Safe Haskell | None |
---|

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

- data T = Cons {}
- 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

# Documentation

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.

# basic helpers

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)`

.
The result is still not unique,
but may be useful for further processing.
*2-2, (base-1)*2+2)

prependDigit :: Int -> T -> TSource

# conversions

commonBasis :: Basis -> Basis -> BasisSource

fromBaseInteger :: Int -> Integer -> TSource

fromBaseRational :: Int -> Rational -> TSource