ersatz-0.6: A monad for expressing SAT or QSAT problems using observable sharing.
Copyright© Edward Kmett 2010-2015 © Eric Mertens 2014 Johan Kiviniemi 2013
LicenseBSD3
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellSafe-Inferred
LanguageHaskell2010

Ersatz.Bits

Description

Bit1 .. Bit8 represent fixed length bit vectors. The most significant bit comes first. Bit1 and Bit2 have modular arithmetic (the result has the same width as the arguments, overflow is ignored).

Bits is an arbitrary length natural number type. The least significant bit comes first. Bits has full arithmetic (the result has large enough width so that there is no overflow).

Synopsis

Fixed length bit vectors

newtype Bit1 Source #

A container of 1 Bit that encodes from and decodes to Word8.

Constructors

Bit1 Bit 

Instances

Instances details
Generic Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Rep Bit1 
Instance details

Defined in Ersatz.Bits

type Rep Bit1 = D1 ('MetaData "Bit1" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'True) (C1 ('MetaCons "Bit1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bit)))

Methods

from :: Bit1 -> Rep Bit1 x #

to :: Rep Bit1 x -> Bit1 #

Num Bit1 Source #

This instance provides modular arithmetic (overflow is ignored).

Instance details

Defined in Ersatz.Bits

Methods

(+) :: Bit1 -> Bit1 -> Bit1 #

(-) :: Bit1 -> Bit1 -> Bit1 #

(*) :: Bit1 -> Bit1 -> Bit1 #

negate :: Bit1 -> Bit1 #

abs :: Bit1 -> Bit1 #

signum :: Bit1 -> Bit1 #

fromInteger :: Integer -> Bit1 #

Show Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bit1 -> ShowS #

show :: Bit1 -> String #

showList :: [Bit1] -> ShowS #

Boolean Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bool :: Bool -> Bit1 Source #

true :: Bit1 Source #

false :: Bit1 Source #

(&&) :: Bit1 -> Bit1 -> Bit1 Source #

(||) :: Bit1 -> Bit1 -> Bit1 Source #

(==>) :: Bit1 -> Bit1 -> Bit1 Source #

not :: Bit1 -> Bit1 Source #

and :: Foldable t => t Bit1 -> Bit1 Source #

or :: Foldable t => t Bit1 -> Bit1 Source #

nand :: Foldable t => t Bit1 -> Bit1 Source #

nor :: Foldable t => t Bit1 -> Bit1 Source #

all :: Foldable t => (a -> Bit1) -> t a -> Bit1 Source #

any :: Foldable t => (a -> Bit1) -> t a -> Bit1 Source #

xor :: Bit1 -> Bit1 -> Bit1 Source #

choose :: Bit1 -> Bit1 -> Bit1 -> Bit1 Source #

HasBits Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit1 -> Bits Source #

Codec Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bit1 
Instance details

Defined in Ersatz.Bits

type Decoded Bit1 = Word8

Methods

decode :: Solution -> Bit1 -> Maybe (Decoded Bit1) Source #

encode :: Decoded Bit1 -> Bit1 Source #

Equatable Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bit1 -> Bit1 -> Bit Source #

(/==) :: Bit1 -> Bit1 -> Bit Source #

Orderable Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bit1 -> Bit1 -> Bit Source #

(<=?) :: Bit1 -> Bit1 -> Bit Source #

(>=?) :: Bit1 -> Bit1 -> Bit Source #

(>?) :: Bit1 -> Bit1 -> Bit Source #

Variable Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Methods

literally :: MonadSAT s m => m Literal -> m Bit1 Source #

type Rep Bit1 Source # 
Instance details

Defined in Ersatz.Bits

type Rep Bit1 = D1 ('MetaData "Bit1" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'True) (C1 ('MetaCons "Bit1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bit)))
type Decoded Bit1 Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bit1 = Word8

data Bit2 Source #

A container of 2 Bits that encodes from and decodes to Word8. MSB is first.

Constructors

Bit2 !Bit !Bit 

Instances

Instances details
Generic Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Rep Bit2 
Instance details

Defined in Ersatz.Bits

type Rep Bit2 = D1 ('MetaData "Bit2" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))

Methods

from :: Bit2 -> Rep Bit2 x #

to :: Rep Bit2 x -> Bit2 #

Num Bit2 Source #

This instance provides modular arithmetic (overflow is ignored).

