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 %*********************************************************
106 -- | Arbitrary-precision integers.
108 = S# Int# -- small integers
110 | J# Int# ByteArray# -- large integers
112 | J# Void BigInteger -- .NET big ints
114 foreign type dotnet "BigInteger" BigInteger
118 Convenient boxed Integer PrimOps.
121 zeroInteger :: Integer
124 int2Integer :: Int -> Integer
125 {-# INLINE int2Integer #-}
126 int2Integer (I# i) = S# i
128 integer2Int :: Integer -> Int
129 integer2Int (S# i) = I# i
130 integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
132 toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
137 %*********************************************************
139 \subsection{Dividing @Integers@}
141 %*********************************************************
144 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
145 quotRemInteger a@(S# (-LEFTMOST_BIT#)) b = quotRemInteger (toBig a) b
146 quotRemInteger (S# i) (S# j)
147 = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j )
148 quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
149 quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
150 quotRemInteger (J# s1 d1) (J# s2 d2)
151 = case (quotRemInteger# s1 d1 s2 d2) of
153 -> (J# s3 d3, J# s4 d4)
155 divModInteger a@(S# (-LEFTMOST_BIT#)) b = divModInteger (toBig a) b
156 divModInteger (S# i) (S# j)
157 = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
158 divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
159 divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
160 divModInteger (J# s1 d1) (J# s2 d2)
161 = case (divModInteger# s1 d1 s2 d2) of
163 -> (J# s3 d3, J# s4 d4)
165 remInteger :: Integer -> Integer -> Integer
167 = error "Prelude.Integral.rem{Integer}: divide by 0"
168 remInteger a@(S# (-LEFTMOST_BIT#)) b = remInteger (toBig a) b
169 remInteger (S# a) (S# b) = S# (remInt# a b)
170 {- Special case doesn't work, because a 1-element J# has the range
171 -(2^32-1) -- 2^32-1, whereas S# has the range -2^31 -- (2^31-1)
172 remInteger ia@(S# a) (J# sb b)
173 | sb ==# 1# = S# (remInt# a (word2Int# (integer2Word# sb b)))
174 | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
176 | otherwise = S# (0# -# a)
178 remInteger ia@(S# _) ib@(J# _ _) = remInteger (toBig ia) ib
179 remInteger (J# sa a) (S# b)
180 = case int2Integer# b of { (# sb, b #) ->
181 case remInteger# sa a sb b of { (# sr, r #) ->
182 S# (integer2Int# sr r) }}
183 remInteger (J# sa a) (J# sb b)
184 = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
186 quotInteger :: Integer -> Integer -> Integer
188 = error "Prelude.Integral.quot{Integer}: divide by 0"
189 quotInteger a@(S# (-LEFTMOST_BIT#)) b = quotInteger (toBig a) b
190 quotInteger (S# a) (S# b) = S# (quotInt# a b)
191 {- Special case disabled, see remInteger above
192 quotInteger (S# a) (J# sb b)
193 | sb ==# 1# = S# (quotInt# a (word2Int# (integer2Word# sb b)))
194 | sb ==# -1# = S# (quotInt# a (0# -# (word2Int# (integer2Word# sb b))))
195 | otherwise = zeroInteger
197 quotInteger ia@(S# _) ib@(J# _ _) = quotInteger (toBig ia) ib
198 quotInteger (J# sa a) (S# b)
199 = case int2Integer# b of { (# sb, b #) ->
200 case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
201 quotInteger (J# sa a) (J# sb b)
202 = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
208 gcdInteger :: Integer -> Integer -> Integer
209 -- SUP: Do we really need the first two cases?
