ppad-fixed-0.1.3: Large fixed-width words and constant-time arithmetic.

Copyright	(c) 2025 Jared Tobin
License	MIT
Maintainer	Jared Tobin <jared@ppad.tech>
Safe Haskell	None
Language	Haskell2010

Data.Word.Limb

Contents

Limb
Bit manipulation and representation
Comparison
Selection
Negation
Arithmetic
Re-exported

Description

The primitive Limb type, as well as operations on it.

All operations run in constant time with respect to inputs, unless specifically indicated otherwise.

Synopsis

newtype Limb :: TYPE 'WordRep = Limb Word#
render :: Limb -> String
and# :: Limb -> Limb -> Limb
or# :: Limb -> Limb -> Limb
not# :: Limb -> Limb
xor# :: Limb -> Limb -> Limb
bits# :: Limb -> Int
shl# :: Limb -> Int# -> Limb
shl1# :: Limb -> (# Limb, Limb #)
shr# :: Limb -> Int# -> Limb
shr1# :: Limb -> (# Limb, Limb #)
eq# :: Limb -> Limb -> Choice
ne# :: Limb -> Limb -> Choice
eq_vartime# :: Limb -> Limb -> Bool
ne_vartime# :: Limb -> Limb -> Bool
nonzero# :: Limb -> Choice
lt# :: Limb -> Limb -> Choice
gt# :: Limb -> Limb -> Choice
select# :: Limb -> Limb -> Choice -> Limb
cswap# :: Limb -> Limb -> Choice -> (# Limb, Limb #)
neg# :: Limb -> Limb
add_o# :: Limb -> Limb -> (# Limb, Limb #)
add_c# :: Limb -> Limb -> Limb -> (# Limb, Limb #)
add_w# :: Limb -> Limb -> Limb
add_s# :: Limb -> Limb -> Limb
sub_b# :: Limb -> Limb -> Limb -> (# Limb, Limb #)
sub_w# :: Limb -> Limb -> Limb
sub_s# :: Limb -> Limb -> Limb
mul_c# :: Limb -> Limb -> (# Limb, Limb #)
mul_w# :: Limb -> Limb -> Limb
mul_s# :: Limb -> Limb -> Limb
mac# :: Limb -> Limb -> Limb -> Limb -> (# Limb, Limb #)
data Word = W# Word#

Limb

newtype Limb :: TYPE 'WordRep Source #

A Limb is the smallest component of a wider word.

Constructors

render :: Limb -> String Source #

Return a Limb value as a String.

Bit manipulation and representation

Arguments

:: Limb	a
-> Limb	b
-> Limb	a & b

Bitwise and.

Arguments

:: Limb	a
-> Limb	b
-> Limb	a \| b

Bitwise or.

Arguments

:: Limb	a
-> Limb	not a

Bitwise not.

Arguments

:: Limb	a
-> Limb	b
-> Limb	a ^ b

Bitwise exclusive or.

Arguments

:: Limb	limb
-> Int	bits required to represent limb

Number of bits required to represent this limb.

Arguments

:: Limb	limb
-> Int#	shift amount
-> Limb	result

Unchecked bit-shift left.

shl1# :: Limb -> (# Limb, Limb #) Source #

Unchecked bit-shift left by 1, returning the result and carry.

Arguments

:: Limb	limb
-> Int#	shift amount
-> Limb	result

Unchecked logical bit-shift right.

shr1# :: Limb -> (# Limb, Limb #) Source #

Unchecked logical bit-shift right by 1, returning the result and carry.

Comparison

eq# :: Limb -> Limb -> Choice Source #

Constant-time equality comparison.

ne# :: Limb -> Limb -> Choice Source #

Constant-time inequality comparison.

eq_vartime# :: Limb -> Limb -> Bool Source #

Variable-time equality comparison.

ne_vartime# :: Limb -> Limb -> Bool Source #

Variable-time inequality comparison.

nonzero# :: Limb -> Choice Source #

Constant-time comparison to zero.

lt# :: Limb -> Limb -> Choice Source #

Constant-time less than comparison.

gt# :: Limb -> Limb -> Choice Source #

Constant-time greater than comparison.

Selection

select# Source #

Arguments

:: Limb	a
-> Limb	b
-> Choice	c
-> Limb	result

Return a if c is truthy, otherwise return b.

cswap# Source #

Arguments

:: Limb	a
-> Limb	b
-> Choice	c
-> (# Limb, Limb #)	result

Return (# b, a #) if c is truthy, otherwise return (# a, b #).

Negation

neg# :: Limb -> Limb Source #

Wrapping (two's complement) negation.

