GHC/Enum.hs

    {-# LANGUAGE BangPatterns #-}
    {-# LANGUAGE CPP #-}
    {-# LANGUAGE MagicHash #-}
    {-# LANGUAGE NoImplicitPrelude #-}
    {-# LANGUAGE StandaloneDeriving #-}
    {-# LANGUAGE Trustworthy #-}
    {-# OPTIONS_HADDOCK not-home #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.Enum
    -- Copyright   :  (c) The University of Glasgow, 1992-2002
    -- License     :  see libraries/base/LICENSE
    --
    -- Maintainer  :  cvs-ghc@haskell.org
    -- Stability   :  internal
    -- Portability :  non-portable (GHC extensions)
    --
    -- The 'Enum' and 'Bounded' classes.
    --
    -----------------------------------------------------------------------------

    #include "MachDeps.h"

    module GHC.Enum(
            Bounded(..), Enum(..),
            boundedEnumFrom, boundedEnumFromThen,
            toEnumError, fromEnumError, succError, predError,

            -- Instances for Bounded and Enum: (), Char, Int

       ) where

    import GHC.Base hiding ( many )
    import GHC.Char
    import GHC.Integer
    import GHC.Num
    import GHC.Show
    default ()              -- Double isn't available yet

    -- | The 'Bounded' class is used to name the upper and lower limits of a
    -- type.  'Ord' is not a superclass of 'Bounded' since types that are not
    -- totally ordered may also have upper and lower bounds.
    --
    -- The 'Bounded' class may be derived for any enumeration type;
    -- 'minBound' is the first constructor listed in the @data@ declaration
    -- and 'maxBound' is the last.
    -- 'Bounded' may also be derived for single-constructor datatypes whose
    -- constituent types are in 'Bounded'.

    class  Bounded a  where
        minBound, maxBound :: a

    -- | Class 'Enum' defines operations on sequentially ordered types.
    --
    -- The @enumFrom@... methods are used in Haskell's translation of
    -- arithmetic sequences.
    --
    -- Instances of 'Enum' may be derived for any enumeration type (types
    -- whose constructors have no fields).  The nullary constructors are
    -- assumed to be numbered left-to-right by 'fromEnum' from @0@ through @n-1@.
    -- See Chapter 10 of the /Haskell Report/ for more details.
    --
    -- For any type that is an instance of class 'Bounded' as well as 'Enum',
    -- the following should hold:
    --
    -- * The calls @'succ' 'maxBound'@ and @'pred' 'minBound'@ should result in
    --   a runtime error.
    --
    -- * 'fromEnum' and 'toEnum' should give a runtime error if the
    --   result value is not representable in the result type.
    --   For example, @'toEnum' 7 :: 'Bool'@ is an error.
    --
    -- * 'enumFrom' and 'enumFromThen' should be defined with an implicit bound,
    --   thus:
    --
    -- >    enumFrom     x   = enumFromTo     x maxBound
    -- >    enumFromThen x y = enumFromThenTo x y bound
    -- >      where
    -- >        bound | fromEnum y >= fromEnum x = maxBound
    -- >              | otherwise                = minBound
    --
    class  Enum a   where
        -- | the successor of a value.  For numeric types, 'succ' adds 1.
        succ                :: a -> a
        -- | the predecessor of a value.  For numeric types, 'pred' subtracts 1.
        pred                :: a -> a
        -- | Convert from an 'Int'.
        toEnum              :: Int -> a
        -- | Convert to an 'Int'.
        -- It is implementation-dependent what 'fromEnum' returns when
        -- applied to a value that is too large to fit in an 'Int'.
        fromEnum            :: a -> Int

        -- | Used in Haskell's translation of @[n..]@ with @[n..] = enumFrom n@,
        --   a possible implementation being @enumFrom n = n : enumFrom (succ n)@.
        --   For example:
        --
        --     * @enumFrom 4 :: [Integer] = [4,5,6,7,...]@
        --     * @enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]@
        enumFrom            :: a -> [a]
        -- | Used in Haskell's translation of @[n,n'..]@
        --   with @[n,n'..] = enumFromThen n n'@, a possible implementation being
        --   @enumFromThen n n' = n : n' : worker (f x) (f x n')@,
        --   @worker s v = v : worker s (s v)@, @x = fromEnum n' - fromEnum n@ and
        --   @f n y
        --     | n > 0 = f (n - 1) (succ y)
        --     | n < 0 = f (n + 1) (pred y)
        --     | otherwise = y@
        --   For example:
        --
        --     * @enumFromThen 4 6 :: [Integer] = [4,6,8,10...]@
        --     * @enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]@
        enumFromThen        :: a -> a -> [a]
        -- | Used in Haskell's translation of @[n..m]@ with
        --   @[n..m] = enumFromTo n m@, a possible implementation being
        --   @enumFromTo n m
        --      | n <= m = n : enumFromTo (succ n) m
        --      | otherwise = []@.
        --   For example:
        --
        --     * @enumFromTo 6 10 :: [Int] = [6,7,8,9,10]@
        --     * @enumFromTo 42 1 :: [Integer] = []@
        enumFromTo          :: a -> a -> [a]
        -- | Used in Haskell's translation of @[n,n'..m]@ with
        --   @[n,n'..m] = enumFromThenTo n n' m@, a possible implementation
        --   being @enumFromThenTo n n' m = worker (f x) (c x) n m@,
        --   @x = fromEnum n' - fromEnum n@, @c x = bool (>=) (<=) (x > 0)@
        --   @f n y
        --      | n > 0 = f (n - 1) (succ y)
        --      | n < 0 = f (n + 1) (pred y)
        --      | otherwise = y@ and
        --   @worker s c v m
        --      | c v m = v : worker s c (s v) m
        --      | otherwise = []@
        --   For example:
        --
        --     * @enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]@
        --     * @enumFromThenTo 6 8 2 :: [Int] = []@
        enumFromThenTo      :: a -> a -> a -> [a]

