|show x will output as much decimalas as
a standard IEEE 754 double if possible.
|(==) and (/=) should not be used as x == y will diverge if
two reals should be equal.
|data CReal |
Real number is represented as a chain of dyadic intervals which
are neither necessarily nested nor bounded away from 0.
On n-th stage computations are performed with precision of n bits.
|type Nat = Word|
|type Chain = Nat -> Interval|
|data PBool |
|PTrue||equivalent to True
|PFalse||equivalent to False
|Indeterminate||neither True nor False.
|min :: CReal -> CReal -> CReal|
|max :: CReal -> CReal -> CReal|
|:: Nat -> CReal||Sequence
|-> Nat -> CReal||Error bounds
|A basic general limit which takes as arguments a sequence of reals and a sequence of
|:: CReal||initial value
|-> CReal -> Nat -> (CReal, CReal)||a function which produces a pair, (next element, error estimate)
from previous one and location
|Similar to lim, but can sometimes be more convenient for some sequences
|:: Nat -> Dyadic||Sequence of dyadics
|-> Nat -> Dyadic||Sequence of (dyadic) error bounds
|Limit of a sequence of rationals.
|:: Nat -> CReal||Sequence of reals
|-> Nat -> CReal||Sequence of series remainders
|Computes an infinite sum of a series
|infSumRec :: CReal -> (CReal -> Nat -> (CReal, CReal)) -> CReal|
|Similar to infSum but can sometimes be more convenient
Second argument is a_0
|approx :: CReal -> Nat -> Either (Dyadic, Word) Dyadic|
approx x n tries to compute a dyadic approximation to x so than |x - d| <= 10^(-n)
If it succeeds it returns Right d where d is a dyadic rational, otherwise it returns
Left (d, n) where d is a dyadic rational and n is the number of accurate decimal places
Approx succeeds if result can be computed with precision less than the square of the number
of required bits of precision.
|pCompare :: CReal -> CReal -> Nat -> POrdering|
| pCompare x y returns a function Nat -> POrdering which
when applied to some n computes approximates with precision n
and then compares the resulting intervals
|(<.) :: CReal -> CReal -> Nat -> PBool|
| x <. y is a function Nat -> PBool which, when
applied to some n , computes the approximation with precision n
and then compares the intervals. If intervals are disjoint then result is
either PTrue or PFalse, otherwise result is Indeterminate.
|(>.) :: CReal -> CReal -> Nat -> PBool|
|Similar to (<.)
|sqrt :: CReal -> CReal|
|exp :: CReal -> CReal|
|log :: CReal -> CReal|
|fromDyadic :: Dyadic -> CReal|
|fromInt :: Int -> CReal|
|fromInt should be preferred over fromIntegral where applicable
|fromWord :: Word -> CReal|
|fromWord should be preferred over fromIntegral where applicable
|fromString :: String -> CReal|
|toString :: Nat -> CReal -> String|
|toString computes the result with specified precision.
|toStringDec :: Nat -> CReal -> String|
|toStringDec tries to compute the result to the number of specified significand digits
|Produced by Haddock version 2.2.2|