2 {-# OPTIONS -fno-implicit-prelude #-}
3 -----------------------------------------------------------------------------
6 -- Copyright : (c) The University of Glasgow 1994-2002
7 -- License : see libraries/base/LICENSE
9 -- Maintainer : cvs-ghc@haskell.org
10 -- Stability : internal
11 -- Portability : non-portable (GHC Extensions)
13 -- The 'Num' class and the 'Integer' type.
15 -----------------------------------------------------------------------------
18 #if SIZEOF_HSWORD == 4
19 #define LEFTMOST_BIT 2147483648
20 #elif SIZEOF_HSWORD == 8
21 #define LEFTMOST_BIT 9223372036854775808
23 #error Please define LEFTMOST_BIT to be 2^(SIZEOF_HSWORD*8-1)
28 import {-# SOURCE #-} GHC.Err
37 default () -- Double isn't available yet,
38 -- and we shouldn't be using defaults anyway
41 %*********************************************************
43 \subsection{Standard numeric class}
45 %*********************************************************
48 class (Eq a, Show a) => Num a where
49 (+), (-), (*) :: a -> a -> a
52 fromInteger :: Integer -> a
57 {-# INLINE subtract #-}
58 subtract :: (Num a) => a -> a -> a
63 %*********************************************************
65 \subsection{Instances for @Int@}
67 %*********************************************************
70 instance Num Int where
75 abs n = if n `geInt` 0 then n else negateInt n
77 signum n | n `ltInt` 0 = negateInt 1
81 fromInteger = integer2Int
83 quotRemInt :: Int -> Int -> (Int, Int)
84 quotRemInt a@(I# _) b@(I# _) = (a `quotInt` b, a `remInt` b)
85 -- OK, so I made it a little stricter. Shoot me. (WDP 94/10)
87 divModInt :: Int -> Int -> (Int, Int)
88 divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
89 -- Stricter. Sorry if you don't like it. (WDP 94/10)
92 %*********************************************************
94 \subsection{The @Integer@ type}
96 %*********************************************************
99 -- | Arbitrary-precision integers.
101 = S# Int# -- small integers
103 | J# Int# ByteArray# -- large integers
105 | J# Void BigInteger -- .NET big ints
107 foreign type dotnet "BigInteger" BigInteger
111 Convenient boxed Integer PrimOps.
114 zeroInteger :: Integer
117 int2Integer :: Int -> Integer
118 {-# INLINE int2Integer #-}
119 int2Integer (I# i) = S# i
121 integer2Int :: Integer -> Int
122 integer2Int (S# i) = I# i
123 integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
125 toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
130 %*********************************************************
132 \subsection{Dividing @Integers@}
134 %*********************************************************
137 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
138 quotRemInteger a@(S# (-LEFTMOST_BIT#)) b = quotRemInteger (toBig a) b
139 quotRemInteger (S# i) (S# j)
140 = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j )
141 quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
142 quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
143 quotRemInteger (J# s1 d1) (J# s2 d2)
144 = case (quotRemInteger# s1 d1 s2 d2) of
146 -> (J# s3 d3, J# s4 d4)
148 divModInteger a@(S# (-LEFTMOST_BIT#)) b = divModInteger (toBig a) b
149 divModInteger (S# i) (S# j)
150 = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
151 divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
152 divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
153 divModInteger (J# s1 d1) (J# s2 d2)
154 = case (divModInteger# s1 d1 s2 d2) of
156 -> (J# s3 d3, J# s4 d4)
158 remInteger :: Integer -> Integer -> Integer
160 = error "Prelude.Integral.rem{Integer}: divide by 0"
161 remInteger a@(S# (-LEFTMOST_BIT#)) b = remInteger (toBig a) b
162 remInteger (S# a) (S# b) = S# (remInt# a b)
163 {- Special case doesn't work, because a 1-element J# has the range
164 -(2^32-1) -- 2^32-1, whereas S# has the range -2^31 -- (2^31-1)
165 remInteger ia@(S# a) (J# sb b)
166 | sb ==# 1# = S# (remInt# a (word2Int# (integer2Word# sb b)))
167 | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
169 | otherwise = S# (0# -# a)
171 remInteger ia@(S# _) ib@(J# _ _) = remInteger (toBig ia) ib
172 remInteger (J# sa a) (S# b)
173 = case int2Integer# b of { (# sb, b #) ->
174 case remInteger# sa a sb b of { (# sr, r #) ->
175 S# (integer2Int# sr r) }}
176 remInteger (J# sa a) (J# sb b)
177 = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
179 quotInteger :: Integer -> Integer -> Integer
181 = error "Prelude.Integral.quot{Integer}: divide by 0"
182 quotInteger a@(S# (-LEFTMOST_BIT#)) b = quotInteger (toBig a) b
183 quotInteger (S# a) (S# b) = S# (quotInt# a b)
184 {- Special case disabled, see remInteger above
185 quotInteger (S# a) (J# sb b)
186 | sb ==# 1# = S# (quotInt# a (word2Int# (integer2Word# sb b)))
187 | sb ==# -1# = S# (quotInt# a (0# -# (word2Int# (integer2Word# sb b))))
188 | otherwise = zeroInteger
190 quotInteger ia@(S# _) ib@(J# _ _) = quotInteger (toBig ia) ib
191 quotInteger (J# sa a) (S# b)
192 = case int2Integer# b of { (# sb, b #) ->
193 case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
194 quotInteger (J# sa a) (J# sb b)
195 = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
201 gcdInteger :: Integer -> Integer -> Integer
202 -- SUP: Do we really need the first two cases?
