NumericPrelude-0.0: An experimental alternative hierarchy of numeric type classes Contents Index

Number.Positional.Check Stability provisional Maintainer numericprelude@henning-thielemann.de

Contents basic helpers conversions

Description

Exact Real Arithmetic (Computable reals?) Inspired by ''The most unreliable technique for computing pi.'' See also http://www.haskell.org/hawiki/ExactRealArithmetic .

Synopsis

data T = Cons { base :: Int exponent :: Int mantissa :: Mantissa } compress :: T -> T carry :: T -> T prependDigit :: Int -> T -> T lift0 :: (Int -> T) -> T lift1 :: (Int -> T -> T) -> T -> T lift2 :: (Int -> T -> T -> T) -> T -> T -> T commonBasis :: Basis -> Basis -> Basis fromBaseInteger :: Int -> Integer -> T fromBaseRational :: Int -> Rational -> T defltBaseRoot :: Basis defltBaseExp :: Exponent defltBase :: Basis defltShow :: T -> String legacyInstance :: a

Documentation

data T

The value Cons b e m represents the number b^e * (m!!0 / 1 + m!!1 / b + m!!2 / b^2 + ...). The interpretation of exponent is chosen such that floor (logBase b (Cons b e m)) == e. That is, it is good for multiplication and logarithms. (Because of the necessity to normalize the multiplication result, the alternative interpretation wouldn't be more complicated.) However for base conversions, roots, conversion to fixed point and working with the fractional part the interpretation b^e * (m!!0 / b + m!!1 / b^2 + m!!2 / b^3 + ...) would fit better. The digits in the mantissa range from 1-base to base-1. The representation is not unique and cannot be made unique in finite time. This way we avoid infinite carry ripples. Constructors Cons base :: Int exponent :: Int mantissa :: Mantissa Instances C T C T C T C T C T C T C T Divisible T Eq T Fractional T Num T Ord T Polar T Power T Real T RealFrac T Show T

basic helpers

compress :: T -> T

Shift digits towards zero by partial application of carries. E.g. 1.8 is converted to 2.(-2) If the digits are in the range (1-base, base-1) the resulting digits are in the range ((1-base)2-2, (base-1)2+2). The result is still not unique, but may be useful for further processing.

carry :: T -> T

perfect carry resolution, works only on finite numbers

prependDigit :: Int -> T -> T

conversions

lift0 :: (Int -> T) -> T

lift1 :: (Int -> T -> T) -> T -> T

lift2 :: (Int -> T -> T -> T) -> T -> T -> T

commonBasis :: Basis -> Basis -> Basis

fromBaseInteger :: Int -> Integer -> T

fromBaseRational :: Int -> Rational -> T

defltBaseRoot :: Basis

defltBaseExp :: Exponent

defltBase :: Basis

defltShow :: T -> String

legacyInstance :: a

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