Safe Haskell	Safe-Inferred
Language	Haskell98

Shelley.Spec.NonIntegral

Synopsis

(***) :: (RealFrac a, Enum a, Show a) => a -> a -> a
exp' :: (RealFrac a, Show a) => a -> a
ln' :: (RealFrac a, Enum a, Show a) => a -> a
findE :: RealFrac a => a -> a -> Integer
splitLn :: (RealFrac a, Show a) => a -> (Integer, a)
scaleExp :: RealFrac a => a -> (Integer, a)
data CompareResult a
- = BELOW a Int
- | ABOVE a Int
- | MaxReached Int
taylorExpCmp :: RealFrac a => a -> a -> a -> CompareResult a

Documentation

(***) :: (RealFrac a, Enum a, Show a) => a -> a -> a Source #

Exponentiation

exp' :: (RealFrac a, Show a) => a -> a Source #

ln' :: (RealFrac a, Enum a, Show a) => a -> a Source #

Compute natural logarithm via continued fraction, first splitting integral part and then using continued fractions approximation for `ln(1+x)`

findE :: RealFrac a => a -> a -> Integer Source #

find n with `e^n<=x<e^(n+1)`

splitLn :: (RealFrac a, Show a) => a -> (Integer, a) Source #

scaleExp :: RealFrac a => a -> (Integer, a) Source #

data CompareResult a Source #

Constructors

BELOW a Int
ABOVE a Int
MaxReached Int

Instances

Instances details

Eq a => Eq (CompareResult a) Source #
Instance details Defined in Shelley.Spec.NonIntegral Methods (==) :: CompareResult a -> CompareResult a -> Bool Source # (/=) :: CompareResult a -> CompareResult a -> Bool Source #
Show a => Show (CompareResult a) Source #
Instance details Defined in Shelley.Spec.NonIntegral Methods showsPrec :: Int -> CompareResult a -> ShowS Source # show :: CompareResult a -> String Source # showList :: [CompareResult a] -> ShowS Source #

taylorExpCmp :: RealFrac a => a -> a -> a -> CompareResult a Source #

Efficient way to compare the result of the Taylor expansion of the exponential function to a threshold value. Using error estimation one can stop early, once it's known the result will certainly be above or below the target value.