    \begin{code}
    {-# OPTIONS_GHC -XNoImplicitPrelude #-}
    {-# OPTIONS_HADDOCK hide #-}
    -----------------------------------------------------------------------------
    -- |
    -- 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.
    --
    -----------------------------------------------------------------------------

    -- #hide
    module GHC.Enum(
            Bounded(..), Enum(..),
            boundedEnumFrom, boundedEnumFromThen,

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

       ) where

    import GHC.Base
    import Data.Tuple       ()              -- for dependencies
    default ()              -- Double isn't available yet
    \end{code}

    %*********************************************************
    %*                                                      *
    \subsection{Class declarations}
    %*                                                      *
    %*********************************************************

    \begin{code}
    -- | 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..]@.
        enumFrom            :: a -> [a]
        -- | Used in Haskell's translation of @[n,n'..]@.
        enumFromThen        :: a -> a -> [a]
        -- | Used in Haskell's translation of @[n..m]@.
        enumFromTo          :: a -> a -> [a]
        -- | Used in Haskell's translation of @[n,n'..m]@.
        enumFromThenTo      :: a -> a -> a -> [a]

        succ                   = toEnum . (`plusInt` oneInt)  . fromEnum
        pred                   = toEnum . (`minusInt` oneInt) . 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
    \end{code}

    %*********************************************************
    %*                                                      *
    \subsection{Tuples}
    %*                                                      *
    %*********************************************************

    \begin{code}
    instance Bounded () where
        minBound = ()
        maxBound = ()

    instance Enum () where
        succ _      = error "Prelude.Enum.().succ: bad argument"
        pred _      = error "Prelude.Enum.().pred: bad argument"

        toEnum x | x == zeroInt = ()
                 | otherwise    = error "Prelude.Enum.().toEnum: bad argument"

        fromEnum () = zeroInt
        enumFrom ()         = [()]
        enumFromThen () ()  = let many = ():many in many
        enumFromTo () ()    = [()]
        enumFromThenTo () () () = let many = ():many in many
    \end{code}

    \begin{code}
    -- Report requires instances up to 15
    instance (Bounded a, Bounded b) => Bounded (a,b) where
       minBound = (minBound, minBound)
       maxBound = (maxBound, maxBound)

    instance (Bounded a, Bounded b, Bounded c) => Bounded (a,b,c) where
       minBound = (minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound)

    instance (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a,b,c,d) where
       minBound = (minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound)

    instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a,b,c,d,e) where
       minBound = (minBound, minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound)

    instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f)
            => Bounded (a,b,c,d,e,f) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound)

    instance (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g)
            => Bounded (a,b,c,d,e,f,g) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound)

    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) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound)

    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) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound, minBound,
                   minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound,
                   maxBound)

    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) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound, minBound,
                   minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound,
                   maxBound, maxBound)

    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) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound, minBound,
                   minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound,
                   maxBound, maxBound, maxBound)

    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) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound, minBound,
                   minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound,
                   maxBound, maxBound, maxBound, maxBound)

    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) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound, minBound,
                   minBound, minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound,
                   maxBound, maxBound, maxBound, maxBound, maxBound)

    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) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound, minBound,
                   minBound, minBound, minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound,
                   maxBound, maxBound, maxBound, maxBound, maxBound, maxBound)

    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) where
       minBound = (minBound, minBound, minBound, minBound, minBound, minBound, minBound, minBound,
                   minBound, minBound, minBound, minBound, minBound, minBound, minBound)
       maxBound = (maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound,
                   maxBound, maxBound, maxBound, maxBound, maxBound, maxBound, maxBound)
    \end{code}

    %*********************************************************
    %*                                                      *
    \subsection{Type @Bool@}
    %*                                                      *
    %*********************************************************

    \begin{code}
    instance Bounded Bool where
      minBound = False
      maxBound = True

    instance Enum Bool where
      succ False = True
      succ True  = error "Prelude.Enum.Bool.succ: bad argument"

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

      toEnum n | n == zeroInt = False
               | n == oneInt  = True
               | otherwise    = error "Prelude.Enum.Bool.toEnum: bad argument"

      fromEnum False = zeroInt
      fromEnum True  = oneInt

      -- Use defaults for the rest
      enumFrom     = boundedEnumFrom
      enumFromThen = boundedEnumFromThen
    \end{code}

    %*********************************************************
    %*                                                      *
    \subsection{Type @Ordering@}
    %*                                                      *
    %*********************************************************

    \begin{code}
    instance Bounded Ordering where
      minBound = LT
      maxBound = GT

    instance Enum Ordering where
      succ LT = EQ
      succ EQ = GT
      succ GT = error "Prelude.Enum.Ordering.succ: bad argument"

