ghc-bignum-1.2: GHC BigNum library
Copyright(c) Sylvain Henry 2019
(c) Herbert Valerio Riedel 2014
LicenseBSD3
Maintainersylvain@haskus.fr
Stabilityprovisional
Portabilitynon-portable (GHC Extensions)
Safe HaskellSafe-Inferred
LanguageHaskell2010

GHC.Num.Integer

Description

The Integer type.

Synopsis

Documentation

data Integer Source #

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 (fit into an Int), IS constructor is used. Otherwise Integer and IN constructors are used to store a BigNat representing respectively the positive or the negative value magnitude.

Invariant: Integer and IN are used iff value doesn't fit in IS

Constructors

IS !Int#

iff value in [minBound::Int, maxBound::Int] range

IP !BigNat#

iff value in ]maxBound::Int, +inf[ range

IN !BigNat#

iff value in ]-inf, minBound::Int[ range

Instances

Instances details
Eq Integer # 
Instance details

Defined in GHC.Num.Integer

Ord Integer # 
Instance details

Defined in GHC.Num.Integer

integerCheck# :: Integer -> Bool# Source #

Check Integer invariants

integerCheck :: Integer -> Bool Source #

Check Integer invariants

integerZero :: Integer Source #

Integer Zero

integerOne :: Integer Source #

Integer One

integerFromBigNat# :: BigNat# -> Integer Source #

Create a positive Integer from a BigNat

integerFromBigNatNeg# :: BigNat# -> Integer Source #

Create a negative Integer from a BigNat

integerFromBigNatSign# :: Int# -> BigNat# -> Integer Source #

Create an Integer from a sign-bit and a BigNat

integerToBigNatSign# :: Integer -> (# Int#, BigNat# #) Source #

Convert an Integer into a sign-bit and a BigNat

integerToBigNatClamp# :: Integer -> BigNat# Source #

Convert an Integer into a BigNat.

Return 0 for negative Integers.

integerFromInt# :: Int# -> Integer Source #

Create an Integer from an Int#

integerFromInt :: Int -> Integer Source #

Create an Integer from an Int

integerToInt# :: Integer -> Int# Source #

Truncates Integer to least-significant Int#

integerToInt :: Integer -> Int Source #

Truncates Integer to least-significant Int#

integerFromWord# :: Word# -> Integer Source #

Convert a Word# into an Integer

integerFromWord :: Word -> Integer Source #

Convert a Word into an Integer

integerFromWordNeg# :: Word# -> Integer Source #

Create a negative Integer with the given Word magnitude

integerFromWordSign# :: Int# -> Word# -> Integer Source #

Create an Integer from a sign and a Word magnitude

integerToWord# :: Integer -> Word# Source #

Truncate an Integer into a Word

integerToWord :: Integer -> Word Source #

Truncate an Integer into a Word

integerFromNatural :: Natural -> Integer Source #

Convert a Natural into an Integer

integerFromWordList :: Bool -> [Word] -> Integer Source #

Convert a list of Word into an Integer

integerToNaturalClamp :: Integer -> Natural Source #

Convert an Integer into a Natural

Return 0 for negative Integers.

integerToNatural :: Integer -> Natural Source #

Convert an Integer into a Natural

Return absolute value

integerToNaturalThrow :: Integer -> Natural Source #

Convert an Integer into a Natural

Throw an Underflow exception if input is negative.

integerIsNegative# :: Integer -> Bool# Source #

Negative predicate

integerIsNegative :: Integer -> Bool Source #

Negative predicate

integerIsZero :: Integer -> Bool Source #

Zero predicate

integerIsOne :: Integer -> Bool Source #

One predicate

integerNe :: Integer -> Integer -> Bool Source #

Not-equal predicate.

integerEq :: Integer -> Integer -> Bool Source #

Equal predicate.

integerLe :: Integer -> Integer -> Bool Source #

Lower-or-equal predicate.

integerLt :: Integer -> Integer -> Bool Source #

Lower predicate.

integerGt :: Integer -> Integer -> Bool Source #

Greater predicate.

integerGe :: Integer -> Integer -> Bool Source #

Greater-or-equal predicate.

integerEq# :: Integer -> Integer -> Bool# Source #

Equal predicate.

integerNe# :: Integer -> Integer -> Bool# Source #

Not-equal predicate.

integerGt# :: Integer -> Integer -> Bool# Source #

Greater predicate.

integerLe# :: Integer -> Integer -> Bool# Source #

Lower-or-equal predicate.

integerLt# :: Integer -> Integer -> Bool# Source #

Lower predicate.

integerGe# :: Integer -> Integer -> Bool# Source #

Greater-or-equal predicate.

integerCompare :: Integer -> Integer -> Ordering Source #

Compare two Integer

integerSub :: Integer -> Integer -> Integer Source #

Subtract one Integer from another.

integerNegate :: Integer -> Integer Source #

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

integerAbs :: Integer -> Integer Source #

Compute absolute value of an Integer

integerSignum :: Integer -> Integer Source #

Return -1, 0, and 1 depending on whether argument is negative, zero, or positive, respectively

integerSignum# :: Integer -> Int# Source #

Return -1#, 0#, and 1# depending on whether argument is negative, zero, or positive, respectively

integerPopCount# :: Integer -> Int# Source #

Count number of set bits. For negative arguments returns the negated population count of the absolute value.

integerBit# :: Word# -> Integer Source #

Positive Integer for which only n-th bit is set

integerBit :: Word -> Integer Source #

Integer for which only n-th bit is set

integerTestBit# :: Integer -> Word# -> Bool# Source #

Test if n-th bit is set.