        succ                   = toEnum . (+ 1)  . fromEnum
        pred                   = toEnum . (subtract 1) . fromEnum
        enumFrom x             = map toEnum [fromEnum x ..]
        enumFromThen x y       = map toEnum [fromEnum x, fromEnum y ..]
        enumFromTo x y         = map toEnum [fromEnum x .. fromEnum y]
        enumFromThenTo x1 x2 y = map toEnum [fromEnum x1, fromEnum x2 .. fromEnum y]

    -- Default methods for bounded enumerations
    boundedEnumFrom :: (Enum a, Bounded a) => a -> [a]
    boundedEnumFrom n = map toEnum [fromEnum n .. fromEnum (maxBound `asTypeOf` n)]

    boundedEnumFromThen :: (Enum a, Bounded a) => a -> a -> [a]
    boundedEnumFromThen n1 n2
      | i_n2 >= i_n1  = map toEnum [i_n1, i_n2 .. fromEnum (maxBound `asTypeOf` n1)]
      | otherwise     = map toEnum [i_n1, i_n2 .. fromEnum (minBound `asTypeOf` n1)]
      where
        i_n1 = fromEnum n1
        i_n2 = fromEnum n2

    ------------------------------------------------------------------------
    -- Helper functions
    ------------------------------------------------------------------------

    {-# NOINLINE toEnumError #-}
    toEnumError :: (Show a) => String -> Int -> (a,a) -> b
    toEnumError inst_ty i bnds =
        errorWithoutStackTrace $ "Enum.toEnum{" ++ inst_ty ++ "}: tag (" ++
                show i ++
                ") is outside of bounds " ++
                show bnds

    {-# NOINLINE fromEnumError #-}
    fromEnumError :: (Show a) => String -> a -> b
    fromEnumError inst_ty x =
        errorWithoutStackTrace $ "Enum.fromEnum{" ++ inst_ty ++ "}: value (" ++
                show x ++
                ") is outside of Int's bounds " ++
                show (minBound::Int, maxBound::Int)

    {-# NOINLINE succError #-}
    succError :: String -> a
    succError inst_ty =
        errorWithoutStackTrace $ "Enum.succ{" ++ inst_ty ++ "}: tried to take `succ' of maxBound"

    {-# NOINLINE predError #-}
    predError :: String -> a
    predError inst_ty =
        errorWithoutStackTrace $ "Enum.pred{" ++ inst_ty ++ "}: tried to take `pred' of minBound"

    ------------------------------------------------------------------------
    -- Tuples
    ------------------------------------------------------------------------

    -- | @since 2.01
    deriving instance Bounded ()

    -- | @since 2.01
    instance Enum () where
        succ _      = errorWithoutStackTrace "Prelude.Enum.().succ: bad argument"
        pred _      = errorWithoutStackTrace "Prelude.Enum.().pred: bad argument"

        toEnum x | x == 0    = ()
                 | otherwise = errorWithoutStackTrace "Prelude.Enum.().toEnum: bad argument"

        fromEnum () = 0
        enumFrom ()         = [()]
        enumFromThen () ()  = let many = ():many in many
        enumFromTo () ()    = [()]
        enumFromThenTo () () () = let many = ():many in many

    -- Report requires instances up to 15
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b)
            => Bounded (a,b)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c)
            => Bounded (a,b,c)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d)
            => Bounded (a,b,c,d)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e)
            => Bounded (a,b,c,d,e)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f)
            => Bounded (a,b,c,d,e,f)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g)
            => Bounded (a,b,c,d,e,f,g)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g, Bounded h)
            => Bounded (a,b,c,d,e,f,g,h)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g, Bounded h, Bounded i)
            => Bounded (a,b,c,d,e,f,g,h,i)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g, Bounded h, Bounded i, Bounded j)
            => Bounded (a,b,c,d,e,f,g,h,i,j)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k)
            => Bounded (a,b,c,d,e,f,g,h,i,j,k)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k,
              Bounded l)
            => Bounded (a,b,c,d,e,f,g,h,i,j,k,l)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k,
              Bounded l, Bounded m)
            => Bounded (a,b,c,d,e,f,g,h,i,j,k,l,m)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k,
              Bounded l, Bounded m, Bounded n)
            => Bounded (a,b,c,d,e,f,g,h,i,j,k,l,m,n)
    -- | @since 2.01
    deriving instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e,
              Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k,
              Bounded l, Bounded m, Bounded n, Bounded o)
            => Bounded (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o)

    ------------------------------------------------------------------------
    -- Bool
    ------------------------------------------------------------------------

