Safe Haskell	Safe
Language	Haskell2010

Precursor.Numeric.Num

Synopsis

Documentation

class Num a where Source #

A class which represents things that can be converted from integer literals

Methods

fromInteger :: Integer -> a Source #

fromInteger :: Num a => Integer -> a Source #

Instances

Num Double Source #
Methods fromInteger :: Integer -> Double Source #
Num Float Source #
Methods fromInteger :: Integer -> Float Source #
Num Int Source #
Methods fromInteger :: Integer -> Int Source #
Num Int8 Source #
Methods fromInteger :: Integer -> Int8 Source #
Num Int16 Source #
Methods fromInteger :: Integer -> Int16 Source #
Num Int32 Source #
Methods fromInteger :: Integer -> Int32 Source #
Num Int64 Source #
Methods fromInteger :: Integer -> Int64 Source #
Num Integer Source #
Methods fromInteger :: Integer -> Integer Source #
Num a => Num (Product a) Source #
Methods fromInteger :: Integer -> Product a Source #
Num a => Num (Sum a) Source #
Methods fromInteger :: Integer -> Sum a Source #

data Double :: * #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Eq Double
Methods (==) :: Double -> Double -> Bool # (/=) :: Double -> Double -> Bool #
Floating Double
Methods pi :: Double # exp :: Double -> Double # log :: Double -> Double # sqrt :: Double -> Double # (**) :: Double -> Double -> Double # logBase :: Double -> Double -> Double # sin :: Double -> Double # cos :: Double -> Double # tan :: Double -> Double # asin :: Double -> Double # acos :: Double -> Double # atan :: Double -> Double # sinh :: Double -> Double # cosh :: Double -> Double # tanh :: Double -> Double # asinh :: Double -> Double # acosh :: Double -> Double # atanh :: Double -> Double # log1p :: Double -> Double # expm1 :: Double -> Double # log1pexp :: Double -> Double # log1mexp :: Double -> Double #
Ord Double
Methods compare :: Double -> Double -> Ordering # (<) :: Double -> Double -> Bool # (<=) :: Double -> Double -> Bool # (>) :: Double -> Double -> Bool # (>=) :: Double -> Double -> Bool # max :: Double -> Double -> Double # min :: Double -> Double -> Double #
RealFloat Double
Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # exponent :: Double -> Int # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isNaN :: Double -> Bool # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # isIEEE :: Double -> Bool # atan2 :: Double -> Double -> Double #
Lift Double
Methods lift :: Double -> Q Exp #
Num Double Source #
Methods fromInteger :: Integer -> Double Source #
Semiring Double Source #
Methods one :: Double Source # zero :: Double Source # (*) :: Double -> Double -> Double Source # (+) :: Double -> Double -> Double Source #
Ring Double Source #
Methods (-) :: Double -> Double -> Double Source #
GTextShowConB arity UDouble
Methods gShowbPrecCon :: ConType -> ShowFunsB arity a -> Int -> UDouble a -> Builder #
GTextShowConT arity UDouble
Methods gShowtPrecCon :: ConType -> ShowFunsT arity a -> Int -> UDouble a -> Text #
GTextShowConTL arity UDouble
Methods gShowtlPrecCon :: ConType -> ShowFunsTL arity a -> Int -> UDouble a -> Text #
IsNullary * UDouble
Methods isNullary :: f a -> Bool #
Functor (URec Double)
Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
Foldable (URec Double)
Methods fold :: Monoid m => URec Double m -> m # foldMap :: Monoid m => (a -> m) -> URec Double a -> m # foldr :: (a -> b -> b) -> b -> URec Double a -> b # foldr' :: (a -> b -> b) -> b -> URec Double a -> b # foldl :: (b -> a -> b) -> b -> URec Double a -> b # foldl' :: (b -> a -> b) -> b -> URec Double a -> b # foldr1 :: (a -> a -> a) -> URec Double a -> a # foldl1 :: (a -> a -> a) -> URec Double a -> a # toList :: URec Double a -> [a] # null :: URec Double a -> Bool # length :: URec Double a -> Int # elem :: Eq a => a -> URec Double a -> Bool # maximum :: Ord a => URec Double a -> a # minimum :: Ord a => URec Double a -> a # sum :: Num a => URec Double a -> a # product :: Num a => URec Double a -> a #
Traversable (URec Double)
Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Generic1 (URec Double)
Associated Types type Rep1 (URec Double :: * -> ) :: -> * # Methods from1 :: URec Double a -> Rep1 (URec Double) a # to1 :: Rep1 (URec Double) a -> URec Double a #
Eq (URec Double p)
Methods (==) :: URec Double p -> URec Double p -> Bool # (/=) :: URec Double p -> URec Double p -> Bool #
Ord (URec Double p)
Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # max :: URec Double p -> URec Double p -> URec Double p # min :: URec Double p -> URec Double p -> URec Double p #
Show (URec Double p)
Methods showsPrec :: Int -> URec Double p -> ShowS # show :: URec Double p -> String # showList :: [URec Double p] -> ShowS #
Generic (URec Double p)
Associated Types type Rep (URec Double p) :: * -> * # Methods from :: URec Double p -> Rep (URec Double p) x # to :: Rep (URec Double p) x -> URec Double p #
data URec Double	Used for marking occurrences of `Double#`
data URec Double = UDouble { uDouble# :: Double# }
type Rep1 (URec Double)
type Rep1 (URec Double) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just Symbol "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UDouble))
type Rep (URec Double p)
type Rep (URec Double p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just Symbol "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UDouble))