Fake 2's complement for negative values (might be slow)

integerTestBit :: Integer -> Word -> Bool Source #

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)

integerShiftR# :: Integer -> Word# -> Integer Source #

Shift-right operation

Fake 2's complement for negative values (might be slow)

integerShiftR :: Integer -> Word -> Integer Source #

Shift-right operation

Fake 2's complement for negative values (might be slow)

integerShiftL# :: Integer -> Word# -> Integer Source #

Shift-left operation

integerShiftL :: Integer -> Word -> Integer Source #

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.

integerOr :: Integer -> Integer -> Integer Source #

Bitwise OR operation

Fake 2's complement for negative values (might be slow)

integerXor :: Integer -> Integer -> Integer Source #

Bitwise XOR operation

Fake 2's complement for negative values (might be slow)

integerAnd :: Integer -> Integer -> Integer Source #

Bitwise AND operation

Fake 2's complement for negative values (might be slow)

integerComplement :: Integer -> Integer Source #

Binary complement of the

integerQuotRem# :: Integer -> Integer -> (# Integer, Integer #) Source #

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) Source #

Simultaneous integerQuot and integerRem.

Divisor must be non-zero otherwise the GHC runtime will terminate with a division-by-zero fault.

integerDivMod# :: Integer -> Integer -> (# Integer, Integer #) Source #

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) Source #

Simultaneous integerDiv and integerMod.

Divisor must be non-zero otherwise the GHC runtime will terminate with a division-by-zero fault.

integerGcd :: Integer -> Integer -> Integer Source #

Compute greatest common divisor.

integerLcm :: Integer -> Integer -> Integer Source #

Compute least common multiple.

integerSqr :: Integer -> Integer Source #

Square a Integer

integerLog2# :: Integer -> Word# Source #

Base 2 logarithm (floor)

For numbers <= 0, return 0

integerLog2 :: Integer -> Word Source #

Base 2 logarithm (floor)

For numbers <= 0, return 0

integerLogBaseWord# :: Word# -> Integer -> Word# Source #

Logarithm (floor) for an arbitrary base

For numbers <= 0, return 0

integerLogBaseWord :: Word -> Integer -> Word Source #

Logarithm (floor) for an arbitrary base

For numbers <= 0, return 0

integerLogBase# :: Integer -> Integer -> Word# Source #

Logarithm (floor) for an arbitrary base

For numbers <= 0, return 0

integerLogBase :: Integer -> Integer -> Word Source #

Logarithm (floor) for an arbitrary base

For numbers <= 0, return 0

integerIsPowerOf2# :: Integer -> (# (# #) | Word# #) Source #

Indicate if the value is a power of two and which one

integerFromInt64# :: Int# -> Integer Source #

Convert an Int64# into an Integer on 64-bit architectures

integerDecodeDouble# :: Double# -> (# Integer, Int# #) Source #

Decode a Double# into (# Integer mantissa, Int# exponent #)

integerEncodeDouble# :: Integer -> Int# -> Double# Source #

Encode (# Integer mantissa, Int# exponent #) into a Double#

integerEncodeDouble :: Integer -> Int -> Double Source #

Encode (Integer mantissa, Int exponent) into a Double

integerEncodeFloat# :: Integer -> Int# -> Float# Source #

Encode (# Integer mantissa, Int# exponent #) into a Float#

TODO: Not sure if it's worth to write Float optimized versions here

integerSizeInBase# :: Word# -> Integer -> Word# Source #

Compute the number of digits of the Integer (without the sign) in the given base.

base must be > 1

integerToAddr# :: Integer -> Addr# -> Bool# -> State# s -> (# State# s, Word# #) Source #

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 Source #

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#.

integerFromAddr# :: Word# -> Addr# -> Bool# -> State# s -> (# State# s, Integer #) Source #

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 Source #

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.

integerToMutableByteArray# :: Integer -> MutableByteArray# s -> Word# -> Bool# -> State# s -> (# State# s, Word# #) Source #

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 Source #

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#.

integerFromByteArray# :: Word# -> ByteArray# -> Word# -> Bool# -> State# s -> (# State# s, Integer #) Source #

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 Source #

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.

integerGcde# :: Integer -> Integer -> (# Integer, Integer, Integer #) Source #

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) Source #

Get the extended GCD of two integers.

`integerGcde a b` returns (g,x,y) where * ax + by = g = |gcd a b|

integerRecipMod# :: Integer -> Natural -> (# Natural | () #) Source #

Computes the modular inverse.

I.e. y = integerRecipMod# x m = x^(-1) mod m

with 0 < y < |m|

integerPowMod# :: Integer -> Integer -> Natural -> (# Natural | () #) Source #

Computes the modular exponentiation.

I.e. y = integer_powmod b e m = b^e mod m

with 0 <= y < abs m

If e is negative, we use integerRecipMod# to try to find a modular multiplicative inverse (which may not exist).