Copyright	(c) Galois Inc 2014-2020
License	BSD3
Maintainer	Joe Hendrix <jhendrix@galois.com>
Stability	provisional
Safe Haskell	Safe-Inferred
Language	Haskell2010

What4.Utils.Complex

Description

This module provides complex numbers without the RealFloat constraints that Data.Complex has. This is useful for representing various intermediate symbolic representations of complex numbers that are not literally number representations.

Synopsis

data Complex a = !a :+ !a
realPart :: Complex a -> a
imagPart :: Complex a -> a
magnitude :: Floating a => Complex a -> a
magnitudeSq :: Num a => Complex a -> a
complexNegate :: Num a => Complex a -> Complex a
complexAdd :: Num a => Complex a -> Complex a -> Complex a
complexSub :: Num a => Complex a -> Complex a -> Complex a
complexMul :: Num a => Complex a -> Complex a -> Complex a
complexDiv :: Fractional a => Complex a -> Complex a -> Complex a
complexRecip :: Fractional a => Complex a -> Complex a
tryComplexSqrt :: (Ord a, Fractional a, Monad m) => (a -> m a) -> Complex a -> m (Complex a)
tryMagnitude :: Num a => (a -> b) -> Complex a -> b
complexAsRational :: Complex Rational -> Maybe Rational

Documentation

data Complex a Source #

A complex pair over an arbitrary type.

Constructors

!a :+ !a infix 6

Instances

Instances details

Functor Complex Source #
Instance details Defined in What4.Utils.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Foldable Complex Source #
Instance details Defined in What4.Utils.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # toList :: Complex a -> [a] # null :: Complex a -> Bool # length :: Complex a -> Int # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # sum :: Num a => Complex a -> a # product :: Num a => Complex a -> a #
Traversable Complex Source #
Instance details Defined in What4.Utils.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Eq a => Eq (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods (==) :: Complex a -> Complex a -> Bool # (/=) :: Complex a -> Complex a -> Bool #
RealFloat a => Floating (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods pi :: Complex a # exp :: Complex a -> Complex a # log :: Complex a -> Complex a # sqrt :: Complex a -> Complex a # (**) :: Complex a -> Complex a -> Complex a # logBase :: Complex a -> Complex a -> Complex a # sin :: Complex a -> Complex a # cos :: Complex a -> Complex a # tan :: Complex a -> Complex a # asin :: Complex a -> Complex a # acos :: Complex a -> Complex a # atan :: Complex a -> Complex a # sinh :: Complex a -> Complex a # cosh :: Complex a -> Complex a # tanh :: Complex a -> Complex a # asinh :: Complex a -> Complex a # acosh :: Complex a -> Complex a # atanh :: Complex a -> Complex a # log1p :: Complex a -> Complex a # expm1 :: Complex a -> Complex a # log1pexp :: Complex a -> Complex a # log1mexp :: Complex a -> Complex a #
Floating a => Fractional (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods (/) :: Complex a -> Complex a -> Complex a # recip :: Complex a -> Complex a # fromRational :: Rational -> Complex a #
Floating a => Num (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods (+) :: Complex a -> Complex a -> Complex a # (-) :: Complex a -> Complex a -> Complex a # (*) :: Complex a -> Complex a -> Complex a # negate :: Complex a -> Complex a # abs :: Complex a -> Complex a # signum :: Complex a -> Complex a # fromInteger :: Integer -> Complex a #
Ord a => Ord (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods compare :: Complex a -> Complex a -> Ordering # (<) :: Complex a -> Complex a -> Bool # (<=) :: Complex a -> Complex a -> Bool # (>) :: Complex a -> Complex a -> Bool # (>=) :: Complex a -> Complex a -> Bool # max :: Complex a -> Complex a -> Complex a # min :: Complex a -> Complex a -> Complex a #
(Ord a, Floating a) => Real (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods toRational :: Complex a -> Rational #
(Ord a, Floating a) => RealFrac (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods properFraction :: Integral b => Complex a -> (b, Complex a) # truncate :: Integral b => Complex a -> b # round :: Integral b => Complex a -> b # ceiling :: Integral b => Complex a -> b # floor :: Integral b => Complex a -> b #
(Eq a, Num a, Show a) => Show (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods showsPrec :: Int -> Complex a -> ShowS # show :: Complex a -> String # showList :: [Complex a] -> ShowS #
Generic (Complex a) Source #
Instance details Defined in What4.Utils.Complex Associated Types type Rep (Complex a) :: Type -> Type # Methods from :: Complex a -> Rep (Complex a) x # to :: Rep (Complex a) x -> Complex a #
Hashable a => Hashable (Complex a) Source #
Instance details Defined in What4.Utils.Complex Methods hashWithSalt :: Int -> Complex a -> Int # hash :: Complex a -> Int #
PolyEq x y => PolyEq (Complex x) (Complex y) Source #
Instance details Defined in What4.Utils.Complex Methods polyEqF :: Complex x -> Complex y -> Maybe (Complex x :~: Complex y) # polyEq :: Complex x -> Complex y -> Bool #
type Rep (Complex a) Source #
Instance details Defined in What4.Utils.Complex type Rep (Complex a) = D1 ('MetaData "Complex" "What4.Utils.Complex" "what4-1.1-F6JmVDCUG2e4tsAmUzrLc2" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))

realPart :: Complex a -> a Source #

imagPart :: Complex a -> a Source #

magnitude :: Floating a => Complex a -> a Source #

magnitudeSq :: Num a => Complex a -> a Source #

Returns square of magnitude.

complexNegate :: Num a => Complex a -> Complex a Source #

complexAdd :: Num a => Complex a -> Complex a -> Complex a Source #

complexSub :: Num a => Complex a -> Complex a -> Complex a Source #

complexMul :: Num a => Complex a -> Complex a -> Complex a Source #

complexDiv :: Fractional a => Complex a -> Complex a -> Complex a Source #

complexRecip :: Fractional a => Complex a -> Complex a Source #

tryComplexSqrt Source #

Arguments

:: (Ord a, Fractional a, Monad m)
=> (a -> m a)	Square-root function defined for non-negative values a.
-> Complex a
-> m (Complex a)

tryMagnitude Source #

Arguments

:: Num a
=> (a -> b)	Sqrt function
-> Complex a
-> b

complexAsRational :: Complex Rational -> Maybe Rational Source #