203 gcdInteger a@(S# (-LEFTMOST_BIT#)) b = gcdInteger (toBig a) b
204 gcdInteger a b@(S# (-LEFTMOST_BIT#)) = gcdInteger a (toBig b)
205 gcdInteger (S# a) (S# b) = case gcdInt (I# a) (I# b) of { I# c -> S# c }
206 gcdInteger ia@(S# 0#) ib@(J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
207 gcdInteger ia@(S# a) ib@(J# sb b)
210 | otherwise = S# (gcdIntegerInt# absSb b absA)
211 where absA = if a <# 0# then negateInt# a else a
212 absSb = if sb <# 0# then negateInt# sb else sb
213 gcdInteger ia@(J# _ _) ib@(S# _) = gcdInteger ib ia
214 gcdInteger (J# 0# _) (J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
215 gcdInteger (J# sa a) (J# sb b)
216 = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
218 lcmInteger :: Integer -> Integer -> Integer
224 = (divExact aa (gcdInteger aa ab)) * ab
228 divExact :: Integer -> Integer -> Integer
229 divExact a@(S# (-LEFTMOST_BIT#)) b = divExact (toBig a) b
230 divExact (S# a) (S# b) = S# (quotInt# a b)
231 divExact (S# a) (J# sb b)
232 = S# (quotInt# a (integer2Int# sb b))
233 divExact (J# sa a) (S# b)
234 = case int2Integer# b of
235 (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
236 divExact (J# sa a) (J# sb b)
237 = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
241 %*********************************************************
243 \subsection{The @Integer@ instances for @Eq@, @Ord@}
245 %*********************************************************
248 instance Eq Integer where
249 (S# i) == (S# j) = i ==# j
250 (S# i) == (J# s d) = cmpIntegerInt# s d i ==# 0#
251 (J# s d) == (S# i) = cmpIntegerInt# s d i ==# 0#
252 (J# s1 d1) == (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ==# 0#
254 (S# i) /= (S# j) = i /=# j
255 (S# i) /= (J# s d) = cmpIntegerInt# s d i /=# 0#
256 (J# s d) /= (S# i) = cmpIntegerInt# s d i /=# 0#
257 (J# s1 d1) /= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) /=# 0#
259 ------------------------------------------------------------------------
260 instance Ord Integer where
261 (S# i) <= (S# j) = i <=# j
262 (J# s d) <= (S# i) = cmpIntegerInt# s d i <=# 0#
263 (S# i) <= (J# s d) = cmpIntegerInt# s d i >=# 0#
264 (J# s1 d1) <= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <=# 0#
266 (S# i) > (S# j) = i ># j
267 (J# s d) > (S# i) = cmpIntegerInt# s d i ># 0#
268 (S# i) > (J# s d) = cmpIntegerInt# s d i <# 0#
269 (J# s1 d1) > (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ># 0#
271 (S# i) < (S# j) = i <# j
272 (J# s d) < (S# i) = cmpIntegerInt# s d i <# 0#
273 (S# i) < (J# s d) = cmpIntegerInt# s d i ># 0#
274 (J# s1 d1) < (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
276 (S# i) >= (S# j) = i >=# j
277 (J# s d) >= (S# i) = cmpIntegerInt# s d i >=# 0#
278 (S# i) >= (J# s d) = cmpIntegerInt# s d i <=# 0#
279 (J# s1 d1) >= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
281 compare (S# i) (S# j)
285 compare (J# s d) (S# i)
286 = case cmpIntegerInt# s d i of { res# ->
287 if res# <# 0# then LT else
288 if res# ># 0# then GT else EQ
290 compare (S# i) (J# s d)
291 = case cmpIntegerInt# s d i of { res# ->
292 if res# ># 0# then LT else
293 if res# <# 0# then GT else EQ
295 compare (J# s1 d1) (J# s2 d2)
296 = case cmpInteger# s1 d1 s2 d2 of { res# ->
297 if res# <# 0# then LT else
298 if res# ># 0# then GT else EQ
303 %*********************************************************
305 \subsection{The @Integer@ instances for @Num@}
307 %*********************************************************
310 instance Num Integer where
314 negate = negateInteger
317 -- ORIG: abs n = if n >= 0 then n else -n
318 abs (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
319 abs (S# i) = case abs (I# i) of I# j -> S# j
320 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
322 signum (S# i) = case signum (I# i) of I# j -> S# j
