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| Synopsis |
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| Documentation |
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| show x will output as much decimalas as
a standard IEEE 754 double if possible.
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| (==) and (/=) should not be used as x == y will diverge if
two reals should be equal.
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| 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.
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| type Nat = Word |
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| type Chain = Nat -> Interval |
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| data PBool |
| Partial booleans
| | Constructors | | PTrue | equivalent to True
| | PFalse | equivalent to False
| | Indeterminate | neither True nor False.
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| | Instances | |
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| min :: CReal -> CReal -> CReal |
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| max :: CReal -> CReal -> CReal |
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| 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.
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| 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
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| limRat |
| :: Nat -> Dyadic | Sequence of dyadics
| | -> Nat -> Dyadic | Sequence of (dyadic) error bounds
| | -> CReal | | | Limit of a sequence of rationals.
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| infSum |
| :: Nat -> CReal | Sequence of reals
| | -> Nat -> CReal | Sequence of series remainders
| | -> CReal | | | Computes an infinite sum of a series
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| infSumRec :: CReal -> (CReal -> Nat -> (CReal, CReal)) -> CReal |
| Similar to infSum but can sometimes be more convenient
Second argument is a_0
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| 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.
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| 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
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| (<.) :: 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.
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| (>.) :: CReal -> CReal -> Nat -> PBool |
| Similar to (<.)
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| sqrt :: CReal -> CReal |
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| exp :: CReal -> CReal |
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| log :: CReal -> CReal |
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| fromDyadic :: Dyadic -> CReal |
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| fromInt :: Int -> CReal |
| fromInt should be preferred over fromIntegral where applicable
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| fromWord :: Word -> CReal |
| fromWord should be preferred over fromIntegral where applicable
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| fromString :: String -> CReal |
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| toString :: Nat -> CReal -> String |
| toString computes the result with specified precision.
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| toStringDec :: Nat -> CReal -> String |
| toStringDec tries to compute the result to the number of specified significand digits
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| Produced by Haddock version 2.2.2 |