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

      toEnum n | n == zeroInt = LT
               | n == oneInt  = EQ
               | n == twoInt  = GT
      toEnum _ = error "Prelude.Enum.Ordering.toEnum: bad argument"

      fromEnum LT = zeroInt
      fromEnum EQ = oneInt
      fromEnum GT = twoInt

      -- Use defaults for the rest
      enumFrom     = boundedEnumFrom
      enumFromThen = boundedEnumFromThen
    \end{code}

    %*********************************************************
    %*                                                      *
    \subsection{Type @Char@}
    %*                                                      *
    %*********************************************************

    \begin{code}
    instance  Bounded Char  where
        minBound =  '\0'
        maxBound =  '\x10FFFF'

    instance  Enum Char  where
        succ (C# c#)
           | not (ord# c# ==# 0x10FFFF#) = C# (chr# (ord# c# +# 1#))
           | otherwise              = error ("Prelude.Enum.Char.succ: bad argument")
        pred (C# c#)
           | not (ord# c# ==# 0#)   = C# (chr# (ord# c# -# 1#))
           | otherwise              = error ("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)

    {-# 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 #-}
    eftCharFB :: (Char -> a -> a) -> a -> Int# -> Int# -> a
    eftCharFB c n x0 y = go x0
                     where
                        go x | x ># y    = n
                             | otherwise = C# (chr# x) `c` go (x +# 1#)

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

    -- For enumFromThenTo we give up on inlining
    {-# NOINLINE [0] efdCharFB #-}
    efdCharFB :: (Char -> a -> a) -> a -> Int# -> Int# -> a
    efdCharFB c n x1 x2
      | 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

    efdChar :: Int# -> Int# -> String
    efdChar x1 x2
      | delta >=# 0# = go_up_char_list x1 delta 0x10FFFF#
      | otherwise    = go_dn_char_list x1 delta 0#
      where
        delta = x2 -# x1

    {-# NOINLINE [0] efdtCharFB #-}
    efdtCharFB :: (Char -> a -> a) -> a -> Int# -> Int# -> Int# -> a
    efdtCharFB c n x1 x2 lim
      | 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

    efdtChar :: Int# -> Int# -> Int# -> String
    efdtChar x1 x2 lim
      | 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 | 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 | 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 | 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 | x <# lim  = []
                | otherwise = C# (chr# x) : go_dn (x +# delta)
    \end{code}

    %*********************************************************
    %*                                                      *
    \subsection{Type @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

    Also NB that the Num class isn't available in this module.

    \begin{code}
    instance  Bounded Int where
        minBound =  minInt
        maxBound =  maxInt

    instance  Enum Int  where
        succ x
           | x == maxBound  = error "Prelude.Enum.succ{Int}: tried to take `succ' of maxBound"
           | otherwise      = x `plusInt` oneInt
        pred x
           | x == minBound  = error "Prelude.Enum.pred{Int}: tried to take `pred' of minBound"
           | otherwise      = x `minusInt` oneInt

        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
     #-}

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

    {-# INLINE [0] eftIntFB #-}
    eftIntFB :: (Int -> r -> r) -> r -> Int# -> Int# -> r
    eftIntFB c n x0 y | x0 ># y    = n
                      | otherwise = go x0
                     where
                       go x = I# x `c` if 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.

    {-# 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
     | x2 >=# x1 = case maxInt of I# y -> efdtIntUp x1 x2 y
     | otherwise = case minInt of I# y -> efdtIntDn x1 x2 y

    efdtInt :: Int# -> Int# -> Int# -> [Int]
    -- [x1,x2..y]
    efdtInt x1 x2 y
     | x2 >=# x1 = efdtIntUp x1 x2 y
     | otherwise = efdtIntDn x1 x2 y

    {-# INLINE [0] efdtIntFB #-}
    efdtIntFB :: (Int -> r -> r) -> r -> Int# -> Int# -> Int# -> r
    efdtIntFB c n x1 x2 y
     | 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!
     | y <# x2   = if 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 | x ># y'  = [I# x]
                               | otherwise = I# x : go_up (x +# delta)
                   in I# x1 : go_up x2

    -- Requires x2 >= x1
    efdtIntUpFB :: (Int -> r -> r) -> r -> Int# -> Int# -> Int# -> r
    efdtIntUpFB c n x1 x2 y    -- Be careful about overflow!
     | y <# x2   = if 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 | 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!
     | y ># x2   = if 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 | x <# y'  = [I# x]
                               | otherwise = I# x : go_dn (x +# delta)
       in I# x1 : go_dn x2

    -- Requires x2 <= x1
    efdtIntDnFB :: (Int -> r -> r) -> r -> Int# -> Int# -> Int# -> r
    efdtIntDnFB c n x1 x2 y    -- Be careful about underflow!
     | y ># x2 = if 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 | x <# y'   = I# x `c` n
                               | otherwise = I# x `c` go_dn (x +# delta)
                   in I# x1 `c` go_dn x2
    \end{code}