    -- | @since 2.01
    deriving instance Bounded Bool

    -- | @since 2.01
    instance Enum Bool where
      succ False = True
      succ True  = errorWithoutStackTrace "Prelude.Enum.Bool.succ: bad argument"

      pred True  = False
      pred False  = errorWithoutStackTrace "Prelude.Enum.Bool.pred: bad argument"

      toEnum n | n == 0    = False
               | n == 1    = True
               | otherwise = errorWithoutStackTrace "Prelude.Enum.Bool.toEnum: bad argument"

      fromEnum False = 0
      fromEnum True  = 1

      -- Use defaults for the rest
      enumFrom     = boundedEnumFrom
      enumFromThen = boundedEnumFromThen

    ------------------------------------------------------------------------
    -- Ordering
    ------------------------------------------------------------------------

    -- | @since 2.01
    deriving instance Bounded Ordering
    -- | @since 2.01
    instance Enum Ordering where
      succ LT = EQ
      succ EQ = GT
      succ GT = errorWithoutStackTrace "Prelude.Enum.Ordering.succ: bad argument"

      pred GT = EQ
      pred EQ = LT
      pred LT = errorWithoutStackTrace "Prelude.Enum.Ordering.pred: bad argument"

      toEnum n | n == 0 = LT
               | n == 1 = EQ
               | n == 2 = GT
      toEnum _ = errorWithoutStackTrace "Prelude.Enum.Ordering.toEnum: bad argument"

      fromEnum LT = 0
      fromEnum EQ = 1
      fromEnum GT = 2

      -- Use defaults for the rest
      enumFrom     = boundedEnumFrom
      enumFromThen = boundedEnumFromThen

    ------------------------------------------------------------------------
    -- Char
    ------------------------------------------------------------------------

    -- | @since 2.01
    instance  Bounded Char  where
        minBound =  '\0'
        maxBound =  '\x10FFFF'

    -- | @since 2.01
    instance  Enum Char  where
        succ (C# c#)
           | isTrue# (ord# c# /=# 0x10FFFF#) = C# (chr# (ord# c# +# 1#))
           | otherwise             = errorWithoutStackTrace ("Prelude.Enum.Char.succ: bad argument")
        pred (C# c#)
           | isTrue# (ord# c# /=# 0#) = C# (chr# (ord# c# -# 1#))
           | otherwise                = errorWithoutStackTrace ("Prelude.Enum.Char.pred: bad argument")

        toEnum   = chr
        fromEnum = ord

        {-# INLINE enumFrom #-}
        enumFrom (C# x) = eftChar (ord# x) 0x10FFFF#
            -- Blarg: technically I guess enumFrom isn't strict!

        {-# INLINE enumFromTo #-}
        enumFromTo (C# x) (C# y) = eftChar (ord# x) (ord# y)

        {-# INLINE enumFromThen #-}
        enumFromThen (C# x1) (C# x2) = efdChar (ord# x1) (ord# x2)

        {-# INLINE enumFromThenTo #-}
        enumFromThenTo (C# x1) (C# x2) (C# y) = efdtChar (ord# x1) (ord# x2) (ord# y)

    -- See Note [How the Enum rules work]
    {-# RULES
    "eftChar"       [~1] forall x y.        eftChar x y       = build (\c n -> eftCharFB c n x y)
    "efdChar"       [~1] forall x1 x2.      efdChar x1 x2     = build (\ c n -> efdCharFB c n x1 x2)
    "efdtChar"      [~1] forall x1 x2 l.    efdtChar x1 x2 l  = build (\ c n -> efdtCharFB c n x1 x2 l)
    "eftCharList"   [1]  eftCharFB  (:) [] = eftChar
    "efdCharList"   [1]  efdCharFB  (:) [] = efdChar
    "efdtCharList"  [1]  efdtCharFB (:) [] = efdtChar
     #-}

    -- We can do better than for Ints because we don't
    -- have hassles about arithmetic overflow at maxBound
    {-# INLINE [0] eftCharFB #-} -- See Note [Inline FB functions] in GHC.List
    eftCharFB :: (Char -> a -> a) -> a -> Int# -> Int# -> a
    eftCharFB c n x0 y = go x0
                     where
                        go x | isTrue# (x ># y) = n
                             | otherwise        = C# (chr# x) `c` go (x +# 1#)

    {-# NOINLINE [1] eftChar #-}
    eftChar :: Int# -> Int# -> String
    eftChar x y | isTrue# (x ># y ) = []
                | otherwise         = C# (chr# x) : eftChar (x +# 1#) y

    -- For enumFromThenTo we give up on inlining
    {-# INLINE [0] efdCharFB #-} -- See Note [Inline FB functions] in GHC.List
    efdCharFB :: (Char -> a -> a) -> a -> Int# -> Int# -> a
    efdCharFB c n x1 x2
      | isTrue# (delta >=# 0#) = go_up_char_fb c n x1 delta 0x10FFFF#
      | otherwise              = go_dn_char_fb c n x1 delta 0#
      where
        !delta = x2 -# x1

    {-# NOINLINE [1] efdChar #-}
    efdChar :: Int# -> Int# -> String
    efdChar x1 x2
      | isTrue# (delta >=# 0#) = go_up_char_list x1 delta 0x10FFFF#
      | otherwise              = go_dn_char_list x1 delta 0#
      where
        !delta = x2 -# x1

