Safe Haskell	None
Language	Haskell98

Number.Positional.Check

Contents

basic helpers
conversions

Description

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

Synopsis

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

Documentation

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.

Constructors

Cons
Fields base :: Basis exponent :: Int mantissa :: Mantissa

Instances

Instances details

Eq T Source #
Instance details Defined in Number.Positional.Check Methods (==) :: T -> T -> Bool # (/=) :: T -> T -> Bool #
Fractional T Source #
Instance details Defined in Number.Positional.Check Methods (/) :: T -> T -> T # recip :: T -> T # fromRational :: Rational -> T #
Num T Source #
Instance details Defined in Number.Positional.Check Methods (+) :: T -> T -> T # (-) :: T -> T -> T # (*) :: T -> T -> T # negate :: T -> T # abs :: T -> T # signum :: T -> T # fromInteger :: Integer -> T #
Ord T Source #
Instance details Defined in Number.Positional.Check Methods compare :: T -> T -> Ordering # (<) :: T -> T -> Bool # (<=) :: T -> T -> Bool # (>) :: T -> T -> Bool # (>=) :: T -> T -> Bool # max :: T -> T -> T # min :: T -> T -> T #
Show T Source #
Instance details Defined in Number.Positional.Check Methods showsPrec :: Int -> T -> ShowS # show :: T -> String # showList :: [T] -> ShowS #
C T Source #
Instance details Defined in Number.Positional.Check Methods zero :: T Source # (+) :: T -> T -> T Source # (-) :: T -> T -> T Source # negate :: T -> T Source #
C T Source #
Instance details Defined in Number.Positional.Check Methods isZero :: T -> Bool Source #
C T Source #
Instance details Defined in Number.Positional.Check Methods (*) :: T -> T -> T Source # one :: T Source # fromInteger :: Integer -> T Source # (^) :: T -> Integer -> T Source #
C T Source #
Instance details Defined in Number.Positional.Check Methods abs :: T -> T Source # signum :: T -> T Source #
C T Source #
Instance details Defined in Number.Positional.Check Methods (/) :: T -> T -> T Source # recip :: T -> T Source # fromRational' :: Rational -> T Source # (^-) :: T -> Integer -> T Source #
C T Source #
Instance details Defined in Number.Positional.Check Methods sqrt :: T -> T Source # root :: Integer -> T -> T Source # (^/) :: T -> Rational -> T Source #
C T Source #
Instance details Defined in Number.Positional.Check Methods pi :: T Source # exp :: T -> T Source # log :: T -> T Source # logBase :: T -> T -> T Source # (**) :: T -> T -> T Source # sin :: T -> T Source # cos :: T -> T Source # tan :: T -> T Source # asin :: T -> T Source # acos :: T -> T Source # atan :: T -> T Source # sinh :: T -> T Source # cosh :: T -> T Source # tanh :: T -> T Source # asinh :: T -> T Source # acosh :: T -> T Source # atanh :: T -> T Source #
C T Source #
Instance details Defined in Number.Positional.Check Methods splitFraction :: C b => T -> (b, T) Source # fraction :: T -> T Source # ceiling :: C b => T -> b Source # floor :: C b => T -> b Source # truncate :: C b => T -> b Source # round :: C b => T -> b Source #
C T Source #
Instance details Defined in Number.Positional.Check
C T Source #
Instance details Defined in Number.Positional.Check Methods atan2 :: T -> T -> T Source #
Power T Source #
Instance details Defined in Number.Positional.Check Methods power :: Rational -> T0 T -> T0 T Source #

basic helpers

compress :: T -> T Source #

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 Source #

perfect carry resolution, works only on finite numbers

prependDigit :: Digit -> T -> T Source #

conversions

lift0 :: (Basis -> T) -> T Source #

lift1 :: (Basis -> T -> T) -> T -> T Source #

lift2 :: (Basis -> T -> T -> T) -> T -> T -> T Source #

commonBasis :: Basis -> Basis -> Basis Source #

fromBaseInteger :: Basis -> Integer -> T Source #

fromBaseRational :: Basis -> Rational -> T Source #

defltBaseRoot :: Basis Source #

defltBaseExp :: Exponent Source #

defltBase :: Basis Source #

defltShow :: T -> String Source #