X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=GHC%2FNum.lhs;h=5dc5e753d1e99633df774f2ec95789e64d37d2c8;hb=be2750a0a11b919fb03cc070074e430f88bdfa90;hp=8bc005b5ed536a06770b112a5375f64af1246932;hpb=260e7f2ed9a43c6ecf5a556d77817f39ed2893ab;p=ghc-base.git

diff --git a/GHC/Num.lhs b/GHC/Num.lhs
index 8bc005b..5dc5e75 100644
--- a/GHC/Num.lhs
+++ b/GHC/Num.lhs
@@ -1,63 +1,92 @@
-% ------------------------------------------------------------------------------
-% $Id: Num.lhs,v 1.3 2001/12/21 15:07:25 simonmar Exp $
-%
-% (c) The University of Glasgow, 1994-2000
-%
-
-\section[GHC.Num]{Module @GHC.Num@}
-
-The class
-
-	Num
-
-and the type
-
-	Integer
-
-
 \begin{code}
-{-# OPTIONS -fno-implicit-prelude #-}
+{-# LANGUAGE CPP, NoImplicitPrelude, MagicHash, UnboxedTuples #-}
+-- We believe we could deorphan this module, by moving lots of things
+-- around, but we haven't got there yet:
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+{-# OPTIONS_HADDOCK hide #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  GHC.Num
+-- Copyright   :  (c) The University of Glasgow 1994-2002
+-- License     :  see libraries/base/LICENSE
+--
+-- Maintainer  :  cvs-ghc@haskell.org
+-- Stability   :  internal
+-- Portability :  non-portable (GHC Extensions)
+--
+-- The 'Num' class and the 'Integer' type.
+--
+-----------------------------------------------------------------------------
 
 #include "MachDeps.h"
 #if SIZEOF_HSWORD == 4
-#define LEFTMOST_BIT 2147483648
+#define DIGITS       9
+#define BASE         1000000000
 #elif SIZEOF_HSWORD == 8
-#define LEFTMOST_BIT 9223372036854775808
+#define DIGITS       18
+#define BASE         1000000000000000000
 #else
-#error Please define LEFTMOST_BIT to be 2^(SIZEOF_HSWORD*8-1)
+#error Please define DIGITS and BASE
+-- DIGITS should be the largest integer such that
+--     10^DIGITS < 2^(SIZEOF_HSWORD * 8 - 1)
+-- BASE should be 10^DIGITS. Note that ^ is not available yet.
 #endif
 
-module GHC.Num where
+-- #hide
+module GHC.Num (module GHC.Num, module GHC.Integer) where
 
-import {-# SOURCE #-} GHC.Err
 import GHC.Base
-import GHC.List
 import GHC.Enum
 import GHC.Show
+import GHC.Integer
 
 infixl 7  *
 infixl 6  +, -
 
-default ()		-- Double isn't available yet, 
-			-- and we shouldn't be using defaults anyway
+default ()              -- Double isn't available yet,
+                        -- and we shouldn't be using defaults anyway
 \end{code}
 
 %*********************************************************
-%*							*
+%*                                                      *
 \subsection{Standard numeric class}
-%*							*
+%*                                                      *
 %*********************************************************
 
 \begin{code}
+-- | Basic numeric class.
+--
+-- Minimal complete definition: all except 'negate' or @(-)@
 class  (Eq a, Show a) => Num a  where
-    (+), (-), (*)	:: a -> a -> a
-    negate		:: a -> a
-    abs, signum		:: a -> a
-    fromInteger		:: Integer -> a
-
-    x - y		= x + negate y
-    negate x		= 0 - x
-
+    (+), (-), (*)       :: a -> a -> a
+    -- | Unary negation.
+    negate              :: a -> a
+    -- | Absolute value.
+    abs                 :: a -> a
+    -- | Sign of a number.
+    -- The functions 'abs' and 'signum' should satisfy the law:
+    --
+    -- > abs x * signum x == x
+    --
+    -- For real numbers, the 'signum' is either @-1@ (negative), @0@ (zero)
+    -- or @1@ (positive).
+    signum              :: a -> a
+    -- | Conversion from an 'Integer'.
+    -- An integer literal represents the application of the function
+    -- 'fromInteger' to the appropriate value of type 'Integer',
+    -- so such literals have type @('Num' a) => a@.
+    fromInteger         :: Integer -> a
+
+    {-# INLINE (-) #-}
+    {-# INLINE negate #-}
+    x - y               = x + negate y
+    negate x            = 0 - x
+
+-- | the same as @'flip' ('-')@.
+--
+-- Because @-@ is treated specially in the Haskell grammar,
+-- @(-@ /e/@)@ is not a section, but an application of prefix negation.
+-- However, @('subtract'@ /exp/@)@ is equivalent to the disallowed section.
 {-# INLINE subtract #-}
 subtract :: (Num a) => a -> a -> a
 subtract x y = y - x
@@ -65,33 +94,28 @@ subtract x y = y - x
 
