1 % ------------------------------------------------------------------------------
2 % $Id: PrelNum.lhs,v 1.39 2001/04/14 22:28:22 qrczak Exp $
4 % (c) The University of Glasgow, 1994-2000
7 \section[PrelNum]{Module @PrelNum@}
19 {-# OPTIONS -fno-implicit-prelude #-}
23 import {-# SOURCE #-} PrelErr
32 default () -- Double isn't available yet,
33 -- and we shouldn't be using defaults anyway
36 %*********************************************************
38 \subsection{Standard numeric class}
40 %*********************************************************
43 class (Eq a, Show a) => Num a where
44 (+), (-), (*) :: a -> a -> a
47 fromInteger :: Integer -> a
52 {-# INLINE subtract #-}
53 subtract :: (Num a) => a -> a -> a
58 %*********************************************************
60 \subsection{Instances for @Int@}
62 %*********************************************************
65 instance Num Int where
70 abs n = if n `geInt` 0 then n else negateInt n
72 signum n | n `ltInt` 0 = negateInt 1
76 fromInteger = integer2Int
81 -- These can't go in PrelBase with the defn of Int, because
82 -- we don't have pairs defined at that time!
84 quotRemInt :: Int -> Int -> (Int, Int)
85 a@(I# _) `quotRemInt` b@(I# _) = (a `quotInt` b, a `remInt` b)
86 -- OK, so I made it a little stricter. Shoot me. (WDP 94/10)
88 divModInt :: Int -> Int -> (Int, Int)
89 divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
90 -- Stricter. Sorry if you don't like it. (WDP 94/10)
94 %*********************************************************
96 \subsection{The @Integer@ type}
98 %*********************************************************
102 = S# Int# -- small integers
103 | J# Int# ByteArray# -- large integers
106 Convenient boxed Integer PrimOps.
109 zeroInteger :: Integer
112 int2Integer :: Int -> Integer
113 {-# INLINE int2Integer #-}
114 int2Integer (I# i) = S# i
116 integer2Int :: Integer -> Int
117 integer2Int (S# i) = I# i
118 integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
120 toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
125 %*********************************************************
127 \subsection{Dividing @Integers@}
129 %*********************************************************
132 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
133 quotRemInteger a@(S# (-2147483648#)) b = quotRemInteger (toBig a) b
134 quotRemInteger (S# i) (S# j)
135 = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j )
136 quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
137 quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
138 quotRemInteger (J# s1 d1) (J# s2 d2)
139 = case (quotRemInteger# s1 d1 s2 d2) of
141 -> (J# s3 d3, J# s4 d4)
143 divModInteger a@(S# (-2147483648#)) b = divModInteger (toBig a) b
144 divModInteger (S# i) (S# j)
145 = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
146 divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
147 divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
148 divModInteger (J# s1 d1) (J# s2 d2)
149 = case (divModInteger# s1 d1 s2 d2) of
151 -> (J# s3 d3, J# s4 d4)
153 remInteger :: Integer -> Integer -> Integer
155 = error "Prelude.Integral.rem{Integer}: divide by 0"
156 remInteger a@(S# (-2147483648#)) b = remInteger (toBig a) b
157 remInteger (S# a) (S# b) = S# (remInt# a b)
158 {- Special case doesn't work, because a 1-element J# has the range
159 -(2^32-1) -- 2^32-1, whereas S# has the range -2^31 -- (2^31-1)
160 remInteger ia@(S# a) (J# sb b)
161 | sb ==# 1# = S# (remInt# a (word2Int# (integer2Word# sb b)))
162 | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
164 | otherwise = S# (0# -# a)
166 remInteger ia@(S# _) ib@(J# _ _) = remInteger (toBig ia) ib
167 remInteger (J# sa a) (S# b)
168 = case int2Integer# b of { (# sb, b #) ->
169 case remInteger# sa a sb b of { (# sr, r #) ->
170 S# (integer2Int# sr r) }}
171 remInteger (J# sa a) (J# sb b)
172 = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
174 quotInteger :: Integer -> Integer -> Integer
176 = error "Prelude.Integral.quot{Integer}: divide by 0"
177 quotInteger a@(S# (-2147483648#)) b = quotInteger (toBig a) b
178 quotInteger (S# a) (S# b) = S# (quotInt# a b)
179 {- Special case disabled, see remInteger above
180 quotInteger (S# a) (J# sb b)
181 | sb ==# 1# = S# (quotInt# a (word2Int# (integer2Word# sb b)))
182 | sb ==# -1# = S# (quotInt# a (0# -# (word2Int# (integer2Word# sb b))))
183 | otherwise = zeroInteger
185 quotInteger ia@(S# _) ib@(J# _ _) = quotInteger (toBig ia) ib
186 quotInteger (J# sa a) (S# b)
187 = case int2Integer# b of { (# sb, b #) ->
188 case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
189 quotInteger (J# sa a) (J# sb b)
190 = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
196 gcdInteger :: Integer -> Integer -> Integer
197 -- SUP: Do we really need the first two cases?