    {-# INLINE [0] efdtCharFB #-} -- See Note [Inline FB functions] in GHC.List
    efdtCharFB :: (Char -> a -> a) -> a -> Int# -> Int# -> Int# -> a
    efdtCharFB c n x1 x2 lim
      | isTrue# (delta >=# 0#) = go_up_char_fb c n x1 delta lim
      | otherwise              = go_dn_char_fb c n x1 delta lim
      where
        !delta = x2 -# x1

    {-# NOINLINE [1] efdtChar #-}
    efdtChar :: Int# -> Int# -> Int# -> String
    efdtChar x1 x2 lim
      | isTrue# (delta >=# 0#) = go_up_char_list x1 delta lim
      | otherwise              = go_dn_char_list x1 delta lim
      where
        !delta = x2 -# x1

    go_up_char_fb :: (Char -> a -> a) -> a -> Int# -> Int# -> Int# -> a
    go_up_char_fb c n x0 delta lim
      = go_up x0
      where
        go_up x | isTrue# (x ># lim) = n
                | otherwise          = C# (chr# x) `c` go_up (x +# delta)

    go_dn_char_fb :: (Char -> a -> a) -> a -> Int# -> Int# -> Int# -> a
    go_dn_char_fb c n x0 delta lim
      = go_dn x0
      where
        go_dn x | isTrue# (x <# lim) = n
                | otherwise          = C# (chr# x) `c` go_dn (x +# delta)

    go_up_char_list :: Int# -> Int# -> Int# -> String
    go_up_char_list x0 delta lim
      = go_up x0
      where
        go_up x | isTrue# (x ># lim) = []
                | otherwise          = C# (chr# x) : go_up (x +# delta)

    go_dn_char_list :: Int# -> Int# -> Int# -> String
    go_dn_char_list x0 delta lim
      = go_dn x0
      where
        go_dn x | isTrue# (x <# lim) = []
                | otherwise          = C# (chr# x) : go_dn (x +# delta)

    ------------------------------------------------------------------------
    -- Int
    ------------------------------------------------------------------------

    {-
    Be careful about these instances.
            (a) remember that you have to count down as well as up e.g. [13,12..0]
            (b) be careful of Int overflow
            (c) remember that Int is bounded, so [1..] terminates at maxInt
    -}

    -- | @since 2.01
    instance  Bounded Int where
        minBound =  minInt
        maxBound =  maxInt

    -- | @since 2.01
    instance  Enum Int  where
        succ x
           | x == maxBound  = errorWithoutStackTrace "Prelude.Enum.succ{Int}: tried to take `succ' of maxBound"
           | otherwise      = x + 1
        pred x
           | x == minBound  = errorWithoutStackTrace "Prelude.Enum.pred{Int}: tried to take `pred' of minBound"
           | otherwise      = x - 1

        toEnum   x = x
        fromEnum x = x

        {-# INLINE enumFrom #-}
        enumFrom (I# x) = eftInt x maxInt#
            where !(I# maxInt#) = maxInt
            -- Blarg: technically I guess enumFrom isn't strict!

        {-# INLINE enumFromTo #-}
        enumFromTo (I# x) (I# y) = eftInt x y

        {-# INLINE enumFromThen #-}
        enumFromThen (I# x1) (I# x2) = efdInt x1 x2

        {-# INLINE enumFromThenTo #-}
        enumFromThenTo (I# x1) (I# x2) (I# y) = efdtInt x1 x2 y

    -----------------------------------------------------
    -- eftInt and eftIntFB deal with [a..b], which is the
    -- most common form, so we take a lot of care
    -- In particular, we have rules for deforestation

    {-# RULES
    "eftInt"        [~1] forall x y. eftInt x y = build (\ c n -> eftIntFB c n x y)
    "eftIntList"    [1] eftIntFB  (:) [] = eftInt
     #-}

    {- Note [How the Enum rules work]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    * Phase 2: eftInt ---> build . eftIntFB
    * Phase 1: inline build; eftIntFB (:) --> eftInt
    * Phase 0: optionally inline eftInt
    -}

    {-# NOINLINE [1] eftInt #-}
    eftInt :: Int# -> Int# -> [Int]
    -- [x1..x2]
    eftInt x0 y | isTrue# (x0 ># y) = []
                | otherwise         = go x0
                   where
                     go x = I# x : if isTrue# (x ==# y)
                                   then []
                                   else go (x +# 1#)

    {-# INLINE [0] eftIntFB #-} -- See Note [Inline FB functions] in GHC.List
    eftIntFB :: (Int -> r -> r) -> r -> Int# -> Int# -> r
    eftIntFB c n x0 y | isTrue# (x0 ># y) = n
                      | otherwise         = go x0
                     where
                       go x = I# x `c` if isTrue# (x ==# y)
                                       then n
                                       else go (x +# 1#)
                            -- Watch out for y=maxBound; hence ==, not >
            -- Be very careful not to have more than one "c"
            -- so that when eftInfFB is inlined we can inline
            -- whatever is bound to "c"

    -----------------------------------------------------
    -- efdInt and efdtInt deal with [a,b..] and [a,b..c].
    -- The code is more complicated because of worries about Int overflow.