 
 %*********************************************************
-%*							*
+%*                                                      *
 \subsection{Instances for @Int@}
-%*							*
+%*                                                      *
 %*********************************************************
 
 \begin{code}
 instance  Num Int  where
-    (+)	   = plusInt
-    (-)	   = minusInt
+    (+)    = plusInt
+    (-)    = minusInt
     negate = negateInt
-    (*)	   = timesInt
+    (*)    = timesInt
     abs n  = if n `geInt` 0 then n else negateInt n
 
     signum n | n `ltInt` 0 = negateInt 1
-	     | n `eqInt` 0 = 0
-	     | otherwise   = 1
+             | n `eqInt` 0 = 0
+             | otherwise   = 1
 
-    fromInteger = integer2Int
-\end{code}
-
-
-\begin{code}
--- These can't go in GHC.Base with the defn of Int, because
--- we don't have pairs defined at that time!
+    {-# INLINE fromInteger #-}	 -- Just to be sure!
+    fromInteger i = I# (toInt# i)
 
 quotRemInt :: Int -> Int -> (Int, Int)
-a@(I# _) `quotRemInt` b@(I# _) = (a `quotInt` b, a `remInt` b)
+quotRemInt a@(I# _) b@(I# _) = (a `quotInt` b, a `remInt` b)
     -- OK, so I made it a little stricter.  Shoot me.  (WDP 94/10)
 
 divModInt ::  Int -> Int -> (Int, Int)
@@ -99,221 +123,107 @@ divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
     -- Stricter.  Sorry if you don't like it.  (WDP 94/10)
 \end{code}
 
-
-%*********************************************************
-%*							*
-\subsection{The @Integer@ type}
-%*							*
 %*********************************************************
-
-\begin{code}
-data Integer	
-   = S# Int#				-- small integers
-#ifndef ILX
-   | J# Int# ByteArray#			-- large integers
-#else
-   | J# Void BigInteger                 -- .NET big ints
-
-foreign type dotnet "BigInteger" BigInteger
-#endif
-\end{code}
-
-Convenient boxed Integer PrimOps. 
-
-\begin{code}
-zeroInteger :: Integer
-zeroInteger = S# 0#
-
-int2Integer :: Int -> Integer
-{-# INLINE int2Integer #-}
-int2Integer (I# i) = S# i
-
-integer2Int :: Integer -> Int
-integer2Int (S# i)   = I# i
-integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
-
-toBig (S# i)     = case int2Integer# i of { (# s, d #) -> J# s d }
-toBig i@(J# _ _) = i
-\end{code}
-
-
-%*********************************************************
-%*							*
-\subsection{Dividing @Integers@}
-%*							*
+%*                                                      *
+\subsection{The @Integer@ instances for @Show@}
+%*                                                      *
 %*********************************************************
 