Instance details

Defined in Ersatz.Bits

Methods

(+) :: Bit2 -> Bit2 -> Bit2 #

(-) :: Bit2 -> Bit2 -> Bit2 #

(*) :: Bit2 -> Bit2 -> Bit2 #

negate :: Bit2 -> Bit2 #

abs :: Bit2 -> Bit2 #

signum :: Bit2 -> Bit2 #

fromInteger :: Integer -> Bit2 #

Show Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bit2 -> ShowS #

show :: Bit2 -> String #

showList :: [Bit2] -> ShowS #

Boolean Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bool :: Bool -> Bit2 Source #

true :: Bit2 Source #

false :: Bit2 Source #

(&&) :: Bit2 -> Bit2 -> Bit2 Source #

(||) :: Bit2 -> Bit2 -> Bit2 Source #

(==>) :: Bit2 -> Bit2 -> Bit2 Source #

not :: Bit2 -> Bit2 Source #

and :: Foldable t => t Bit2 -> Bit2 Source #

or :: Foldable t => t Bit2 -> Bit2 Source #

nand :: Foldable t => t Bit2 -> Bit2 Source #

nor :: Foldable t => t Bit2 -> Bit2 Source #

all :: Foldable t => (a -> Bit2) -> t a -> Bit2 Source #

any :: Foldable t => (a -> Bit2) -> t a -> Bit2 Source #

xor :: Bit2 -> Bit2 -> Bit2 Source #

choose :: Bit2 -> Bit2 -> Bit2 -> Bit2 Source #

HasBits Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit2 -> Bits Source #

Codec Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bit2 
Instance details

Defined in Ersatz.Bits

type Decoded Bit2 = Word8

Methods

decode :: Solution -> Bit2 -> Maybe (Decoded Bit2) Source #

encode :: Decoded Bit2 -> Bit2 Source #

Equatable Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bit2 -> Bit2 -> Bit Source #

(/==) :: Bit2 -> Bit2 -> Bit Source #

Orderable Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bit2 -> Bit2 -> Bit Source #

(<=?) :: Bit2 -> Bit2 -> Bit Source #

(>=?) :: Bit2 -> Bit2 -> Bit Source #

(>?) :: Bit2 -> Bit2 -> Bit Source #

Variable Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Methods

literally :: MonadSAT s m => m Literal -> m Bit2 Source #

type Rep Bit2 Source # 
Instance details

Defined in Ersatz.Bits

type Rep Bit2 = D1 ('MetaData "Bit2" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))
type Decoded Bit2 Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bit2 = Word8

data Bit3 Source #

A container of 3 Bits that encodes from and decodes to Word8. MSB is first.

Constructors

Bit3 !Bit !Bit !Bit 

Instances

Instances details
Generic Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Rep Bit3 
Instance details

Defined in Ersatz.Bits

type Rep Bit3 = D1 ('MetaData "Bit3" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))))

Methods

from :: Bit3 -> Rep Bit3 x #

to :: Rep Bit3 x -> Bit3 #

Show Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bit3 -> ShowS #

show :: Bit3 -> String #

showList :: [Bit3] -> ShowS #

Boolean Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bool :: Bool -> Bit3 Source #

true :: Bit3 Source #

false :: Bit3 Source #

(&&) :: Bit3 -> Bit3 -> Bit3 Source #

(||) :: Bit3 -> Bit3 -> Bit3 Source #

(==>) :: Bit3 -> Bit3 -> Bit3 Source #

not :: Bit3 -> Bit3 Source #

and :: Foldable t => t Bit3 -> Bit3 Source #

or :: Foldable t => t Bit3 -> Bit3 Source #

nand :: Foldable t => t Bit3 -> Bit3 Source #

nor :: Foldable t => t Bit3 -> Bit3 Source #

all :: Foldable t => (a -> Bit3) -> t a -> Bit3 Source #

any :: Foldable t => (a -> Bit3) -> t a -> Bit3 Source #

xor :: Bit3 -> Bit3 -> Bit3 Source #

choose :: Bit3 -> Bit3 -> Bit3 -> Bit3 Source #

HasBits Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit3 -> Bits Source #

Codec Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bit3 
Instance details

Defined in Ersatz.Bits

type Decoded Bit3 = Word8

Methods

decode :: Solution -> Bit3 -> Maybe (Decoded Bit3) Source #

encode :: Decoded Bit3 -> Bit3 Source #

Equatable Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bit3 -> Bit3 -> Bit Source #

