{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE DeriveTraversable #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -Wall #-}
module NumHask.Data.LogField
(
LogField (),
logField,
fromLogField,
logToLogField,
logFromLogField,
accurateSum,
accurateProduct,
pow,
)
where
import Data.Data (Data)
import qualified Data.Foldable as F
import GHC.Generics (Generic, Generic1)
import NumHask.Algebra.Additive
import NumHask.Algebra.Field
import NumHask.Algebra.Lattice
import NumHask.Algebra.Multiplicative
import NumHask.Algebra.Ring
import NumHask.Analysis.Metric
import NumHask.Data.Integral
import NumHask.Data.Rational
import Prelude hiding (Num (..), exp, fromIntegral, log, negate)
newtype LogField a
= LogField a
deriving
( LogField a -> LogField a -> Bool
(LogField a -> LogField a -> Bool)
-> (LogField a -> LogField a -> Bool) -> Eq (LogField a)
forall a. Eq a => LogField a -> LogField a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: LogField a -> LogField a -> Bool
$c/= :: forall a. Eq a => LogField a -> LogField a -> Bool
== :: LogField a -> LogField a -> Bool
$c== :: forall a. Eq a => LogField a -> LogField a -> Bool
Eq,
Eq (LogField a)
Eq (LogField a)
-> (LogField a -> LogField a -> Ordering)
-> (LogField a -> LogField a -> Bool)
-> (LogField a -> LogField a -> Bool)
-> (LogField a -> LogField a -> Bool)
-> (LogField a -> LogField a -> Bool)
-> (LogField a -> LogField a -> LogField a)
-> (LogField a -> LogField a -> LogField a)
-> Ord (LogField a)
LogField a -> LogField a -> Bool
LogField a -> LogField a -> Ordering
LogField a -> LogField a -> LogField a
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall a. Ord a => Eq (LogField a)
forall a. Ord a => LogField a -> LogField a -> Bool
forall a. Ord a => LogField a -> LogField a -> Ordering
forall a. Ord a => LogField a -> LogField a -> LogField a
min :: LogField a -> LogField a -> LogField a
$cmin :: forall a. Ord a => LogField a -> LogField a -> LogField a
max :: LogField a -> LogField a -> LogField a
$cmax :: forall a. Ord a => LogField a -> LogField a -> LogField a
>= :: LogField a -> LogField a -> Bool
$c>= :: forall a. Ord a => LogField a -> LogField a -> Bool
> :: LogField a -> LogField a -> Bool
$c> :: forall a. Ord a => LogField a -> LogField a -> Bool
<= :: LogField a -> LogField a -> Bool
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< :: LogField a -> LogField a -> Bool
$c< :: forall a. Ord a => LogField a -> LogField a -> Bool
compare :: LogField a -> LogField a -> Ordering
$ccompare :: forall a. Ord a => LogField a -> LogField a -> Ordering
$cp1Ord :: forall a. Ord a => Eq (LogField a)
Ord,
ReadPrec [LogField a]
ReadPrec (LogField a)
Int -> ReadS (LogField a)
ReadS [LogField a]
(Int -> ReadS (LogField a))
-> ReadS [LogField a]
-> ReadPrec (LogField a)
-> ReadPrec [LogField a]
-> Read (LogField a)
forall a. Read a => ReadPrec [LogField a]
forall a. Read a => ReadPrec (LogField a)
forall a. Read a => Int -> ReadS (LogField a)
forall a. Read a => ReadS [LogField a]
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
readListPrec :: ReadPrec [LogField a]
$creadListPrec :: forall a. Read a => ReadPrec [LogField a]
readPrec :: ReadPrec (LogField a)
$creadPrec :: forall a. Read a => ReadPrec (LogField a)
readList :: ReadS [LogField a]
$creadList :: forall a. Read a => ReadS [LogField a]
readsPrec :: Int -> ReadS (LogField a)
$creadsPrec :: forall a. Read a => Int -> ReadS (LogField a)
Read,
Typeable (LogField a)
DataType
Constr
Typeable (LogField a)
-> (forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
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-> (LogField a -> Constr)
-> (LogField a -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c (LogField a)))
-> (forall (t :: * -> * -> *) (c :: * -> *).
