1 % ------------------------------------------------------------------------------
2 % $Id: Num.lhs,v 1.2 2001/07/31 13:09:11 simonmar Exp $
4 % (c) The University of Glasgow, 1994-2000
7 \section[GHC.Num]{Module @GHC.Num@}
19 {-# OPTIONS -fno-implicit-prelude #-}
22 #if WORD_SIZE_IN_BYTES == 4
23 #define LEFTMOST_BIT 2147483648
24 #elif WORD_SIZE_IN_BYTES == 8
25 #define LEFTMOST_BIT 9223372036854775808
27 #error Please define LEFTMOST_BIT to be 2^(WORD_SIZE_IN_BYTES*8-1)
32 import {-# SOURCE #-} GHC.Err
41 default () -- Double isn't available yet,
42 -- and we shouldn't be using defaults anyway
45 %*********************************************************
47 \subsection{Standard numeric class}
49 %*********************************************************
52 class (Eq a, Show a) => Num a where
53 (+), (-), (*) :: a -> a -> a
56 fromInteger :: Integer -> a
61 {-# INLINE subtract #-}
62 subtract :: (Num a) => a -> a -> a
67 %*********************************************************
69 \subsection{Instances for @Int@}
71 %*********************************************************
74 instance Num Int where
79 abs n = if n `geInt` 0 then n else negateInt n
81 signum n | n `ltInt` 0 = negateInt 1
85 fromInteger = integer2Int
90 -- These can't go in GHC.Base with the defn of Int, because
91 -- we don't have pairs defined at that time!
93 quotRemInt :: Int -> Int -> (Int, Int)
94 a@(I# _) `quotRemInt` b@(I# _) = (a `quotInt` b, a `remInt` b)
95 -- OK, so I made it a little stricter. Shoot me. (WDP 94/10)
97 divModInt :: Int -> Int -> (Int, Int)
98 divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
99 -- Stricter. Sorry if you don't like it. (WDP 94/10)
103 %*********************************************************
105 \subsection{The @Integer@ type}
107 %*********************************************************
111 = S# Int# -- small integers
112 | J# Int# ByteArray# -- large integers
115 Convenient boxed Integer PrimOps.
118 zeroInteger :: Integer
121 int2Integer :: Int -> Integer
122 {-# INLINE int2Integer #-}
123 int2Integer (I# i) = S# i
125 integer2Int :: Integer -> Int
126 integer2Int (S# i) = I# i
127 integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
129 toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
134 %*********************************************************
136 \subsection{Dividing @Integers@}
138 %*********************************************************
141 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
142 quotRemInteger a@(S# (-LEFTMOST_BIT#)) b = quotRemInteger (toBig a) b
143 quotRemInteger (S# i) (S# j)
144 = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j )
145 quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
146 quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
147 quotRemInteger (J# s1 d1) (J# s2 d2)
148 = case (quotRemInteger# s1 d1 s2 d2) of
150 -> (J# s3 d3, J# s4 d4)
152 divModInteger a@(S# (-LEFTMOST_BIT#)) b = divModInteger (toBig a) b
153 divModInteger (S# i) (S# j)
154 = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
155 divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
156 divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
157 divModInteger (J# s1 d1) (J# s2 d2)
158 = case (divModInteger# s1 d1 s2 d2) of
160 -> (J# s3 d3, J# s4 d4)
162 remInteger :: Integer -> Integer -> Integer
164 = error "Prelude.Integral.rem{Integer}: divide by 0"
165 remInteger a@(S# (-LEFTMOST_BIT#)) b = remInteger (toBig a) b
166 remInteger (S# a) (S# b) = S# (remInt# a b)
167 {- Special case doesn't work, because a 1-element J# has the range
168 -(2^32-1) -- 2^32-1, whereas S# has the range -2^31 -- (2^31-1)
169 remInteger ia@(S# a) (J# sb b)
170 | sb ==# 1# = S# (remInt# a (word2Int# (integer2Word# sb b)))
171 | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
173 | otherwise = S# (0# -# a)
175 remInteger ia@(S# _) ib@(J# _ _) = remInteger (toBig ia) ib
176 remInteger (J# sa a) (S# b)
177 = case int2Integer# b of { (# sb, b #) ->
178 case remInteger# sa a sb b of { (# sr, r #) ->
179 S# (integer2Int# sr r) }}
180 remInteger (J# sa a) (J# sb b)
181 = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
183 quotInteger :: Integer -> Integer -> Integer
185 = error "Prelude.Integral.quot{Integer}: divide by 0"
186 quotInteger a@(S# (-LEFTMOST_BIT#)) b = quotInteger (toBig a) b
187 quotInteger (S# a) (S# b) = S# (quotInt# a b)
188 {- Special case disabled, see remInteger above
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
194 quotInteger ia@(S# _) ib@(J# _ _) = quotInteger (toBig ia) ib
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 -- SUP: Do we really need the first two cases?