 \begin{code}
-quotRemInteger :: Integer -> Integer -> (Integer, Integer)
-quotRemInteger a@(S# (-LEFTMOST_BIT#)) b = quotRemInteger (toBig a) b
-quotRemInteger (S# i) (S# j)
-  = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j ) 
-quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
-quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
-quotRemInteger (J# s1 d1) (J# s2 d2)
-  = case (quotRemInteger# s1 d1 s2 d2) of
-	  (# s3, d3, s4, d4 #)
-	    -> (J# s3 d3, J# s4 d4)
-
-divModInteger a@(S# (-LEFTMOST_BIT#)) b = divModInteger (toBig a) b
-divModInteger (S# i) (S# j)
-  = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j) 
-divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
-divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
-divModInteger (J# s1 d1) (J# s2 d2)
-  = case (divModInteger# s1 d1 s2 d2) of
-	  (# s3, d3, s4, d4 #)
-	    -> (J# s3 d3, J# s4 d4)
-
-remInteger :: Integer -> Integer -> Integer
-remInteger ia 0
-  = error "Prelude.Integral.rem{Integer}: divide by 0"
-remInteger a@(S# (-LEFTMOST_BIT#)) b = remInteger (toBig a) b
-remInteger (S# a) (S# b) = S# (remInt# a b)
-{- Special case doesn't work, because a 1-element J# has the range
-   -(2^32-1) -- 2^32-1, whereas S# has the range -2^31 -- (2^31-1)
-remInteger ia@(S# a) (J# sb b)
-  | sb ==# 1#  = S# (remInt# a (word2Int# (integer2Word# sb b)))
-  | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
-  | 0# <# sb   = ia
-  | otherwise  = S# (0# -# a)
--}
-remInteger ia@(S# _) ib@(J# _ _) = remInteger (toBig ia) ib
-remInteger (J# sa a) (S# b)
-  = case int2Integer# b of { (# sb, b #) ->
-    case remInteger# sa a sb b of { (# sr, r #) ->
-    S# (integer2Int# sr r) }}
-remInteger (J# sa a) (J# sb b)
-  = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
-
-quotInteger :: Integer -> Integer -> Integer
-quotInteger ia 0
-  = error "Prelude.Integral.quot{Integer}: divide by 0"
-quotInteger a@(S# (-LEFTMOST_BIT#)) b = quotInteger (toBig a) b
-quotInteger (S# a) (S# b) = S# (quotInt# a b)
-{- Special case disabled, see remInteger above
-quotInteger (S# a) (J# sb b)
-  | sb ==# 1#  = S# (quotInt# a (word2Int# (integer2Word# sb b)))
-  | sb ==# -1# = S# (quotInt# a (0# -# (word2Int# (integer2Word# sb b))))
-  | otherwise  = zeroInteger
--}
-quotInteger ia@(S# _) ib@(J# _ _) = quotInteger (toBig ia) ib
-quotInteger (J# sa a) (S# b)
-  = case int2Integer# b of { (# sb, b #) ->
-    case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
-quotInteger (J# sa a) (J# sb b)
-  = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
-\end{code}
-
-
-
-\begin{code}
-gcdInteger :: Integer -> Integer -> Integer
--- SUP: Do we really need the first two cases?
-gcdInteger a@(S# (-LEFTMOST_BIT#)) b = gcdInteger (toBig a) b
-gcdInteger a b@(S# (-LEFTMOST_BIT#)) = gcdInteger a (toBig b)
-gcdInteger (S# a) (S# b) = case gcdInt (I# a) (I# b) of { I# c -> S# c }
-gcdInteger ia@(S# 0#) ib@(J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
-gcdInteger ia@(S# a)  ib@(J# sb b)
-  | a  ==# 0#  = abs ib
-  | sb ==# 0#  = abs ia
-  | otherwise  = S# (gcdIntegerInt# absSb b absA)
-       where absA  = if a  <# 0# then negateInt# a  else a
-             absSb = if sb <# 0# then negateInt# sb else sb
-gcdInteger ia@(J# _ _) ib@(S# _) = gcdInteger ib ia
-gcdInteger (J# 0# _) (J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
-gcdInteger (J# sa a) (J# sb b)
-  = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
-
-lcmInteger :: Integer -> Integer -> Integer
-lcmInteger a 0
-  = zeroInteger
-lcmInteger 0 b
-  = zeroInteger
-lcmInteger a b
-  = (divExact aa (gcdInteger aa ab)) * ab
-  where aa = abs a
-        ab = abs b
-
-divExact :: Integer -> Integer -> Integer
-divExact a@(S# (-LEFTMOST_BIT#)) b = divExact (toBig a) b
-divExact (S# a) (S# b) = S# (quotInt# a b)
-divExact (S# a) (J# sb b)
-  = S# (quotInt# a (integer2Int# sb b))
-divExact (J# sa a) (S# b)
-  = case int2Integer# b of
-     (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
-divExact (J# sa a) (J# sb b)
-  = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
-\end{code}
+instance Show Integer where
+    showsPrec p n r
+        | p > 6 && n < 0 = '(' : integerToString n (')' : r)
+        -- Minor point: testing p first gives better code
+        -- in the not-uncommon case where the p argument
+        -- is a constant
+        | otherwise = integerToString n r
+    showList = showList__ (showsPrec 0)
 