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Int -> (forall d. Data d => d -> u) -> LogField a -> u)
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-> Data (LogField a)
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dataCast2 :: (forall d e. (Data d, Data e) => c (t d e))
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dataTypeOf :: LogField a -> DataType
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toConstr :: LogField a -> Constr
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(forall b r. Data b => c (b -> r) -> c r)
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gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
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$cgfoldl :: forall a (c :: * -> *).
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(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> LogField a -> c (LogField a)
$cp1Data :: forall a. Data a => Typeable (LogField a)
Data,
(forall x. LogField a -> Rep (LogField a) x)
-> (forall x. Rep (LogField a) x -> LogField a)
-> Generic (LogField a)
forall x. Rep (LogField a) x -> LogField a
forall x. LogField a -> Rep (LogField a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (LogField a) x -> LogField a
forall a x. LogField a -> Rep (LogField a) x
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Generic,
(forall a. LogField a -> Rep1 LogField a)
-> (forall a. Rep1 LogField a -> LogField a) -> Generic1 LogField
forall a. Rep1 LogField a -> LogField a
forall a. LogField a -> Rep1 LogField a
forall k (f :: k -> *).
(forall (a :: k). f a -> Rep1 f a)
-> (forall (a :: k). Rep1 f a -> f a) -> Generic1 f
$cto1 :: forall a. Rep1 LogField a -> LogField a
$cfrom1 :: forall a. LogField a -> Rep1 LogField a
Generic1,
a -> LogField b -> LogField a
(a -> b) -> LogField a -> LogField b
(forall a b. (a -> b) -> LogField a -> LogField b)
-> (forall a b. a -> LogField b -> LogField a) -> Functor LogField
forall a b. a -> LogField b -> LogField a
forall a b. (a -> b) -> LogField a -> LogField b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
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fmap :: (a -> b) -> LogField a -> LogField b
$cfmap :: forall a b. (a -> b) -> LogField a -> LogField b
Functor,
LogField a -> Bool
(a -> m) -> LogField a -> m
(a -> b -> b) -> b -> LogField a -> b
(forall m. Monoid m => LogField m -> m)
-> (forall m a. Monoid m => (a -> m) -> LogField a -> m)
-> (forall m a. Monoid m => (a -> m) -> LogField a -> m)
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-> (forall b a. (b -> a -> b) -> b -> LogField a -> b)
-> (forall b a. (b -> a -> b) -> b -> LogField a -> b)
-> (forall a. (a -> a -> a) -> LogField a -> a)
-> (forall a. (a -> a -> a) -> LogField a -> a)
-> (forall a. LogField a -> [a])
-> (forall a. LogField a -> Bool)
-> (forall a. LogField a -> Int)
-> (forall a. Eq a => a -> LogField a -> Bool)
-> (forall a. Ord a => LogField a -> a)
-> (forall a. Ord a => LogField a -> a)
-> (forall a. Num a => LogField a -> a)
-> (forall a. Num a => LogField a -> a)
-> Foldable LogField
forall a. Eq a => a -> LogField a -> Bool
forall a. Num a => LogField a -> a
forall a. Ord a => LogField a -> a
forall m. Monoid m => LogField m -> m
forall a. LogField a -> Bool
forall a. LogField a -> Int
forall a. LogField a -> [a]
forall a. (a -> a -> a) -> LogField a -> a
forall m a. Monoid m => (a -> m) -> LogField a -> m
forall b a. (b -> a -> b) -> b -> LogField a -> b
forall a b. (a -> b -> b) -> b -> LogField a -> b
forall (t :: * -> *).
