Numeric.Log

Documentation

newtype Log a

Log-domain Float and Double values.

Constructors

Exp

Fields

• ln :: a

Instances

Monad Log

Methods

(>>=) :: Log a -> (a -> Log b) -> Log b

(>>) :: Log a -> Log b -> Log b

return :: a -> Log a

fail :: String -> Log a

Functor Log

Methods

fmap :: (a -> b) -> Log a -> Log b

(<$) :: a -> Log b -> Log a

Applicative Log

Methods

pure :: a -> Log a

(<*>) :: Log (a -> b) -> Log a -> Log b

(*>) :: Log a -> Log b -> Log b

(<*) :: Log a -> Log b -> Log a

Foldable Log

Methods

fold :: Monoid m => Log m -> m

foldMap :: Monoid m => (a -> m) -> Log a -> m

foldr :: (a -> b -> b) -> b -> Log a -> b

foldr' :: (a -> b -> b) -> b -> Log a -> b

foldl :: (b -> a -> b) -> b -> Log a -> b

foldl' :: (b -> a -> b) -> b -> Log a -> b

foldr1 :: (a -> a -> a) -> Log a -> a

foldl1 :: (a -> a -> a) -> Log a -> a

toList :: Log a -> [a]

null :: Log a -> Bool

length :: Log a -> Int

elem :: Eq a => a -> Log a -> Bool

maximum :: Ord a => Log a -> a

minimum :: Ord a => Log a -> a

sum :: Num a => Log a -> a

product :: Num a => Log a -> a

Traversable Log

Methods

traverse :: Applicative f => (a -> f b) -> Log a -> f (Log b)

sequenceA :: Applicative f => Log (f a) -> f (Log a)

mapM :: Monad m => (a -> m b) -> Log a -> m (Log b)

sequence :: Monad m => Log (m a) -> m (Log a)

Serial1 Log

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Log a -> m ()

deserializeWith :: MonadGet m => m a -> m (Log a)

Comonad Log

Methods

extract :: Log a -> a

duplicate :: Log a -> Log (Log a)

extend :: (Log a -> b) -> Log a -> Log b

ComonadApply Log

Methods

(<@>) :: Log (a -> b) -> Log a -> Log b

(@>) :: Log a -> Log b -> Log b

(<@) :: Log a -> Log b -> Log a

Distributive Log

Methods

distribute :: Functor f => f (Log a) -> Log (f a)

collect :: Functor f => (a -> Log b) -> f a -> Log (f b)

distributeM :: Monad m => m (Log a) -> Log (m a)

collectM :: Monad m => (a -> Log b) -> m a -> Log (m b)

Hashable1 Log

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Log a -> Int

Traversable1 Log

Methods

traverse1 :: Apply f => (a -> f b) -> Log a -> f (Log b)

sequence1 :: Apply f => Log (f b) -> f (Log b)

Apply Log

Methods

(<.>) :: Log (a -> b) -> Log a -> Log b

(.>) :: Log a -> Log b -> Log b

(<.) :: Log a -> Log b -> Log a

Bind Log

Methods

(>>-) :: Log a -> (a -> Log b) -> Log b

join :: Log (Log a) -> Log a

Extend Log

Methods

duplicated :: Log a -> Log (Log a)

extended :: (Log a -> b) -> Log a -> Log b

Foldable1 Log

Methods

fold1 :: Semigroup m => Log m -> m

foldMap1 :: Semigroup m => (a -> m) -> Log a -> m

toNonEmpty :: Log a -> NonEmpty a

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

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Log a) -> m (Vector (Log a))

basicUnsafeThaw :: PrimMonad m => Vector (Log a) -> m (Mutable Vector (PrimState m) (Log a))

basicLength :: Vector (Log a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Log a) -> Vector (Log a)

basicUnsafeIndexM :: Monad m => Vector (Log a) -> Int -> m (Log a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Log a) -> Vector (Log a) -> m ()

elemseq :: Vector (Log a) -> Log a -> b -> b

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

Methods

basicLength :: MVector s (Log a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Log a) -> MVector s (Log a)

basicOverlaps :: MVector s (Log a) -> MVector s (Log a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Log a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Log a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Log a -> m (MVector (PrimState m) (Log a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Log a) -> Int -> m (Log a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Log a) -> Int -> Log a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Log a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Log a) -> Log a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Log a) -> MVector (PrimState m) (Log a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Log a) -> MVector (PrimState m) (Log a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Log a) -> Int -> m (MVector (PrimState m) (Log a))

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

Methods

succ :: Log a -> Log a

pred :: Log a -> Log a

toEnum :: Int -> Log a

fromEnum :: Log a -> Int

enumFrom :: Log a -> [Log a]

enumFromThen :: Log a -> Log a -> [Log a]

enumFromTo :: Log a -> Log a -> [Log a]

enumFromThenTo :: Log a -> Log a -> Log a -> [Log a]

Eq a => Eq (Log a)

