Number.Positional.Check

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

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

Fields

• base :: Basis
• exponent :: Int
• mantissa :: Mantissa

Instances

Eq T

Defined in Number.Positional.Check

Methods

(==) :: T -> T -> Bool

(/=) :: T -> T -> Bool

Fractional T

Defined in Number.Positional.Check

Methods

(/) :: T -> T -> T

recip :: T -> T

fromRational :: Rational -> T

Num T

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

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

Defined in Number.Positional.Check

Methods

showsPrec :: Int -> T -> ShowS

show :: T -> String

showList :: [T] -> ShowS

C T

Defined in Number.Positional.Check

Methods

zero :: T

(+) :: T -> T -> T

(-) :: T -> T -> T

negate :: T -> T

C T

Defined in Number.Positional.Check

Methods

isZero :: T -> Bool

C T

Defined in Number.Positional.Check

Methods

(*) :: T -> T -> T

one :: T

fromInteger :: Integer -> T

(^) :: T -> Integer -> T

C T

Defined in Number.Positional.Check

Methods

abs :: T -> T

signum :: T -> T

C T

Defined in Number.Positional.Check

Methods

(/) :: T -> T -> T

recip :: T -> T

fromRational' :: Rational -> T

(^-) :: T -> Integer -> T

C T

Defined in Number.Positional.Check

Methods

sqrt :: T -> T

root :: Integer -> T -> T

(^/) :: T -> Rational -> T

C T

Defined in Number.Positional.Check

Methods

pi :: T

exp :: T -> T

log :: T -> T

logBase :: T -> T -> T

(**) :: T -> T -> T

sin :: T -> T

cos :: T -> T

tan :: T -> T

asin :: T -> T

acos :: T -> T

atan :: T -> T

sinh :: T -> T

cosh :: T -> T

tanh :: T -> T

asinh :: T -> T

acosh :: T -> T

atanh :: T -> T

C T

Defined in Number.Positional.Check

Methods

splitFraction :: C b => T -> (b, T)

fraction :: T -> T

ceiling :: C b => T -> b

floor :: C b => T -> b

truncate :: C b => T -> b

round :: C b => T -> b

C T

Defined in Number.Positional.Check

C T

Defined in Number.Positional.Check

Methods

atan2 :: T -> T -> T

Power T

Defined in Number.Positional.Check

Methods

power :: Rational -> T0 T -> T0 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 :: Digit -> T -> T

conversions

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