    -- See Note [How the Enum rules work]
    {-# RULES
    "efdtInt"       [~1] forall x1 x2 y.
                         efdtInt x1 x2 y = build (\ c n -> efdtIntFB c n x1 x2 y)
    "efdtIntUpList" [1]  efdtIntFB (:) [] = efdtInt
     #-}

    efdInt :: Int# -> Int# -> [Int]
    -- [x1,x2..maxInt]
    efdInt x1 x2
     | isTrue# (x2 >=# x1) = case maxInt of I# y -> efdtIntUp x1 x2 y
     | otherwise           = case minInt of I# y -> efdtIntDn x1 x2 y

    {-# NOINLINE [1] efdtInt #-}
    efdtInt :: Int# -> Int# -> Int# -> [Int]
    -- [x1,x2..y]
    efdtInt x1 x2 y
     | isTrue# (x2 >=# x1) = efdtIntUp x1 x2 y
     | otherwise           = efdtIntDn x1 x2 y

    {-# INLINE [0] efdtIntFB #-} -- See Note [Inline FB functions] in GHC.List
    efdtIntFB :: (Int -> r -> r) -> r -> Int# -> Int# -> Int# -> r
    efdtIntFB c n x1 x2 y
     | isTrue# (x2 >=# x1) = efdtIntUpFB c n x1 x2 y
     | otherwise           = efdtIntDnFB c n x1 x2 y

    -- Requires x2 >= x1
    efdtIntUp :: Int# -> Int# -> Int# -> [Int]
    efdtIntUp x1 x2 y    -- Be careful about overflow!
     | isTrue# (y <# x2) = if isTrue# (y <# x1) then [] else [I# x1]
     | otherwise = -- Common case: x1 <= x2 <= y
                   let !delta = x2 -# x1 -- >= 0
                       !y' = y -# delta  -- x1 <= y' <= y; hence y' is representable

                       -- Invariant: x <= y
                       -- Note that: z <= y' => z + delta won't overflow
                       -- so we are guaranteed not to overflow if/when we recurse
                       go_up x | isTrue# (x ># y') = [I# x]
                               | otherwise         = I# x : go_up (x +# delta)
                   in I# x1 : go_up x2

    -- Requires x2 >= x1
    {-# INLINE [0] efdtIntUpFB #-} -- See Note [Inline FB functions] in GHC.List
    efdtIntUpFB :: (Int -> r -> r) -> r -> Int# -> Int# -> Int# -> r
    efdtIntUpFB c n x1 x2 y    -- Be careful about overflow!
     | isTrue# (y <# x2) = if isTrue# (y <# x1) then n else I# x1 `c` n
     | otherwise = -- Common case: x1 <= x2 <= y
                   let !delta = x2 -# x1 -- >= 0
                       !y' = y -# delta  -- x1 <= y' <= y; hence y' is representable

                       -- Invariant: x <= y
                       -- Note that: z <= y' => z + delta won't overflow
                       -- so we are guaranteed not to overflow if/when we recurse
                       go_up x | isTrue# (x ># y') = I# x `c` n
                               | otherwise         = I# x `c` go_up (x +# delta)
                   in I# x1 `c` go_up x2

    -- Requires x2 <= x1
    efdtIntDn :: Int# -> Int# -> Int# -> [Int]
    efdtIntDn x1 x2 y    -- Be careful about underflow!
     | isTrue# (y ># x2) = if isTrue# (y ># x1) then [] else [I# x1]
     | otherwise = -- Common case: x1 >= x2 >= y
                   let !delta = x2 -# x1 -- <= 0
                       !y' = y -# delta  -- y <= y' <= x1; hence y' is representable

                       -- Invariant: x >= y
                       -- Note that: z >= y' => z + delta won't underflow
                       -- so we are guaranteed not to underflow if/when we recurse
                       go_dn x | isTrue# (x <# y') = [I# x]
                               | otherwise         = I# x : go_dn (x +# delta)
       in I# x1 : go_dn x2

    -- Requires x2 <= x1
    {-# INLINE [0] efdtIntDnFB #-} -- See Note [Inline FB functions] in GHC.List
    efdtIntDnFB :: (Int -> r -> r) -> r -> Int# -> Int# -> Int# -> r
    efdtIntDnFB c n x1 x2 y    -- Be careful about underflow!
     | isTrue# (y ># x2) = if isTrue# (y ># x1) then n else I# x1 `c` n
     | otherwise = -- Common case: x1 >= x2 >= y
                   let !delta = x2 -# x1 -- <= 0
                       !y' = y -# delta  -- y <= y' <= x1; hence y' is representable

                       -- Invariant: x >= y
                       -- Note that: z >= y' => z + delta won't underflow
                       -- so we are guaranteed not to underflow if/when we recurse
                       go_dn x | isTrue# (x <# y') = I# x `c` n
                               | otherwise         = I# x `c` go_dn (x +# delta)
                   in I# x1 `c` go_dn x2

    ------------------------------------------------------------------------
    -- Word
    ------------------------------------------------------------------------

    -- | @since 2.01
    instance Bounded Word where
        minBound = 0

        -- use unboxed literals for maxBound, because GHC doesn't optimise
        -- (fromInteger 0xffffffff :: Word).
    #if WORD_SIZE_IN_BITS == 32
        maxBound = W# 0xFFFFFFFF##
    #elif WORD_SIZE_IN_BITS == 64
        maxBound = W# 0xFFFFFFFFFFFFFFFF##
    #else
    #error Unhandled value for WORD_SIZE_IN_BITS
    #endif

    -- | @since 2.01
    instance Enum Word where
        succ x
            | x /= maxBound = x + 1
            | otherwise     = succError "Word"
        pred x
            | x /= minBound = x - 1
            | otherwise     = predError "Word"
        toEnum i@(I# i#)
            | i >= 0        = W# (int2Word# i#)
            | otherwise     = toEnumError "Word" i (minBound::Word, maxBound::Word)
        fromEnum x@(W# x#)
            | x <= maxIntWord = I# (word2Int# x#)
            | otherwise       = fromEnumError "Word" x

        {-# INLINE enumFrom #-}
        enumFrom (W# x#)      = eftWord x# maxWord#
            where !(W# maxWord#) = maxBound
            -- Blarg: technically I guess enumFrom isn't strict!

