Posit.Internal.PositC

Library implementing standard 'Posit-3.2' numbers, as defined by the Posit Working Group 23 June 2018.

Documentation

class PositC (es :: ES) where

The Posit class is an approximation of ℝ, it is like a sampling on the Projective Real line ℙ(ℝ) with Maybe ℚ as the internal type. The es is an index that controlls the log2 word size of the Posit's fininte precision representation.

Minimal complete definition

encode, decode, exponentSize, unReal, mostPosVal, leastPosVal, leastNegVal, mostNegVal, buildIntRep, mkIntRep, formRegime, formExponent, formFraction, regime2Integer, findRegimeFormat, countRegimeBits, exponent2Nat, fraction2Posit, displayBin

Associated Types

type IntN es = r | r -> es

Type of the Finite Precision Representation, in our case Int8, Int16, Int32, Int64, Int128, Int256. The es of kind ES will determine a result of r such that you can determine the es by the r

Methods

encode

Arguments

:: Maybe Rational

-> IntN es

Maybe you have some Rational Number and you want to encode it as some integer with a finite integer log2 word size.

Transform to/from the Infinite Precision Representation

decode

Arguments

:: IntN es

-> Maybe Rational

You have an integer with a finite integer log2 word size decode it and Maybe it is Rational

exponentSize

Arguments

:: Natural

The exponent size, es is a Natural number

Exponent Size based on the Posit Exponent kind ES

nBytes

Arguments

:: Natural

nBytes the number of bytes of the Posit Representation

Various other size definitions used in the Posit format with their default definitions

nBits

Arguments

:: Natural

nBits the number of bits of the Posit Representation

signBitSize

Arguments

:: Natural

signBitSize the size of the sign bit

uSeed

Arguments

:: Natural

uSeed scaling factor for the regime of the Posit Representation

unReal

Arguments

:: IntN es

unReal is something that is not Real, the integer value that is not a Real number

Integer Representation of common bounds

mostPosVal :: IntN es

leastPosVal :: IntN es

leastNegVal :: IntN es

mostNegVal :: IntN es

maxPosRat :: Rational

minPosRat :: Rational

maxNegRat :: Rational

minNegRat :: Rational

log_uSeed :: (Integer, Rational) -> (Integer, Rational)

getRegime :: Rational -> (Integer, Rational)

posit2TupPosit :: Rational -> (Bool, Integer, Natural, Rational)

buildIntRep :: Rational -> IntN es

mkIntRep :: Integer -> Natural -> Rational -> IntN es

formRegime :: Integer -> (IntN es, Integer)

formExponent :: Natural -> Integer -> (IntN es, Integer)

formFraction :: Rational -> Integer -> IntN es

tupPosit2Posit :: (Bool, Integer, Natural, Rational) -> Maybe Rational

regime2Integer :: IntN es -> (Integer, Int)

findRegimeFormat :: IntN es -> Bool

countRegimeBits :: Bool -> IntN es -> Int

exponent2Nat :: Int -> IntN es -> Natural

fraction2Posit :: Int -> IntN es -> Rational

displayBin :: IntN es -> String

decimalPrec :: Int

Instances

PositC 'I

Defined in Posit.Internal.PositC

Associated Types

type IntN 'I = (r :: Type)

Methods

encode :: Maybe Rational -> IntN 'I

decode :: IntN 'I -> Maybe Rational

exponentSize :: Natural

nBytes :: Natural

nBits :: Natural

signBitSize :: Natural

uSeed :: Natural

unReal :: IntN 'I

mostPosVal :: IntN 'I

leastPosVal :: IntN 'I

leastNegVal :: IntN 'I

mostNegVal :: IntN 'I

maxPosRat :: Rational

minPosRat :: Rational

maxNegRat :: Rational

minNegRat :: Rational

log_uSeed :: (Integer, Rational) -> (Integer, Rational)

getRegime :: Rational -> (Integer, Rational)

posit2TupPosit :: Rational -> (Bool, Integer, Natural, Rational)

buildIntRep :: Rational -> IntN 'I

mkIntRep :: Integer -> Natural -> Rational -> IntN 'I

formRegime :: Integer -> (IntN 'I, Integer)

formExponent :: Natural -> Integer -> (IntN 'I, Integer)

formFraction :: Rational -> Integer -> IntN 'I

tupPosit2Posit :: (Bool, Integer, Natural, Rational) -> Maybe Rational

regime2Integer :: IntN 'I -> (Integer, Int)

findRegimeFormat :: IntN 'I -> Bool

countRegimeBits :: Bool -> IntN 'I -> Int

exponent2Nat :: Int -> IntN 'I -> Natural

fraction2Posit :: Int -> IntN 'I -> Rational

displayBin :: IntN 'I -> String

decimalPrec :: Int

PositC 'II

Defined in Posit.Internal.PositC

Associated Types

type IntN 'II = (r :: Type)