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-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
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-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
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-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
product :: LogField a -> a
$cproduct :: forall a. Num a => LogField a -> a
sum :: LogField a -> a
$csum :: forall a. Num a => LogField a -> a
minimum :: LogField a -> a
$cminimum :: forall a. Ord a => LogField a -> a
maximum :: LogField a -> a
$cmaximum :: forall a. Ord a => LogField a -> a
elem :: a -> LogField a -> Bool
$celem :: forall a. Eq a => a -> LogField a -> Bool
length :: LogField a -> Int
$clength :: forall a. LogField a -> Int
null :: LogField a -> Bool
$cnull :: forall a. LogField a -> Bool
toList :: LogField a -> [a]
$ctoList :: forall a. LogField a -> [a]
foldl1 :: (a -> a -> a) -> LogField a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> LogField a -> a
foldr1 :: (a -> a -> a) -> LogField a -> a
$cfoldr1 :: forall a. (a -> a -> a) -> LogField a -> a
foldl' :: (b -> a -> b) -> b -> LogField a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> LogField a -> b
foldl :: (b -> a -> b) -> b -> LogField a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> LogField a -> b
foldr' :: (a -> b -> b) -> b -> LogField a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> LogField a -> b
foldr :: (a -> b -> b) -> b -> LogField a -> b
$cfoldr :: forall a b. (a -> b -> b) -> b -> LogField a -> b
foldMap' :: (a -> m) -> LogField a -> m
$cfoldMap' :: forall m a. Monoid m => (a -> m) -> LogField a -> m
foldMap :: (a -> m) -> LogField a -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> LogField a -> m
fold :: LogField m -> m
$cfold :: forall m. Monoid m => LogField m -> m
Foldable,
Functor LogField
Foldable LogField
Functor LogField
-> Foldable LogField
-> (forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> LogField a -> f (LogField b))
-> (forall (f :: * -> *) a.
Applicative f =>
LogField (f a) -> f (LogField a))
-> (forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> LogField a -> m (LogField b))
-> (forall (m :: * -> *) a.
Monad m =>
LogField (m a) -> m (LogField a))
-> Traversable LogField
(a -> f b) -> LogField a -> f (LogField b)
forall (t :: * -> *).
Functor t
-> Foldable t
-> (forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (m :: * -> *) a. Monad m => LogField (m a) -> m (LogField a)
forall (f :: * -> *) a.
Applicative f =>
LogField (f a) -> f (LogField a)
forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> LogField a -> m (LogField b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> LogField a -> f (LogField b)
sequence :: LogField (m a) -> m (LogField a)
$csequence :: forall (m :: * -> *) a. Monad m => LogField (m a) -> m (LogField a)
mapM :: (a -> m b) -> LogField a -> m (LogField b)
$cmapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> LogField a -> m (LogField b)
sequenceA :: LogField (f a) -> f (LogField a)
$csequenceA :: forall (f :: * -> *) a.
Applicative f =>
LogField (f a) -> f (LogField a)
traverse :: (a -> f b) -> LogField a -> f (LogField b)
$ctraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> LogField a -> f (LogField b)
$cp2Traversable :: Foldable LogField
$cp1Traversable :: Functor LogField
Traversable
)
instance (ExpField a, Show a) => Show (LogField a) where
showsPrec :: Int -> LogField a -> ShowS
showsPrec Int
p (LogField a
x) =
let y :: a
y = a -> a
forall a. ExpField a => a -> a
exp a
x
in a
y a -> ShowS -> ShowS
`seq` Bool -> ShowS -> ShowS
showParen (Int
p Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
9) (String -> ShowS
showString String
"LogField " ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> a -> ShowS
forall a. Show a => Int -> a -> ShowS
showsPrec Int
11 a
y)
logField :: (ExpField a) => a -> LogField a
{-# INLINE [0] logField #-}
logField :: a -> LogField a
logField = a -> LogField a
forall a. a -> LogField a
LogField (a -> LogField a) -> (a -> a) -> a -> LogField a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> a
forall a. ExpField a => a -> a
log
logToLogField :: a -> LogField a
logToLogField :: a -> LogField a
logToLogField = a -> LogField a
forall a. a -> LogField a
LogField
fromLogField :: ExpField a => LogField a -> a
{-# INLINE [0] fromLogField #-}
fromLogField :: LogField a -> a
fromLogField (LogField a
x) = a -> a
forall a. ExpField a => a -> a
exp a
x
logFromLogField :: LogField a -> a
logFromLogField :: LogField a -> a
logFromLogField (LogField a
x) = a
x
{-# RULES
"log/fromLogField" forall x.
