{-# LANGUAGE CPP, ForeignFunctionInterface, MultiParamTypeClasses #-}
{-# OPTIONS_GHC
-XGeneralizedNewtypeDeriving
-XScopedTypeVariables
-XInstanceSigs
#-}
{-# OPTIONS_GHC -Wall -fwarn-tabs #-}
{-# OPTIONS_GHC -O2 -fexcess-precision -fenable-rewrite-rules #-}
module Data.Number.LogFloat
(
module Data.Number.Transfinite
, LogFloat()
, logFloat
, fromLogFloat
, logToLogFloat
, logFromLogFloat
, sum, product
, pow
, log1p, expm1
) where
import Prelude hiding (log, sum, product, isInfinite, isNaN)
import Data.Number.Transfinite
import Data.Number.PartialOrd
import Data.Number.LogFloat.Raw
import Data.Array.Base (IArray(..))
import Data.Array.Unboxed (UArray)
#ifdef __HUGS__
import Hugs.IOExts (unsafeCoerce)
#elif __NHC__
import NonStdUnsafeCoerce (unsafeCoerce)
#elif __GLASGOW_HASKELL__ >= 710
import Unsafe.Coerce (unsafeCoerce)
import Data.Ix (Ix)
#endif
#ifdef __GLASGOW_HASKELL__
import Foreign.Storable (Storable)
#endif
newtype LogFloat = LogFloat Double
deriving
( LogFloat -> LogFloat -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: LogFloat -> LogFloat -> Bool
$c/= :: LogFloat -> LogFloat -> Bool
== :: LogFloat -> LogFloat -> Bool
$c== :: LogFloat -> LogFloat -> Bool
Eq
, Eq LogFloat
LogFloat -> LogFloat -> Bool
LogFloat -> LogFloat -> Ordering
LogFloat -> LogFloat -> LogFloat
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
min :: LogFloat -> LogFloat -> LogFloat
$cmin :: LogFloat -> LogFloat -> LogFloat
max :: LogFloat -> LogFloat -> LogFloat
$cmax :: LogFloat -> LogFloat -> LogFloat
>= :: LogFloat -> LogFloat -> Bool
$c>= :: LogFloat -> LogFloat -> Bool
> :: LogFloat -> LogFloat -> Bool
$c> :: LogFloat -> LogFloat -> Bool
<= :: LogFloat -> LogFloat -> Bool
$c<= :: LogFloat -> LogFloat -> Bool
< :: LogFloat -> LogFloat -> Bool
$c< :: LogFloat -> LogFloat -> Bool
compare :: LogFloat -> LogFloat -> Ordering
$ccompare :: LogFloat -> LogFloat -> Ordering
Ord
#ifdef __GLASGOW_HASKELL__
#if __GLASGOW_HASKELL__ < 710
, IArray UArray
#endif
, Ptr LogFloat -> IO LogFloat
Ptr LogFloat -> Int -> IO LogFloat
Ptr LogFloat -> Int -> LogFloat -> IO ()
Ptr LogFloat -> LogFloat -> IO ()
LogFloat -> Int
forall b. Ptr b -> Int -> IO LogFloat
forall b. Ptr b -> Int -> LogFloat -> IO ()
forall a.