325 cmp = cmpIntegerInt# s d 0#
327 if cmp ># 0# then S# 1#
328 else if cmp ==# 0# then S# 0#
329 else S# (negateInt# 1#)
331 plusInteger i1@(S# i) i2@(S# j) = case addIntC# i j of { (# r, c #) ->
332 if c ==# 0# then S# r
333 else toBig i1 + toBig i2 }
334 plusInteger i1@(J# _ _) i2@(S# _) = i1 + toBig i2
335 plusInteger i1@(S# _) i2@(J# _ _) = toBig i1 + i2
336 plusInteger (J# s1 d1) (J# s2 d2) = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
338 minusInteger i1@(S# i) i2@(S# j) = case subIntC# i j of { (# r, c #) ->
339 if c ==# 0# then S# r
340 else toBig i1 - toBig i2 }
341 minusInteger i1@(J# _ _) i2@(S# _) = i1 - toBig i2
342 minusInteger i1@(S# _) i2@(J# _ _) = toBig i1 - i2
343 minusInteger (J# s1 d1) (J# s2 d2) = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
345 timesInteger i1@(S# i) i2@(S# j) = if mulIntMayOflo# i j ==# 0#
347 else toBig i1 * toBig i2
348 timesInteger i1@(J# _ _) i2@(S# _) = i1 * toBig i2
349 timesInteger i1@(S# _) i2@(J# _ _) = toBig i1 * i2
350 timesInteger (J# s1 d1) (J# s2 d2) = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
352 negateInteger (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
353 negateInteger (S# i) = S# (negateInt# i)
354 negateInteger (J# s d) = J# (negateInt# s) d
358 %*********************************************************
360 \subsection{The @Integer@ instance for @Enum@}
362 %*********************************************************
365 instance Enum Integer where
368 toEnum n = int2Integer n
369 fromEnum n = integer2Int n
371 {-# INLINE enumFrom #-}
372 {-# INLINE enumFromThen #-}
373 {-# INLINE enumFromTo #-}
374 {-# INLINE enumFromThenTo #-}
375 enumFrom x = enumDeltaInteger x 1
376 enumFromThen x y = enumDeltaInteger x (y-x)
377 enumFromTo x lim = enumDeltaToInteger x 1 lim
378 enumFromThenTo x y lim = enumDeltaToInteger x (y-x) lim
381 "enumDeltaInteger" [~1] forall x y. enumDeltaInteger x y = build (\c _ -> enumDeltaIntegerFB c x y)
382 "efdtInteger" [~1] forall x y l.enumDeltaToInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
383 "enumDeltaInteger" [1] enumDeltaIntegerFB (:) = enumDeltaInteger
384 "enumDeltaToInteger" [1] enumDeltaToIntegerFB (:) [] = enumDeltaToInteger
387 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
388 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
390 enumDeltaInteger :: Integer -> Integer -> [Integer]
391 enumDeltaInteger x d = x : enumDeltaInteger (x+d) d
393 enumDeltaToIntegerFB c n x delta lim
394 | delta >= 0 = up_fb c n x delta lim
395 | otherwise = dn_fb c n x delta lim
397 enumDeltaToInteger x delta lim
398 | delta >= 0 = up_list x delta lim
399 | otherwise = dn_list x delta lim
401 up_fb c n x delta lim = go (x::Integer)
404 | otherwise = x `c` go (x+delta)
405 dn_fb c n x delta lim = go (x::Integer)
408 | otherwise = x `c` go (x+delta)
410 up_list x delta lim = go (x::Integer)
413 | otherwise = x : go (x+delta)
414 dn_list x delta lim = go (x::Integer)
417 | otherwise = x : go (x+delta)
422 %*********************************************************
424 \subsection{The @Integer@ instances for @Show@}
426 %*********************************************************
429 instance Show Integer where
431 | p > 6 && n < 0 = '(' : jtos n (')' : r)
432 -- Minor point: testing p first gives better code
433 -- in the not-uncommon case where the p argument
435 | otherwise = jtos n r
436 showList = showList__ (showsPrec 0)
438 jtos :: Integer -> String -> String
440 | n < 0 = '-' : jtos' (-n) cs
441 | otherwise = jtos' n cs
443 jtos' :: Integer -> String -> String
445 | n' < 10 = case unsafeChr (ord '0' + fromInteger n') of
447 | otherwise = case unsafeChr (ord '0' + fromInteger r) of
448 c@(C# _) -> jtos' q (c:cs')
450 (q,r) = n' `quotRemInteger` 10