(/==) :: Bit3 -> Bit3 -> Bit Source #

Orderable Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bit3 -> Bit3 -> Bit Source #

(<=?) :: Bit3 -> Bit3 -> Bit Source #

(>=?) :: Bit3 -> Bit3 -> Bit Source #

(>?) :: Bit3 -> Bit3 -> Bit Source #

Variable Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Methods

literally :: MonadSAT s m => m Literal -> m Bit3 Source #

type Rep Bit3 Source # 
Instance details

Defined in Ersatz.Bits

type Rep Bit3 = D1 ('MetaData "Bit3" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))))
type Decoded Bit3 Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bit3 = Word8

data Bit4 Source #

A container of 4 Bits that encodes from and decodes to Word8. MSB is first.

Constructors

Bit4 !Bit !Bit !Bit !Bit 

Instances

Instances details
Generic Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Rep Bit4 
Instance details

Defined in Ersatz.Bits

type Rep Bit4 = D1 ('MetaData "Bit4" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit4" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))))

Methods

from :: Bit4 -> Rep Bit4 x #

to :: Rep Bit4 x -> Bit4 #

Show Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bit4 -> ShowS #

show :: Bit4 -> String #

showList :: [Bit4] -> ShowS #

Boolean Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bool :: Bool -> Bit4 Source #

true :: Bit4 Source #

false :: Bit4 Source #

(&&) :: Bit4 -> Bit4 -> Bit4 Source #

(||) :: Bit4 -> Bit4 -> Bit4 Source #

(==>) :: Bit4 -> Bit4 -> Bit4 Source #

not :: Bit4 -> Bit4 Source #

and :: Foldable t => t Bit4 -> Bit4 Source #

or :: Foldable t => t Bit4 -> Bit4 Source #

nand :: Foldable t => t Bit4 -> Bit4 Source #

nor :: Foldable t => t Bit4 -> Bit4 Source #

all :: Foldable t => (a -> Bit4) -> t a -> Bit4 Source #

any :: Foldable t => (a -> Bit4) -> t a -> Bit4 Source #

xor :: Bit4 -> Bit4 -> Bit4 Source #

choose :: Bit4 -> Bit4 -> Bit4 -> Bit4 Source #

HasBits Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit4 -> Bits Source #

Codec Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bit4 
Instance details

Defined in Ersatz.Bits

type Decoded Bit4 = Word8

Methods

decode :: Solution -> Bit4 -> Maybe (Decoded Bit4) Source #

encode :: Decoded Bit4 -> Bit4 Source #

Equatable Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bit4 -> Bit4 -> Bit Source #

(/==) :: Bit4 -> Bit4 -> Bit Source #

Orderable Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bit4 -> Bit4 -> Bit Source #

(<=?) :: Bit4 -> Bit4 -> Bit Source #

(>=?) :: Bit4 -> Bit4 -> Bit Source #

(>?) :: Bit4 -> Bit4 -> Bit Source #

Variable Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Methods

literally :: MonadSAT s m => m Literal -> m Bit4 Source #

type Rep Bit4 Source # 
Instance details

Defined in Ersatz.Bits

type Rep Bit4 = D1 ('MetaData "Bit4" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit4" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))))
type Decoded Bit4 Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bit4 = Word8

data Bit5 Source #

A container of 5 Bits that encodes from and decodes to Word8. MSB is first.

Constructors

Bit5 !Bit !Bit !Bit !Bit !Bit 

Instances

Instances details
Generic Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Rep Bit5 
Instance details

Defined in Ersatz.Bits

type Rep Bit5 = D1 ('MetaData "Bit5" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit5" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))))

Methods

from :: Bit5 -> Rep Bit5 x #

to :: Rep Bit5 x -> Bit5 #

Show Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bit5 -> ShowS #

show :: Bit5 -> String #

showList :: [Bit5] -> ShowS #

Boolean Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bool :: Bool -> Bit5 Source #