198 gcdInteger a@(S# (-2147483648#)) b = gcdInteger (toBig a) b
199 gcdInteger a b@(S# (-2147483648#)) = gcdInteger a (toBig b)
200 gcdInteger (S# a) (S# b) = case gcdInt (I# a) (I# b) of { I# c -> S# c }
201 gcdInteger ia@(S# 0#) ib@(J# 0# _) = error "PrelNum.gcdInteger: gcd 0 0 is undefined"
202 gcdInteger ia@(S# a) ib@(J# sb b)
205 | otherwise = S# (gcdIntegerInt# absSb b absA)
206 where absA = if a <# 0# then negateInt# a else a
207 absSb = if sb <# 0# then negateInt# sb else sb
208 gcdInteger ia@(J# _ _) ib@(S# _) = gcdInteger ib ia
209 gcdInteger (J# 0# _) (J# 0# _) = error "PrelNum.gcdInteger: gcd 0 0 is undefined"
210 gcdInteger (J# sa a) (J# sb b)
211 = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
213 lcmInteger :: Integer -> Integer -> Integer
219 = (divExact aa (gcdInteger aa ab)) * ab
223 divExact :: Integer -> Integer -> Integer
224 divExact a@(S# (-2147483648#)) b = divExact (toBig a) b
225 divExact (S# a) (S# b) = S# (quotInt# a b)
226 divExact (S# a) (J# sb b)
227 = S# (quotInt# a (integer2Int# sb b))
228 divExact (J# sa a) (S# b)
229 = case int2Integer# b of
230 (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
231 divExact (J# sa a) (J# sb b)
232 = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
236 %*********************************************************
238 \subsection{The @Integer@ instances for @Eq@, @Ord@}
240 %*********************************************************
243 instance Eq Integer where
244 (S# i) == (S# j) = i ==# j
245 (S# i) == (J# s d) = cmpIntegerInt# s d i ==# 0#
246 (J# s d) == (S# i) = cmpIntegerInt# s d i ==# 0#
247 (J# s1 d1) == (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ==# 0#
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 ------------------------------------------------------------------------
255 instance Ord Integer where
256 (S# i) <= (S# j) = i <=# j
257 (J# s d) <= (S# i) = cmpIntegerInt# s d i <=# 0#
258 (S# i) <= (J# s d) = 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 (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 compare (S# i) (S# j)
280 compare (J# s d) (S# i)
281 = case cmpIntegerInt# s d i of { res# ->
282 if res# <# 0# then LT else
283 if res# ># 0# then GT else EQ
285 compare (S# i) (J# s d)
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 (J# s1 d1) (J# s2 d2)
291 = case cmpInteger# s1 d1 s2 d2 of { res# ->
292 if res# <# 0# then LT else
293 if res# ># 0# then GT else EQ
298 %*********************************************************
300 \subsection{The @Integer@ instances for @Num@}
302 %*********************************************************
305 instance Num Integer where
309 negate = negateInteger
312 -- ORIG: abs n = if n >= 0 then n else -n
313 abs (S# (-2147483648#)) = 2147483648
314 abs (S# i) = case abs (I# i) of I# j -> S# j
315 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
317 signum (S# i) = case signum (I# i) of I# j -> S# j
320 cmp = cmpIntegerInt# s d 0#
322 if cmp ># 0# then S# 1#
323 else if cmp ==# 0# then S# 0#
324 else S# (negateInt# 1#)
326 plusInteger i1@(S# i) i2@(S# j) = case addIntC# i j of { (# r, c #) ->
327 if c ==# 0# then S# r
328 else toBig i1 + toBig i2 }
329 plusInteger i1@(J# _ _) i2@(S# _) = i1 + toBig i2
330 plusInteger i1@(S# _) i2@(J# _ _) = toBig i1 + i2
