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
86 -- These can't go in GHC.Base with the defn of Int, because
87 -- we don't have pairs defined at that time!
89 quotRemInt :: Int -> Int -> (Int, Int)
90 a@(I# _) `quotRemInt` b@(I# _) = (a `quotInt` b, a `remInt` b)
91 -- OK, so I made it a little stricter. Shoot me. (WDP 94/10)
93 divModInt :: Int -> Int -> (Int, Int)
94 divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
95 -- Stricter. Sorry if you don't like it. (WDP 94/10)
99 %*********************************************************
101 \subsection{The @Integer@ type}
103 %*********************************************************
107 = S# Int# -- small integers
109 | J# Int# ByteArray# -- large integers
111 | J# Void BigInteger -- .NET big ints
113 foreign type dotnet "BigInteger" BigInteger
117 Convenient boxed Integer PrimOps.
120 zeroInteger :: Integer
123 int2Integer :: Int -> Integer
124 {-# INLINE int2Integer #-}
125 int2Integer (I# i) = S# i
127 integer2Int :: Integer -> Int
128 integer2Int (S# i) = I# i
129 integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
131 toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
136 %*********************************************************
138 \subsection{Dividing @Integers@}
140 %*********************************************************
143 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
144 quotRemInteger a@(S# (-LEFTMOST_BIT#)) b = quotRemInteger (toBig a) b
145 quotRemInteger (S# i) (S# j)
146 = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j )
147 quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
148 quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
149 quotRemInteger (J# s1 d1) (J# s2 d2)
150 = case (quotRemInteger# s1 d1 s2 d2) of
152 -> (J# s3 d3, J# s4 d4)
154 divModInteger a@(S# (-LEFTMOST_BIT#)) b = divModInteger (toBig a) b
155 divModInteger (S# i) (S# j)
156 = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
157 divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
158 divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
159 divModInteger (J# s1 d1) (J# s2 d2)
160 = case (divModInteger# s1 d1 s2 d2) of
162 -> (J# s3 d3, J# s4 d4)
164 remInteger :: Integer -> Integer -> Integer
166 = error "Prelude.Integral.rem{Integer}: divide by 0"
167 remInteger a@(S# (-LEFTMOST_BIT#)) b = remInteger (toBig a) b
168 remInteger (S# a) (S# b) = S# (remInt# a b)
169 {- Special case doesn't work, because a 1-element J# has the range
170 -(2^32-1) -- 2^32-1, whereas S# has the range -2^31 -- (2^31-1)
171 remInteger ia@(S# a) (J# sb b)
172 | sb ==# 1# = S# (remInt# a (word2Int# (integer2Word# sb b)))
173 | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
175 | otherwise = S# (0# -# a)
177 remInteger ia@(S# _) ib@(J# _ _) = remInteger (toBig ia) ib
178 remInteger (J# sa a) (S# b)
179 = case int2Integer# b of { (# sb, b #) ->
180 case remInteger# sa a sb b of { (# sr, r #) ->
181 S# (integer2Int# sr r) }}
182 remInteger (J# sa a) (J# sb b)
183 = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
185 quotInteger :: Integer -> Integer -> Integer
187 = error "Prelude.Integral.quot{Integer}: divide by 0"
188 quotInteger a@(S# (-LEFTMOST_BIT#)) b = quotInteger (toBig a) b
189 quotInteger (S# a) (S# b) = S# (quotInt# a b)
190 {- Special case disabled, see remInteger above
191 quotInteger (S# a) (J# sb b)
192 | sb ==# 1# = S# (quotInt# a (word2Int# (integer2Word# sb b)))
193 | sb ==# -1# = S# (quotInt# a (0# -# (word2Int# (integer2Word# sb b))))
194 | otherwise = zeroInteger
196 quotInteger ia@(S# _) ib@(J# _ _) = quotInteger (toBig ia) ib
197 quotInteger (J# sa a) (S# b)
198 = case int2Integer# b of { (# sb, b #) ->
199 case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
200 quotInteger (J# sa a) (J# sb b)
201 = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
207 gcdInteger :: Integer -> Integer -> Integer
208 -- SUP: Do we really need the first two cases?