(a -> Int)
-> (a -> Int)
-> (Ptr a -> Int -> IO a)
-> (Ptr a -> Int -> a -> IO ())
-> (forall b. Ptr b -> Int -> IO a)
-> (forall b. Ptr b -> Int -> a -> IO ())
-> (Ptr a -> IO a)
-> (Ptr a -> a -> IO ())
-> Storable a
poke :: Ptr LogFloat -> LogFloat -> IO ()
$cpoke :: Ptr LogFloat -> LogFloat -> IO ()
peek :: Ptr LogFloat -> IO LogFloat
$cpeek :: Ptr LogFloat -> IO LogFloat
pokeByteOff :: forall b. Ptr b -> Int -> LogFloat -> IO ()
$cpokeByteOff :: forall b. Ptr b -> Int -> LogFloat -> IO ()
peekByteOff :: forall b. Ptr b -> Int -> IO LogFloat
$cpeekByteOff :: forall b. Ptr b -> Int -> IO LogFloat
pokeElemOff :: Ptr LogFloat -> Int -> LogFloat -> IO ()
$cpokeElemOff :: Ptr LogFloat -> Int -> LogFloat -> IO ()
peekElemOff :: Ptr LogFloat -> Int -> IO LogFloat
$cpeekElemOff :: Ptr LogFloat -> Int -> IO LogFloat
alignment :: LogFloat -> Int
$calignment :: LogFloat -> Int
sizeOf :: LogFloat -> Int
$csizeOf :: LogFloat -> Int
Storable
#endif
)
#if __GLASGOW_HASKELL__ >= 710
instance IArray UArray LogFloat where
{-# INLINE bounds #-}
bounds :: forall i. Ix i => UArray i LogFloat -> (i, i)
bounds :: forall i. Ix i => UArray i LogFloat -> (i, i)
bounds = forall a b. a -> b
unsafeCoerce (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> (i, i)
bounds :: UArray i Double -> (i, i))
{-# INLINE numElements #-}
numElements :: forall i. Ix i => UArray i LogFloat -> Int
numElements :: forall i. Ix i => UArray i LogFloat -> Int
numElements = forall a b. a -> b
unsafeCoerce (forall (a :: * -> * -> *) e i. (IArray a e, Ix i) => a i e -> Int
numElements :: UArray i Double -> Int)
{-# INLINE unsafeArray #-}
unsafeArray
:: forall i. Ix i => (i,i) -> [(Int,LogFloat)] -> UArray i LogFloat
unsafeArray :: forall i. Ix i => (i, i) -> [(Int, LogFloat)] -> UArray i LogFloat
unsafeArray = forall a b. a -> b
unsafeCoerce (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
(i, i) -> [(Int, e)] -> a i e
unsafeArray
:: (i,i) -> [(Int,Double)] -> UArray i Double)
{-# INLINE unsafeAt #-}
unsafeAt :: forall i. Ix i => UArray i LogFloat -> Int -> LogFloat
unsafeAt :: forall i. Ix i => UArray i LogFloat -> Int -> LogFloat
unsafeAt = forall a b. a -> b
unsafeCoerce (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
unsafeAt :: UArray i Double -> Int -> Double)
{-# INLINE unsafeReplace #-}
unsafeReplace
:: forall i. Ix i
=> UArray i LogFloat -> [(Int,LogFloat)] -> UArray i LogFloat
unsafeReplace :: forall i.
Ix i =>
UArray i LogFloat -> [(Int, LogFloat)] -> UArray i LogFloat
unsafeReplace = forall a b. a -> b
unsafeCoerce (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> [(Int, e)] -> a i e
unsafeReplace
:: UArray i Double -> [(Int,Double)] -> UArray i Double)
{-# INLINE unsafeAccum #-}
unsafeAccum
:: forall i e. Ix i
=> (LogFloat -> e -> LogFloat)
-> UArray i LogFloat -> [(Int,e)] -> UArray i LogFloat
unsafeAccum :: forall i e'.
Ix i =>
(LogFloat -> e' -> LogFloat)
-> UArray i LogFloat -> [(Int, e')] -> UArray i LogFloat
unsafeAccum = forall a b. a -> b
unsafeCoerce (forall (a :: * -> * -> *) e i e'.
(IArray a e, Ix i) =>
(e -> e' -> e) -> a i e -> [(Int, e')] -> a i e
unsafeAccum
:: (Double -> e -> Double)
-> UArray i Double -> [(Int,e)] -> UArray i Double)
{-# INLINE unsafeAccumArray #-}
unsafeAccumArray
:: forall i e. Ix i
=> (LogFloat -> e -> LogFloat)
-> LogFloat -> (i,i) -> [(Int,e)] -> UArray i LogFloat
unsafeAccumArray :: forall i e'.
Ix i =>
(LogFloat -> e' -> LogFloat)
-> LogFloat -> (i, i) -> [(Int, e')] -> UArray i LogFloat
unsafeAccumArray = forall a b. a -> b
unsafeCoerce (forall (a :: * -> * -> *) e i e'.
(IArray a e, Ix i) =>
(e -> e' -> e) -> e -> (i, i) -> [(Int, e')] -> a i e
unsafeAccumArray
:: (Double -> e -> Double)
-> Double -> (i,i) -> [(Int,e)] -> UArray i Double)
#elif __HUGS__ || __NHC__
(~>) :: (a -> b) -> (d -> c) -> (b -> d) -> a -> c
{-# INLINE (~>) #-}
infixr 2 ~>
f ~> g = (. f) . (g .)