210 gcdInteger a@(S# (-LEFTMOST_BIT#)) b = gcdInteger (toBig a) b
211 gcdInteger a b@(S# (-LEFTMOST_BIT#)) = gcdInteger a (toBig b)
212 gcdInteger (S# a) (S# b) = case gcdInt (I# a) (I# b) of { I# c -> S# c }
213 gcdInteger ia@(S# 0#) ib@(J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
214 gcdInteger ia@(S# a) ib@(J# sb b)
217 | otherwise = S# (gcdIntegerInt# absSb b absA)
218 where absA = if a <# 0# then negateInt# a else a
219 absSb = if sb <# 0# then negateInt# sb else sb
220 gcdInteger ia@(J# _ _) ib@(S# _) = gcdInteger ib ia
221 gcdInteger (J# 0# _) (J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
222 gcdInteger (J# sa a) (J# sb b)
223 = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
225 lcmInteger :: Integer -> Integer -> Integer
231 = (divExact aa (gcdInteger aa ab)) * ab
235 divExact :: Integer -> Integer -> Integer
236 divExact a@(S# (-LEFTMOST_BIT#)) b = divExact (toBig a) b
237 divExact (S# a) (S# b) = S# (quotInt# a b)
238 divExact (S# a) (J# sb b)
239 = S# (quotInt# a (integer2Int# sb b))
240 divExact (J# sa a) (S# b)
241 = case int2Integer# b of
242 (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
243 divExact (J# sa a) (J# sb b)
244 = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
248 %*********************************************************
250 \subsection{The @Integer@ instances for @Eq@, @Ord@}
252 %*********************************************************
255 instance Eq Integer where
256 (S# i) == (S# j) = i ==# j
257 (S# i) == (J# s d) = cmpIntegerInt# s d i ==# 0#
258 (J# s d) == (S# i) = cmpIntegerInt# s d i ==# 0#
259 (J# s1 d1) == (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ==# 0#
261 (S# i) /= (S# j) = i /=# j
262 (S# i) /= (J# s d) = cmpIntegerInt# s d i /=# 0#
263 (J# s d) /= (S# i) = cmpIntegerInt# s d i /=# 0#
264 (J# s1 d1) /= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) /=# 0#
266 ------------------------------------------------------------------------
267 instance Ord Integer where
268 (S# i) <= (S# j) = i <=# j
269 (J# s d) <= (S# i) = cmpIntegerInt# s d i <=# 0#
270 (S# i) <= (J# s d) = cmpIntegerInt# s d i >=# 0#
271 (J# s1 d1) <= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <=# 0#
273 (S# i) > (S# j) = i ># j
274 (J# s d) > (S# i) = cmpIntegerInt# s d i ># 0#
275 (S# i) > (J# s d) = cmpIntegerInt# s d i <# 0#
276 (J# s1 d1) > (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ># 0#
278 (S# i) < (S# j) = i <# j
279 (J# s d) < (S# i) = cmpIntegerInt# s d i <# 0#
280 (S# i) < (J# s d) = cmpIntegerInt# s d i ># 0#
281 (J# s1 d1) < (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
283 (S# i) >= (S# j) = i >=# j
284 (J# s d) >= (S# i) = cmpIntegerInt# s d i >=# 0#
285 (S# i) >= (J# s d) = cmpIntegerInt# s d i <=# 0#
286 (J# s1 d1) >= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
288 compare (S# i) (S# j)
292 compare (J# s d) (S# i)
293 = case cmpIntegerInt# s d i of { res# ->
294 if res# <# 0# then LT else
295 if res# ># 0# then GT else EQ
297 compare (S# i) (J# s d)
298 = case cmpIntegerInt# s d i of { res# ->
299 if res# ># 0# then LT else
300 if res# <# 0# then GT else EQ
302 compare (J# s1 d1) (J# s2 d2)
303 = case cmpInteger# s1 d1 s2 d2 of { res# ->
304 if res# <# 0# then LT else
305 if res# ># 0# then GT else EQ
310 %*********************************************************
312 \subsection{The @Integer@ instances for @Num@}
314 %*********************************************************
317 instance Num Integer where
321 negate = negateInteger
324 -- ORIG: abs n = if n >= 0 then n else -n
325 abs (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
326 abs (S# i) = case abs (I# i) of I# j -> S# j
327 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
329 signum (S# i) = case signum (I# i) of I# j -> S# j