log (fromLogField x) =
logFromLogField x
"fromLogField/LogField" forall x. fromLogField (LogField x) = x
#-}
log1p :: ExpField a => a -> a
{-# INLINE [0] log1p #-}
log1p :: a -> a
log1p a
x = a -> a
forall a. ExpField a => a -> a
log (a
forall a. Multiplicative a => a
one a -> a -> a
forall a. Additive a => a -> a -> a
+ a
x)
expm1 :: (ExpField a) => a -> a
{-# INLINE [0] expm1 #-}
expm1 :: a -> a
expm1 a
x = a -> a
forall a. ExpField a => a -> a
exp a
x a -> a -> a
forall a. Subtractive a => a -> a -> a
- a
forall a. Multiplicative a => a
one
{-# RULES
"expm1/log1p" forall x. expm1 (log1p x) = x
"log1p/expm1" forall x. log1p (expm1 x) = x
#-}
instance
(ExpField a, LowerBoundedField a, Ord a) =>
Additive (LogField a)
where
x :: LogField a
x@(LogField a
x') + :: LogField a -> LogField a -> LogField a
+ y :: LogField a
y@(LogField a
y')
| LogField a
x LogField a -> LogField a -> Bool
forall a. Eq a => a -> a -> Bool
== LogField a
forall a. Additive a => a
zero Bool -> Bool -> Bool
&& LogField a
y LogField a -> LogField a -> Bool
forall a. Eq a => a -> a -> Bool
== LogField a
forall a. Additive a => a
zero = LogField a
forall a. Additive a => a
zero
| LogField a
x LogField a -> LogField a -> Bool
forall a. Eq a => a -> a -> Bool
== LogField a
forall a. Additive a => a
zero = LogField a
y
| LogField a
y LogField a -> LogField a -> Bool
forall a. Eq a => a -> a -> Bool
== LogField a
forall a. Additive a => a
zero = LogField a
x
| LogField a
x LogField a -> LogField a -> Bool
forall a. Ord a => a -> a -> Bool
>= LogField a
y = a -> LogField a
forall a. a -> LogField a
LogField (a
x' a -> a -> a
forall a. Additive a => a -> a -> a
+ a -> a
forall a. ExpField a => a -> a
log1p (a -> a
forall a. ExpField a => a -> a
exp (a
y' a -> a -> a
forall a. Subtractive a => a -> a -> a
- a
x')))
| Bool
otherwise = a -> LogField a
forall a. a -> LogField a
LogField (a
y' a -> a -> a
forall a. Additive a => a -> a -> a
+ a -> a
forall a. ExpField a => a -> a
log1p (a -> a
forall a. ExpField a => a -> a
exp (a
x' a -> a -> a
forall a. Subtractive a => a -> a -> a
- a
y')))
zero :: LogField a
zero = a -> LogField a
forall a. a -> LogField a
LogField a
forall a. LowerBoundedField a => a
negInfinity
instance
(ExpField a, Ord a, LowerBoundedField a, UpperBoundedField a) =>
Subtractive (LogField a)
where
negate :: LogField a -> LogField a
negate LogField a
x
| LogField a
x LogField a -> LogField a -> Bool
forall a. Eq a => a -> a -> Bool
== LogField a
forall a. Additive a => a
zero = LogField a
forall a. Additive a => a
zero
| Bool
otherwise = LogField a
forall a. UpperBoundedField a => a
nan
instance
(LowerBoundedField a, Eq a) =>
Multiplicative (LogField a)
where
(LogField a
x) * :: LogField a -> LogField a -> LogField a
* (LogField a
y)
| a
x a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
forall a. LowerBoundedField a => a
negInfinity Bool -> Bool -> Bool
|| a
y a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
forall a. LowerBoundedField a => a
negInfinity = a -> LogField a
forall a. a -> LogField a
LogField a
forall a. LowerBoundedField a => a
negInfinity
| Bool
otherwise = a -> LogField a
forall a. a -> LogField a
LogField (a
x a -> a -> a
forall a. Additive a => a -> a -> a
+ a
y)
one :: LogField a
one = a -> LogField a
forall a. a -> LogField a
LogField a
forall a. Additive a => a
zero
instance
(LowerBoundedField a, Eq a) =>
Divisive (LogField a)
where
recip :: LogField a -> LogField a
recip (LogField a
x) = a -> LogField a
forall a. a -> LogField a
LogField (a -> LogField a) -> a -> LogField a
forall a b. (a -> b) -> a -> b
$ a -> a
forall a. Subtractive a => a -> a
negate a
x
instance
(Ord a, LowerBoundedField a, ExpField a) =>
Distributive (LogField a)
instance (Field (LogField a), ExpField a, LowerBoundedField a, Ord a) => ExpField (LogField a) where
exp :: LogField a -> LogField a
exp (LogField a
x) = a -> LogField a
forall a. a -> LogField a
LogField (a -> LogField a) -> a -> LogField a
forall a b. (a -> b) -> a -> b
$ a -> a
forall a. ExpField a => a -> a
exp a
x
log :: LogField a -> LogField a
log (LogField a
x) = a -> LogField a
forall a. a -> LogField a
LogField (a -> LogField a) -> a -> LogField a
forall a b. (a -> b) -> a -> b
$ a -> a
forall a. ExpField a => a -> a
log a
x
** :: LogField a -> LogField a -> LogField a
(**) LogField a
x (LogField a
y) = LogField a -> a -> LogField a
forall a.