($::) :: a -> (a -> b) -> b
{-# INLINE ($::) #-}
infixl 1 $::
($::) = flip ($)
{-# INLINE logFromLFAssocs #-}
logFromLFAssocs :: [(Int, LogFloat)] -> [(Int, Double)]
#if __GLASGOW_HASKELL__ >= 710
logFromLFAssocs = coerce
#else
logFromLFAssocs = unsafeCoerce
#endif
{-# INLINE logFromLFUArray #-}
logFromLFUArray :: UArray a LogFloat -> UArray a Double
logFromLFUArray = unsafeCoerce
{-# INLINE unsafeLogToLFUArray #-}
unsafeLogToLFUArray :: UArray a Double -> UArray a LogFloat
unsafeLogToLFUArray = unsafeCoerce
{-# INLINE unsafeLogToLFFunc #-}
unsafeLogToLFFunc :: (LogFloat -> a -> LogFloat) -> (Double -> a -> Double)
unsafeLogToLFFunc = ($:: unsafeLogToLogFloat ~> id ~> logFromLogFloat)
{-# INLINE unsafeLogToLogFloat #-}
unsafeLogToLogFloat :: Double -> LogFloat
unsafeLogToLogFloat = LogFloat
instance IArray UArray LogFloat where
{-# INLINE bounds #-}
bounds = bounds . logFromLFUArray
#if (!(defined(__HUGS__))) || (__HUGS__ > 200609)
{-# INLINE numElements #-}
numElements = numElements . logFromLFUArray
#endif
{-# INLINE unsafeArray #-}
unsafeArray = unsafeArray $:: id ~> logFromLFAssocs ~> unsafeLogToLFUArray
{-# INLINE unsafeAt #-}
unsafeAt = unsafeAt $:: logFromLFUArray ~> id ~> unsafeLogToLogFloat
{-# INLINE unsafeReplace #-}
unsafeReplace = unsafeReplace
$:: logFromLFUArray ~> logFromLFAssocs ~> unsafeLogToLFUArray
{-# INLINE unsafeAccum #-}
unsafeAccum = unsafeAccum
$:: unsafeLogToLFFunc ~> logFromLFUArray ~> id ~> unsafeLogToLFUArray
{-# INLINE unsafeAccumArray #-}
unsafeAccumArray = unsafeAccumArray
$:: unsafeLogToLFFunc ~> logFromLogFloat ~> id ~> id ~> unsafeLogToLFUArray
#endif
instance PartialOrd LogFloat where
cmp :: LogFloat -> LogFloat -> Maybe Ordering
cmp (LogFloat Double
x) (LogFloat Double
y)
| forall a. Transfinite a => a -> Bool
isNaN Double
x Bool -> Bool -> Bool
|| forall a. Transfinite a => a -> Bool
isNaN Double
y = forall a. Maybe a
Nothing
| Bool
otherwise = forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$! Double
x forall a. Ord a => a -> a -> Ordering
`compare` Double
y
instance Read LogFloat where
readsPrec :: Int -> ReadS LogFloat
readsPrec Int
p String
s =
[(Double -> LogFloat
LogFloat (forall a. (Floating a, Transfinite a) => a -> a
log Double
x), String
r) | (Double
x, String
r) <- forall a. Read a => Int -> ReadS a
readsPrec Int
p String
s, Bool -> Bool
not (forall a. Transfinite a => a -> Bool
isNaN Double
x), Double
x forall a. Ord a => a -> a -> Bool
>= Double
0]
errorOutOfRange :: String -> a
{-# NOINLINE errorOutOfRange #-}
errorOutOfRange :: forall a. String -> a
errorOutOfRange String
fun =
forall a. HasCallStack => String -> a
error forall a b. (a -> b) -> a -> b
$! String
"Data.Number.LogFloat."forall a. [a] -> [a] -> [a]
++String
funforall a. [a] -> [a] -> [a]
++ String
": argument out of range"
guardNonNegative :: String -> Double -> Double
guardNonNegative :: String -> Double -> Double
guardNonNegative String
fun Double
x
| forall a. Transfinite a => a -> Bool
isNaN Double
x Bool -> Bool -> Bool
|| Double
x forall a. Ord a => a -> a -> Bool
< Double
0 = forall a. String -> a
errorOutOfRange String
fun
| Bool
otherwise = Double
x
guardIsANumber :: String -> Double -> Double
guardIsANumber :: String -> Double -> Double
guardIsANumber String
fun Double
x
| forall a. Transfinite a => a -> Bool
isNaN Double
x = forall a. String -> a
errorOutOfRange String
fun
| Bool
otherwise = Double
x
logFloat :: Double -> LogFloat
{-# INLINE [0] logFloat #-}
logFloat :: Double -> LogFloat
