might be slow) integerTestBit# :: Integer -> Word# -> Bool# -- | Test if n-th bit is set. For negative Integers it tests the -- n-th bit of the negated argument. -- -- Fake 2's complement for negative values (might be slow) integerTestBit :: Integer -> Word -> Bool -- | Shift-right operation -- -- Fake 2's complement for negative values (might be slow) integerShiftR# :: Integer -> Word# -> Integer -- | Shift-right operation -- -- Fake 2's complement for negative values (might be slow) integerShiftR :: Integer -> Word -> Integer -- | Shift-left operation integerShiftL# :: Integer -> Word# -> Integer -- | Shift-left operation -- -- Remember that bits are stored in sign-magnitude form, hence the -- behavior of negative Integers is different from negative Int's -- behavior. integerShiftL :: Integer -> Word -> Integer -- | Bitwise OR operation -- -- Fake 2's complement for negative values (might be slow) integerOr :: Integer -> Integer -> Integer -- | Bitwise XOR operation -- -- Fake 2's complement for negative values (might be slow) integerXor :: Integer -> Integer -> Integer -- | Bitwise AND operation -- -- Fake 2's complement for negative values (might be slow) integerAnd :: Integer -> Integer -> Integer -- | Binary complement of the integerComplement :: Integer -> Integer -- | Compute the number of digits of the Integer (without the sign) in the -- given base. -- -- base must be > 1 integerSizeInBase# :: Word# -> Integer -> Word# instance GHC.Classes.Eq GHC.Num.Integer.Integer instance GHC.Classes.Ord GHC.Num.Integer.Integer module GHC.Num.Backend.Native -- | ghc-bignum backend name backendName :: [Char] count_words_bits :: Word# -> (# Word#, Word# #) count_words_bits_int :: Word# -> (# Int#, Int# #) bignat_compare :: WordArray# -> WordArray# -> Int# bignat_add :: MutableWordArray# s -> WordArray# -> WordArray# -> State# s -> State# s bignat_add_word :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> State# RealWorld bignat_sub_word :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> (# State# RealWorld, Bool# #) bignat_mul_word :: MutableWordArray# RealWorld -> WordArray# -> Word# -> State# RealWorld -> State# RealWorld bignat_mul :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld bignat_sub :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> (# State# RealWorld, Bool# #) bignat_popcount :: WordArray# -> Word# bignat_shiftl :: MutableWordArray# s -> WordArray# -> Word# -> State# s -> State# s bignat_shiftr :: MutableWordArray# s -> WordArray# -> Word# -> State# s -> State# s bignat_shiftr_neg :: MutableWordArray# s -> WordArray# -> Word# -> State# s -> State# s bignat_or :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld bignat_xor :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld bignat_and :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld bignat_and_not :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld bignat_quotrem :: MutableWordArray# s -> MutableWordArray# s -> WordArray# -> WordArray# -> State# s -> State# s bignat_quot :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld bignat_rem :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld -- | Perform quotRem on normalized inputs: * highest bit of B is set * A is -- trimmed * A >= B * B > 1 bignat_quotrem_normalized :: MutableWordArray# s -> MutableWordArray# s -> WordArray# -> State# s -> State# s bignat_quotrem_word :: MutableWordArray# s -> WordArray# -> Word# -> State# s -> (# State# s, Word# #) bignat_quot_word :: MutableWordArray# s -> WordArray# -> Word# -> State# s -> State# s bignat_rem_word :: WordArray# -> Word# -> Word# bignat_gcd :: MutableWordArray# s -> WordArray# -> WordArray# -> State# s -> State# s bignat_gcd_word :: WordArray# -> Word# -> Word# -- | This operation doesn't really belongs here, but GMP's one is much -- faster than this simple implementation (basic Euclid algorithm). -- -- Ideally we should make an implementation as fast as GMP's one and put -- it into GHC.Num.Primitives. bignat_gcd_word_word :: Word# -> Word# -> Word# bignat_encode_double :: WordArray# -> Int# -> Double# bignat_powmod_word :: WordArray# -> WordArray# -> Word# -> Word# bignat_powmod :: MutableWordArray# RealWorld -> WordArray# -> WordArray# -> WordArray# -> State# RealWorld -> State# RealWorld bignat_powmod_words :: Word# -> Word# -> Word# -> Word# integer_gcde :: Integer -> Integer -> (# Integer, Integer, Integer #) integer_recip_mod :: Integer -> Natural -> (# Natural | () #) integer_powmod :: Integer -> Natural -> Natural -> Natural