209 gcdInteger a@(S# (-LEFTMOST_BIT#)) b = gcdInteger (toBig a) b
210 gcdInteger a b@(S# (-LEFTMOST_BIT#)) = gcdInteger a (toBig b)
211 gcdInteger (S# a) (S# b) = case gcdInt (I# a) (I# b) of { I# c -> S# c }
212 gcdInteger ia@(S# 0#) ib@(J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
213 gcdInteger ia@(S# a) ib@(J# sb b)
216 | otherwise = S# (gcdIntegerInt# absSb b absA)
217 where absA = if a <# 0# then negateInt# a else a
218 absSb = if sb <# 0# then negateInt# sb else sb
219 gcdInteger ia@(J# _ _) ib@(S# _) = gcdInteger ib ia
220 gcdInteger (J# 0# _) (J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
221 gcdInteger (J# sa a) (J# sb b)
222 = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
224 lcmInteger :: Integer -> Integer -> Integer
230 = (divExact aa (gcdInteger aa ab)) * ab
234 divExact :: Integer -> Integer -> Integer
235 divExact a@(S# (-LEFTMOST_BIT#)) b = divExact (toBig a) b
236 divExact (S# a) (S# b) = S# (quotInt# a b)
237 divExact (S# a) (J# sb b)
238 = S# (quotInt# a (integer2Int# sb b))
239 divExact (J# sa a) (S# b)
240 = case int2Integer# b of
241 (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
242 divExact (J# sa a) (J# sb b)
243 = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
247 %*********************************************************
249 \subsection{The @Integer@ instances for @Eq@, @Ord@}
251 %*********************************************************
254 instance Eq Integer where
255 (S# i) == (S# j) = i ==# j
256 (S# i) == (J# s d) = cmpIntegerInt# s d i ==# 0#
257 (J# s d) == (S# i) = cmpIntegerInt# s d i ==# 0#
258 (J# s1 d1) == (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ==# 0#
260 (S# i) /= (S# j) = i /=# j
261 (S# i) /= (J# s d) = cmpIntegerInt# s d i /=# 0#
262 (J# s d) /= (S# i) = cmpIntegerInt# s d i /=# 0#
263 (J# s1 d1) /= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) /=# 0#
265 ------------------------------------------------------------------------
266 instance Ord Integer where
267 (S# i) <= (S# j) = i <=# j
268 (J# s d) <= (S# i) = cmpIntegerInt# s d i <=# 0#
269 (S# i) <= (J# s d) = cmpIntegerInt# s d i >=# 0#
270 (J# s1 d1) <= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <=# 0#
272 (S# i) > (S# j) = i ># j
273 (J# s d) > (S# i) = cmpIntegerInt# s d i ># 0#
274 (S# i) > (J# s d) = cmpIntegerInt# s d i <# 0#
275 (J# s1 d1) > (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ># 0#
277 (S# i) < (S# j) = i <# j
278 (J# s d) < (S# i) = cmpIntegerInt# s d i <# 0#
279 (S# i) < (J# s d) = cmpIntegerInt# s d i ># 0#
280 (J# s1 d1) < (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
282 (S# i) >= (S# j) = i >=# j
283 (J# s d) >= (S# i) = cmpIntegerInt# s d i >=# 0#
284 (S# i) >= (J# s d) = cmpIntegerInt# s d i <=# 0#
285 (J# s1 d1) >= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
287 compare (S# i) (S# j)
291 compare (J# s d) (S# i)
292 = case cmpIntegerInt# s d i of { res# ->
293 if res# <# 0# then LT else
294 if res# ># 0# then GT else EQ
296 compare (S# i) (J# s d)
297 = case cmpIntegerInt# s d i of { res# ->
298 if res# ># 0# then LT else
299 if res# <# 0# then GT else EQ
301 compare (J# s1 d1) (J# s2 d2)
302 = case cmpInteger# s1 d1 s2 d2 of { res# ->
303 if res# <# 0# then LT else
304 if res# ># 0# then GT else EQ
309 %*********************************************************
311 \subsection{The @Integer@ instances for @Num@}
313 %*********************************************************
316 instance Num Integer where
320 negate = negateInteger
323 -- ORIG: abs n = if n >= 0 then n else -n
324 abs (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
325 abs (S# i) = case abs (I# i) of I# j -> S# j
326 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
328 signum (S# i) = case signum (I# i) of I# j -> S# j
