Copyright | (c) Edward Kmett 2013-2015 |
---|---|
License | BSD3 |
Maintainer | Edward Kmett <[email protected]> |
Stability | experimental |
Portability | non-portable |
Safe Haskell | Trustworthy |
Language | Haskell2010 |
Numeric.Log
Description
Documentation
Log
-domain Float
and Double
values.
Instances
Foldable1 Log Source # | |||||
Defined in Numeric.Log Methods fold1 :: Semigroup m => Log m -> m # foldMap1 :: Semigroup m => (a -> m) -> Log a -> m # foldMap1' :: Semigroup m => (a -> m) -> Log a -> m # toNonEmpty :: Log a -> NonEmpty a # maximum :: Ord a => Log a -> a # minimum :: Ord a => Log a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Log a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Log a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Log a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Log a -> b # | |||||
Eq1 Log Source # | |||||
Serial1 Log Source # | |||||
Defined in Numeric.Log Methods serializeWith :: MonadPut m => (a -> m ()) -> Log a -> m () # deserializeWith :: MonadGet m => m a -> m (Log a) # | |||||
Comonad Log Source # | |||||
ComonadApply Log Source # | |||||
Distributive Log Source # | |||||
Applicative Log Source # | |||||
Functor Log Source # | |||||
Monad Log Source # | |||||
Foldable Log Source # | |||||
Defined in Numeric.Log Methods fold :: Monoid m => Log m -> m # foldMap :: Monoid m => (a -> m) -> Log a -> 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 # elem :: Eq a => a -> Log a -> Bool # maximum :: Ord a => Log a -> a # | |||||
Traversable Log Source # | |||||
Hashable1 Log Source # | |||||
Defined in Numeric.Log | |||||
Apply Log Source # | |||||
Bind Log Source # | |||||
Extend Log Source # | |||||
Traversable1 Log Source # | |||||
(RealFloat a, Unbox a) => Vector Vector (Log a) Source # | |||||
Defined in Numeric.Log Methods basicUnsafeFreeze :: Mutable Vector s (Log a) -> ST s (Vector (Log a)) basicUnsafeThaw :: Vector (Log a) -> ST s (Mutable Vector s (Log a)) basicLength :: Vector (Log a) -> Int basicUnsafeSlice :: Int -> Int -> Vector (Log a) -> Vector (Log a) basicUnsafeIndexM :: Vector (Log a) -> Int -> Box (Log a) basicUnsafeCopy :: Mutable Vector s (Log a) -> Vector (Log a) -> ST s () | |||||
Unbox a => MVector MVector (Log a) Source # | |||||
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 :: Int -> ST s (MVector s (Log a)) basicInitialize :: MVector s (Log a) -> ST s () basicUnsafeReplicate :: Int -> Log a -> ST s (MVector s (Log a)) basicUnsafeRead :: MVector s (Log a) -> Int -> ST s (Log a) basicUnsafeWrite :: MVector s (Log a) -> Int -> Log a -> ST s () basicClear :: MVector s (Log a) -> ST s () basicSet :: MVector s (Log a) -> Log a -> ST s () basicUnsafeCopy :: MVector s (Log a) -> MVector s (Log a) -> ST s () basicUnsafeMove :: MVector s (Log a) -> MVector s (Log a) -> ST s () basicUnsafeGrow :: MVector s (Log a) -> Int -> ST s (MVector s (Log a)) | |||||
Binary a => Binary (Log a) Source # | |||||
Serial a => Serial (Log a) Source # | |||||
Defined in Numeric.Log | |||||
Serialize a => Serialize (Log a) Source # | |||||
NFData a => NFData (Log a) Source # | |||||
Defined in Numeric.Log | |||||
RealFloat a => Monoid (Log a) Source # | |||||
RealFloat a => Semigroup (Log a) Source # | |||||
Data a => Data (Log a) Source # | |||||
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) # 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 :: forall r r'. (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, Enum a) => Enum (Log a) Source # | |||||
RealFloat a => Floating (Log a) Source # | |||||
Storable a => Storable (Log a) Source # | |||||
Generic (Log a) Source # | |||||
Defined in Numeric.Log Associated Types
| |||||
RealFloat a => Num (Log a) Source # | |||||
(Floating a, Read a) => Read (Log a) Source # | |||||
RealFloat a => Fractional (Log a) Source # | |||||
(RealFloat a, Ord a) => Real (Log a) Source # | |||||
Defined in Numeric.Log Methods toRational :: Log a -> Rational # | |||||
RealFloat a => RealFrac (Log a) Source # | |||||
(Floating a, Show a) => Show (Log a) Source # | |||||
Eq a => Eq (Log a) Source # | |||||
Ord a => Ord (Log a) Source # | |||||
Hashable a => Hashable (Log a) Source # | |||||
Defined in Numeric.Log | |||||
(RealFloat a, Unbox a) => Unbox (Log a) Source # | |||||
Defined in Numeric.Log | |||||
newtype MVector s (Log a) Source # | |||||
Defined in Numeric.Log | |||||
type Rep (Log a) Source # | |||||
Defined in Numeric.Log | |||||
newtype Vector (Log a) Source # | |||||
Defined in Numeric.Log |
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.