data Float :: * #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Eq Float
Methods (==) :: Float -> Float -> Bool # (/=) :: Float -> Float -> Bool #
Floating Float
Methods pi :: Float # exp :: Float -> Float # log :: Float -> Float # sqrt :: Float -> Float # (**) :: Float -> Float -> Float # logBase :: Float -> Float -> Float # sin :: Float -> Float # cos :: Float -> Float # tan :: Float -> Float # asin :: Float -> Float # acos :: Float -> Float # atan :: Float -> Float # sinh :: Float -> Float # cosh :: Float -> Float # tanh :: Float -> Float # asinh :: Float -> Float # acosh :: Float -> Float # atanh :: Float -> Float # log1p :: Float -> Float # expm1 :: Float -> Float # log1pexp :: Float -> Float # log1mexp :: Float -> Float #
Ord Float
Methods compare :: Float -> Float -> Ordering # (<) :: Float -> Float -> Bool # (<=) :: Float -> Float -> Bool # (>) :: Float -> Float -> Bool # (>=) :: Float -> Float -> Bool # max :: Float -> Float -> Float # min :: Float -> Float -> Float #
RealFloat Float
Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # exponent :: Float -> Int # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isNaN :: Float -> Bool # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # isIEEE :: Float -> Bool # atan2 :: Float -> Float -> Float #
Lift Float
Methods lift :: Float -> Q Exp #
Num Float Source #
Methods fromInteger :: Integer -> Float Source #
Semiring Float Source #
Methods one :: Float Source # zero :: Float Source # (*) :: Float -> Float -> Float Source # (+) :: Float -> Float -> Float Source #
Ring Float Source #
Methods (-) :: Float -> Float -> Float Source #
GTextShowConB arity UFloat
Methods gShowbPrecCon :: ConType -> ShowFunsB arity a -> Int -> UFloat a -> Builder #
GTextShowConT arity UFloat
Methods gShowtPrecCon :: ConType -> ShowFunsT arity a -> Int -> UFloat a -> Text #
GTextShowConTL arity UFloat
Methods gShowtlPrecCon :: ConType -> ShowFunsTL arity a -> Int -> UFloat a -> Text #
IsNullary * UFloat
Methods isNullary :: f a -> Bool #
Functor (URec Float)
Methods fmap :: (a -> b) -> URec Float a -> URec Float b # (<$) :: a -> URec Float b -> URec Float a #
Foldable (URec Float)
Methods fold :: Monoid m => URec Float m -> m # foldMap :: Monoid m => (a -> m) -> URec Float a -> m # foldr :: (a -> b -> b) -> b -> URec Float a -> b # foldr' :: (a -> b -> b) -> b -> URec Float a -> b # foldl :: (b -> a -> b) -> b -> URec Float a -> b # foldl' :: (b -> a -> b) -> b -> URec Float a -> b # foldr1 :: (a -> a -> a) -> URec Float a -> a # foldl1 :: (a -> a -> a) -> URec Float a -> a # toList :: URec Float a -> [a] # null :: URec Float a -> Bool # length :: URec Float a -> Int # elem :: Eq a => a -> URec Float a -> Bool # maximum :: Ord a => URec Float a -> a # minimum :: Ord a => URec Float a -> a # sum :: Num a => URec Float a -> a # product :: Num a => URec Float a -> a #
Traversable (URec Float)
Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Generic1 (URec Float)
Associated Types type Rep1 (URec Float :: * -> ) :: -> * # Methods from1 :: URec Float a -> Rep1 (URec Float) a # to1 :: Rep1 (URec Float) a -> URec Float a #
Eq (URec Float p)
Methods (==) :: URec Float p -> URec Float p -> Bool # (/=) :: URec Float p -> URec Float p -> Bool #
Ord (URec Float p)
Methods compare :: URec Float p -> URec Float p -> Ordering # (<) :: URec Float p -> URec Float p -> Bool # (<=) :: URec Float p -> URec Float p -> Bool # (>) :: URec Float p -> URec Float p -> Bool # (>=) :: URec Float p -> URec Float p -> Bool # max :: URec Float p -> URec Float p -> URec Float p # min :: URec Float p -> URec Float p -> URec Float p #
Show (URec Float p)
Methods showsPrec :: Int -> URec Float p -> ShowS # show :: URec Float p -> String # showList :: [URec Float p] -> ShowS #
Generic (URec Float p)
Associated Types type Rep (URec Float p) :: * -> * # Methods from :: URec Float p -> Rep (URec Float p) x # to :: Rep (URec Float p) x -> URec Float p #
data URec Float	Used for marking occurrences of `Float#`
data URec Float = UFloat { uFloat# :: Float# }
type Rep1 (URec Float)
type Rep1 (URec Float) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just Symbol "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UFloat))
type Rep (URec Float p)
type Rep (URec Float p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just Symbol "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UFloat))

