Safe Haskell	None
Language	Haskell2010

Circuit.Arithmetic

Description

Definition of arithmetic circuits: one with a single multiplication gate with affine inputs and another variant with an arbitrary number of such gates.

Synopsis

data Gate i f
- = Mul {
  - mulLeft :: AffineCircuit i f
  - mulRight :: AffineCircuit i f
  - mulOutput :: i
  }
- | Equal {
  - eqInput :: i
  - eqMagic :: i
  - eqOutput :: i
  }
- | Split {
  - splitInput :: i
  - splitOutputs :: [i]
  }
mapVarsGate :: (i -> j) -> Gate i f -> Gate j f
collectInputsGate :: Ord i => Gate i f -> [i]
outputWires :: Gate i f -> [i]
newtype ArithCircuit f = ArithCircuit [Gate Wire f]
fetchVars :: AffineCircuit Wire f -> [Wire]
generateRoots :: Applicative m => m f -> ArithCircuit f -> m [[f]]
validArithCircuit :: ArithCircuit f -> Bool
data Wire
- = InputWire Int
- | IntermediateWire Int
- | OutputWire Int
evalGate :: (Bits f, Fractional f) => (i -> vars -> Maybe f) -> (i -> f -> vars -> vars) -> vars -> Gate i f -> vars
evalArithCircuit :: forall f vars. (Bits f, Fractional f) => (Wire -> vars -> Maybe f) -> (Wire -> f -> vars -> vars) -> ArithCircuit f -> vars -> vars
unsplit :: Num f => [Wire] -> AffineCircuit Wire f

Documentation

data Gate i f Source #

An arithmetic circuit with a single multiplication gate.

Constructors

Mul
Fields mulLeft :: AffineCircuit i f mulRight :: AffineCircuit i f mulOutput :: i
Equal
Fields eqInput :: i eqMagic :: i eqOutput :: i
Split
Fields splitInput :: i splitOutputs :: [i]

Instances

(Eq f, Eq i) => Eq (Gate i f) Source #
Instance details Defined in Circuit.Arithmetic Methods (==) :: Gate i f -> Gate i f -> Bool # (/=) :: Gate i f -> Gate i f -> Bool #
(Show f, Show i) => Show (Gate i f) Source #
Instance details Defined in Circuit.Arithmetic Methods showsPrec :: Int -> Gate i f -> ShowS # show :: Gate i f -> String # showList :: [Gate i f] -> ShowS #
Generic (Gate i f) Source #
Instance details Defined in Circuit.Arithmetic Associated Types type Rep (Gate i f) :: Type -> Type # Methods from :: Gate i f -> Rep (Gate i f) x # to :: Rep (Gate i f) x -> Gate i f #
(ToJSON i, ToJSON f) => ToJSON (Gate i f) Source #
Instance details Defined in Circuit.Arithmetic Methods toJSON :: Gate i f -> Value # toEncoding :: Gate i f -> Encoding # toJSONList :: [Gate i f] -> Value # toEncodingList :: [Gate i f] -> Encoding #
(FromJSON i, FromJSON f) => FromJSON (Gate i f) Source #
Instance details Defined in Circuit.Arithmetic Methods parseJSON :: Value -> Parser (Gate i f) # parseJSONList :: Value -> Parser [Gate i f] #
(NFData f, NFData i) => NFData (Gate i f) Source #
Instance details Defined in Circuit.Arithmetic Methods rnf :: Gate i f -> () #
(Pretty i, Show f) => Pretty (Gate i f) Source #
Instance details Defined in Circuit.Arithmetic Methods pretty :: Gate i f -> Doc # prettyList :: [Gate i f] -> Doc #
type Rep (Gate i f) Source #
Instance details Defined in Circuit.Arithmetic type Rep (Gate i f) = D1 (MetaData "Gate" "Circuit.Arithmetic" "arithmetic-circuits-0.2.0-6zOfGRHnhI9W2wAnMDkNU" False) (C1 (MetaCons "Mul" PrefixI True) (S1 (MetaSel (Just "mulLeft") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 (AffineCircuit i f)) :: (S1 (MetaSel (Just "mulRight") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 (AffineCircuit i f)) :: S1 (MetaSel (Just "mulOutput") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 i))) :+: (C1 (MetaCons "Equal" PrefixI True) (S1 (MetaSel (Just "eqInput") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 i) :: (S1 (MetaSel (Just "eqMagic") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 i) :: S1 (MetaSel (Just "eqOutput") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 i))) :+: C1 (MetaCons "Split" PrefixI True) (S1 (MetaSel (Just "splitInput") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 i) :*: S1 (MetaSel (Just "splitOutputs") NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 [i]))))

mapVarsGate :: (i -> j) -> Gate i f -> Gate j f Source #

Apply mapping to variable names, i.e. rename variables. (Ideally the mapping is injective.)

collectInputsGate :: Ord i => Gate i f -> [i] Source #

outputWires :: Gate i f -> [i] Source #

List output wires of a gate

newtype ArithCircuit f Source #

A circuit is a list of multiplication gates along with their output wire labels (which can be intermediate or actual outputs).