+-- Divide an conquer implementation of string conversion
+integerToString :: Integer -> String -> String
+integerToString n0 cs0
+    | n0 < 0    = '-' : integerToString' (- n0) cs0
+    | otherwise = integerToString' n0 cs0
+    where
+    integerToString' :: Integer -> String -> String
+    integerToString' n cs
+        | n < BASE  = jhead (fromInteger n) cs
+        | otherwise = jprinth (jsplitf (BASE*BASE) n) cs
+
+    -- Split n into digits in base p. We first split n into digits
+    -- in base p*p and then split each of these digits into two.
+    -- Note that the first 'digit' modulo p*p may have a leading zero
+    -- in base p that we need to drop - this is what jsplith takes care of.
+    -- jsplitb the handles the remaining digits.
+    jsplitf :: Integer -> Integer -> [Integer]
+    jsplitf p n
+        | p > n     = [n]
+        | otherwise = jsplith p (jsplitf (p*p) n)
+
+    jsplith :: Integer -> [Integer] -> [Integer]
+    jsplith p (n:ns) =
+        case n `quotRemInteger` p of
+        (# q, r #) ->
+            if q > 0 then q : r : jsplitb p ns
+                     else     r : jsplitb p ns
+    jsplith _ [] = error "jsplith: []"
+
+    jsplitb :: Integer -> [Integer] -> [Integer]
+    jsplitb _ []     = []
+    jsplitb p (n:ns) = case n `quotRemInteger` p of
+                       (# q, r #) ->
+                           q : r : jsplitb p ns
+
+    -- Convert a number that has been split into digits in base BASE^2
+    -- this includes a last splitting step and then conversion of digits
+    -- that all fit into a machine word.
+    jprinth :: [Integer] -> String -> String
+    jprinth (n:ns) cs =
+        case n `quotRemInteger` BASE of
+        (# q', r' #) ->
+            let q = fromInteger q'
+                r = fromInteger r'
+            in if q > 0 then jhead q $ jblock r $ jprintb ns cs
+                        else jhead r $ jprintb ns cs
+    jprinth [] _ = error "jprinth []"
+
+    jprintb :: [Integer] -> String -> String
+    jprintb []     cs = cs
+    jprintb (n:ns) cs = case n `quotRemInteger` BASE of
+                        (# q', r' #) ->
+                            let q = fromInteger q'
+                                r = fromInteger r'
+                            in jblock q $ jblock r $ jprintb ns cs
+
+    -- Convert an integer that fits into a machine word. Again, we have two
+    -- functions, one that drops leading zeros (jhead) and one that doesn't
+    -- (jblock)
+    jhead :: Int -> String -> String
+    jhead n cs
+        | n < 10    = case unsafeChr (ord '0' + n) of
+            c@(C# _) -> c : cs
+        | otherwise = case unsafeChr (ord '0' + r) of
+            c@(C# _) -> jhead q (c : cs)
+        where
+        (q, r) = n `quotRemInt` 10
 
-%*********************************************************
-%*							*
-\subsection{The @Integer@ instances for @Eq@, @Ord@}
-%*							*
-%*********************************************************
+    jblock = jblock' {- ' -} DIGITS
 
-\begin{code}
-instance  Eq Integer  where
-    (S# i)     ==  (S# j)     = i ==# j
-    (S# i)     ==  (J# s d)   = cmpIntegerInt# s d i ==# 0#
-    (J# s d)   ==  (S# i)     = cmpIntegerInt# s d i ==# 0#
-    (J# s1 d1) ==  (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ==# 0#
-
-    (S# i)     /=  (S# j)     = i /=# j
-    (S# i)     /=  (J# s d)   = cmpIntegerInt# s d i /=# 0#
-    (J# s d)   /=  (S# i)     = cmpIntegerInt# s d i /=# 0#
-    (J# s1 d1) /=  (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) /=# 0#
-
-------------------------------------------------------------------------
-instance  Ord Integer  where
-    (S# i)     <=  (S# j)     = i <=# j
-    (J# s d)   <=  (S# i)     = cmpIntegerInt# s d i <=# 0#
-    (S# i)     <=  (J# s d)   = cmpIntegerInt# s d i >=# 0#
-    (J# s1 d1) <=  (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <=# 0#
-
-    (S# i)     >   (S# j)     = i ># j
-    (J# s d)   >   (S# i)     = cmpIntegerInt# s d i ># 0#
-    (S# i)     >   (J# s d)   = cmpIntegerInt# s d i <# 0#
-    (J# s1 d1) >   (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ># 0#
-
-    (S# i)     <   (S# j)     = i <# j
-    (J# s d)   <   (S# i)     = cmpIntegerInt# s d i <# 0#
-    (S# i)     <   (J# s d)   = cmpIntegerInt# s d i ># 0#
-    (J# s1 d1) <   (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
-
-    (S# i)     >=  (S# j)     = i >=# j
-    (J# s d)   >=  (S# i)     = cmpIntegerInt# s d i >=# 0#
-    (S# i)     >=  (J# s d)   = cmpIntegerInt# s d i <=# 0#
-    (J# s1 d1) >=  (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
-
-    compare (S# i)  (S# j)
-       | i ==# j = EQ
-       | i <=# j = LT
-       | otherwise = GT
-    compare (J# s d) (S# i)
-       = case cmpIntegerInt# s d i of { res# ->
-	 if res# <# 0# then LT else 
-	 if res# ># 0# then GT else EQ
-	 }
-    compare (S# i) (J# s d)
-       = case cmpIntegerInt# s d i of { res# ->
-	 if res# ># 0# then LT else 
-	 if res# <# 0# then GT else EQ
-	 }
-    compare (J# s1 d1) (J# s2 d2)
-       = case cmpInteger# s1 d1 s2 d2 of { res# ->
-	 if res# <# 0# then LT else 
-	 if res# ># 0# then GT else EQ
-	 }
+    jblock' :: Int -> Int -> String -> String
+    jblock' d n cs
+        | d == 1    = case unsafeChr (ord '0' + n) of
+             c@(C# _) -> c : cs
+        | otherwise = case unsafeChr (ord '0' + r) of
+             c@(C# _) -> jblock' (d - 1) q (c : cs)
+        where
+        (q, r) = n `quotRemInt` 10
 \end{code}
 
