Numeric.Log

Documentation

newtype Log a

Log-domain Float and Double values.

Constructors

Exp

Fields

ln :: a

Instances

Monad Log

Functor Log

Applicative Log

Foldable Log

Traversable Log

Serial1 Log

Comonad Log

ComonadApply Log

Distributive Log

Hashable1 Log

Traversable1 Log

Apply Log

Bind Log

Extend Log

Foldable1 Log

(RealFloat a, Unbox a) => Vector Vector (Log a)

(RealFloat a, Unbox a) => MVector MVector (Log a)

(RealFloat a, Precise a, Enum a) => Enum (Log a)

Eq a => Eq (Log a)

(RealFloat a, Precise a) => Floating (Log a)

(Precise a, RealFloat a, Eq a) => Fractional (Log a)

Data a => Data (Log a)

(Precise a, RealFloat a) => Num (Log a)

Ord a => Ord (Log a)

(Floating a, Read a) => Read (Log a)

(Precise a, RealFloat a, Ord a) => Real (Log a)

(Precise a, RealFloat a) => RealFrac (Log a)

(Floating a, Show a) => Show (Log a)

Generic (Log a)

Storable a => Storable (Log a)

(Precise a, RealFloat a) => Monoid (Log a)

Binary a => Binary (Log a)

Serial a => Serial (Log a)

Serialize a => Serialize (Log a)

NFData a => NFData (Log a)

Hashable a => Hashable (Log a)

SafeCopy a => SafeCopy (Log a)

(RealFloat a, Unbox a) => Unbox (Log a)

data MVector s (Log a) = MV_Log (MVector s a)

type Rep (Log a)

data Vector (Log a) = V_Log (Vector a)

class Floating a => Precise a where

This provides log1p and expm1 for working more accurately with small numbers.

Minimal complete definition

log1p, expm1

Methods

log1p :: a -> a

Computes log(1 + x)

This is far enough from 0 that the Taylor series is defined.

This can provide much more accurate answers for logarithms of numbers close to 1 (x near 0).

These arise when working wth log-scale probabilities a lot.

expm1 :: a -> a

The Taylor series for exp(x) is given by

exp(x) = 1 + x + x^2/2! + ...

When x is small, the leading 1 consumes all of the available precision.

This computes:

exp(x) - 1 = x + x^2/2! + ..

which can afford you a great deal of additional precision if you move things around algebraically to provide the 1 by other means.

log1pexp :: a -> a

log1mexp :: a -> a

Instances

Precise Double

Precise Float

(RealFloat a, Precise a) => Precise (Complex a)

sum :: (RealFloat a, Ord a, Precise a, Foldable f) => f (Log a) -> Log a

Efficiently and accurately compute the sum of a set of log-domain numbers

While folding with (+) accomplishes the same end, it requires an additional n-2 logarithms to sum n terms. In addition, here we introduce fewer opportunities for round-off error.

While for small quantities the naive sum accumulates error,

>>> let xs = Prelude.replicate 40000 (Exp 1e-4) :: [Log Float]
>>> Prelude.sum xs ~= 4.00e4
True

This sum gives a more accurate result,

>>> Numeric.Log.sum xs ~= 4.00e4
True

NB: This does require two passes over the data.