        {-# INLINE enumFromTo #-}
        enumFromTo (W# x) (W# y) = eftWord x y

        {-# INLINE enumFromThen #-}
        enumFromThen (W# x1) (W# x2) = efdWord x1 x2

        {-# INLINE enumFromThenTo #-}
        enumFromThenTo (W# x1) (W# x2) (W# y) = efdtWord x1 x2 y

    maxIntWord :: Word
    -- The biggest word representable as an Int
    maxIntWord = W# (case maxInt of I# i -> int2Word# i)

    -----------------------------------------------------
    -- eftWord and eftWordFB deal with [a..b], which is the
    -- most common form, so we take a lot of care
    -- In particular, we have rules for deforestation

    {-# RULES
    "eftWord"        [~1] forall x y. eftWord x y = build (\ c n -> eftWordFB c n x y)
    "eftWordList"    [1] eftWordFB  (:) [] = eftWord
     #-}

    -- The Enum rules for Word work much the same way that they do for Int.
    -- See Note [How the Enum rules work].

    {-# NOINLINE [1] eftWord #-}
    eftWord :: Word# -> Word# -> [Word]
    -- [x1..x2]
    eftWord x0 y | isTrue# (x0 `gtWord#` y) = []
                 | otherwise                = go x0
                    where
                      go x = W# x : if isTrue# (x `eqWord#` y)
                                    then []
                                    else go (x `plusWord#` 1##)

    {-# INLINE [0] eftWordFB #-} -- See Note [Inline FB functions] in GHC.List
    eftWordFB :: (Word -> r -> r) -> r -> Word# -> Word# -> r
    eftWordFB c n x0 y | isTrue# (x0 `gtWord#` y) = n
                       | otherwise                = go x0
                      where
                        go x = W# x `c` if isTrue# (x `eqWord#` y)
                                        then n
                                        else go (x `plusWord#` 1##)
                            -- Watch out for y=maxBound; hence ==, not >
            -- Be very careful not to have more than one "c"
            -- so that when eftInfFB is inlined we can inline
            -- whatever is bound to "c"

    -----------------------------------------------------
    -- efdWord and efdtWord deal with [a,b..] and [a,b..c].
    -- The code is more complicated because of worries about Word overflow.

    -- See Note [How the Enum rules work]
    {-# RULES
    "efdtWord"       [~1] forall x1 x2 y.
                         efdtWord x1 x2 y = build (\ c n -> efdtWordFB c n x1 x2 y)
    "efdtWordUpList" [1]  efdtWordFB (:) [] = efdtWord
     #-}

    efdWord :: Word# -> Word# -> [Word]
    -- [x1,x2..maxWord]
    efdWord x1 x2
     | isTrue# (x2 `geWord#` x1) = case maxBound of W# y -> efdtWordUp x1 x2 y
     | otherwise                 = case minBound of W# y -> efdtWordDn x1 x2 y

    {-# NOINLINE [1] efdtWord #-}
    efdtWord :: Word# -> Word# -> Word# -> [Word]
    -- [x1,x2..y]
    efdtWord x1 x2 y
     | isTrue# (x2 `geWord#` x1) = efdtWordUp x1 x2 y
     | otherwise                 = efdtWordDn x1 x2 y

    {-# INLINE [0] efdtWordFB #-} -- See Note [Inline FB functions] in GHC.List
    efdtWordFB :: (Word -> r -> r) -> r -> Word# -> Word# -> Word# -> r
    efdtWordFB c n x1 x2 y
     | isTrue# (x2 `geWord#` x1) = efdtWordUpFB c n x1 x2 y
     | otherwise                 = efdtWordDnFB c n x1 x2 y

    -- Requires x2 >= x1
    efdtWordUp :: Word# -> Word# -> Word# -> [Word]
    efdtWordUp x1 x2 y    -- Be careful about overflow!
     | isTrue# (y `ltWord#` x2) = if isTrue# (y `ltWord#` x1) then [] else [W# x1]
     | otherwise = -- Common case: x1 <= x2 <= y
                   let !delta = x2 `minusWord#` x1 -- >= 0
                       !y' = y `minusWord#` delta  -- x1 <= y' <= y; hence y' is representable

                       -- Invariant: x <= y
                       -- Note that: z <= y' => z + delta won't overflow
                       -- so we are guaranteed not to overflow if/when we recurse
                       go_up x | isTrue# (x `gtWord#` y') = [W# x]
                               | otherwise                = W# x : go_up (x `plusWord#` delta)
                   in W# x1 : go_up x2

