numeric-prelude-0.4.1: An experimental alternative hierarchy of numeric type classes

Safe HaskellNone




Interface to Number.Positional which dynamically checks for equal bases.



data T Source

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.




base :: Int
exponent :: Int
mantissa :: Mantissa


Eq T 
Fractional T 
Num T 
Ord T 
Show T 
C T 
C T 
C T 
C T 
C T 
C T 
C T 
C T 
C T 
C T 
Power T 

basic helpers

compress :: T -> TSource

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 -> TSource

perfect carry resolution, works only on finite numbers


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

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

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