Crypto.Lol.Types.Unsafe.Complex

Data type, functions, and instances for complex numbers. This module is "unsafe" because it exports the Complex constructor. This module should only be used to make tensor-specific instances for Complex. The safe way to use this type is to import Crypto.Lol.Types.

Documentation

newtype Complex a

Newtype wrapper (with slightly different instances) for Number.Complex.

Constructors

Complex' (T a)

Instances

Transcendental a => CRTrans Maybe (Complex a)

For testing ergonomics, we also have a Maybe instance of CRTrans for complex numbers.

Defined in Crypto.Lol.CRTrans

Methods

crtInfo :: Reflects m Int => TaggedT m Maybe (CRTInfo (Complex a))

Transcendental a => CRTrans Identity (Complex a)

Complex numbers have CRTrans for any index \(m\)

Defined in Crypto.Lol.CRTrans

Methods

crtInfo :: Reflects m Int => TaggedT m Identity (CRTInfo (Complex a))

Eq a => Eq (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

(==) :: Complex a -> Complex a -> Bool

(/=) :: Complex a -> Complex a -> Bool

Show a => Show (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

showsPrec :: Int -> Complex a -> ShowS

show :: Complex a -> String

showList :: [Complex a] -> ShowS

Random a => Random (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

randomR :: RandomGen g => (Complex a, Complex a) -> g -> (Complex a, g)

random :: RandomGen g => g -> (Complex a, g)

randomRs :: RandomGen g => (Complex a, Complex a) -> g -> [Complex a]

randoms :: RandomGen g => g -> [Complex a]

randomRIO :: (Complex a, Complex a) -> IO (Complex a)

randomIO :: IO (Complex a)

NFData a => NFData (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

rnf :: Complex a -> ()

C a => C (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

(/) :: Complex a -> Complex a -> Complex a

recip :: Complex a -> Complex a

fromRational' :: Rational -> Complex a

(^-) :: Complex a -> Integer -> Complex a

Field a => C (Complex a)

Custom instance replacing the one provided by numeric prelude: it always returns 0 as the remainder of a division. (The NP instance sometimes has precision issues, because it yields nonzero remainders, which is a problem for divG methods.)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

div :: Complex a -> Complex a -> Complex a

mod :: Complex a -> Complex a -> Complex a

divMod :: Complex a -> Complex a -> (Complex a, Complex a)

C a => C (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

(*) :: Complex a -> Complex a -> Complex a

one :: Complex a

fromInteger :: Integer -> Complex a

(^) :: Complex a -> Integer -> Complex a

C a => C (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

isZero :: Complex a -> Bool

C a => C (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

zero :: Complex a

(+) :: Complex a -> Complex a -> Complex a

(-) :: Complex a -> Complex a -> Complex a

negate :: Complex a -> Complex a

Transcendental a => CRTEmbed (Complex a)

Self-embed

Defined in Crypto.Lol.CRTrans

Associated Types

type CRTExt (Complex a) :: Type

Methods

toExt :: Complex a -> CRTExt (Complex a)

fromExt :: CRTExt (Complex a) -> Complex a

ApproxEqual (Complex Double)

Defined in Crypto.Lol.Utils.Tests

Methods

(=~=) :: Complex Double -> Complex Double -> Bool

Show (ArgType (Complex Double))

Defined in Crypto.Lol.Utils.ShowType

Methods

showsPrec :: Int -> ArgType (Complex Double) -> ShowS

show :: ArgType (Complex Double) -> String

showList :: [ArgType (Complex Double)] -> ShowS

type CRTExt (Complex a)

Defined in Crypto.Lol.CRTrans

type CRTExt (Complex a) = Complex a

roundComplex :: (RealRing a, ToInteger b) => Complex a -> (b, b)

Rounds the real and imaginary components to the nearest integer.

cis :: Transcendental a => a -> Complex a

cis \(t\) is a complex value with magnitude 1 and phase \(t \bmod 2\cdot\pi\)).

real :: Complex a -> a

Real component of a complex number.

imag :: Complex a -> a

Imaginary component of a complex number.

fromReal :: Additive a => a -> Complex a

Embeds a scalar as the real component of a complex number.