Methods

(==) :: Log a -> Log a -> Bool

(/=) :: Log a -> Log a -> Bool

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

Methods

pi :: Log a

exp :: Log a -> Log a

log :: Log a -> Log a

sqrt :: Log a -> Log a

(**) :: Log a -> Log a -> Log a

logBase :: Log a -> Log a -> Log a

sin :: Log a -> Log a

cos :: Log a -> Log a

tan :: Log a -> Log a

asin :: Log a -> Log a

acos :: Log a -> Log a

atan :: Log a -> Log a

sinh :: Log a -> Log a

cosh :: Log a -> Log a

tanh :: Log a -> Log a

asinh :: Log a -> Log a

acosh :: Log a -> Log a

atanh :: Log a -> Log a

log1p :: Log a -> Log a

expm1 :: Log a -> Log a

log1pexp :: Log a -> Log a

log1mexp :: Log a -> Log a

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

Methods

(/) :: Log a -> Log a -> Log a

recip :: Log a -> Log a

fromRational :: Rational -> Log a

Data a => Data (Log a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Log a -> c (Log a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Log a)

toConstr :: Log a -> Constr

dataTypeOf :: Log a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Log a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Log a))

gmapT :: (forall b. Data b => b -> b) -> Log a -> Log a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Log a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Log a -> r

gmapQ :: (forall d. Data d => d -> u) -> Log a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Log a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Log a -> m (Log a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Log a -> m (Log a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Log a -> m (Log a)

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

Methods

(+) :: Log a -> Log a -> Log a

(-) :: Log a -> Log a -> Log a

(*) :: Log a -> Log a -> Log a

negate :: Log a -> Log a

abs :: Log a -> Log a

signum :: Log a -> Log a

fromInteger :: Integer -> Log a

Ord a => Ord (Log a)

Methods

compare :: Log a -> Log a -> Ordering

(<) :: Log a -> Log a -> Bool

(<=) :: Log a -> Log a -> Bool

(>) :: Log a -> Log a -> Bool

(>=) :: Log a -> Log a -> Bool

max :: Log a -> Log a -> Log a

min :: Log a -> Log a -> Log a

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

Methods

readsPrec :: Int -> ReadS (Log a)

readList :: ReadS [Log a]

readPrec :: ReadPrec (Log a)

readListPrec :: ReadPrec [Log a]

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

Methods

toRational :: Log a -> Rational

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

Methods

properFraction :: Integral b => Log a -> (b, Log a)

truncate :: Integral b => Log a -> b

round :: Integral b => Log a -> b

ceiling :: Integral b => Log a -> b

floor :: Integral b => Log a -> b

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

Methods

showsPrec :: Int -> Log a -> ShowS

show :: Log a -> String

showList :: [Log a] -> ShowS

Generic (Log a)

Associated Types

type Rep (Log a) :: * -> *

Methods

from :: Log a -> Rep (Log a) x

to :: Rep (Log a) x -> Log a

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

Methods

mempty :: Log a

mappend :: Log a -> Log a -> Log a

mconcat :: [Log a] -> Log a

Storable a => Storable (Log a)

Methods

sizeOf :: Log a -> Int

alignment :: Log a -> Int

peekElemOff :: Ptr (Log a) -> Int -> IO (Log a)

pokeElemOff :: Ptr (Log a) -> Int -> Log a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Log a)

pokeByteOff :: Ptr b -> Int -> Log a -> IO ()

peek :: Ptr (Log a) -> IO (Log a)

poke :: Ptr (Log a) -> Log a -> IO ()

Binary a => Binary (Log a)

Methods

put :: Log a -> Put

get :: Get (Log a)

putList :: [Log a] -> Put

Serial a => Serial (Log a)

Methods

serialize :: MonadPut m => Log a -> m ()

deserialize :: MonadGet m => m (Log a)

Serialize a => Serialize (Log a)

Methods

put :: Putter (Log a)

get :: Get (Log a)

NFData a => NFData (Log a)

Methods

rnf :: Log a -> ()

Hashable a => Hashable (Log a)

Methods

hashWithSalt :: Int -> Log a -> Int

hash :: Log a -> Int

SafeCopy a => SafeCopy (Log a)

Methods

version :: Version (Log a)

kind :: Kind (Log a)

getCopy :: Contained (Get (Log a))

putCopy :: Log a -> Contained Put

internalConsistency :: Consistency (Log a)

objectProfile :: Profile (Log a)

errorTypeName :: Proxy (Log a) -> String

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

data MVector s (Log a)

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

type Rep (Log a)

type Rep (Log a) = D1 (MetaData "Log" "Numeric.Log" "log-domain-0.11.2-DbezXHV18ePDSndewx7hTA" True) (C1 (MetaCons "Exp" PrefixI True) (S1 (MetaSel (Just Symbol "ln") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

data Vector (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

Methods

log1p :: Double -> Double

expm1 :: Double -> Double

log1pexp :: Double -> Double

log1mexp :: Double -> Double

Precise Float

Methods

log1p :: Float -> Float

expm1 :: Float -> Float

log1pexp :: Float -> Float

log1mexp :: Float -> Float

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

Methods

log1p :: Complex a -> Complex a

expm1 :: Complex a -> Complex a

log1pexp :: Complex a -> Complex a

log1mexp :: Complex a -> 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.