Copyright	(c) Edward Kmett 2013-2015
License	BSD3
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Trustworthy
Language	Haskell98

Numeric.Log

Description

Synopsis

Documentation

newtype Log a Source #

Log-domain Float and Double values.

Constructors

Exp
Fields ln :: a

Instances

Monad Log Source #
Methods (>>=) :: Log a -> (a -> Log b) -> Log b # (>>) :: Log a -> Log b -> Log b # return :: a -> Log a # fail :: String -> Log a #
Functor Log Source #
Methods fmap :: (a -> b) -> Log a -> Log b # (<$) :: a -> Log b -> Log a #
Applicative Log Source #
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 Source #
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 Source #
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 Source #
Methods serializeWith :: MonadPut m => (a -> m ()) -> Log a -> m () # deserializeWith :: MonadGet m => m a -> m (Log a) #
Comonad Log Source #
Methods extract :: Log a -> a # duplicate :: Log a -> Log (Log a) # extend :: (Log a -> b) -> Log a -> Log b #
ComonadApply Log Source #
Methods (<@>) :: Log (a -> b) -> Log a -> Log b # (@>) :: Log a -> Log b -> Log b # (<@) :: Log a -> Log b -> Log a #
Distributive Log Source #
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 Source #
Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Log a -> Int #
Traversable1 Log Source #
Methods traverse1 :: Apply f => (a -> f b) -> Log a -> f (Log b) # sequence1 :: Apply f => Log (f b) -> f (Log b) #
Apply Log Source #
Methods (<.>) :: Log (a -> b) -> Log a -> Log b # (.>) :: Log a -> Log b -> Log b # (<.) :: Log a -> Log b -> Log a #
Bind Log Source #
Methods (>>-) :: Log a -> (a -> Log b) -> Log b # join :: Log (Log a) -> Log a #
Extend Log Source #
Methods duplicated :: Log a -> Log (Log a) # extended :: (Log a -> b) -> Log a -> Log b #
Foldable1 Log Source #
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) Source #
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) Source #
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) Source #
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) Source #
Methods (==) :: Log a -> Log a -> Bool # (/=) :: Log a -> Log a -> Bool #
(RealFloat a, Precise a) => Floating (Log a) Source #
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) Source #
Methods (/) :: Log a -> Log a -> Log a # recip :: Log a -> Log a # fromRational :: Rational -> Log a #
Data a => Data (Log a) Source #
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) Source #
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) Source #
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) Source #
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) Source #
Methods toRational :: Log a -> Rational #
(Precise a, RealFloat a) => RealFrac (Log a) Source #
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) Source #
Methods showsPrec :: Int -> Log a -> ShowS # show :: Log a -> String # showList :: [Log a] -> ShowS #
Generic (Log a) Source #
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) Source #
Methods mempty :: Log a # mappend :: Log a -> Log a -> Log a # mconcat :: [Log a] -> Log a #
Storable a => Storable (Log a) Source #
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) Source #
Methods put :: Log a -> Put # get :: Get (Log a) # putList :: [Log a] -> Put #
Serial a => Serial (Log a) Source #
Methods serialize :: MonadPut m => Log a -> m () # deserialize :: MonadGet m => m (Log a) #
Serialize a => Serialize (Log a) Source #
Methods put :: Putter (Log a) # get :: Get (Log a) #
NFData a => NFData (Log a) Source #
Methods rnf :: Log a -> () #
Hashable a => Hashable (Log a) Source #
Methods hashWithSalt :: Int -> Log a -> Int # hash :: Log a -> Int #
SafeCopy a => SafeCopy (Log a) Source #
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) Source #

data MVector s (Log a) Source #
data MVector s (Log a) = MV_Log (MVector s a)
type Rep (Log a) Source #
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) Source #
data Vector (Log a) = V_Log (Vector a)

class Floating a => Precise a where Source #

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

Minimal complete definition

log1p, expm1

Methods

log1p :: a -> a Source #

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 Source #

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 Source #

log1mexp :: a -> a Source #

Instances

Precise Double Source #
Methods log1p :: Double -> Double Source # expm1 :: Double -> Double Source # log1pexp :: Double -> Double Source # log1mexp :: Double -> Double Source #
Precise Float Source #
Methods log1p :: Float -> Float Source # expm1 :: Float -> Float Source # log1pexp :: Float -> Float Source # log1mexp :: Float -> Float Source #
(RealFloat a, Precise a) => Precise (Complex a) Source #
Methods log1p :: Complex a -> Complex a Source # expm1 :: Complex a -> Complex a Source # log1pexp :: Complex a -> Complex a Source # log1mexp :: Complex a -> Complex a Source #

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

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.