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

newtype Log a = Exp {
- ln :: a
}
sum :: (RealFloat a, Foldable f) => f (Log a) -> Log a

Documentation

newtype Log a Source #

Log-domain Float and Double values.

Constructors

Exp
Fields ln :: a

Instances

Monad Log Source #
Instance details Defined in Numeric.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 Source #
Instance details Defined in Numeric.Log Methods fmap :: (a -> b) -> Log a -> Log b # (<$) :: a -> Log b -> Log a #
Applicative Log Source #
Instance details Defined in Numeric.Log Methods pure :: a -> Log a # (<>) :: Log (a -> b) -> Log a -> Log b # liftA2 :: (a -> b -> c) -> Log a -> Log b -> Log c # (>) :: Log a -> Log b -> Log b # (<*) :: Log a -> Log b -> Log a #
Foldable Log Source #
Instance details Defined in Numeric.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 Source #
Instance details Defined in Numeric.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) #
Comonad Log Source #
Instance details Defined in Numeric.Log Methods extract :: Log a -> a duplicate :: Log a -> Log (Log a) extend :: (Log a -> b) -> Log a -> Log b
ComonadApply Log Source #
Instance details Defined in Numeric.Log Methods (<@>) :: Log (a -> b) -> Log a -> Log b (@>) :: Log a -> Log b -> Log b (<@) :: Log a -> Log b -> Log a
Serial1 Log Source #
Instance details Defined in Numeric.Log Methods serializeWith :: MonadPut m => (a -> m ()) -> Log a -> m () deserializeWith :: MonadGet m => m a -> m (Log a)
Distributive Log Source #
Instance details Defined in Numeric.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)
Apply Log Source #
Instance details Defined in Numeric.Log Methods (<.>) :: Log (a -> b) -> Log a -> Log b (.>) :: Log a -> Log b -> Log b (<.) :: Log a -> Log b -> Log a liftF2 :: (a -> b -> c) -> Log a -> Log b -> Log c
Bind Log Source #
Instance details Defined in Numeric.Log Methods (>>-) :: Log a -> (a -> Log b) -> Log b join :: Log (Log a) -> Log a
Extend Log Source #
Instance details Defined in Numeric.Log Methods duplicated :: Log a -> Log (Log a) extended :: (Log a -> b) -> Log a -> Log b
Hashable1 Log Source #
Instance details Defined in Numeric.Log Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Log a -> Int
Foldable1 Log Source #
Instance details Defined in Numeric.Log Methods fold1 :: Semigroup m => Log m -> m foldMap1 :: Semigroup m => (a -> m) -> Log a -> m toNonEmpty :: Log a -> NonEmpty a
Traversable1 Log Source #
Instance details Defined in Numeric.Log Methods traverse1 :: Apply f => (a -> f b) -> Log a -> f (Log b) sequence1 :: Apply f => Log (f b) -> f (Log b)
(RealFloat a, Unbox a) => Vector Vector (Log a) Source #
Instance details Defined in Numeric.Log 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
Unbox a => MVector MVector (Log a) Source #
Instance details Defined in Numeric.Log 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, Enum a) => Enum (Log a) Source #
Instance details Defined in Numeric.Log 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 #
Instance details Defined in Numeric.Log Methods (==) :: Log a -> Log a -> Bool # (/=) :: Log a -> Log a -> Bool #
RealFloat a => Floating (Log a) Source #
Instance details Defined in Numeric.Log 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 #
RealFloat a => Fractional (Log a) Source #
Instance details Defined in Numeric.Log Methods (/) :: Log a -> Log a -> Log a # recip :: Log a -> Log a # fromRational :: Rational -> Log a #
Data a => Data (Log a) Source #
Instance details Defined in Numeric.Log 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) #
RealFloat a => Num (Log a) Source #
Instance details Defined in Numeric.Log 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 #
Instance details Defined in Numeric.Log 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 #
Instance details Defined in Numeric.Log Methods readsPrec :: Int -> ReadS (Log a) # readList :: ReadS [Log a] # readPrec :: ReadPrec (Log a) # readListPrec :: ReadPrec [Log a] #
(RealFloat a, Ord a) => Real (Log a) Source #
Instance details Defined in Numeric.Log Methods toRational :: Log a -> Rational #
RealFloat a => RealFrac (Log a) Source #
Instance details Defined in Numeric.Log 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 #
Instance details Defined in Numeric.Log Methods showsPrec :: Int -> Log a -> ShowS # show :: Log a -> String # showList :: [Log a] -> ShowS #
Generic (Log a) Source #
Instance details Defined in Numeric.Log Associated Types type Rep (Log a) :: Type -> Type # Methods from :: Log a -> Rep (Log a) x # to :: Rep (Log a) x -> Log a #
RealFloat a => Semigroup (Log a) Source #
Instance details Defined in Numeric.Log Methods (<>) :: Log a -> Log a -> Log a # sconcat :: NonEmpty (Log a) -> Log a # stimes :: Integral b => b -> Log a -> Log a #
RealFloat a => Monoid (Log a) Source #
Instance details Defined in Numeric.Log Methods mempty :: Log a # mappend :: Log a -> Log a -> Log a # mconcat :: [Log a] -> Log a #
Storable a => Storable (Log a) Source #
Instance details Defined in Numeric.Log 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 #
Instance details Defined in Numeric.Log Methods put :: Log a -> Put # get :: Get (Log a) # putList :: [Log a] -> Put #
NFData a => NFData (Log a) Source #
Instance details Defined in Numeric.Log Methods rnf :: Log a -> () #
Serial a => Serial (Log a) Source #
Instance details Defined in Numeric.Log Methods serialize :: MonadPut m => Log a -> m () deserialize :: MonadGet m => m (Log a)
Hashable a => Hashable (Log a) Source #
Instance details Defined in Numeric.Log Methods hashWithSalt :: Int -> Log a -> Int hash :: Log a -> Int
Serialize a => Serialize (Log a) Source #
Instance details Defined in Numeric.Log Methods put :: Putter (Log a) get :: Get (Log a)
(RealFloat a, Unbox a) => Unbox (Log a) Source #
Instance details Defined in Numeric.Log
newtype MVector s (Log a) Source #
Instance details Defined in Numeric.Log newtype MVector s (Log a) = MV_Log (MVector s a)
type Rep (Log a) Source #
Instance details Defined in Numeric.Log type Rep (Log a) = D1 (MetaData "Log" "Numeric.Log" "log-domain-0.13-inplace" True) (C1 (MetaCons "Exp" PrefixI True) (S1 (MetaSel (Just "ln") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
newtype Vector (Log a) Source #
Instance details Defined in Numeric.Log newtype Vector (Log a) = V_Log (Vector a)

sum :: (RealFloat 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.