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.

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.

Instances

Eq CReal
Fractional CReal
Num CReal
Read CReal
Show CReal

type Nat = Word Source

type Chain = Nat -> Interval Source

data PBool Source

Partial booleans

Constructors

PTrue	equivalent to True
PFalse	equivalent to False
Indeterminate	neither True nor False.

Instances

Eq PBool
Ord PBool
Show PBool

min :: CReal -> CReal -> CReal Source

max :: CReal -> CReal -> CReal Source

lim Source

Arguments

:: (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 Source

Arguments

:: 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 Source

Arguments

:: (Nat -> Dyadic)	Sequence of dyadics
-> (Nat -> Dyadic)	Sequence of (dyadic) error bounds
-> CReal

Limit of a sequence of rationals.

infSum Source

Arguments

:: (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 Source

Similar to infSum but can sometimes be more convenient Second argument is a_0

approx :: CReal -> Nat -> Either (Dyadic, Word) Dyadic Source

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 Source

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 Source

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 Source

Similar to (<.)

sqrt :: CReal -> CReal Source

exp :: CReal -> CReal Source

log :: CReal -> CReal Source

fromDyadic :: Dyadic -> CReal Source

fromInt :: Int -> CReal Source

fromInt should be preferred over fromIntegral where applicable

fromWord :: Word -> CReal Source

fromWord should be preferred over fromIntegral where applicable

fromString :: String -> CReal Source

toString :: Nat -> CReal -> String Source

toString computes the result with specified precision.

toStringDec :: Nat -> CReal -> String Source

toStringDec tries to compute the result to the number of specified significand digits