(ExpField a, LowerBoundedField a, Ord a) =>
LogField a -> a -> LogField a
pow LogField a
x (a -> LogField a) -> a -> LogField a
forall a b. (a -> b) -> a -> b
$ a -> a
forall a. ExpField a => a -> a
exp a
y
instance (FromIntegral a b, ExpField a) => FromIntegral (LogField a) b where
fromIntegral :: b -> LogField a
fromIntegral = a -> LogField a
forall a. ExpField a => a -> LogField a
logField (a -> LogField a) -> (b -> a) -> b -> LogField a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. b -> a
forall a b. FromIntegral a b => b -> a
fromIntegral
instance (ToIntegral a b, ExpField a) => ToIntegral (LogField a) b where
toIntegral :: LogField a -> b
toIntegral = a -> b
forall a b. ToIntegral a b => a -> b
toIntegral (a -> b) -> (LogField a -> a) -> LogField a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. LogField a -> a
forall a. ExpField a => LogField a -> a
fromLogField
instance (FromRatio a b, ExpField a) => FromRatio (LogField a) b where
fromRatio :: Ratio b -> LogField a
fromRatio = a -> LogField a
forall a. ExpField a => a -> LogField a
logField (a -> LogField a) -> (Ratio b -> a) -> Ratio b -> LogField a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Ratio b -> a
forall a b. FromRatio a b => Ratio b -> a
fromRatio
instance (ToRatio a b, ExpField a) => ToRatio (LogField a) b where
toRatio :: LogField a -> Ratio b
toRatio = a -> Ratio b
forall a b. ToRatio a b => a -> Ratio b
toRatio (a -> Ratio b) -> (LogField a -> a) -> LogField a -> Ratio b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. LogField a -> a
forall a. ExpField a => LogField a -> a
fromLogField
instance (Ord a) => JoinSemiLattice (LogField a) where
\/ :: LogField a -> LogField a -> LogField a
(\/) = LogField a -> LogField a -> LogField a
forall a. Ord a => a -> a -> a
min
instance (Ord a) => MeetSemiLattice (LogField a) where
/\ :: LogField a -> LogField a -> LogField a
(/\) = LogField a -> LogField a -> LogField a
forall a. Ord a => a -> a -> a
max
instance
(Epsilon a, ExpField a, LowerBoundedField a, UpperBoundedField a, Ord a) =>
Epsilon (LogField a)
where
epsilon :: LogField a
epsilon = a -> LogField a
forall a. ExpField a => a -> LogField a
logField a
forall a. Epsilon a => a
epsilon
nearZero :: LogField a -> Bool
nearZero (LogField a
x) = a -> Bool
forall a. Epsilon a => a -> Bool
nearZero (a -> Bool) -> a -> Bool
forall a b. (a -> b) -> a -> b
$ a -> a
forall a. ExpField a => a -> a
exp a
x
aboutEqual :: LogField a -> LogField a -> Bool
aboutEqual (LogField a
x) (LogField a
y) = a -> a -> Bool
forall a. Epsilon a => a -> a -> Bool
aboutEqual (a -> a
forall a. ExpField a => a -> a
exp a
x) (a -> a
forall a. ExpField a => a -> a
exp a
y)
instance (Ord a, ExpField a, LowerBoundedField a, UpperBoundedField a) => Field (LogField a)
instance
(Ord a, ExpField a, LowerBoundedField a, UpperBoundedField a) =>
LowerBoundedField (LogField a)
instance
(Ord a, ExpField a, LowerBoundedField a, UpperBoundedField a) =>
UpperBoundedField (LogField a)
instance
(Ord a, LowerBoundedField a, UpperBoundedField a, ExpField a) =>
Signed (LogField a)
where
sign :: LogField a -> LogField a
sign LogField a
a
| LogField a
a LogField a -> LogField a -> Bool
