Numeric.Basics

Constants

pattern M_E :: (Eq a, Fractional a) => Fractional a => a

\( e \)

pattern M_LOG2E :: (Eq a, Fractional a) => Fractional a => a

\( \log_2 e \)

pattern M_LOG10E :: (Eq a, Fractional a) => Fractional a => a

\( \log_{10} e \)

pattern M_LN2 :: (Eq a, Fractional a) => Fractional a => a

\( \log_e 2 \)

pattern M_LN10 :: (Eq a, Fractional a) => Fractional a => a

\( \log_e 10 \)

pattern M_SQRT2 :: (Eq a, Fractional a) => Fractional a => a

\( \sqrt{2} \)

pattern M_SQRT1_2 :: (Eq a, Fractional a) => Fractional a => a

\( \frac{1}{\sqrt{2}} \)

pattern M_PI :: (Eq a, Fractional a) => Fractional a => a

\( \pi \)

pattern M_PI_2 :: (Eq a, Fractional a) => Fractional a => a

\( \frac{\pi}{2} \)

pattern M_PI_3 :: (Eq a, Fractional a) => Fractional a => a

\( \frac{\pi}{3} \)

pattern M_PI_4 :: (Eq a, Fractional a) => Fractional a => a

\( \frac{\pi}{4} \)

pattern M_1_PI :: (Eq a, Fractional a) => Fractional a => a

\( \frac{1}{\pi} \)

pattern M_2_PI :: (Eq a, Fractional a) => Fractional a => a

\( \frac{2}{\pi} \)

pattern M_2_SQRTPI :: (Eq a, Fractional a) => Fractional a => a

\( \frac{2}{\sqrt{\pi}} \)

class (Eq a, Floating a) => Epsilon a where

Define a meaningful precision for complex floating-point operations.

Methods

epsilon :: a

A small positive number that depends on the type of a. Compare your values to epsilon to tell if they are near zero.

Instances

Epsilon Double

Defined in Numeric.Basics

Methods

epsilon :: Double

Epsilon Float

Defined in Numeric.Basics

Methods

epsilon :: Float

Epsilon (DFBackend t ds) => Epsilon (DataFrame t ds)

Defined in Numeric.DataFrame.Type

Methods

epsilon :: DataFrame t ds

(Epsilon (DataFrame ts ('[] :: [Nat])), KnownBackends ts ('[] :: [Nat]), Eq (DataFrame ts ('[] :: [XNat]))) => Epsilon (DataFrame ts ('[] :: [XNat]))

Defined in Numeric.DataFrame.Type

Methods

epsilon :: DataFrame ts '[]

pattern M_EPS :: Epsilon a => a

A small positive number that depends on the type of a.

Functions

class (Real a, PrimBytes a) => RealExtras a where

Extra functions for Real types.

Minimal complete definition

Nothing

Methods

copysign :: a -> a -> a

copysign x y returns a value with the magnitude of x and the sign of y.

NB: in future, this function is to reimplemented using primops and should behave the same way as its C analogue.

Instances

RealExtras Double

Defined in Numeric.Basics

Methods

copysign :: Double -> Double -> Double

RealExtras Float

Defined in Numeric.Basics

Methods

copysign :: Float -> Float -> Float

RealExtras Int

Defined in Numeric.Basics

Methods

copysign :: Int -> Int -> Int

RealExtras Int8

Defined in Numeric.Basics

Methods

copysign :: Int8 -> Int8 -> Int8

RealExtras Int16

Defined in Numeric.Basics

Methods

copysign :: Int16 -> Int16 -> Int16

RealExtras Int32

Defined in Numeric.Basics

Methods

copysign :: Int32 -> Int32 -> Int32

RealExtras Int64

Defined in Numeric.Basics

Methods

copysign :: Int64 -> Int64 -> Int64

RealExtras Word

Defined in Numeric.Basics

Methods

copysign :: Word -> Word -> Word

RealExtras Word8

Defined in Numeric.Basics

Methods

copysign :: Word8 -> Word8 -> Word8

RealExtras Word16

Defined in Numeric.Basics

Methods

copysign :: Word16 -> Word16 -> Word16

RealExtras Word32

Defined in Numeric.Basics

Methods

copysign :: Word32 -> Word32 -> Word32

RealExtras Word64

Defined in Numeric.Basics

Methods

copysign :: Word64 -> Word64 -> Word64

RealExtras (DFBackend t ds) => RealExtras (DataFrame t ds)