331 plusInteger (J# s1 d1) (J# s2 d2) = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
333 minusInteger i1@(S# i) i2@(S# j) = case subIntC# i j of { (# r, c #) ->
334 if c ==# 0# then S# r
335 else toBig i1 - toBig i2 }
336 minusInteger i1@(J# _ _) i2@(S# _) = i1 - toBig i2
337 minusInteger i1@(S# _) i2@(J# _ _) = toBig i1 - i2
338 minusInteger (J# s1 d1) (J# s2 d2) = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
340 timesInteger i1@(S# i) i2@(S# j) = case mulIntC# i j of { (# r, c #) ->
341 if c ==# 0# then S# r
342 else toBig i1 * toBig i2 }
343 timesInteger i1@(J# _ _) i2@(S# _) = i1 * toBig i2
344 timesInteger i1@(S# _) i2@(J# _ _) = toBig i1 * i2
345 timesInteger (J# s1 d1) (J# s2 d2) = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
347 negateInteger (S# (-2147483648#)) = 2147483648
348 negateInteger (S# i) = S# (negateInt# i)
349 negateInteger (J# s d) = J# (negateInt# s) d
353 %*********************************************************
355 \subsection{The @Integer@ instance for @Enum@}
357 %*********************************************************
360 instance Enum Integer where
363 toEnum n = int2Integer n
364 fromEnum n = integer2Int n
366 {-# INLINE enumFrom #-}
367 {-# INLINE enumFromThen #-}
368 {-# INLINE enumFromTo #-}
369 {-# INLINE enumFromThenTo #-}
370 enumFrom x = efdInteger x 1
371 enumFromThen x y = efdInteger x (y-x)
372 enumFromTo x lim = efdtInteger x 1 lim
373 enumFromThenTo x y lim = efdtInteger x (y-x) lim
376 efdInteger = enumDeltaIntegerList
377 efdtInteger = enumDeltaToIntegerList
380 "efdInteger" forall x y. efdInteger x y = build (\c _ -> enumDeltaIntegerFB c x y)
381 "efdtInteger" forall x y l.efdtInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
382 "enumDeltaInteger" enumDeltaIntegerFB (:) = enumDeltaIntegerList
383 "enumDeltaToInteger" enumDeltaToIntegerFB (:) [] = enumDeltaToIntegerList
386 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
387 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
389 enumDeltaIntegerList :: Integer -> Integer -> [Integer]
390 enumDeltaIntegerList x d = x : enumDeltaIntegerList (x+d) d
392 enumDeltaToIntegerFB c n x delta lim
393 | delta >= 0 = up_fb c n x delta lim
394 | otherwise = dn_fb c n x delta lim
396 enumDeltaToIntegerList x delta lim
397 | delta >= 0 = up_list x delta lim
398 | otherwise = dn_list x delta lim
400 up_fb c n x delta lim = go (x::Integer)
403 | otherwise = x `c` go (x+delta)
404 dn_fb c n x delta lim = go (x::Integer)
407 | otherwise = x `c` go (x+delta)
409 up_list x delta lim = go (x::Integer)
412 | otherwise = x : go (x+delta)
413 dn_list x delta lim = go (x::Integer)
416 | otherwise = x : go (x+delta)
421 %*********************************************************
423 \subsection{The @Integer@ instances for @Show@}
425 %*********************************************************
428 instance Show Integer where
430 | n < 0 && p > 6 = '(' : jtos n (')' : r)
431 | otherwise = jtos n r
432 showList = showList__ (showsPrec 0)
434 jtos :: Integer -> String -> String
436 | n < 0 = '-' : jtos' (-n) cs
437 | otherwise = jtos' n cs
439 jtos' :: Integer -> String -> String
441 | n' < 10 = case unsafeChr (ord '0' + fromInteger n') of
443 | otherwise = case unsafeChr (ord '0' + fromInteger r) of
444 c@(C# _) -> jtos' q (c:cs')
446 (q,r) = n' `quotRemInteger` 10