 
 %*********************************************************
-%*							*
+%*                                                      *
 \subsection{The @Integer@ instances for @Num@}
-%*							*
+%*                                                      *
 %*********************************************************
 
 \begin{code}
@@ -321,145 +231,85 @@ instance  Num Integer  where
     (+) = plusInteger
     (-) = minusInteger
     (*) = timesInteger
-    negate	   = negateInteger
-    fromInteger	x  =  x
-
-    -- ORIG: abs n = if n >= 0 then n else -n
-    abs (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
-    abs (S# i) = case abs (I# i) of I# j -> S# j
-    abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
-
-    signum (S# i) = case signum (I# i) of I# j -> S# j
-    signum (J# s d)
-      = let
-	    cmp = cmpIntegerInt# s d 0#
-	in
-	if      cmp >#  0# then S# 1#
-	else if cmp ==# 0# then S# 0#
-	else			S# (negateInt# 1#)
-
-plusInteger i1@(S# i) i2@(S# j)  = case addIntC# i j of { (# r, c #) ->
-				   if c ==# 0# then S# r
-				   else toBig i1 + toBig i2 }
-plusInteger i1@(J# _ _) i2@(S# _) = i1 + toBig i2
-plusInteger i1@(S# _) i2@(J# _ _) = toBig i1 + i2
-plusInteger (J# s1 d1) (J# s2 d2) = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
-
-minusInteger i1@(S# i) i2@(S# j)   = case subIntC# i j of { (# r, c #) ->
-				     if c ==# 0# then S# r
-				     else toBig i1 - toBig i2 }
-minusInteger i1@(J# _ _) i2@(S# _) = i1 - toBig i2
-minusInteger i1@(S# _) i2@(J# _ _) = toBig i1 - i2
-minusInteger (J# s1 d1) (J# s2 d2) = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
-
-timesInteger i1@(S# i) i2@(S# j)   = if   mulIntMayOflo# i j ==# 0#
-                                     then S# (i *# j)
-                                     else toBig i1 * toBig i2 
-timesInteger i1@(J# _ _) i2@(S# _) = i1 * toBig i2
-timesInteger i1@(S# _) i2@(J# _ _) = toBig i1 * i2
-timesInteger (J# s1 d1) (J# s2 d2) = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
-
-negateInteger (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
-negateInteger (S# i)		  = S# (negateInt# i)
-negateInteger (J# s d)		  = J# (negateInt# s) d
+    negate         = negateInteger
+    fromInteger x  =  x
+
+    abs = absInteger
+    signum = signumInteger
 \end{code}
 
 
 %*********************************************************
-%*							*
+%*                                                      *
 \subsection{The @Integer@ instance for @Enum@}
-%*							*
+%*                                                      *
 %*********************************************************
 
 \begin{code}
 instance  Enum Integer  where
-    succ x		 = x + 1
-    pred x		 = x - 1
-    toEnum n		 = int2Integer n
-    fromEnum n		 = integer2Int n
+    succ x               = x + 1
+    pred x               = x - 1
+    toEnum (I# n)        = smallInteger n
+    fromEnum n           = I# (toInt# n)
 