Defined in Numeric.DataFrame.Type

Methods

copysign :: DataFrame t ds -> DataFrame t ds -> DataFrame t ds

(RealExtras (DataFrame t ('[] :: [Nat])), KnownBackend t ('[] :: [Nat]), Eq t) => RealExtras (DataFrame t ('[] :: [XNat]))

Defined in Numeric.DataFrame.Type

Methods

copysign :: DataFrame t '[] -> DataFrame t '[] -> DataFrame t '[]

class (Epsilon a, RealExtras a, RealFloat a) => RealFloatExtras a where

Extra functions for RealFrac types.

Minimal complete definition

maxFinite

Methods

hypot :: a -> a -> a

\( \sqrt{ x^2 + y^2 } \).

NB: in future, this function is to reimplemented using primops and should behave the same way as its C analogue.

maxFinite :: a

Maximum finite number representable by this FP type.

Instances

RealFloatExtras Double

Defined in Numeric.Basics

Methods

hypot :: Double -> Double -> Double

maxFinite :: Double

RealFloatExtras Float

Defined in Numeric.Basics

Methods

hypot :: Float -> Float -> Float

maxFinite :: Float

RealFloatExtras (DFBackend t ds) => RealFloatExtras (DataFrame t ds)

Defined in Numeric.DataFrame.Type

Methods

hypot :: DataFrame t ds -> DataFrame t ds -> DataFrame t ds

maxFinite :: DataFrame t ds

(RealFloatExtras (DataFrame t ('[] :: [Nat])), KnownBackend t ('[] :: [Nat]), Eq t) => RealFloatExtras (DataFrame t ('[] :: [XNat]))

Defined in Numeric.DataFrame.Type

Methods

hypot :: DataFrame t '[] -> DataFrame t '[] -> DataFrame t '[]

maxFinite :: DataFrame t '[]

negateUnless :: Num t => Bool -> t -> t

Negate if False. This is a useful alternative to signum, when signum 0 == 0 causing some troubles.

Exceptions

type IterativeMethod = HasCallStack

This is just an alias for the HasCallStack constraint. It servers two goals:

1. Document functions that use iterative methods and can fail (supposedly in extremely rare cases).
2. Provide a call stack in case of failure.

Use tooManyIterations function where necessary if you implement an iterative algorithm and annotate your implementation function with IterativeMethod constraint.

data TooManyIterations

Typically, this exception can occur in an iterative algorithm; when the number of iterations exceeds a pre-defined limit, but the stop condition is not fulfilled.

Use the IterativeMethod constraint to annotate functions that throw this exception.

Instances

Eq TooManyIterations

Note, this instance ignores oodCallStack

Defined in Numeric.Basics

Methods

(==) :: TooManyIterations -> TooManyIterations -> Bool

(/=) :: TooManyIterations -> TooManyIterations -> Bool

Ord TooManyIterations

Note, this instance ignores oodCallStack

Defined in Numeric.Basics

Methods

compare :: TooManyIterations -> TooManyIterations -> Ordering

(<) :: TooManyIterations -> TooManyIterations -> Bool

(<=) :: TooManyIterations -> TooManyIterations -> Bool

(>) :: TooManyIterations -> TooManyIterations -> Bool

(>=) :: TooManyIterations -> TooManyIterations -> Bool

max :: TooManyIterations -> TooManyIterations -> TooManyIterations

min :: TooManyIterations -> TooManyIterations -> TooManyIterations

Show TooManyIterations

Defined in Numeric.Basics

Methods

showsPrec :: Int -> TooManyIterations -> ShowS

show :: TooManyIterations -> String

showList :: [TooManyIterations] -> ShowS

Exception TooManyIterations

Defined in Numeric.Basics

Methods

toException :: TooManyIterations -> SomeException

fromException :: SomeException -> Maybe TooManyIterations

displayException :: TooManyIterations -> String

tooManyIterations

Arguments

:: IterativeMethod

=> String

Label (e.g. function name)

-> a

Throw a TooManyIterations exception.