Numeric.MixedTypes.Elementary

Square root

class CanSqrt t where

A replacement for Prelude's sqrt. If Floating t, then one can use the default implementation to mirror Prelude's sqrt.

Minimal complete definition

Nothing

Associated Types

type SqrtType t

type SqrtType t = t

Methods

sqrt :: t -> SqrtType t

default sqrt :: (SqrtType t ~ t, Floating t) => t -> SqrtType t

Instances

CanSqrt Double

Defined in Numeric.MixedTypes.Elementary

Associated Types

type SqrtType Double

Methods

sqrt :: Double -> SqrtType Double

(CanSqrt a, CanTestPosNeg a, CanMinMaxThis a Integer) => CanSqrt (CN a)

Defined in Numeric.MixedTypes.Elementary

Associated Types

type SqrtType (CN a)

Methods

sqrt :: CN a -> SqrtType (CN a)

type CanSqrtSameType t = (CanSqrt t, SqrtType t ~ t)

specCanSqrtReal :: _ => T t -> Spec

HSpec properties that each implementation of CanSqrt should satisfy.

Exp

class CanExp t where

A replacement for Prelude's exp. If Floating t, then one can use the default implementation to mirror Prelude's exp.

Minimal complete definition

Nothing

Associated Types

type ExpType t

type ExpType t = t

Methods

exp :: t -> ExpType t

default exp :: (ExpType t ~ t, Floating t) => t -> ExpType t

Instances

CanExp Double

Defined in Numeric.MixedTypes.Elementary

Associated Types

type ExpType Double

Methods

exp :: Double -> ExpType Double

(CanExp t, CanSinCos t, CanMulAsymmetric (ExpType t) (SinCosType t)) => CanExp (Complex t)

Defined in Numeric.MixedTypes.Complex

Associated Types

type ExpType (Complex t)

Methods

exp :: Complex t -> ExpType (Complex t)

CanExp a => CanExp (CN a)

Defined in Numeric.MixedTypes.Elementary

Associated Types

type ExpType (CN a)

Methods

exp :: CN a -> ExpType (CN a)

type CanExpSameType t = (CanExp t, ExpType t ~ t)

specCanExpReal :: _ => T t -> Spec

HSpec properties that each implementation of CanExp should satisfy.

Log

class CanLog t where

A replacement for Prelude's log. If Floating t, then one can use the default implementation to mirror Prelude's log.

Minimal complete definition

Nothing

Associated Types

type LogType t

type LogType t = t

Methods

log :: t -> LogType t

default log :: (LogType t ~ t, Floating t) => t -> LogType t

Instances

CanLog Double

Defined in Numeric.MixedTypes.Elementary

Associated Types

type LogType Double

Methods

log :: Double -> LogType Double

(CanLog a, CanTestPosNeg a) => CanLog (CN a)

Defined in Numeric.MixedTypes.Elementary

Associated Types

type LogType (CN a)

Methods

log :: CN a -> LogType (CN a)

type CanLogSameType t = (CanLog t, LogType t ~ t)

specCanLogReal :: _ => T t -> Spec

HSpec properties that each implementation of CanLog should satisfy.

powUsingExpLog :: (CanLogSameType t, CanExpSameType t, CanTestInteger t, CanTestZero t) => t -> (t -> t -> t) -> (t -> t) -> t -> t -> t

Sine and cosine

class CanSinCos t where

A replacement for Prelude's cos and sin. If Floating t, then one can use the default implementation to mirror Prelude's sin, cos.

Minimal complete definition

Nothing

Associated Types

type SinCosType t

type SinCosType t = t

Methods

cos :: t -> SinCosType t

default cos :: (SinCosType t ~ t, Floating t) => t -> SinCosType t

sin :: t -> SinCosType t

default sin :: (SinCosType t ~ t, Floating t) => t -> SinCosType t

Instances

CanSinCos Double

Defined in Numeric.MixedTypes.Elementary

Associated Types

type SinCosType Double

Methods

cos :: Double -> SinCosType Double

sin :: Double -> SinCosType Double

CanSinCos a => CanSinCos (CN a)

Defined in Numeric.MixedTypes.Elementary

Associated Types

type SinCosType (CN a)

Methods

cos :: CN a -> SinCosType (CN a)

sin :: CN a -> SinCosType (CN a)

type CanSinCosSameType t = (CanSinCos t, SinCosType t ~ t)

specCanSinCosReal :: _ => T t -> Spec

HSpec properties that each implementation of CanSinCos should satisfy.

Derived partially from http://math.stackexchange.com/questions/1303044/axiomatic-definition-of-sin-and-cos

approxPi :: Floating t => t

Approximate pi, synonym for Prelude's pi.

We do not define (exect) pi in this package as we have no type that can represent it exactly.