    -- Requires x2 >= x1
    {-# INLINE [0] efdtWordUpFB #-} -- See Note [Inline FB functions] in GHC.List
    efdtWordUpFB :: (Word -> r -> r) -> r -> Word# -> Word# -> Word# -> r
    efdtWordUpFB c n x1 x2 y    -- Be careful about overflow!
     | isTrue# (y `ltWord#` x2) = if isTrue# (y `ltWord#` x1) then n else W# x1 `c` n
     | otherwise = -- Common case: x1 <= x2 <= y
                   let !delta = x2 `minusWord#` x1 -- >= 0
                       !y' = y `minusWord#` delta  -- x1 <= y' <= y; hence y' is representable

                       -- Invariant: x <= y
                       -- Note that: z <= y' => z + delta won't overflow
                       -- so we are guaranteed not to overflow if/when we recurse
                       go_up x | isTrue# (x `gtWord#` y') = W# x `c` n
                               | otherwise                = W# x `c` go_up (x `plusWord#` delta)
                   in W# x1 `c` go_up x2

    -- Requires x2 <= x1
    efdtWordDn :: Word# -> Word# -> Word# -> [Word]
    efdtWordDn x1 x2 y    -- Be careful about underflow!
     | isTrue# (y `gtWord#` x2) = if isTrue# (y `gtWord#` x1) then [] else [W# x1]
     | otherwise = -- Common case: x1 >= x2 >= y
                   let !delta = x2 `minusWord#` x1 -- <= 0
                       !y' = y `minusWord#` delta  -- y <= y' <= x1; hence y' is representable

                       -- Invariant: x >= y
                       -- Note that: z >= y' => z + delta won't underflow
                       -- so we are guaranteed not to underflow if/when we recurse
                       go_dn x | isTrue# (x `ltWord#` y') = [W# x]
                               | otherwise                = W# x : go_dn (x `plusWord#` delta)
       in W# x1 : go_dn x2

    -- Requires x2 <= x1
    {-# INLINE [0] efdtWordDnFB #-} -- See Note [Inline FB functions] in GHC.List
    efdtWordDnFB :: (Word -> r -> r) -> r -> Word# -> Word# -> Word# -> r
    efdtWordDnFB c n x1 x2 y    -- Be careful about underflow!
     | isTrue# (y `gtWord#` x2) = if isTrue# (y `gtWord#` x1) then n else W# x1 `c` n
     | otherwise = -- Common case: x1 >= x2 >= y
                   let !delta = x2 `minusWord#` x1 -- <= 0
                       !y' = y `minusWord#` delta  -- y <= y' <= x1; hence y' is representable

                       -- Invariant: x >= y
                       -- Note that: z >= y' => z + delta won't underflow
                       -- so we are guaranteed not to underflow if/when we recurse
                       go_dn x | isTrue# (x `ltWord#` y') = W# x `c` n
                               | otherwise                = W# x `c` go_dn (x `plusWord#` delta)
                   in W# x1 `c` go_dn x2

    ------------------------------------------------------------------------
    -- Integer
    ------------------------------------------------------------------------

    -- | @since 2.01
    instance  Enum Integer  where
        succ x               = x + 1
        pred x               = x - 1
        toEnum (I# n)        = smallInteger n
        fromEnum n           = I# (integerToInt n)

        {-# INLINE enumFrom #-}
        {-# INLINE enumFromThen #-}
        {-# INLINE enumFromTo #-}
        {-# INLINE enumFromThenTo #-}
        enumFrom x             = enumDeltaInteger   x 1
        enumFromThen x y       = enumDeltaInteger   x (y-x)
        enumFromTo x lim       = enumDeltaToInteger x 1     lim
        enumFromThenTo x y lim = enumDeltaToInteger x (y-x) lim

    -- See Note [How the Enum rules work]
    {-# RULES
    "enumDeltaInteger"      [~1] forall x y.   enumDeltaInteger x y         = build (\c _ -> enumDeltaIntegerFB c x y)
    "efdtInteger"           [~1] forall x d l. enumDeltaToInteger x d l     = build (\c n -> enumDeltaToIntegerFB  c n x d l)
    "efdtInteger1"          [~1] forall x l.   enumDeltaToInteger x 1 l     = build (\c n -> enumDeltaToInteger1FB c n x l)

    "enumDeltaToInteger1FB" [1] forall c n x.  enumDeltaToIntegerFB c n x 1 = enumDeltaToInteger1FB c n x

    "enumDeltaInteger"      [1] enumDeltaIntegerFB    (:)     = enumDeltaInteger
    "enumDeltaToInteger"    [1] enumDeltaToIntegerFB  (:) []  = enumDeltaToInteger
    "enumDeltaToInteger1"   [1] enumDeltaToInteger1FB (:) []  = enumDeltaToInteger1
     #-}

    {- Note [Enum Integer rules for literal 1]
    The "1" rules above specialise for the common case where delta = 1,
    so that we can avoid the delta>=0 test in enumDeltaToIntegerFB.
    Then enumDeltaToInteger1FB is nice and small and can be inlined,
    which would allow the constructor to be inlined and good things to happen.

