2 % (c) The AQUA Project, Glasgow University, 1994-1996
5 \section[PrelNum]{Module @PrelNum@}
17 {-# OPTIONS -fno-implicit-prelude #-}
21 import {-# SOURCE #-} PrelErr
30 default () -- Double isn't available yet,
31 -- and we shouldn't be using defaults anyway
34 %*********************************************************
36 \subsection{Standard numeric class}
38 %*********************************************************
41 class (Eq a, Show a) => Num a where
42 (+), (-), (*) :: a -> a -> a
45 fromInteger :: Integer -> a
46 fromInt :: Int -> a -- partain: Glasgow extension
50 fromInt (I# i#) = fromInteger (S# i#)
51 -- Go via the standard class-op if the
52 -- non-standard one ain't provided
55 A few small numeric functions
58 subtract :: (Num a) => a -> a -> a
59 {-# INLINE subtract #-}
63 ord_0 = fromInt (ord '0')
67 %*********************************************************
69 \subsection{Instances for @Int@}
71 %*********************************************************
74 instance Num Int where
76 (-) x y = minusInt x y
77 negate x = negateInt x
78 (*) x y = timesInt x y
79 abs n = if n `geInt` 0 then n else (negateInt n)
81 signum n | n `ltInt` 0 = negateInt 1
85 fromInteger n = integer2Int n
91 -- These can't go in PrelBase with the defn of Int, because
92 -- we don't have pairs defined at that time!
94 quotRemInt :: Int -> Int -> (Int, Int)
95 a@(I# _) `quotRemInt` b@(I# _) = (a `quotInt` b, a `remInt` b)
96 -- OK, so I made it a little stricter. Shoot me. (WDP 94/10)
98 divModInt :: Int -> Int -> (Int, Int)
99 divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
100 -- Stricter. Sorry if you don't like it. (WDP 94/10)
104 %*********************************************************
106 \subsection{The @Integer@ type}
108 %*********************************************************
112 = S# Int# -- small integers
113 | J# Int# ByteArray# -- large integers
116 Convenient boxed Integer PrimOps.
119 zeroInteger :: Integer
122 int2Integer :: Int -> Integer
123 {-# INLINE int2Integer #-}
124 int2Integer (I# i) = S# i
126 integer2Int :: Integer -> Int
127 integer2Int (S# i) = I# i
128 integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
130 addr2Integer :: Addr# -> Integer
131 {-# INLINE addr2Integer #-}
132 addr2Integer x = case addr2Integer# x of (# s, d #) -> J# s d
134 toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
139 %*********************************************************
141 \subsection{Dividing @Integers@}
143 %*********************************************************
146 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
147 quotRemInteger i1@(S# i) i2@(S# j)
148 | i ==# -2147483648# = quotRemInteger (toBig i1) i2
149 | otherwise = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j )
150 quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
151 quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
152 quotRemInteger (J# s1 d1) (J# s2 d2)
153 = case (quotRemInteger# s1 d1 s2 d2) of
155 -> (J# s3 d3, J# s4 d4)
157 divModInteger i1@(S# i) i2@(S# j)
158 | i ==# -2147483648# = divModInteger (toBig i1) i2
159 | otherwise = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
160 divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
161 divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
162 divModInteger (J# s1 d1) (J# s2 d2)
163 = case (divModInteger# s1 d1 s2 d2) of
165 -> (J# s3 d3, J# s4 d4)
167 remInteger :: Integer -> Integer -> Integer
169 = error "Prelude.Integral.rem{Integer}: divide by 0"
170 remInteger ia@(S# a) ib@(S# b)
171 | a ==# -2147483648# = remInteger (toBig ia) ib
172 | otherwise = S# (remInt# a b)
173 remInteger ia@(S# a) (J# sb b)
174 | sb ==# 1# = S# (remInt# a (word2Int# (integer2Word# sb b)))
175 | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
