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 a@(S# (-2147483648#)) b = quotRemInteger (toBig a) b
148 quotRemInteger (S# i) (S# j)
149 = 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 a@(S# (-2147483648#)) b = divModInteger (toBig a) b
158 divModInteger (S# i) (S# j)
159 = 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 a@(S# (-2147483648#)) b = remInteger (toBig a) b
171 remInteger (S# a) (S# b) = S# (remInt# a b)
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)
177 remInteger (J# sa a) (S# b)
178 = case int2Integer# b of { (# sb, b #) ->
179 case remInteger# sa a sb b of { (# sr, r #) ->
180 S# (sr *# (word2Int# (integer2Word# sr r))) }}
181 remInteger (J# sa a) (J# sb b)
182 = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
184 quotInteger :: Integer -> Integer -> Integer
186 = error "Prelude.Integral.quot{Integer}: divide by 0"
187 quotInteger a@(S# (-2147483648#)) b = quotInteger (toBig a) b
188 quotInteger (S# a) (S# b) = S# (quotInt# a b)
189 quotInteger (S# a) (J# sb b)
190 | sb ==# 1# = S# (quotInt# a (word2Int# (integer2Word# sb b)))
191 | sb ==# -1# = S# (quotInt# a (0# -# (word2Int# (integer2Word# sb b))))
192 | otherwise = zeroInteger
193 quotInteger (J# sa a) (S# b)
194 = case int2Integer# b of { (# sb, b #) ->
195 case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
196 quotInteger (J# sa a) (J# sb b)
197 = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
203 gcdInteger :: Integer -> Integer -> Integer
204 gcdInteger a@(S# (-2147483648#)) b = gcdInteger (toBig a) b
205 gcdInteger a b@(S# (-2147483648#)) = gcdInteger a (toBig b)
206 gcdInteger (S# a) (S# b) = S# (gcdInt# a b)
207 gcdInteger ia@(S# a) ib@(J# sb b)
210 | otherwise = S# (gcdIntegerInt# sb b a)
211 gcdInteger ia@(J# sa a) ib@(S# b)
214 | otherwise = S# (gcdIntegerInt# sa a b)
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# (-2147483648#)) 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 (sb *# (word2Int# (integer2Word# 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
311 (+) i1@(S# i) i2@(S# j)
312 = case addIntC# i j of { (# r, c #) ->
313 if c ==# 0# then S# r
314 else toBig i1 + toBig i2 }
315 (+) i1@(J# _ _) i2@(S# _) = i1 + toBig i2
316 (+) i1@(S# _) i2@(J# _ _) = toBig i1 + i2
317 (+) (J# s1 d1) (J# s2 d2)
318 = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
320 (-) i1@(S# i) i2@(S# j)
321 = case subIntC# i j of { (# r, c #) ->
322 if c ==# 0# then S# r
323 else toBig i1 - toBig i2 }
324 (-) i1@(J# _ _) i2@(S# _) = i1 - toBig i2
325 (-) i1@(S# _) i2@(J# _ _) = toBig i1 - i2
326 (-) (J# s1 d1) (J# s2 d2)
327 = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
329 (*) i1@(S# i) i2@(S# j)
330 = case mulIntC# i j of { (# r, c #) ->
331 if c ==# 0# then S# r
332 else toBig i1 * toBig i2 }
333 (*) i1@(J# _ _) i2@(S# _) = i1 * toBig i2
334 (*) i1@(S# _) i2@(J# _ _) = toBig i1 * i2
335 (*) (J# s1 d1) (J# s2 d2)
336 = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
338 negate (S# (-2147483648#)) = 2147483648
339 negate (S# i) = S# (negateInt# i)
340 negate (J# s d) = J# (negateInt# s) d
342 -- ORIG: abs n = if n >= 0 then n else -n
344 abs (S# (-2147483648#)) = 2147483648
345 abs (S# i) = case abs (I# i) of I# j -> S# j
346 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
348 signum (S# i) = case signum (I# i) of I# j -> S# j
351 cmp = cmpIntegerInt# s d 0#
353 if cmp ># 0# then S# 1#
354 else if cmp ==# 0# then S# 0#
355 else S# (negateInt# 1#)
359 fromInt (I# i) = S# i
363 %*********************************************************
365 \subsection{The @Integer@ instance for @Enum@}
367 %*********************************************************
370 instance Enum Integer where
373 toEnum n = int2Integer n
374 fromEnum n = integer2Int n
376 {-# INLINE enumFrom #-}
377 {-# INLINE enumFromThen #-}
378 {-# INLINE enumFromTo #-}
379 {-# INLINE enumFromThenTo #-}
380 enumFrom x = build (\c _ -> enumDeltaIntegerFB c x 1)
381 enumFromThen x y = build (\c _ -> enumDeltaIntegerFB c x (y-x))
382 enumFromTo x lim = build (\c n -> enumDeltaToIntegerFB c n x 1 lim)
383 enumFromThenTo x y lim = build (\c n -> enumDeltaToIntegerFB c n x (y-x) lim)
385 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
386 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
388 enumDeltaIntegerList :: Integer -> Integer -> [Integer]
389 enumDeltaIntegerList x d = x : enumDeltaIntegerList (x+d) d
391 enumDeltaToIntegerFB c n x delta lim
392 | delta >= 0 = up_fb c n x delta lim
393 | otherwise = dn_fb c n x delta lim
395 enumDeltaToIntegerList x delta lim
396 | delta >= 0 = up_list x delta lim
397 | otherwise = dn_list x delta lim
399 up_fb c n x delta lim = go (x::Integer)
402 | otherwise = x `c` go (x+delta)
403 dn_fb c n x delta lim = go (x::Integer)
406 | otherwise = x `c` go (x+delta)
408 up_list x delta lim = go (x::Integer)
411 | otherwise = x : go (x+delta)
412 dn_list x delta lim = go (x::Integer)
415 | otherwise = x : go (x+delta)
418 "enumDeltaInteger" enumDeltaIntegerFB (:) = enumDeltaIntegerList
419 "enumDeltaToInteger" enumDeltaToIntegerFB (:) [] = enumDeltaToIntegerList
424 %*********************************************************
426 \subsection{The @Integer@ instances for @Show@}
428 %*********************************************************
431 instance Show Integer where
432 showsPrec x = showSignedInteger x
433 showList = showList__ (showsPrec 0)
435 showSignedInteger :: Int -> Integer -> ShowS
436 showSignedInteger p n r
437 | n < 0 && p > 6 = '(':jtos n (')':r)
438 | otherwise = jtos n r
440 jtos :: Integer -> String -> String
442 | i < 0 = '-' : jtos' (-i) rs
443 | otherwise = jtos' i rs
445 jtos' :: Integer -> String -> String
447 | n < 10 = chr (fromInteger n + (ord_0::Int)) : cs
448 | otherwise = jtos' q (chr (integer2Int r + (ord_0::Int)) : cs)
450 (q,r) = n `quotRemInteger` 10