true :: Bit5 Source #

false :: Bit5 Source #

(&&) :: Bit5 -> Bit5 -> Bit5 Source #

(||) :: Bit5 -> Bit5 -> Bit5 Source #

(==>) :: Bit5 -> Bit5 -> Bit5 Source #

not :: Bit5 -> Bit5 Source #

and :: Foldable t => t Bit5 -> Bit5 Source #

or :: Foldable t => t Bit5 -> Bit5 Source #

nand :: Foldable t => t Bit5 -> Bit5 Source #

nor :: Foldable t => t Bit5 -> Bit5 Source #

all :: Foldable t => (a -> Bit5) -> t a -> Bit5 Source #

any :: Foldable t => (a -> Bit5) -> t a -> Bit5 Source #

xor :: Bit5 -> Bit5 -> Bit5 Source #

choose :: Bit5 -> Bit5 -> Bit5 -> Bit5 Source #

HasBits Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit5 -> Bits Source #

Codec Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bit5 
Instance details

Defined in Ersatz.Bits

type Decoded Bit5 = Word8

Methods

decode :: Solution -> Bit5 -> Maybe (Decoded Bit5) Source #

encode :: Decoded Bit5 -> Bit5 Source #

Equatable Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bit5 -> Bit5 -> Bit Source #

(/==) :: Bit5 -> Bit5 -> Bit Source #

Orderable Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bit5 -> Bit5 -> Bit Source #

(<=?) :: Bit5 -> Bit5 -> Bit Source #

(>=?) :: Bit5 -> Bit5 -> Bit Source #

(>?) :: Bit5 -> Bit5 -> Bit Source #

Variable Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Methods

literally :: MonadSAT s m => m Literal -> m Bit5 Source #

type Rep Bit5 Source # 
Instance details

Defined in Ersatz.Bits

type Rep Bit5 = D1 ('MetaData "Bit5" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit5" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))))
type Decoded Bit5 Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bit5 = Word8

data Bit6 Source #

A container of 6 Bits that encodes from and decodes to Word8. MSB is first.

Constructors

Bit6 !Bit !Bit !Bit !Bit !Bit !Bit 

Instances

Instances details
Generic Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Rep Bit6 
Instance details

Defined in Ersatz.Bits

type Rep Bit6 = D1 ('MetaData "Bit6" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit6" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))))

Methods

from :: Bit6 -> Rep Bit6 x #

to :: Rep Bit6 x -> Bit6 #

Show Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bit6 -> ShowS #

show :: Bit6 -> String #

showList :: [Bit6] -> ShowS #

Boolean Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bool :: Bool -> Bit6 Source #

true :: Bit6 Source #

false :: Bit6 Source #

(&&) :: Bit6 -> Bit6 -> Bit6 Source #

(||) :: Bit6 -> Bit6 -> Bit6 Source #

(==>) :: Bit6 -> Bit6 -> Bit6 Source #

not :: Bit6 -> Bit6 Source #

and :: Foldable t => t Bit6 -> Bit6 Source #

or :: Foldable t => t Bit6 -> Bit6 Source #

nand :: Foldable t => t Bit6 -> Bit6 Source #

nor :: Foldable t => t Bit6 -> Bit6 Source #

all :: Foldable t => (a -> Bit6) -> t a -> Bit6 Source #

any :: Foldable t => (a -> Bit6) -> t a -> Bit6 Source #

xor :: Bit6 -> Bit6 -> Bit6 Source #

choose :: Bit6 -> Bit6 -> Bit6 -> Bit6 Source #

HasBits Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit6 -> Bits Source #

Codec Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bit6 
Instance details

Defined in Ersatz.Bits

type Decoded Bit6 = Word8

Methods

decode :: Solution -> Bit6 -> Maybe (Decoded Bit6) Source #

encode :: Decoded Bit6 -> Bit6 Source #

Equatable Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bit6 -> Bit6 -> Bit Source #

(/==) :: Bit6 -> Bit6 -> Bit Source #

Orderable Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bit6 -> Bit6 -> Bit Source #

(<=?) :: Bit6 -> Bit6 -> Bit Source #

(>=?) :: Bit6 -> Bit6 -> Bit Source #

(>?) :: Bit6 -> Bit6 -> Bit Source #

Variable Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Methods

literally :: MonadSAT s m => m Literal -> m Bit6 Source #

type Rep Bit6 Source # 
Instance details

Defined in Ersatz.Bits

type Rep Bit6 = D1 ('MetaData "Bit6" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit6" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))))
type Decoded Bit6 Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bit6 = Word8

data Bit7 Source #

A container of 7 Bits that encodes from and decodes to Word8. MSB is first.