Methods

encode :: Maybe Rational -> IntN 'II

decode :: IntN 'II -> Maybe Rational

exponentSize :: Natural

nBytes :: Natural

nBits :: Natural

signBitSize :: Natural

uSeed :: Natural

unReal :: IntN 'II

mostPosVal :: IntN 'II

leastPosVal :: IntN 'II

leastNegVal :: IntN 'II

mostNegVal :: IntN 'II

maxPosRat :: Rational

minPosRat :: Rational

maxNegRat :: Rational

minNegRat :: Rational

log_uSeed :: (Integer, Rational) -> (Integer, Rational)

getRegime :: Rational -> (Integer, Rational)

posit2TupPosit :: Rational -> (Bool, Integer, Natural, Rational)

buildIntRep :: Rational -> IntN 'II

mkIntRep :: Integer -> Natural -> Rational -> IntN 'II

formRegime :: Integer -> (IntN 'II, Integer)

formExponent :: Natural -> Integer -> (IntN 'II, Integer)

formFraction :: Rational -> Integer -> IntN 'II

tupPosit2Posit :: (Bool, Integer, Natural, Rational) -> Maybe Rational

regime2Integer :: IntN 'II -> (Integer, Int)

findRegimeFormat :: IntN 'II -> Bool

countRegimeBits :: Bool -> IntN 'II -> Int

exponent2Nat :: Int -> IntN 'II -> Natural

fraction2Posit :: Int -> IntN 'II -> Rational

displayBin :: IntN 'II -> String

decimalPrec :: Int

PositC 'III

Defined in Posit.Internal.PositC

Associated Types

type IntN 'III = (r :: Type)

Methods

encode :: Maybe Rational -> IntN 'III

decode :: IntN 'III -> Maybe Rational

exponentSize :: Natural

nBytes :: Natural

nBits :: Natural

signBitSize :: Natural

uSeed :: Natural

unReal :: IntN 'III

mostPosVal :: IntN 'III

leastPosVal :: IntN 'III

leastNegVal :: IntN 'III

mostNegVal :: IntN 'III

maxPosRat :: Rational

minPosRat :: Rational

maxNegRat :: Rational

minNegRat :: Rational

log_uSeed :: (Integer, Rational) -> (Integer, Rational)

getRegime :: Rational -> (Integer, Rational)

posit2TupPosit :: Rational -> (Bool, Integer, Natural, Rational)

buildIntRep :: Rational -> IntN 'III

mkIntRep :: Integer -> Natural -> Rational -> IntN 'III

formRegime :: Integer -> (IntN 'III, Integer)

formExponent :: Natural -> Integer -> (IntN 'III, Integer)

formFraction :: Rational -> Integer -> IntN 'III

tupPosit2Posit :: (Bool, Integer, Natural, Rational) -> Maybe Rational

regime2Integer :: IntN 'III -> (Integer, Int)

findRegimeFormat :: IntN 'III -> Bool

countRegimeBits :: Bool -> IntN 'III -> Int

exponent2Nat :: Int -> IntN 'III -> Natural

fraction2Posit :: Int -> IntN 'III -> Rational

displayBin :: IntN 'III -> String

decimalPrec :: Int

PositC 'IV

Defined in Posit.Internal.PositC

Associated Types

type IntN 'IV = (r :: Type)

Methods

encode :: Maybe Rational -> IntN 'IV

decode :: IntN 'IV -> Maybe Rational

exponentSize :: Natural

nBytes :: Natural

nBits :: Natural

signBitSize :: Natural

uSeed :: Natural

unReal :: IntN 'IV

mostPosVal :: IntN 'IV

leastPosVal :: IntN 'IV

leastNegVal :: IntN 'IV

mostNegVal :: IntN 'IV

maxPosRat :: Rational

minPosRat :: Rational

maxNegRat :: Rational

minNegRat :: Rational

log_uSeed :: (Integer, Rational) -> (Integer, Rational)

getRegime :: Rational -> (Integer, Rational)

posit2TupPosit :: Rational -> (Bool, Integer, Natural, Rational)

buildIntRep :: Rational -> IntN 'IV

mkIntRep :: Integer -> Natural -> Rational -> IntN 'IV

formRegime :: Integer -> (IntN 'IV, Integer)

formExponent :: Natural -> Integer -> (IntN 'IV, Integer)

formFraction :: Rational -> Integer -> IntN 'IV

tupPosit2Posit :: (Bool, Integer, Natural, Rational) -> Maybe Rational

regime2Integer :: IntN 'IV -> (Integer, Int)

findRegimeFormat :: IntN 'IV -> Bool

countRegimeBits :: Bool -> IntN 'IV -> Int

exponent2Nat :: Int -> IntN 'IV -> Natural

fraction2Posit :: Int -> IntN 'IV -> Rational

displayBin :: IntN 'IV -> String

decimalPrec :: Int

PositC 'V

Defined in Posit.Internal.PositC

Associated Types

type IntN 'V = (r :: Type)