331 cmp = cmpIntegerInt# s d 0#
333 if cmp ># 0# then S# 1#
334 else if cmp ==# 0# then S# 0#
335 else S# (negateInt# 1#)
337 plusInteger i1@(S# i) i2@(S# j) = case addIntC# i j of { (# r, c #) ->
338 if c ==# 0# then S# r
339 else toBig i1 + toBig i2 }
340 plusInteger i1@(J# _ _) i2@(S# _) = i1 + toBig i2
341 plusInteger i1@(S# _) i2@(J# _ _) = toBig i1 + i2
342 plusInteger (J# s1 d1) (J# s2 d2) = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
344 minusInteger i1@(S# i) i2@(S# j) = case subIntC# i j of { (# r, c #) ->
345 if c ==# 0# then S# r
346 else toBig i1 - toBig i2 }
347 minusInteger i1@(J# _ _) i2@(S# _) = i1 - toBig i2
348 minusInteger i1@(S# _) i2@(J# _ _) = toBig i1 - i2
349 minusInteger (J# s1 d1) (J# s2 d2) = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
351 timesInteger i1@(S# i) i2@(S# j) = if mulIntMayOflo# i j ==# 0#
353 else toBig i1 * toBig i2
354 timesInteger i1@(J# _ _) i2@(S# _) = i1 * toBig i2
355 timesInteger i1@(S# _) i2@(J# _ _) = toBig i1 * i2
356 timesInteger (J# s1 d1) (J# s2 d2) = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
358 negateInteger (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
359 negateInteger (S# i) = S# (negateInt# i)
360 negateInteger (J# s d) = J# (negateInt# s) d
364 %*********************************************************
366 \subsection{The @Integer@ instance for @Enum@}
368 %*********************************************************
371 instance Enum Integer where
374 toEnum n = int2Integer n
375 fromEnum n = integer2Int n
377 {-# INLINE enumFrom #-}
378 {-# INLINE enumFromThen #-}
379 {-# INLINE enumFromTo #-}
380 {-# INLINE enumFromThenTo #-}
381 enumFrom x = enumDeltaInteger x 1
382 enumFromThen x y = enumDeltaInteger x (y-x)
383 enumFromTo x lim = enumDeltaToInteger x 1 lim
384 enumFromThenTo x y lim = enumDeltaToInteger x (y-x) lim
387 "enumDeltaInteger" [~1] forall x y. enumDeltaInteger x y = build (\c _ -> enumDeltaIntegerFB c x y)
388 "efdtInteger" [~1] forall x y l.enumDeltaToInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
389 "enumDeltaInteger" [1] enumDeltaIntegerFB (:) = enumDeltaInteger
390 "enumDeltaToInteger" [1] enumDeltaToIntegerFB (:) [] = enumDeltaToInteger
393 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
394 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
396 enumDeltaInteger :: Integer -> Integer -> [Integer]
397 enumDeltaInteger x d = x : enumDeltaInteger (x+d) d
399 enumDeltaToIntegerFB c n x delta lim
400 | delta >= 0 = up_fb c n x delta lim
401 | otherwise = dn_fb c n x delta lim
403 enumDeltaToInteger x delta lim
404 | delta >= 0 = up_list x delta lim
405 | otherwise = dn_list x delta lim
407 up_fb c n x delta lim = go (x::Integer)
410 | otherwise = x `c` go (x+delta)
411 dn_fb c n x delta lim = go (x::Integer)
414 | otherwise = x `c` go (x+delta)
416 up_list x delta lim = go (x::Integer)
419 | otherwise = x : go (x+delta)
420 dn_list x delta lim = go (x::Integer)
423 | otherwise = x : go (x+delta)
428 %*********************************************************
430 \subsection{The @Integer@ instances for @Show@}
432 %*********************************************************
435 instance Show Integer where
437 | p > 6 && n < 0 = '(' : jtos n (')' : r)
438 -- Minor point: testing p first gives better code
439 -- in the not-uncommon case where the p argument
441 | otherwise = jtos n r
442 showList = showList__ (showsPrec 0)
444 jtos :: Integer -> String -> String
446 | n < 0 = '-' : jtos' (-n) cs
447 | otherwise = jtos' n cs
449 jtos' :: Integer -> String -> String
451 | n' < 10 = case unsafeChr (ord '0' + fromInteger n') of
453 | otherwise = case unsafeChr (ord '0' + fromInteger r) of
454 c@(C# _) -> jtos' q (c:cs')
456 (q,r) = n' `quotRemInteger` 10