data Int :: * #

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

Bounded Int
Methods minBound :: Int # maxBound :: Int #
Enum Int
Methods succ :: Int -> Int # pred :: Int -> Int # toEnum :: Int -> Int # fromEnum :: Int -> Int # enumFrom :: Int -> [Int] # enumFromThen :: Int -> Int -> [Int] # enumFromTo :: Int -> Int -> [Int] # enumFromThenTo :: Int -> Int -> Int -> [Int] #
Eq Int
Methods (==) :: Int -> Int -> Bool # (/=) :: Int -> Int -> Bool #
Integral Int
Methods quot :: Int -> Int -> Int # rem :: Int -> Int -> Int # div :: Int -> Int -> Int # mod :: Int -> Int -> Int # quotRem :: Int -> Int -> (Int, Int) # divMod :: Int -> Int -> (Int, Int) # toInteger :: Int -> Integer #
Num Int
Methods (+) :: Int -> Int -> Int # (-) :: Int -> Int -> Int # (*) :: Int -> Int -> Int # negate :: Int -> Int # abs :: Int -> Int # signum :: Int -> Int # fromInteger :: Integer -> Int #
Ord Int
Methods compare :: Int -> Int -> Ordering # (<) :: Int -> Int -> Bool # (<=) :: Int -> Int -> Bool # (>) :: Int -> Int -> Bool # (>=) :: Int -> Int -> Bool # max :: Int -> Int -> Int # min :: Int -> Int -> Int #
Real Int
Methods toRational :: Int -> Rational #
Lift Int
Methods lift :: Int -> Q Exp #
Num Int Source #
Methods fromInteger :: Integer -> Int Source #
Semiring Int Source #
Methods one :: Int Source # zero :: Int Source # (*) :: Int -> Int -> Int Source # (+) :: Int -> Int -> Int Source #
Integral Int Source #
Methods divMod :: Int -> Int -> (Int, Int) Source # (//) :: Int -> Int -> Int Source # (%) :: Int -> Int -> Int Source #
Ring Int Source #
Methods (-) :: Int -> Int -> Int Source #
GTextShowConB arity UInt
Methods gShowbPrecCon :: ConType -> ShowFunsB arity a -> Int -> UInt a -> Builder #
GTextShowConT arity UInt
Methods gShowtPrecCon :: ConType -> ShowFunsT arity a -> Int -> UInt a -> Text #
GTextShowConTL arity UInt
Methods gShowtlPrecCon :: ConType -> ShowFunsTL arity a -> Int -> UInt a -> Text #
IsNullary * UInt
Methods isNullary :: f a -> Bool #
Functor (URec Int)
Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
Foldable (URec Int)
Methods fold :: Monoid m => URec Int m -> m # foldMap :: Monoid m => (a -> m) -> URec Int a -> m # foldr :: (a -> b -> b) -> b -> URec Int a -> b # foldr' :: (a -> b -> b) -> b -> URec Int a -> b # foldl :: (b -> a -> b) -> b -> URec Int a -> b # foldl' :: (b -> a -> b) -> b -> URec Int a -> b # foldr1 :: (a -> a -> a) -> URec Int a -> a # foldl1 :: (a -> a -> a) -> URec Int a -> a # toList :: URec Int a -> [a] # null :: URec Int a -> Bool # length :: URec Int a -> Int # elem :: Eq a => a -> URec Int a -> Bool # maximum :: Ord a => URec Int a -> a # minimum :: Ord a => URec Int a -> a # sum :: Num a => URec Int a -> a # product :: Num a => URec Int a -> a #
Traversable (URec Int)
Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Generic1 (URec Int)
Associated Types type Rep1 (URec Int :: * -> ) :: -> * # Methods from1 :: URec Int a -> Rep1 (URec Int) a # to1 :: Rep1 (URec Int) a -> URec Int a #
Eq (URec Int p)
Methods (==) :: URec Int p -> URec Int p -> Bool # (/=) :: URec Int p -> URec Int p -> Bool #
Ord (URec Int p)
Methods compare :: URec Int p -> URec Int p -> Ordering # (<) :: URec Int p -> URec Int p -> Bool # (<=) :: URec Int p -> URec Int p -> Bool # (>) :: URec Int p -> URec Int p -> Bool # (>=) :: URec Int p -> URec Int p -> Bool # max :: URec Int p -> URec Int p -> URec Int p # min :: URec Int p -> URec Int p -> URec Int p #
Show (URec Int p)
Methods showsPrec :: Int -> URec Int p -> ShowS # show :: URec Int p -> String # showList :: [URec Int p] -> ShowS #
Generic (URec Int p)
Associated Types type Rep (URec Int p) :: * -> * # Methods from :: URec Int p -> Rep (URec Int p) x # to :: Rep (URec Int p) x -> URec Int p #
data URec Int	Used for marking occurrences of `Int#`
data URec Int = UInt { uInt# :: Int# }
type Rep1 (URec Int)
type Rep1 (URec Int) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just Symbol "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UInt))
type Rep (URec Int p)
type Rep (URec Int p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just Symbol "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UInt))

