X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=GHC%2FNum.lhs;h=540204d3a6b1f3b9dd53e05c78492e73d21f6c3a;hb=567080c906535534628b1ab83a4a4425dcd4bb5e;hp=c8355314885216eef68631d53841de257ccb52ab;hpb=7f1f4e7a695c402ddd3a1dc2cc7114e649a78ebc;p=haskell-directory.git

diff --git a/GHC/Num.lhs b/GHC/Num.lhs
index c835531..540204d 100644
--- a/GHC/Num.lhs
+++ b/GHC/Num.lhs
@@ -1,28 +1,39 @@
-% ------------------------------------------------------------------------------
-% $Id: Num.lhs,v 1.1 2001/06/28 14:15:03 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 #-}
-
+{-# OPTIONS_GHC -fno-implicit-prelude #-}
+-----------------------------------------------------------------------------
+-- |
+-- 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)
+-- DIGITS should be the largest integer such that 10^DIGITS < LEFTMOST_BIT
+-- BASE should be 10^DIGITS. Note that ^ is not available yet.
+#endif
+
+-- #hide
 module GHC.Num where
 
 import {-# SOURCE #-} GHC.Err
 import GHC.Base
-import GHC.List
 import GHC.Enum
 import GHC.Show
 
@@ -40,15 +51,37 @@ default ()		-- Double isn't available yet,
 %*********************************************************
 
 \begin{code}
+-- | Basic numeric class.
+--
+-- Minimal complete definition: all except 'negate' or @(-)@
 class  (Eq a, Show a) => Num a  where
     (+), (-), (*)	:: a -> a -> a
+    -- | Unary negation.
     negate		:: a -> a
-    abs, signum		:: 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
 
     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
@@ -74,15 +107,9 @@ instance  Num Int  where
 	     | 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!
 
 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)
@@ -90,7 +117,6 @@ 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}
@@ -98,9 +124,16 @@ divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
 %*********************************************************
 
 \begin{code}
+-- | Arbitrary-precision integers.
 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. 
@@ -130,7 +163,7 @@ toBig i@(J# _ _) = i
 
 \begin{code}
 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
-quotRemInteger a@(S# (-2147483648#)) b = quotRemInteger (toBig a) b
+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)
@@ -140,7 +173,7 @@ quotRemInteger (J# s1 d1) (J# s2 d2)
 	  (# s3, d3, s4, d4 #)
 	    -> (J# s3 d3, J# s4 d4)
 
-divModInteger a@(S# (-2147483648#)) b = divModInteger (toBig a) b
+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)
@@ -153,7 +186,7 @@ divModInteger (J# s1 d1) (J# s2 d2)
 remInteger :: Integer -> Integer -> Integer
 remInteger ia 0
   = error "Prelude.Integral.rem{Integer}: divide by 0"
-remInteger a@(S# (-2147483648#)) b = remInteger (toBig a) b
+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)
@@ -174,7 +207,7 @@ remInteger (J# sa a) (J# sb b)
 quotInteger :: Integer -> Integer -> Integer
 quotInteger ia 0
   = error "Prelude.Integral.quot{Integer}: divide by 0"
-quotInteger a@(S# (-2147483648#)) b = quotInteger (toBig a) b
+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)
@@ -195,8 +228,8 @@ quotInteger (J# sa a) (J# sb b)
 \begin{code}
 gcdInteger :: Integer -> Integer -> Integer
 -- SUP: Do we really need the first two cases?
-gcdInteger a@(S# (-2147483648#)) b = gcdInteger (toBig a) b
-gcdInteger a b@(S# (-2147483648#)) = gcdInteger a (toBig b)
+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)
@@ -221,7 +254,7 @@ lcmInteger a b
         ab = abs b
 
 divExact :: Integer -> Integer -> Integer
-divExact a@(S# (-2147483648#)) b = divExact (toBig a) b
+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))
@@ -310,7 +343,7 @@ instance  Num Integer  where
     fromInteger	x  =  x
 
     -- ORIG: abs n = if n >= 0 then n else -n
-    abs (S# (-2147483648#)) = 2147483648
+    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
 
@@ -337,14 +370,14 @@ 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)   = case mulIntC# i j of { (# r, c #) ->
-				     if c ==# 0# then S# r
-				     else toBig i1 * toBig i2 }
+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# (-2147483648#)) = 2147483648
+negateInteger (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
 negateInteger (S# i)		  = S# (negateInt# i)
 negateInteger (J# s d)		  = J# (negateInt# s) d
 \end{code}
@@ -367,33 +400,29 @@ instance  Enum Integer  where
     {-# 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
+enumDeltaInteger :: Integer -> Integer -> [Integer]
+enumDeltaInteger x d = x : enumDeltaInteger (x+d) d
 
 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 x delta lim
   | delta >= 0 = up_list x delta lim
   | otherwise  = dn_list x delta lim
 
@@ -427,21 +456,88 @@ dn_list x delta lim = go (x::Integer)
 \begin{code}
 instance Show Integer where
     showsPrec p n r
-        | n < 0 && p > 6 = '(' : jtos 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)
 
+-- Divide an conquer implementation of string conversion
 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')
+    jtos' 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) =
+        if q > 0 then fromInteger q : fromInteger r : jsplitb p ns
+                 else fromInteger r : jsplitb p ns
         where
-        (q,r) = n' `quotRemInteger` 10
+        (q, r) = n `quotRemInteger` p
+
+    jsplitb :: Integer -> [Integer] -> [Integer]
+    jsplitb p []     = []
+    jsplitb p (n:ns) = q : r : jsplitb p ns
+        where
+        (q, r) = n `quotRemInteger` p
+
+    -- 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 =
+        if q > 0 then jhead q $ jblock r $ jprintb ns cs
+                 else jhead r $ jprintb ns cs
+        where
+        (q', r') = n `quotRemInteger` BASE
+        q = fromInteger q'
+        r = fromInteger r'
+
+    jprintb :: [Integer] -> String -> String
+    jprintb []     cs = cs
+    jprintb (n:ns) cs = jblock q $ jblock r $ jprintb ns cs
+        where
+        (q', r') = n `quotRemInteger` BASE
+        q = fromInteger q'
+        r = fromInteger r'
+
+    -- 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
+
+    jblock = jblock' {- ' -} DIGITS
+
+    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}