Methods

encode :: Maybe Rational -> IntN 'V

decode :: IntN 'V -> Maybe Rational

exponentSize :: Natural

nBytes :: Natural

nBits :: Natural

signBitSize :: Natural

uSeed :: Natural

unReal :: IntN 'V

mostPosVal :: IntN 'V

leastPosVal :: IntN 'V

leastNegVal :: IntN 'V

mostNegVal :: IntN 'V

maxPosRat :: Rational

minPosRat :: Rational

maxNegRat :: Rational

minNegRat :: Rational

log_uSeed :: (Integer, Rational) -> (Integer, Rational)

getRegime :: Rational -> (Integer, Rational)

posit2TupPosit :: Rational -> (Bool, Integer, Natural, Rational)

buildIntRep :: Rational -> IntN 'V

mkIntRep :: Integer -> Natural -> Rational -> IntN 'V

formRegime :: Integer -> (IntN 'V, Integer)

formExponent :: Natural -> Integer -> (IntN 'V, Integer)

formFraction :: Rational -> Integer -> IntN 'V

tupPosit2Posit :: (Bool, Integer, Natural, Rational) -> Maybe Rational

regime2Integer :: IntN 'V -> (Integer, Int)

findRegimeFormat :: IntN 'V -> Bool

countRegimeBits :: Bool -> IntN 'V -> Int

exponent2Nat :: Int -> IntN 'V -> Natural

fraction2Posit :: Int -> IntN 'V -> Rational

displayBin :: IntN 'V -> String

decimalPrec :: Int

PositC 'Z

Defined in Posit.Internal.PositC

Associated Types

type IntN 'Z = (r :: Type)

Methods

encode :: Maybe Rational -> IntN 'Z

decode :: IntN 'Z -> Maybe Rational

exponentSize :: Natural

nBytes :: Natural

nBits :: Natural

signBitSize :: Natural

uSeed :: Natural

unReal :: IntN 'Z

mostPosVal :: IntN 'Z

leastPosVal :: IntN 'Z

leastNegVal :: IntN 'Z

mostNegVal :: IntN 'Z

maxPosRat :: Rational

minPosRat :: Rational

maxNegRat :: Rational

minNegRat :: Rational

log_uSeed :: (Integer, Rational) -> (Integer, Rational)

getRegime :: Rational -> (Integer, Rational)

posit2TupPosit :: Rational -> (Bool, Integer, Natural, Rational)

buildIntRep :: Rational -> IntN 'Z

mkIntRep :: Integer -> Natural -> Rational -> IntN 'Z

formRegime :: Integer -> (IntN 'Z, Integer)

formExponent :: Natural -> Integer -> (IntN 'Z, Integer)

formFraction :: Rational -> Integer -> IntN 'Z

tupPosit2Posit :: (Bool, Integer, Natural, Rational) -> Maybe Rational

regime2Integer :: IntN 'Z -> (Integer, Int)

findRegimeFormat :: IntN 'Z -> Bool

countRegimeBits :: Bool -> IntN 'Z -> Int

exponent2Nat :: Int -> IntN 'Z -> Natural

fraction2Posit :: Int -> IntN 'Z -> Rational

displayBin :: IntN 'Z -> String

decimalPrec :: Int

data ES

The Exponent Size ES kind, the constructor for the Type is a Roman Numeral.

Constructors

Z

I

II

III

IV

V

Orphan instances

Storable Int128

Methods

sizeOf :: Int128 -> Int

alignment :: Int128 -> Int

peekElemOff :: Ptr Int128 -> Int -> IO Int128

pokeElemOff :: Ptr Int128 -> Int -> Int128 -> IO ()

peekByteOff :: Ptr b -> Int -> IO Int128

pokeByteOff :: Ptr b -> Int -> Int128 -> IO ()

peek :: Ptr Int128 -> IO Int128

poke :: Ptr Int128 -> Int128 -> IO ()

Storable Int256

Methods

sizeOf :: Int256 -> Int

alignment :: Int256 -> Int

peekElemOff :: Ptr Int256 -> Int -> IO Int256

pokeElemOff :: Ptr Int256 -> Int -> Int256 -> IO ()

peekByteOff :: Ptr b -> Int -> IO Int256

pokeByteOff :: Ptr b -> Int -> Int256 -> IO ()

peek :: Ptr Int256 -> IO Int256

poke :: Ptr Int256 -> Int256 -> IO ()

Storable Word128

Methods

sizeOf :: Word128 -> Int

alignment :: Word128 -> Int

peekElemOff :: Ptr Word128 -> Int -> IO Word128

pokeElemOff :: Ptr Word128 -> Int -> Word128 -> IO ()

peekByteOff :: Ptr b -> Int -> IO Word128

pokeByteOff :: Ptr b -> Int -> Word128 -> IO ()

peek :: Ptr Word128 -> IO Word128

poke :: Ptr Word128 -> Word128 -> IO ()