332 cmp = cmpIntegerInt# s d 0#
334 if cmp ># 0# then S# 1#
335 else if cmp ==# 0# then S# 0#
336 else S# (negateInt# 1#)
338 plusInteger i1@(S# i) i2@(S# j) = case addIntC# i j of { (# r, c #) ->
339 if c ==# 0# then S# r
340 else toBig i1 + toBig i2 }
341 plusInteger i1@(J# _ _) i2@(S# _) = i1 + toBig i2
342 plusInteger i1@(S# _) i2@(J# _ _) = toBig i1 + i2
343 plusInteger (J# s1 d1) (J# s2 d2) = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
345 minusInteger i1@(S# i) i2@(S# j) = case subIntC# i j of { (# r, c #) ->
346 if c ==# 0# then S# r
347 else toBig i1 - toBig i2 }
348 minusInteger i1@(J# _ _) i2@(S# _) = i1 - toBig i2
349 minusInteger i1@(S# _) i2@(J# _ _) = toBig i1 - i2
350 minusInteger (J# s1 d1) (J# s2 d2) = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
352 timesInteger i1@(S# i) i2@(S# j) = if mulIntMayOflo# i j ==# 0#
354 else toBig i1 * toBig i2
355 timesInteger i1@(J# _ _) i2@(S# _) = i1 * toBig i2
356 timesInteger i1@(S# _) i2@(J# _ _) = toBig i1 * i2
357 timesInteger (J# s1 d1) (J# s2 d2) = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
359 negateInteger (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
360 negateInteger (S# i) = S# (negateInt# i)
361 negateInteger (J# s d) = J# (negateInt# s) d
365 %*********************************************************
367 \subsection{The @Integer@ instance for @Enum@}
369 %*********************************************************
372 instance Enum Integer where
375 toEnum n = int2Integer n
376 fromEnum n = integer2Int n
378 {-# INLINE enumFrom #-}
379 {-# INLINE enumFromThen #-}
380 {-# INLINE enumFromTo #-}
381 {-# INLINE enumFromThenTo #-}
382 enumFrom x = enumDeltaInteger x 1
383 enumFromThen x y = enumDeltaInteger x (y-x)
384 enumFromTo x lim = enumDeltaToInteger x 1 lim
385 enumFromThenTo x y lim = enumDeltaToInteger x (y-x) lim
388 "enumDeltaInteger" [~1] forall x y. enumDeltaInteger x y = build (\c _ -> enumDeltaIntegerFB c x y)
389 "efdtInteger" [~1] forall x y l.enumDeltaToInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
390 "enumDeltaInteger" [1] enumDeltaIntegerFB (:) = enumDeltaInteger
391 "enumDeltaToInteger" [1] enumDeltaToIntegerFB (:) [] = enumDeltaToInteger
394 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
395 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
397 enumDeltaInteger :: Integer -> Integer -> [Integer]
398 enumDeltaInteger x d = x : enumDeltaInteger (x+d) d
400 enumDeltaToIntegerFB c n x delta lim
401 | delta >= 0 = up_fb c n x delta lim
402 | otherwise = dn_fb c n x delta lim
404 enumDeltaToInteger x delta lim
405 | delta >= 0 = up_list x delta lim
406 | otherwise = dn_list x delta lim
408 up_fb c n x delta lim = go (x::Integer)
411 | otherwise = x `c` go (x+delta)
412 dn_fb c n x delta lim = go (x::Integer)
415 | otherwise = x `c` go (x+delta)
417 up_list x delta lim = go (x::Integer)
420 | otherwise = x : go (x+delta)
421 dn_list x delta lim = go (x::Integer)
424 | otherwise = x : go (x+delta)
429 %*********************************************************
431 \subsection{The @Integer@ instances for @Show@}
433 %*********************************************************
436 instance Show Integer where
438 | p > 6 && n < 0 = '(' : jtos n (')' : r)
439 -- Minor point: testing p first gives better code
440 -- in the not-uncommon case where the p argument
442 | otherwise = jtos n r
443 showList = showList__ (showsPrec 0)
445 jtos :: Integer -> String -> String
447 | n < 0 = '-' : jtos' (-n) cs
448 | otherwise = jtos' n cs
450 jtos' :: Integer -> String -> String
452 | n' < 10 = case unsafeChr (ord '0' + fromInteger n') of
454 | otherwise = case unsafeChr (ord '0' + fromInteger r) of
455 c@(C# _) -> jtos' q (c:cs')
457 (q,r) = n' `quotRemInteger` 10