Posit

Library implementing standard Posit Numbers (Posit Standard version 3.2.0.0, with some improvements) a fixed width word size of 2^es bytes.

Main Exported Types

type Posit8 = Posit Z

An 8-bit Posit number with es ~ Z

type Posit16 = Posit I

An 16-bit Posit number with es ~ I

type Posit32 = Posit II

An 32-bit Posit number with es ~ II

type Posit64 = Posit III

An 64-bit Posit number with es ~ III

type Posit128 = Posit IV

An 128-bit Posit number with es ~ IV

type Posit256 = Posit V

An 256-bit Posit number with es ~ V

Patterns for Matching Exported Types

pattern NaR :: PositC es => Posit es

Not a Real Number, the Posit is like a Maybe type, it's either a real number or not

A pattern for Exception handling when a value is Not a Real number (NaR).

pattern R :: PositC es => Rational -> Posit es

A Real or at least Rational Number, rounded to the nearest Posit Rational representation

A pattern for the non-Exceptional case, yielding a Rational, will make a total function when paired with NaR, if the Rational implementation is total.

Fused Operation Interface defined by the Posit Standard

class Num a => FusedOps a where

A class that delays the rounding operation until the end for some operations

Methods

fma :: a -> a -> a -> a

Fused Multiply Add: (a * b) + c

fam :: a -> a -> a -> a

Fused Add Multiply: (a + b) * c

fmms :: a -> a -> a -> a -> a

Fused Multiply Multiply Subtract: (a * b) - (c * d)

fsum3 :: a -> a -> a -> a

Fused Sum of 3 values: a + b + c

fsum4 :: a -> a -> a -> a -> a

Fused Sum of 4 values: a + b + c + d

fsumL :: Foldable t => t a -> a

Fused Sum of a List of Posits

fdot3 :: a -> a -> a -> a -> a -> a -> a

Fused Dot Product of 3 element vector: (a1 * b1) + (a2 * b2) + (a3 * b3)

fdot4 :: a -> a -> a -> a -> a -> a -> a -> a -> a

Fused Dot Product of 4 element vector: (a0 * b0) + (a1 * b1) + (a2 * b2) + (a3 * b3)

fdotL :: Foldable t => t a -> t a -> a

Fused Dot Product of Two Lists

fsm :: a -> a -> a -> a

Fused Subtract Multiply: a - (b * c)

Instances

FusedOps Rational

Defined in Posit

Methods

fma :: Rational -> Rational -> Rational -> Rational

fam :: Rational -> Rational -> Rational -> Rational

fmms :: Rational -> Rational -> Rational -> Rational -> Rational

fsum3 :: Rational -> Rational -> Rational -> Rational

fsum4 :: Rational -> Rational -> Rational -> Rational -> Rational

fsumL :: Foldable t => t Rational -> Rational

fdot3 :: Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational

fdot4 :: Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational

fdotL :: Foldable t => t Rational -> t Rational -> Rational

fsm :: Rational -> Rational -> Rational -> Rational

Posits are Convertable between different Posit representations

class Convertible a b where

A Convertible class that will cast or convert between two different Posit es types

Methods

convert :: a -> b

Additional functions to show the Posit in different formats

class AltShow a where

A Alternative to the typical Show class to assist in displaying the Posit es type in different formats

Methods

displayBinary :: a -> String

Display the Posit in its Binary Representation

displayIntegral :: a -> String

Display the Posit in its Integral Representation

displayRational :: a -> String

Display the Posit as a Rational

displayDecimal :: a -> String

Display the Posit as a Decimal until the Repetend occurs

Additional Special Functions

class AltFloating p where

Methods

phi :: p

gamma :: p -> p

sinc :: p -> p

expm1 :: p -> p

Instances

AltFloating Posit128

Defined in Posit

Methods

phi :: Posit128

gamma :: Posit128 -> Posit128

sinc :: Posit128 -> Posit128

expm1 :: Posit128 -> Posit128

AltFloating Posit16

Defined in Posit

Methods

phi :: Posit16

gamma :: Posit16 -> Posit16

sinc :: Posit16 -> Posit16

expm1 :: Posit16 -> Posit16

AltFloating Posit256

Defined in Posit

Methods

phi :: Posit256

gamma :: Posit256 -> Posit256

sinc :: Posit256 -> Posit256

expm1 :: Posit256 -> Posit256

AltFloating Posit32

Defined in Posit

Methods

phi :: Posit32

gamma :: Posit32 -> Posit32

sinc :: Posit32 -> Posit32

expm1 :: Posit32 -> Posit32

AltFloating Posit64

Defined in Posit

Methods

phi :: Posit64

gamma :: Posit64 -> Posit64

sinc :: Posit64 -> Posit64

expm1 :: Posit64 -> Posit64

AltFloating Posit8

Defined in Posit

Methods

phi :: Posit8

gamma :: Posit8 -> Posit8

sinc :: Posit8 -> Posit8

expm1 :: Posit8 -> Posit8

Functions to lift functions of Integers or Rationals to operate on Posit Types

viaIntegral :: forall es. PositC es => (IntN es -> IntN es) -> Posit es -> Posit es

viaRational :: (PositC es, Ord (IntN es), Num (IntN es)) => (Rational -> Rational) -> Posit es -> Posit es

viaRational2 :: (PositC es, Ord (IntN es), Num (IntN es)) => (Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es

viaRational3 :: (PositC es, Ord (IntN es), Num (IntN es)) => (Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es

viaRational4 :: (PositC es, Ord (IntN es), Num (IntN es)) => (Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es

viaRational6 :: (PositC es, Ord (IntN es), Num (IntN es)) => (Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es

viaRational8 :: (PositC es, Ord (IntN es), Num (IntN es)) => (Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es