forall a. Eq a => a -> a -> Bool
== LogField a
forall a. LowerBoundedField a => a
negInfinity = LogField a
forall a. Additive a => a
zero
| Bool
otherwise = LogField a
forall a. Multiplicative a => a
one
abs :: LogField a -> LogField a
abs = LogField a -> LogField a
forall a. a -> a
id
pow :: (ExpField a, LowerBoundedField a, Ord a) => LogField a -> a -> LogField a
{-# INLINE pow #-}
infixr 8 `pow`
pow :: LogField a -> a -> LogField a
pow x :: LogField a
x@(LogField a
x') a
m
| LogField a
x LogField a -> LogField a -> Bool
forall a. Eq a => a -> a -> Bool
== LogField a
forall a. Additive a => a
zero Bool -> Bool -> Bool
&& a
m a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
forall a. Additive a => a
zero = a -> LogField a
forall a. a -> LogField a
LogField a
forall a. Additive a => a
zero
| LogField a
x LogField a -> LogField a -> Bool
forall a. Eq a => a -> a -> Bool
== LogField a
forall a. Additive a => a
zero = LogField a
x
| Bool
otherwise = a -> LogField a
forall a. a -> LogField a
LogField (a -> LogField a) -> a -> LogField a
forall a b. (a -> b) -> a -> b
$ a
m a -> a -> a
forall a. Multiplicative a => a -> a -> a
* a
x'
{-# INLINE accurateSum #-}
accurateSum :: (ExpField a, Foldable f, Ord a) => f (LogField a) -> LogField a
accurateSum :: f (LogField a) -> LogField a
accurateSum f (LogField a)
xs = a -> LogField a
forall a. a -> LogField a
LogField (a
theMax a -> a -> a
forall a. Additive a => a -> a -> a
+ a -> a
forall a. ExpField a => a -> a
log a
theSum)
where
LogField a
theMax = f (LogField a) -> LogField a
forall (t :: * -> *) a. (Foldable t, Ord a) => t a -> a
maximum f (LogField a)
xs
theSum :: a
theSum = (a -> LogField a -> a) -> a -> f (LogField a) -> a
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
F.foldl' (\a
acc (LogField a
x) -> a
acc a -> a -> a
forall a. Additive a => a -> a -> a
+ a -> a
forall a. ExpField a => a -> a
exp (a
x a -> a -> a
forall a. Subtractive a => a -> a -> a
- a
theMax)) a
forall a. Additive a => a
zero f (LogField a)
xs
{-# INLINE accurateProduct #-}
accurateProduct :: (ExpField a, Foldable f) => f (LogField a) -> LogField a
accurateProduct :: f (LogField a) -> LogField a
accurateProduct = a -> LogField a
forall a. a -> LogField a
LogField (a -> LogField a)
-> (f (LogField a) -> a) -> f (LogField a) -> LogField a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a, a) -> a
forall a b. (a, b) -> a
fst ((a, a) -> a) -> (f (LogField a) -> (a, a)) -> f (LogField a) -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (LogField a -> (a, a) -> (a, a))
-> (a, a) -> f (LogField a) -> (a, a)
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
F.foldr LogField a -> (a, a) -> (a, a)
forall b. Subtractive b => LogField b -> (b, b) -> (b, b)
kahanPlus (a
forall a. Additive a => a
zero, a
forall a. Additive a => a
zero)
where
kahanPlus :: LogField b -> (b, b) -> (b, b)
kahanPlus (LogField b
x) (b
t, b
c) =
let y :: b
y = b
x b -> b -> b
forall a. Subtractive a => a -> a -> a
- b
c
t' :: b
t' = b
t b -> b -> b
forall a. Additive a => a -> a -> a
+ b
y
c' :: b
c' = (b
t' b -> b -> b
forall a. Subtractive a => a -> a -> a
- b
t) b -> b -> b
forall a. Subtractive a => a -> a -> a
- b
y
in (b
t', b
c')