logFloat = Double -> LogFloat
LogFloat forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. (Floating a, Transfinite a) => a -> a
log forall b c a. (b -> c) -> (a -> b) -> a -> c
. String -> Double -> Double
guardNonNegative String
"logFloat"
logToLogFloat :: Double -> LogFloat
logToLogFloat :: Double -> LogFloat
logToLogFloat = Double -> LogFloat
LogFloat forall b c a. (b -> c) -> (a -> b) -> a -> c
. String -> Double -> Double
guardIsANumber String
"logToLogFloat"
fromLogFloat :: LogFloat -> Double
{-# INLINE [0] fromLogFloat #-}
fromLogFloat :: LogFloat -> Double
fromLogFloat (LogFloat Double
x) = forall a. Floating a => a -> a
exp Double
x
logFromLogFloat :: LogFloat -> Double
logFromLogFloat :: LogFloat -> Double
logFromLogFloat (LogFloat Double
x) = Double
x
{-# RULES
-- Out of log-domain and back in
"log/fromLogFloat" forall x. log (fromLogFloat x) = logFromLogFloat x
"logFloat/fromLogFloat" forall x. logFloat (fromLogFloat x) = x
-- Into log-domain and back out
"fromLogFloat/logFloat" forall x. fromLogFloat (logFloat x) = x
#-}
instance Show LogFloat where
showsPrec :: Int -> LogFloat -> ShowS
showsPrec Int
p (LogFloat Double
x) =
let y :: Double
y = forall a. Floating a => a -> a
exp Double
x in Double
y seq :: forall a b. a -> b -> b
`seq`
Bool -> ShowS -> ShowS
showParen (Int
p forall a. Ord a => a -> a -> Bool
> Int
9)
( String -> ShowS
showString String
"logFloat "
forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Show a => Int -> a -> ShowS
showsPrec Int
11 Double
y
)
ordered :: Ord a => a -> a -> (a -> a -> b) -> b
ordered :: forall a b. Ord a => a -> a -> (a -> a -> b) -> b
ordered a
x a
y a -> a -> b
k
| a
x forall a. Ord a => a -> a -> Bool
<= a
y = a -> a -> b
k a
x a
y
| Bool
otherwise = a -> a -> b
k a
y a
x
{-# INLINE ordered #-}
instance Num LogFloat where
* :: LogFloat -> LogFloat -> LogFloat
(*) (LogFloat Double
x) (LogFloat Double
y)
| forall a. Transfinite a => a -> Bool
isInfinite Double
x Bool -> Bool -> Bool
&& forall a. Transfinite a => a -> Bool
isInfinite Double
y Bool -> Bool -> Bool
&& Double
x forall a. Eq a => a -> a -> Bool
== forall a. Num a => a -> a
negate Double
y =
Double -> LogFloat
LogFloat forall a. Transfinite a => a
negativeInfinity
| Bool
otherwise =
Double -> LogFloat
LogFloat (Double
x forall a. Num a => a -> a -> a
+ Double
y)
+ :: LogFloat -> LogFloat -> LogFloat
(+) (LogFloat Double
x) (LogFloat Double
y)
| forall a. Transfinite a => a -> Bool
isInfinite Double
x Bool -> Bool -> Bool
&& forall a. Transfinite a => a -> Bool
isInfinite Double
y Bool -> Bool -> Bool
&& Double
x forall a. Eq a => a -> a -> Bool
== Double
y =
Double -> LogFloat
LogFloat Double
x
| Bool
otherwise =
forall a b. Ord a => a -> a -> (a -> a -> b) -> b
ordered Double
x Double
y forall a b. (a -> b) -> a -> b
$ \Double
n Double
m ->
Double -> LogFloat
LogFloat (Double
m forall a. Num a => a -> a -> a
+ Double -> Double
log1pexp (Double
n forall a. Num a => a -> a -> a
- Double
m))
(-) (LogFloat Double
x) (LogFloat Double
y)
| Double
x forall a. Eq a => a -> a -> Bool
== forall a. Transfinite a => a
negativeInfinity Bool -> Bool -> Bool
&& Double
y forall a. Eq a => a -> a -> Bool
== forall a. Transfinite a => a
negativeInfinity =
Double -> LogFloat
LogFloat forall a. Transfinite a => a
negativeInfinity
| Bool
otherwise =
forall a b. Ord a => a -> a -> (a -> a -> b) -> b
ordered Double
x Double
y forall a b. (a -> b) -> a -> b
$ \Double
n Double
m ->
Double -> LogFloat