177 | otherwise = S# (0# -# a)
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# (sr *# (word2Int# (integer2Word# 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 ia@(S# a) ib@(S# b)
189 | a ==# -2147483648# = quotInteger (toBig ia) ib
190 | otherwise = S# (quotInt# a b)
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
195 quotInteger (J# sa a) (S# b)
196 = case int2Integer# b of { (# sb, b #) ->
197 case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
198 quotInteger (J# sa a) (J# sb b)
199 = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
205 gcdInteger :: Integer -> Integer -> Integer
206 gcdInteger ia@(S# a) ib@(S# b)
207 | a ==# -2147483648# = gcdInteger (toBig ia) ib
208 | otherwise = S# (gcdInt# a b)
209 gcdInteger ia@(S# a) ib@(J# sb b)
212 | otherwise = S# (gcdIntegerInt# sb b a)
213 gcdInteger ia@(J# sa a) ib@(S# b)
216 | otherwise = S# (gcdIntegerInt# sa a b)
217 gcdInteger (J# sa a) (J# sb b)
218 = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
220 lcmInteger :: Integer -> Integer -> Integer
226 = (divExact aa (gcdInteger aa ab)) * ab
230 divExact :: Integer -> Integer -> Integer
231 divExact ia@(S# a) ib@(S# b)
232 | a ==# -2147483648# = divExact (toBig ia) ib
233 | otherwise = S# (quotInt# a b)
234 divExact (S# a) (J# sb b)
235 = S# (quotInt# a (sb *# (word2Int# (integer2Word# sb b))))
236 divExact (J# sa a) (S# b)
237 = case int2Integer# b of
238 (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
239 divExact (J# sa a) (J# sb b)
240 = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
244 %*********************************************************
246 \subsection{The @Integer@ instances for @Eq@, @Ord@}
248 %*********************************************************
251 instance Eq Integer where
252 (S# i) == (S# j) = i ==# j
253 (S# i) == (J# s d) = cmpIntegerInt# s d i ==# 0#
254 (J# s d) == (S# i) = cmpIntegerInt# s d i ==# 0#
255 (J# s1 d1) == (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ==# 0#
257 (S# i) /= (S# j) = i /=# j
258 (S# i) /= (J# s d) = cmpIntegerInt# s d i /=# 0#
259 (J# s d) /= (S# i) = cmpIntegerInt# s d i /=# 0#
260 (J# s1 d1) /= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) /=# 0#
262 ------------------------------------------------------------------------
263 instance Ord Integer where
264 (S# i) <= (S# j) = i <=# j
265 (J# s d) <= (S# i) = cmpIntegerInt# s d i <=# 0#
266 (S# i) <= (J# s d) = cmpIntegerInt# s d i >=# 0#
267 (J# s1 d1) <= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <=# 0#
269 (S# i) > (S# j) = i ># j
270 (J# s d) > (S# i) = cmpIntegerInt# s d i ># 0#
271 (S# i) > (J# s d) = cmpIntegerInt# s d i <# 0#
272 (J# s1 d1) > (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ># 0#
274 (S# i) < (S# j) = i <# j
275 (J# s d) < (S# i) = cmpIntegerInt# s d i <# 0#
276 (S# i) < (J# s d) = cmpIntegerInt# s d i ># 0#
277 (J# s1 d1) < (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
279 (S# i) >= (S# j) = i >=# j
280 (J# s d) >= (S# i) = cmpIntegerInt# s d i >=# 0#
281 (S# i) >= (J# s d) = cmpIntegerInt# s d i <=# 0#
282 (J# s1 d1) >= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
284 compare (S# i) (S# j)
288 compare (J# s d) (S# i)
289 = case cmpIntegerInt# s d i of { res# ->
290 if res# <# 0# then LT else
291 if res# ># 0# then GT else EQ
293 compare (S# i) (J# s d)
294 = case cmpIntegerInt# s d i of { res# ->
295 if res# ># 0# then LT else
296 if res# <# 0# then GT else EQ
298 compare (J# s1 d1) (J# s2 d2)
299 = case cmpInteger# s1 d1 s2 d2 of { res# ->
300 if res# <# 0# then LT else
301 if res# ># 0# then GT else EQ
306 %*********************************************************
308 \subsection{The @Integer@ instances for @Num@}
310 %*********************************************************
313 instance Num Integer where