Constructors

Bit7 !Bit !Bit !Bit !Bit !Bit !Bit !Bit 

Instances

Instances details
Generic Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Rep Bit7 
Instance details

Defined in Ersatz.Bits

type Rep Bit7 = D1 ('MetaData "Bit7" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit7" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))) :*: ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))))

Methods

from :: Bit7 -> Rep Bit7 x #

to :: Rep Bit7 x -> Bit7 #

Show Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bit7 -> ShowS #

show :: Bit7 -> String #

showList :: [Bit7] -> ShowS #

Boolean Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bool :: Bool -> Bit7 Source #

true :: Bit7 Source #

false :: Bit7 Source #

(&&) :: Bit7 -> Bit7 -> Bit7 Source #

(||) :: Bit7 -> Bit7 -> Bit7 Source #

(==>) :: Bit7 -> Bit7 -> Bit7 Source #

not :: Bit7 -> Bit7 Source #

and :: Foldable t => t Bit7 -> Bit7 Source #

or :: Foldable t => t Bit7 -> Bit7 Source #

nand :: Foldable t => t Bit7 -> Bit7 Source #

nor :: Foldable t => t Bit7 -> Bit7 Source #

all :: Foldable t => (a -> Bit7) -> t a -> Bit7 Source #

any :: Foldable t => (a -> Bit7) -> t a -> Bit7 Source #

xor :: Bit7 -> Bit7 -> Bit7 Source #

choose :: Bit7 -> Bit7 -> Bit7 -> Bit7 Source #

HasBits Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit7 -> Bits Source #

Codec Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bit7 
Instance details

Defined in Ersatz.Bits

type Decoded Bit7 = Word8

Methods

decode :: Solution -> Bit7 -> Maybe (Decoded Bit7) Source #

encode :: Decoded Bit7 -> Bit7 Source #

Equatable Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bit7 -> Bit7 -> Bit Source #

(/==) :: Bit7 -> Bit7 -> Bit Source #

Orderable Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bit7 -> Bit7 -> Bit Source #

(<=?) :: Bit7 -> Bit7 -> Bit Source #

(>=?) :: Bit7 -> Bit7 -> Bit Source #

(>?) :: Bit7 -> Bit7 -> Bit Source #

Variable Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Methods

literally :: MonadSAT s m => m Literal -> m Bit7 Source #

type Rep Bit7 Source # 
Instance details

Defined in Ersatz.Bits

type Rep Bit7 = D1 ('MetaData "Bit7" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit7" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))) :*: ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))))
type Decoded Bit7 Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bit7 = Word8

data Bit8 Source #

A container of 8 Bits that encodes from and decodes to Word8. MSB is first.

Constructors

Bit8 !Bit !Bit !Bit !Bit !Bit !Bit !Bit !Bit 

Instances

Instances details
Generic Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Rep Bit8 
Instance details

Defined in Ersatz.Bits

type Rep Bit8 = D1 ('MetaData "Bit8" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit8" 'PrefixI 'False) (((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))) :*: ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))))

Methods

from :: Bit8 -> Rep Bit8 x #

to :: Rep Bit8 x -> Bit8 #

Show Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bit8 -> ShowS #

show :: Bit8 -> String #

showList :: [Bit8] -> ShowS #

Boolean Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bool :: Bool -> Bit8 Source #

true :: Bit8 Source #

false :: Bit8 Source #

(&&) :: Bit8 -> Bit8 -> Bit8 Source #

(||) :: Bit8 -> Bit8 -> Bit8 Source #

(==>) :: Bit8 -> Bit8 -> Bit8 Source #

not :: Bit8 -> Bit8 Source #

and :: Foldable t => t Bit8 -> Bit8 Source #

or :: Foldable t => t Bit8 -> Bit8 Source #

nand :: Foldable t => t Bit8 -> Bit8 Source #

nor :: Foldable t => t Bit8 -> Bit8 Source #

all :: Foldable t => (a -> Bit8) -> t a -> Bit8 Source #

any :: Foldable t => (a -> Bit8) -> t a -> Bit8 Source #

xor :: Bit8 -> Bit8 -> Bit8 Source #

choose :: Bit8 -> Bit8 -> Bit8 -> Bit8 Source #

HasBits Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit8 -> Bits Source #

Codec Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bit8 
Instance details

Defined in Ersatz.Bits

type Decoded Bit8 = Word8

Methods

decode :: Solution -> Bit8 -> Maybe (Decoded Bit8) Source #

encode :: Decoded Bit8 -> Bit8 Source #

Equatable Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bit8 -> Bit8 -> Bit Source #

(/==) :: Bit8 -> Bit8 -> Bit Source #

Orderable Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bit8 -> Bit8 -> Bit Source #

