Safe Haskell	None
Language	Haskell2010

Data.CReal

Description

This module exports everything you need to use exact real numbers

Synopsis

Documentation

data CReal n Source

The type CReal represents a fast binary Cauchy sequence. This is a Cauchy sequence with the invariant that the pth element will be within 2^-p of the true value. Internally this sequence is represented as a function from Ints to Integers.

Instances

KnownNat n => Eq (CReal n) Source	Values of type `CReal p` are compared for equality at precision `p`. This may cause values which differ by less than 2^-p to compare as equal. `>>>` `0 == (0.1 :: CReal 1)`True
Methods (==) :: CReal n -> CReal n -> Bool (/=) :: CReal n -> CReal n -> Bool
Floating (CReal n) Source
Methods pi :: CReal n exp :: CReal n -> CReal n log :: CReal n -> CReal n sqrt :: CReal n -> CReal n (**) :: CReal n -> CReal n -> CReal n logBase :: CReal n -> CReal n -> CReal n sin :: CReal n -> CReal n cos :: CReal n -> CReal n tan :: CReal n -> CReal n asin :: CReal n -> CReal n acos :: CReal n -> CReal n atan :: CReal n -> CReal n sinh :: CReal n -> CReal n cosh :: CReal n -> CReal n tanh :: CReal n -> CReal n asinh :: CReal n -> CReal n acosh :: CReal n -> CReal n atanh :: CReal n -> CReal n
Fractional (CReal n) Source	Taking the reciprocal of zero will not terminate
Methods (/) :: CReal n -> CReal n -> CReal n recip :: CReal n -> CReal n fromRational :: Rational -> CReal n
Num (CReal n) Source	`signum (x :: CReal p)` returns the sign of `x` at precision `p`. It's important to remember that this may not represent the actual sign of `x` if the distance between `x` and zero is less than 2^-`p`. This is a little bit of a fudge, but it's probably better than failing to terminate when trying to find the sign of zero. The class still respects the abs-signum law though. `>>>` `signum (0.1 :: CReal 2)`0.0 `>>>` `signum (0.1 :: CReal 3)`1.0
Methods (+) :: CReal n -> CReal n -> CReal n (-) :: CReal n -> CReal n -> CReal n (*) :: CReal n -> CReal n -> CReal n negate :: CReal n -> CReal n abs :: CReal n -> CReal n signum :: CReal n -> CReal n fromInteger :: Integer -> CReal n
KnownNat n => Ord (CReal n) Source	Like equality values of type `CReal p` are compared at precision `p`.
Methods compare :: CReal n -> CReal n -> Ordering (<) :: CReal n -> CReal n -> Bool (<=) :: CReal n -> CReal n -> Bool (>) :: CReal n -> CReal n -> Bool (>=) :: CReal n -> CReal n -> Bool max :: CReal n -> CReal n -> CReal n min :: CReal n -> CReal n -> CReal n
KnownNat n => Show (CReal n) Source	A CReal with precision p is shown as a decimal number d such that d is within 2^-p of the true value. `>>>` `show (47176870 :: CReal 0)`"47176870"
Methods showsPrec :: Int -> CReal n -> ShowS show :: CReal n -> String showList :: [CReal n] -> ShowS

atPrecision :: CReal n -> Int -> Integer Source

x `atPrecision` p returns the numerator of the pth element in the Cauchy sequence represented by x. The denominator is 2^p.

>>> 10 `atPrecision` 10
10240

crealPrecision :: KnownNat n => CReal n -> Int Source

crealPrecision x returns the type level parameter representing x's default precision.

>>> crealPrecision (1 :: CReal 10)
10