     {-# INLINE enumFrom #-}
     {-# INLINE enumFromThen #-}
     {-# INLINE enumFromTo #-}
     {-# INLINE enumFromThenTo #-}
-    enumFrom x             = efdInteger  x 1
-    enumFromThen x y       = efdInteger  x (y-x)
-    enumFromTo x lim	   = efdtInteger x 1     lim
-    enumFromThenTo x y lim = efdtInteger x (y-x) lim
-
-
-efdInteger  = enumDeltaIntegerList
-efdtInteger = enumDeltaToIntegerList
+    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
 
 {-# RULES
-"efdInteger"		forall x y.  efdInteger x y	    = build (\c _ -> enumDeltaIntegerFB c x y)
-"efdtInteger"		forall x y l.efdtInteger x y l	    = build (\c n -> enumDeltaToIntegerFB c n x y l)
-"enumDeltaInteger" 	enumDeltaIntegerFB   (:)    = enumDeltaIntegerList
-"enumDeltaToInteger" 	enumDeltaToIntegerFB (:) [] = enumDeltaToIntegerList
+"enumDeltaInteger"      [~1] forall x y.  enumDeltaInteger x y     = build (\c _ -> enumDeltaIntegerFB c x y)
+"efdtInteger"           [~1] forall x y l.enumDeltaToInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
+"enumDeltaInteger"      [1] enumDeltaIntegerFB   (:)    = enumDeltaInteger
+"enumDeltaToInteger"    [1] enumDeltaToIntegerFB (:) [] = enumDeltaToInteger
  #-}
 
 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
-enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
-
-enumDeltaIntegerList :: Integer -> Integer -> [Integer]
-enumDeltaIntegerList x d = x : enumDeltaIntegerList (x+d) d
-
+enumDeltaIntegerFB c x d = x `seq` (x `c` enumDeltaIntegerFB c (x+d) d)
+
+enumDeltaInteger :: Integer -> Integer -> [Integer]
+enumDeltaInteger x d = x `seq` (x : enumDeltaInteger (x+d) d)
+-- strict accumulator, so
+--     head (drop 1000000 [1 .. ]
+-- works
+
+{-# NOINLINE [0] enumDeltaToIntegerFB #-}
+-- 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
 
-enumDeltaToIntegerList x delta lim
+enumDeltaToInteger :: Integer -> Integer -> Integer -> [Integer]
+enumDeltaToInteger x delta lim
   | delta >= 0 = up_list x delta lim
   | otherwise  = dn_list x delta lim
 
-up_fb c n x delta lim = go (x::Integer)
-		      where
-			go x | x > lim   = n
-			     | otherwise = x `c` go (x+delta)
-dn_fb c n x delta lim = go (x::Integer)
-		      where
-			go x | x < lim   = n
-			     | otherwise = x `c` go (x+delta)
-
-up_list x delta lim = go (x::Integer)
-		    where
-			go x | x > lim   = []
-			     | otherwise = x : go (x+delta)
-dn_list x delta lim = go (x::Integer)
-		    where
-			go x | x < lim   = []
-			     | otherwise = x : go (x+delta)
-
+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)
 \end{code}
 
-
-%*********************************************************
-%*							*
-\subsection{The @Integer@ instances for @Show@}
-%*							*
-%*********************************************************
-
-\begin{code}
-instance Show Integer where
-    showsPrec p n r
-        | p > 6 && n < 0 = '(' : jtos n (')' : r)
-		-- Minor point: testing p first gives better code 
-		-- in the not-uncommon case where the p argument
-		-- is a constant
-        | otherwise      = jtos n r
-    showList = showList__ (showsPrec 0)
-
-jtos :: Integer -> String -> String
-jtos n cs
-    | n < 0     = '-' : jtos' (-n) cs
-    | otherwise = jtos' n cs
-    where
-    jtos' :: Integer -> String -> String
-    jtos' n' cs'
-        | n' < 10    = case unsafeChr (ord '0' + fromInteger n') of
-            c@(C# _) -> c:cs'
-        | otherwise = case unsafeChr (ord '0' + fromInteger r) of
-            c@(C# _) -> jtos' q (c:cs')
-        where
-        (q,r) = n' `quotRemInteger` 10
-\end{code}