(<=?) :: Bit8 -> Bit8 -> Bit Source #

(>=?) :: Bit8 -> Bit8 -> Bit Source #

(>?) :: Bit8 -> Bit8 -> Bit Source #

Variable Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Methods

literally :: MonadSAT s m => m Literal -> m Bit8 Source #

type Rep Bit8 Source # 
Instance details

Defined in Ersatz.Bits

type Rep Bit8 = D1 ('MetaData "Bit8" "Ersatz.Bits" "ersatz-0.6-AqdcKC2j1aSLWyGA90SA2m" 'False) (C1 ('MetaCons "Bit8" 'PrefixI 'False) (((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit))) :*: ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Bit)))))
type Decoded Bit8 Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bit8 = Word8

Variable length bit vectors

newtype Bits Source #

A container of Bits that is suitable for comparisons and arithmetic. Bits are stored with least significant bit first to enable phantom false values to be truncated.

Constructors

Bits [Bit] 

Instances

Instances details
Num Bits Source #

This instance provides full arithmetic. The result has large enough width so that there is no overflow.

Subtraction is modified: a - b denotes max 0 (a - b).

Width of a + b is 1 + max (width a) (width b), width of a * b is (width a) + (width b), width of a - b is max (width a) (width b).

fromInteger will raise error for negative arguments.

Instance details

Defined in Ersatz.Bits

Methods

(+) :: Bits -> Bits -> Bits #

(-) :: Bits -> Bits -> Bits #

(*) :: Bits -> Bits -> Bits #

negate :: Bits -> Bits #

abs :: Bits -> Bits #

signum :: Bits -> Bits #

fromInteger :: Integer -> Bits #

Show Bits Source # 
Instance details

Defined in Ersatz.Bits

Methods

showsPrec :: Int -> Bits -> ShowS #

show :: Bits -> String #

showList :: [Bits] -> ShowS #

HasBits Bits Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bits -> Bits Source #

Codec Bits Source # 
Instance details

Defined in Ersatz.Bits

Associated Types

type Decoded Bits 
Instance details

Defined in Ersatz.Bits

type Decoded Bits = Integer

Methods

decode :: Solution -> Bits -> Maybe (Decoded Bits) Source #

encode :: Decoded Bits -> Bits Source #

Equatable Bits Source # 
Instance details

Defined in Ersatz.Bits

Methods

(===) :: Bits -> Bits -> Bit Source #

(/==) :: Bits -> Bits -> Bit Source #

Orderable Bits Source # 
Instance details

Defined in Ersatz.Bits

Methods

(<?) :: Bits -> Bits -> Bit Source #

(<=?) :: Bits -> Bits -> Bit Source #

(>=?) :: Bits -> Bits -> Bit Source #

(>?) :: Bits -> Bits -> Bit Source #

type Decoded Bits Source # 
Instance details

Defined in Ersatz.Bits

type Decoded Bits = Integer

class HasBits a where Source #

HasBits provides the bits method for embedding fixed with numeric encoding types into the arbitrary width Bits type.

Methods

bits :: a -> Bits Source #

Instances

Instances details
HasBits Bit Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit -> Bits Source #

HasBits Bit1 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit1 -> Bits Source #

HasBits Bit2 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit2 -> Bits Source #

HasBits Bit3 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit3 -> Bits Source #

HasBits Bit4 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit4 -> Bits Source #

HasBits Bit5 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit5 -> Bits Source #

HasBits Bit6 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit6 -> Bits Source #

HasBits Bit7 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit7 -> Bits Source #

HasBits Bit8 Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bit8 -> Bits Source #

HasBits Bits Source # 
Instance details

Defined in Ersatz.Bits

Methods

bits :: Bits -> Bits Source #

isEven :: HasBits b => b -> Bit Source #

Predicate for even-valued Bitss.

isOdd :: HasBits b => b -> Bit Source #

Predicate for odd-valued Bitss.

sumBit :: Foldable t => t Bit -> Bits Source #

Optimization of sumBits enabled when summing individual Bits.

sumBits :: (Foldable t, HasBits a) => t a -> Bits Source #

Compute the sum of a source of Bits values.

Adders

fullAdder Source #

Arguments

:: Bit 
-> Bit 
-> Bit 
-> (Bit, Bit)

(sum, carry)

Compute the sum and carry bit from adding three bits.

halfAdder Source #

Arguments

:: Bit 
-> Bit 
-> (Bit, Bit)

(sum, carry)

Compute the sum and carry bit from adding two bits.