Arithmetic

add_o# Source #

Arguments

:: Limb	augend
-> Limb	addend
-> (# Limb, Limb #)	(# sum, carry #)

Overflowing addition, computing augend + addend, returning the sum and carry.

add_c# Source #

Arguments

:: Limb	augend
-> Limb	addend
-> Limb	carry
-> (# Limb, Limb #)	(# sum, new carry #)

Carrying addition, computing augend + addend + carry, returning the sum and new carry.

add_w# Source #

Arguments

:: Limb	augend
-> Limb	addend
-> Limb	sum

Wrapping addition, computing augend + addend, returning the sum (discarding overflow).

add_s# :: Limb -> Limb -> Limb Source #

Saturating addition, computing augend + addend, returning the sum (clamping to the maximum representable value in the case of overflow).

sub_b# Source #

Arguments

:: Limb	minuend
-> Limb	subtrahend
-> Limb	borrow
-> (# Limb, Limb #)	(# difference, new borrow #)

Borrowing subtraction, computing minuend - (subtrahend + borrow), returning the difference and new borrow mask.

sub_w# Source #

Arguments

:: Limb	minuend
-> Limb	subtrahend
-> Limb	difference

Wrapping subtraction, computing minuend - subtrahend, returning the difference (and discarding underflow).

sub_s# Source #

Arguments

:: Limb	minuend
-> Limb	subtrahend
-> Limb	difference

Saturating subtraction, computing minuend - subtrahend, returning the difference (and clamping to zero in the case of underflow).

mul_c# Source #

Arguments

:: Limb	multiplicand
-> Limb	multiplier
-> (# Limb, Limb #)	(# low, high #) product

Widening multiplication, returning low and high words of the product.

mul_w# Source #

Arguments

:: Limb	multiplicand
-> Limb	multiplier
-> Limb	low word of product

Wrapping multiplication, returning only the low word of the product.

mul_s# Source #

Arguments

:: Limb	multiplicand
-> Limb	multiplier
-> Limb	clamped low word of product

Saturating multiplication, returning only the low word of the product, and clamping to the maximum value in the case of overflow.

Arguments

:: Limb	a (multiplicand)
-> Limb	b (multiplier)
-> Limb	m (addend)
-> Limb	c (carry)
-> (# Limb, Limb #)	a * b + m + c

Multiply-add-carry, computing a * b + m + c, returning the result along with the new carry.

Re-exported

data Word #

A Word is an unsigned integral type, with the same size as Int.

Constructors

Instances

Instances details

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word #

toConstr :: Word -> Constr #

dataTypeOf :: Word -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) #

gmapT :: (forall b. Data b => b -> b) -> Word -> Word #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r #

gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word #

Since: base-2.1

Instance details

Defined in Foreign.Storable

Methods

sizeOf :: Word -> Int #

alignment :: Word -> Int #

peekElemOff :: Ptr Word -> Int -> IO Word #

pokeElemOff :: Ptr Word -> Int -> Word -> IO () #

peekByteOff :: Ptr b -> Int -> IO Word #

pokeByteOff :: Ptr b -> Int -> Word -> IO () #

peek :: Ptr Word -> IO Word #

poke :: Ptr Word -> Word -> IO () #

Since: base-2.1

Instance details

Defined in GHC.Bits

Methods

(.&.) :: Word -> Word -> Word #

(.|.) :: Word -> Word -> Word #

xor :: Word -> Word -> Word #

complement :: Word -> Word #

shift :: Word -> Int -> Word #

rotate :: Word -> Int -> Word #

zeroBits :: Word #

bit :: Int -> Word #

setBit :: Word -> Int -> Word #

clearBit :: Word -> Int -> Word #

complementBit :: Word -> Int -> Word #

testBit :: Word -> Int -> Bool #

bitSizeMaybe :: Word -> Maybe Int #

bitSize :: Word -> Int #

isSigned :: Word -> Bool #

shiftL :: Word -> Int -> Word #

unsafeShiftL :: Word -> Int -> Word #

shiftR :: Word -> Int -> Word #

unsafeShiftR :: Word -> Int -> Word #

rotateL :: Word -> Int -> Word #

rotateR :: Word -> Int -> Word #

popCount :: Word -> Int #

FiniteBits Word

Since: base-4.6.0.0

Instance details

Defined in GHC.Bits

Methods

finiteBitSize :: Word -> Int #

countLeadingZeros :: Word -> Int #

countTrailingZeros :: Word -> Int #

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: Word #

maxBound :: Word #

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Word -> Word #

pred :: Word -> Word #

toEnum :: Int -> Word #

fromEnum :: Word -> Int #

enumFrom :: Word -> [Word] #

enumFromThen :: Word -> Word -> [Word] #

enumFromTo :: Word -> Word -> [Word] #

enumFromThenTo :: Word -> Word -> Word -> [Word] #

Since: base-4.6.0.0

Instance details

Defined in GHC.Ix

Methods

range :: (Word, Word) -> [Word] #

index :: (Word, Word) -> Word -> Int #

unsafeIndex :: (Word, Word) -> Word -> Int #

inRange :: (Word, Word) -> Word -> Bool #

rangeSize :: (Word, Word) -> Int #

unsafeRangeSize :: (Word, Word) -> Int #

Since: base-2.1

Instance details

Defined in GHC.Num

Methods

(+) :: Word -> Word -> Word #

(-) :: Word -> Word -> Word #

(*) :: Word -> Word -> Word #

negate :: Word -> Word #

abs :: Word -> Word #

signum :: Word -> Word #

fromInteger :: Integer -> Word #

Since: base-4.5.0.0

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Word #

readList :: ReadS [Word] #

readPrec :: ReadPrec Word #

readListPrec :: ReadPrec [Word] #

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

quot :: Word -> Word -> Word #

rem :: Word -> Word -> Word #

div :: Word -> Word -> Word #

mod :: Word -> Word -> Word #

quotRem :: Word -> Word -> (Word, Word) #

divMod :: Word -> Word -> (Word, Word) #

toInteger :: Word -> Integer #

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

toRational :: Word -> Rational #

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Word -> ShowS #

show :: Word -> String #

showList :: [Word] -> ShowS #

Since: base-2.1

Instance details

Defined in Text.Printf

Methods

formatArg :: Word -> FieldFormatter #

parseFormat :: Word -> ModifierParser #

Instance details

Defined in Control.DeepSeq

Methods

rnf :: Word -> () #

Instance details

Defined in GHC.Classes

Methods

(==) :: Word -> Word -> Bool #

(/=) :: Word -> Word -> Bool #

Instance details

Defined in GHC.Classes

Methods

compare :: Word -> Word -> Ordering #

(<) :: Word -> Word -> Bool #

(<=) :: Word -> Word -> Bool #

(>) :: Word -> Word -> Bool #

(>=) :: Word -> Word -> Bool #

max :: Word -> Word -> Word #

min :: Word -> Word -> Word #

Generic1 (URec Word :: k -> Type)

Instance details

Defined in GHC.Generics

Associated Types

type Rep1 (URec Word :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (URec Word :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Word a -> Rep1 (URec Word :: k -> Type) a #

to1 :: forall (a :: k). Rep1 (URec Word :: k -> Type) a -> URec Word a #

Foldable (UWord :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => UWord m -> m #

foldMap :: Monoid m => (a -> m) -> UWord a -> m #

foldMap' :: Monoid m => (a -> m) -> UWord a -> m #

foldr :: (a -> b -> b) -> b -> UWord a -> b #

foldr' :: (a -> b -> b) -> b -> UWord a -> b #

foldl :: (b -> a -> b) -> b -> UWord a -> b #

foldl' :: (b -> a -> b) -> b -> UWord a -> b #

foldr1 :: (a -> a -> a) -> UWord a -> a #

foldl1 :: (a -> a -> a) -> UWord a -> a #

toList :: UWord a -> [a] #

null :: UWord a -> Bool #

length :: UWord a -> Int #

elem :: Eq a => a -> UWord a -> Bool #

maximum :: Ord a => UWord a -> a #

minimum :: Ord a => UWord a -> a #

sum :: Num a => UWord a -> a #

product :: Num a => UWord a -> a #

Traversable (UWord :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UWord a -> f (UWord b) #

sequenceA :: Applicative f => UWord (f a) -> f (UWord a) #

mapM :: Monad m => (a -> m b) -> UWord a -> m (UWord b) #

sequence :: Monad m => UWord (m a) -> m (UWord a) #

Functor (URec Word :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b #

(<$) :: a -> URec Word b -> URec Word a #

Generic (URec Word p)

Instance details

Defined in GHC.Generics

Associated Types

type Rep (URec Word p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (URec Word p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: Type -> Type)))

Methods

from :: URec Word p -> Rep (URec Word p) x #

to :: Rep (URec Word p) x -> URec Word p #

Show (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

showsPrec :: Int -> URec Word p -> ShowS #

show :: URec Word p -> String #

showList :: [URec Word p] -> ShowS #

Eq (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Word p -> URec Word p -> Bool #

(/=) :: URec Word p -> URec Word p -> Bool #

Ord (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

compare :: URec Word p -> URec Word p -> Ordering #

(<) :: URec Word p -> URec Word p -> Bool #

(<=) :: URec Word p -> URec Word p -> Bool #

(>) :: URec Word p -> URec Word p -> Bool #

(>=) :: URec Word p -> URec Word p -> Bool #

max :: URec Word p -> URec Word p -> URec Word p #

min :: URec Word p -> URec Word p -> URec Word p #

data URec Word (p :: k)

Used for marking occurrences of Word#

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

data URec Word (p :: k) = UWord {

uWord# :: Word#

}

type Rep1 (URec Word :: k -> Type)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

type Rep1 (URec Word :: k -> Type) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: k -> Type)))

type Rep (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

type Rep (URec Word p) = D1 ('MetaData "URec" "GHC.Generics" "base" 'False) (C1 ('MetaCons "UWord" 'PrefixI 'True) (S1 ('MetaSel ('Just "uWord#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UWord :: Type -> Type)))