



Synopsis 



Documentation 

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 nth stage computations are performed with precision of n bits.
 Instances  


type Nat = Word 

type Chain = Nat > Interval 

data PBool 
Partial booleans
 Constructors  PTrue  equivalent to True
 PFalse  equivalent to False
 Indeterminate  neither True nor False.

 Instances  


min :: CReal > CReal > CReal 

max :: CReal > CReal > CReal 

lim 
:: Nat > CReal  Sequence
 > Nat > CReal  Error bounds
 > CReal   A basic general limit which takes as arguments a sequence of reals and a sequence of
error bounds.



limRec 
:: CReal  initial value
 > CReal > Nat > (CReal, CReal)  a function which produces a pair, (next element, error estimate)
from previous one and location
 > CReal   Similar to lim, but can sometimes be more convenient for some sequences



limRat 
:: Nat > Dyadic  Sequence of dyadics
 > Nat > Dyadic  Sequence of (dyadic) error bounds
 > CReal   Limit of a sequence of rationals.



infSum 
:: Nat > CReal  Sequence of reals
 > Nat > CReal  Sequence of series remainders
 > CReal   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 