    We match on the literal "1" both in phase 2 (rule "efdtInteger1") and
    phase 1 (rule "enumDeltaToInteger1FB"), just for belt and braces

    We do not do it for Int this way because hand-tuned code already exists, and
    the special case varies more from the general case, due to the issue of overflows.
    -}

    {-# INLINE [0] enumDeltaIntegerFB #-}
    -- See Note [Inline FB functions] in GHC.List
    enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
    enumDeltaIntegerFB c x0 d = go x0
      where go x = x `seq` (x `c` go (x+d))

    {-# NOINLINE [1] enumDeltaInteger #-}
    enumDeltaInteger :: Integer -> Integer -> [Integer]
    enumDeltaInteger x d = x `seq` (x : enumDeltaInteger (x+d) d)
    -- strict accumulator, so
    --     head (drop 1000000 [1 .. ]
    -- works

    {-# INLINE [0] enumDeltaToIntegerFB #-}
    -- See Note [Inline FB functions] in GHC.List
    -- Don't inline this until RULE "enumDeltaToInteger" has had a chance to fire
    enumDeltaToIntegerFB :: (Integer -> a -> a) -> a
                         -> Integer -> Integer -> Integer -> a
    enumDeltaToIntegerFB c n x delta lim
      | delta >= 0 = up_fb c n x delta lim
      | otherwise  = dn_fb c n x delta lim

    {-# INLINE [0] enumDeltaToInteger1FB #-}
    -- See Note [Inline FB functions] in GHC.List
    -- Don't inline this until RULE "enumDeltaToInteger" has had a chance to fire
    enumDeltaToInteger1FB :: (Integer -> a -> a) -> a
                          -> Integer -> Integer -> a
    enumDeltaToInteger1FB c n x0 lim = go (x0 :: Integer)
                          where
                            go x | x > lim   = n
                                 | otherwise = x `c` go (x+1)

    {-# NOINLINE [1] enumDeltaToInteger #-}
    enumDeltaToInteger :: Integer -> Integer -> Integer -> [Integer]
    enumDeltaToInteger x delta lim
      | delta >= 0 = up_list x delta lim
      | otherwise  = dn_list x delta lim

    {-# NOINLINE [1] enumDeltaToInteger1 #-}
    enumDeltaToInteger1 :: Integer -> Integer -> [Integer]
    -- Special case for Delta = 1
    enumDeltaToInteger1 x0 lim = go (x0 :: Integer)
                          where
                            go x | x > lim   = []
                                 | otherwise = x : go (x+1)

    up_fb :: (Integer -> a -> a) -> a -> Integer -> Integer -> Integer -> a
    up_fb c n x0 delta lim = go (x0 :: Integer)
                          where
                            go x | x > lim   = n
                                 | otherwise = x `c` go (x+delta)
    dn_fb :: (Integer -> a -> a) -> a -> Integer -> Integer -> Integer -> a
    dn_fb c n x0 delta lim = go (x0 :: Integer)
                          where
                            go x | x < lim   = n
                                 | otherwise = x `c` go (x+delta)

    up_list :: Integer -> Integer -> Integer -> [Integer]
    up_list x0 delta lim = go (x0 :: Integer)
                        where
                            go x | x > lim   = []
                                 | otherwise = x : go (x+delta)
    dn_list :: Integer -> Integer -> Integer -> [Integer]
    dn_list x0 delta lim = go (x0 :: Integer)
                        where
                            go x | x < lim   = []
                                 | otherwise = x : go (x+delta)

    ------------------------------------------------------------------------
    -- Natural
    ------------------------------------------------------------------------

    -- | @since 4.8.0.0
    instance Enum Natural where
        succ n = n `plusNatural`  wordToNaturalBase 1##
        pred n = n `minusNatural` wordToNaturalBase 1##

        toEnum = intToNatural

    #if defined(MIN_VERSION_integer_gmp)
        fromEnum (NatS# w)
          | i >= 0    = i
          | otherwise = errorWithoutStackTrace "fromEnum: out of Int range"
          where
            i = I# (word2Int# w)
    #endif
        fromEnum n = fromEnum (naturalToInteger n)

        enumFrom x        = enumDeltaNatural      x (wordToNaturalBase 1##)
        enumFromThen x y
          | x <= y        = enumDeltaNatural      x (y-x)
          | otherwise     = enumNegDeltaToNatural x (x-y) (wordToNaturalBase 0##)

        enumFromTo x lim  = enumDeltaToNatural    x (wordToNaturalBase 1##) lim
        enumFromThenTo x y lim
          | x <= y        = enumDeltaToNatural    x (y-x) lim
          | otherwise     = enumNegDeltaToNatural x (x-y) lim

    -- Helpers for 'Enum Natural'; TODO: optimise & make fusion work

    enumDeltaNatural :: Natural -> Natural -> [Natural]
    enumDeltaNatural !x d = x : enumDeltaNatural (x+d) d

    enumDeltaToNatural :: Natural -> Natural -> Natural -> [Natural]
    enumDeltaToNatural x0 delta lim = go x0
      where
        go x | x > lim   = []
             | otherwise = x : go (x+delta)

    enumNegDeltaToNatural :: Natural -> Natural -> Natural -> [Natural]
    enumNegDeltaToNatural x0 ndelta lim = go x0
      where
        go x | x < lim     = []
             | x >= ndelta = x : go (x-ndelta)
             | otherwise   = [x]

    -- Instances from GHC.Types

    -- | @since 4.10.0.0
    deriving instance Bounded VecCount
    -- | @since 4.10.0.0
    deriving instance Enum VecCount

    -- | @since 4.10.0.0
    deriving instance Bounded VecElem
    -- | @since 4.10.0.0
    deriving instance Enum VecElem