LogFloat (String -> Double -> Double
guardIsANumber String
"(-)" (Double
m forall a. Num a => a -> a -> a
+ Double -> Double
log1mexp (Double
n forall a. Num a => a -> a -> a
- Double
m)))
signum :: LogFloat -> LogFloat
signum (LogFloat Double
x)
| Double
x forall a. Eq a => a -> a -> Bool
== forall a. Transfinite a => a
negativeInfinity = LogFloat
0
| Double
x forall a. Ord a => a -> a -> Bool
> forall a. Transfinite a => a
negativeInfinity = LogFloat
1
| Bool
otherwise = forall a. String -> a
errorOutOfRange String
"signum"
negate :: LogFloat -> LogFloat
negate LogFloat
_ = forall a. String -> a
errorOutOfRange String
"negate"
abs :: LogFloat -> LogFloat
abs = forall a. a -> a
id
fromInteger :: Integer -> LogFloat
fromInteger = Double -> LogFloat
LogFloat forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. (Floating a, Transfinite a) => a -> a
log forall b c a. (b -> c) -> (a -> b) -> a -> c
. String -> Double -> Double
guardNonNegative String
"fromInteger" forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Num a => Integer -> a
fromInteger
instance Fractional LogFloat where
/ :: LogFloat -> LogFloat -> LogFloat
(/) (LogFloat Double
x) (LogFloat Double
y)
| forall a. Transfinite a => a -> Bool
isInfinite Double
x Bool -> Bool -> Bool
&& forall a. Transfinite a => a -> Bool
isInfinite Double
y Bool -> Bool -> Bool
&& Double
x forall a. Eq a => a -> a -> Bool
== Double
y = forall a. String -> a
errorOutOfRange String
"(/)"
| Double
x forall a. Eq a => a -> a -> Bool
== forall a. Transfinite a => a
negativeInfinity = Double -> LogFloat
LogFloat forall a. Transfinite a => a
negativeInfinity
| Bool
otherwise = Double -> LogFloat
LogFloat (Double
x forall a. Num a => a -> a -> a
- Double
y)
fromRational :: Rational -> LogFloat
fromRational = Double -> LogFloat
LogFloat forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. (Floating a, Transfinite a) => a -> a
log
forall b c a. (b -> c) -> (a -> b) -> a -> c
. String -> Double -> Double
guardNonNegative String
"fromRational" forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Fractional a => Rational -> a
fromRational
instance Real LogFloat where
toRational :: LogFloat -> Rational
toRational (LogFloat Double
x)
| forall a. Transfinite a => a -> Bool
isInfinite Double
ex Bool -> Bool -> Bool
|| forall a. Transfinite a => a -> Bool
isNaN Double
ex = forall a. String -> a
errorOutOfRange String
"toRational"
| Bool
otherwise = forall a. Real a => a -> Rational
toRational Double
ex
where
ex :: Double
ex = forall a. Floating a => a -> a
exp Double
x
pow :: LogFloat -> Double -> LogFloat
{-# INLINE pow #-}
infixr 8 `pow`
pow :: LogFloat -> Double -> LogFloat
pow (LogFloat Double
x) Double
m
| forall a. Transfinite a => a -> Bool
isNaN Double
mx = Double -> LogFloat
LogFloat Double
0
| Bool
otherwise = Double -> LogFloat
LogFloat Double
mx
where
mx :: Double
mx = Double
m forall a. Num a => a -> a -> a
* Double
x
sum :: [LogFloat] -> LogFloat
sum :: [LogFloat] -> LogFloat
sum = Double -> LogFloat
LogFloat forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Double] -> Double
logSumExp forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap LogFloat -> Double
logFromLogFloat
product :: [LogFloat] -> LogFloat
product :: [LogFloat] -> LogFloat
product = Double -> LogFloat
LogFloat forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Double] -> Double
kahanSum forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap LogFloat -> Double
logFromLogFloat