314 (+) i1@(S# i) i2@(S# j)
315 = case addIntC# i j of { (# r, c #) ->
316 if c ==# 0# then S# r
317 else toBig i1 + toBig i2 }
318 (+) i1@(J# _ _) i2@(S# _) = i1 + toBig i2
319 (+) i1@(S# _) i2@(J# _ _) = toBig i1 + i2
320 (+) (J# s1 d1) (J# s2 d2)
321 = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
323 (-) i1@(S# i) i2@(S# j)
324 = case subIntC# i j of { (# r, c #) ->
325 if c ==# 0# then S# r
326 else toBig i1 - toBig i2 }
327 (-) i1@(J# _ _) i2@(S# _) = i1 - toBig i2
328 (-) i1@(S# _) i2@(J# _ _) = toBig i1 - i2
329 (-) (J# s1 d1) (J# s2 d2)
330 = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
332 (*) i1@(S# i) i2@(S# j)
333 = case mulIntC# i j of { (# r, c #) ->
334 if c ==# 0# then S# r
335 else toBig i1 * toBig i2 }
336 (*) i1@(J# _ _) i2@(S# _) = i1 * toBig i2
337 (*) i1@(S# _) i2@(J# _ _) = toBig i1 * i2
338 (*) (J# s1 d1) (J# s2 d2)
339 = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
341 negate (S# (-2147483648#)) = 2147483648
342 negate (S# i) = S# (negateInt# i)
343 negate (J# s d) = J# (negateInt# s) d
345 -- ORIG: abs n = if n >= 0 then n else -n
347 abs (S# (-2147483648#)) = 2147483648
348 abs (S# i) = case abs (I# i) of I# j -> S# j
349 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
351 signum (S# i) = case signum (I# i) of I# j -> S# j
354 cmp = cmpIntegerInt# s d 0#
356 if cmp ># 0# then S# 1#
357 else if cmp ==# 0# then S# 0#
358 else S# (negateInt# 1#)
362 fromInt (I# i) = S# i
366 %*********************************************************
368 \subsection{The @Integer@ instance for @Enum@}
370 %*********************************************************
373 instance Enum Integer where
376 toEnum n = int2Integer n
377 fromEnum n = integer2Int n
379 {-# INLINE enumFrom #-}
380 {-# INLINE enumFromThen #-}
381 {-# INLINE enumFromTo #-}
382 {-# INLINE enumFromThenTo #-}
383 enumFrom x = build (\c _ -> enumDeltaIntegerFB c x 1)
384 enumFromThen x y = build (\c _ -> enumDeltaIntegerFB c x (y-x))
385 enumFromTo x lim = build (\c n -> enumDeltaToIntegerFB c n x 1 lim)
386 enumFromThenTo x y lim = build (\c n -> enumDeltaToIntegerFB c n x (y-x) lim)
388 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
389 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
391 enumDeltaIntegerList :: Integer -> Integer -> [Integer]
392 enumDeltaIntegerList x d = x : enumDeltaIntegerList (x+d) d
394 enumDeltaToIntegerFB c n x delta lim
395 | delta >= 0 = up_fb c n x delta lim
396 | otherwise = dn_fb c n x delta lim
398 enumDeltaToIntegerList x delta lim
399 | delta >= 0 = up_list x delta lim
400 | otherwise = dn_list x delta lim
402 up_fb c n x delta lim = go (x::Integer)
405 | otherwise = x `c` go (x+delta)
406 dn_fb c n x delta lim = go (x::Integer)
409 | otherwise = x `c` go (x+delta)
411 up_list x delta lim = go (x::Integer)
414 | otherwise = x : go (x+delta)
415 dn_list x delta lim = go (x::Integer)
418 | otherwise = x : go (x+delta)
421 "enumDeltaInteger" enumDeltaIntegerFB (:) = enumDeltaIntegerList
422 "enumDeltaToInteger" enumDeltaToIntegerFB (:) [] = enumDeltaToIntegerList
427 %*********************************************************
429 \subsection{The @Integer@ instances for @Show@}
431 %*********************************************************
434 instance Show Integer where
435 showsPrec x = showSignedInteger x
436 showList = showList__ (showsPrec 0)
438 showSignedInteger :: Int -> Integer -> ShowS
439 showSignedInteger p n r
440 | n < 0 && p > 6 = '(':jtos n (')':r)
441 | otherwise = jtos n r
443 jtos :: Integer -> String -> String
445 | i < 0 = '-' : jtos' (-i) rs
446 | otherwise = jtos' i rs
448 jtos' :: Integer -> String -> String
450 | n < 10 = chr (fromInteger n + (ord_0::Int)) : cs
451 | otherwise = jtos' q (chr (integer2Int r + (ord_0::Int)) : cs)
453 (q,r) = n `quotRemInteger` 10