Constructors

ArithCircuit [Gate Wire f]

Instances

Eq f => Eq (ArithCircuit f) Source #
Instance details Defined in Circuit.Arithmetic Methods (==) :: ArithCircuit f -> ArithCircuit f -> Bool # (/=) :: ArithCircuit f -> ArithCircuit f -> Bool #
Show f => Show (ArithCircuit f) Source #
Instance details Defined in Circuit.Arithmetic Methods showsPrec :: Int -> ArithCircuit f -> ShowS # show :: ArithCircuit f -> String # showList :: [ArithCircuit f] -> ShowS #
Generic (ArithCircuit f) Source #
Instance details Defined in Circuit.Arithmetic Associated Types type Rep (ArithCircuit f) :: Type -> Type # Methods from :: ArithCircuit f -> Rep (ArithCircuit f) x # to :: Rep (ArithCircuit f) x -> ArithCircuit f #
ToJSON f => ToJSON (ArithCircuit f) Source #
Instance details Defined in Circuit.Arithmetic Methods toJSON :: ArithCircuit f -> Value # toEncoding :: ArithCircuit f -> Encoding # toJSONList :: [ArithCircuit f] -> Value # toEncodingList :: [ArithCircuit f] -> Encoding #
FromJSON f => FromJSON (ArithCircuit f) Source #
Instance details Defined in Circuit.Arithmetic Methods parseJSON :: Value -> Parser (ArithCircuit f) # parseJSONList :: Value -> Parser [ArithCircuit f] #
NFData f => NFData (ArithCircuit f) Source #
Instance details Defined in Circuit.Arithmetic Methods rnf :: ArithCircuit f -> () #
Show f => Pretty (ArithCircuit f) Source #
Instance details Defined in Circuit.Arithmetic Methods pretty :: ArithCircuit f -> Doc # prettyList :: [ArithCircuit f] -> Doc #
type Rep (ArithCircuit f) Source #
Instance details Defined in Circuit.Arithmetic type Rep (ArithCircuit f) = D1 (MetaData "ArithCircuit" "Circuit.Arithmetic" "arithmetic-circuits-0.2.0-6zOfGRHnhI9W2wAnMDkNU" True) (C1 (MetaCons "ArithCircuit" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [Gate Wire f])))

fetchVars :: AffineCircuit Wire f -> [Wire] Source #

generateRoots :: Applicative m => m f -> ArithCircuit f -> m [[f]] Source #

Generate enough roots for a circuit

validArithCircuit :: ArithCircuit f -> Bool Source #

Check whether an arithmetic circuit does not refer to intermediate wires before they are defined and whether output wires are not used as input wires.

data Wire Source #

Wires are can be labeled in the ways given in this data type

Constructors

InputWire Int
IntermediateWire Int
OutputWire Int

Instances

Eq Wire Source #
Instance details Defined in Circuit.Arithmetic Methods (==) :: Wire -> Wire -> Bool # (/=) :: Wire -> Wire -> Bool #
Ord Wire Source #
Instance details Defined in Circuit.Arithmetic Methods compare :: Wire -> Wire -> Ordering # (<) :: Wire -> Wire -> Bool # (<=) :: Wire -> Wire -> Bool # (>) :: Wire -> Wire -> Bool # (>=) :: Wire -> Wire -> Bool # max :: Wire -> Wire -> Wire # min :: Wire -> Wire -> Wire #
Show Wire Source #
Instance details Defined in Circuit.Arithmetic Methods showsPrec :: Int -> Wire -> ShowS # show :: Wire -> String # showList :: [Wire] -> ShowS #
Generic Wire Source #
Instance details Defined in Circuit.Arithmetic Associated Types type Rep Wire :: Type -> Type # Methods from :: Wire -> Rep Wire x # to :: Rep Wire x -> Wire #
ToJSON Wire Source #
Instance details Defined in Circuit.Arithmetic Methods toJSON :: Wire -> Value # toEncoding :: Wire -> Encoding # toJSONList :: [Wire] -> Value # toEncodingList :: [Wire] -> Encoding #
FromJSON Wire Source #
Instance details Defined in Circuit.Arithmetic Methods parseJSON :: Value -> Parser Wire # parseJSONList :: Value -> Parser [Wire] #
NFData Wire Source #
Instance details Defined in Circuit.Arithmetic Methods rnf :: Wire -> () #
Pretty Wire Source #
Instance details Defined in Circuit.Arithmetic Methods pretty :: Wire -> Doc # prettyList :: [Wire] -> Doc #
type Rep Wire Source #
Instance details Defined in Circuit.Arithmetic type Rep Wire = D1 (MetaData "Wire" "Circuit.Arithmetic" "arithmetic-circuits-0.2.0-6zOfGRHnhI9W2wAnMDkNU" False) (C1 (MetaCons "InputWire" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Int)) :+: (C1 (MetaCons "IntermediateWire" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Int)) :+: C1 (MetaCons "OutputWire" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedStrict) (Rec0 Int))))

evalGate Source #

Arguments

:: (Bits f, Fractional f)
=> (i -> vars -> Maybe f)	lookup a value at a wire
-> (i -> f -> vars -> vars)	update a value at a wire
-> vars	context before evaluation
-> Gate i f	gate
-> vars	context after evaluation

Evaluate a single gate

evalArithCircuit Source #

Arguments

:: (Bits f, Fractional f)
=> (Wire -> vars -> Maybe f)	lookup a value at a wire
-> (Wire -> f -> vars -> vars)	update a value at a wire
-> ArithCircuit f	circuit to evaluate
-> vars	input variables
-> vars	input and output variables

Evaluate an arithmetic circuit on a given environment containing the inputs. Outputs the entire environment (outputs, intermediate values and inputs).

unsplit Source #

Arguments

:: Num f
=> [Wire]	(binary) wires containing a binary expansion, small-endian
-> AffineCircuit Wire f

Turn a binary expansion back into a single value.