data Integer :: * #

Invariant: Jn# and Jp# are used iff value doesn't fit in S#

Useful properties resulting from the invariants:

```
abs (S# _) <= abs (Jp# _)
```
```
abs (S# _) <  abs (Jn# _)
```

Instances

Enum Integer
Methods succ :: Integer -> Integer # pred :: Integer -> Integer # toEnum :: Int -> Integer # fromEnum :: Integer -> Int # enumFrom :: Integer -> [Integer] # enumFromThen :: Integer -> Integer -> [Integer] # enumFromTo :: Integer -> Integer -> [Integer] # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] #
Eq Integer
Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Integral Integer
Methods quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) # divMod :: Integer -> Integer -> (Integer, Integer) # toInteger :: Integer -> Integer #
Num Integer
Methods (+) :: Integer -> Integer -> Integer # (-) :: Integer -> Integer -> Integer # (*) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # abs :: Integer -> Integer # signum :: Integer -> Integer # fromInteger :: Integer -> Integer #
Ord Integer
Methods compare :: Integer -> Integer -> Ordering # (<) :: Integer -> Integer -> Bool # (<=) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool # (>=) :: Integer -> Integer -> Bool # max :: Integer -> Integer -> Integer # min :: Integer -> Integer -> Integer #
Real Integer
Methods toRational :: Integer -> Rational #
Lift Integer
Methods lift :: Integer -> Q Exp #
Num Integer Source #
Methods fromInteger :: Integer -> Integer Source #
Semiring Integer Source #
Methods one :: Integer Source # zero :: Integer Source # (*) :: Integer -> Integer -> Integer Source # (+) :: Integer -> Integer -> Integer Source #
Integral Integer Source #
Methods divMod :: Integer -> Integer -> (Integer, Integer) Source # (//) :: Integer -> Integer -> Integer Source # (%) :: Integer -> Integer -> Integer Source #
Ring Integer Source #
Methods (-) :: Integer -> Integer -> Integer Source #