Safe Haskell	Safe-Inferred
Language	Haskell2010

Cardano.Ledger.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

Show a ⇒ Show (CompareResult a) Source #
Instance details Defined in Cardano.Ledger.NonIntegral Methods showsPrec ∷ Int → CompareResult a → ShowS # show ∷ CompareResult a → String # showList ∷ [CompareResult a] → ShowS #
Eq a ⇒ Eq (CompareResult a) Source #
Instance details Defined in Cardano.Ledger.NonIntegral Methods (==) ∷ CompareResult a → CompareResult a → Bool # (/=) ∷ CompareResult a → CompareResult a → Bool #

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.