207 gcdInteger a@(S# (-LEFTMOST_BIT#)) b = gcdInteger (toBig a) b
208 gcdInteger a b@(S# (-LEFTMOST_BIT#)) = gcdInteger a (toBig b)
209 gcdInteger (S# a) (S# b) = case gcdInt (I# a) (I# b) of { I# c -> S# c }
210 gcdInteger ia@(S# 0#) ib@(J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
211 gcdInteger ia@(S# a) ib@(J# sb b)
214 | otherwise = S# (gcdIntegerInt# absSb b absA)
215 where absA = if a <# 0# then negateInt# a else a
216 absSb = if sb <# 0# then negateInt# sb else sb
217 gcdInteger ia@(J# _ _) ib@(S# _) = gcdInteger ib ia
218 gcdInteger (J# 0# _) (J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
219 gcdInteger (J# sa a) (J# sb b)
220 = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
222 lcmInteger :: Integer -> Integer -> Integer
228 = (divExact aa (gcdInteger aa ab)) * ab
232 divExact :: Integer -> Integer -> Integer
233 divExact a@(S# (-LEFTMOST_BIT#)) b = divExact (toBig a) b
234 divExact (S# a) (S# b) = S# (quotInt# a b)
235 divExact (S# a) (J# sb b)
236 = S# (quotInt# a (integer2Int# sb b))
237 divExact (J# sa a) (S# b)
238 = case int2Integer# b of
239 (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
240 divExact (J# sa a) (J# sb b)
241 = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
245 %*********************************************************
247 \subsection{The @Integer@ instances for @Eq@, @Ord@}
249 %*********************************************************
252 instance Eq Integer where
253 (S# i) == (S# j) = i ==# j
254 (S# i) == (J# s d) = cmpIntegerInt# s d i ==# 0#
255 (J# s d) == (S# i) = cmpIntegerInt# s d i ==# 0#
256 (J# s1 d1) == (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ==# 0#
258 (S# i) /= (S# j) = i /=# j
259 (S# i) /= (J# s d) = cmpIntegerInt# s d i /=# 0#
260 (J# s d) /= (S# i) = cmpIntegerInt# s d i /=# 0#
261 (J# s1 d1) /= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) /=# 0#
263 ------------------------------------------------------------------------
264 instance Ord Integer where
265 (S# i) <= (S# j) = i <=# j
266 (J# s d) <= (S# i) = cmpIntegerInt# s d i <=# 0#
267 (S# i) <= (J# s d) = cmpIntegerInt# s d i >=# 0#
268 (J# s1 d1) <= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <=# 0#
270 (S# i) > (S# j) = i ># j
271 (J# s d) > (S# i) = cmpIntegerInt# s d i ># 0#
272 (S# i) > (J# s d) = cmpIntegerInt# s d i <# 0#
273 (J# s1 d1) > (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ># 0#
275 (S# i) < (S# j) = i <# j
276 (J# s d) < (S# i) = cmpIntegerInt# s d i <# 0#
277 (S# i) < (J# s d) = cmpIntegerInt# s d i ># 0#
278 (J# s1 d1) < (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
280 (S# i) >= (S# j) = i >=# j
281 (J# s d) >= (S# i) = cmpIntegerInt# s d i >=# 0#
282 (S# i) >= (J# s d) = cmpIntegerInt# s d i <=# 0#
283 (J# s1 d1) >= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
285 compare (S# i) (S# j)
289 compare (J# s d) (S# i)
290 = case cmpIntegerInt# s d i of { res# ->
291 if res# <# 0# then LT else
292 if res# ># 0# then GT else EQ
294 compare (S# i) (J# s d)
295 = case cmpIntegerInt# s d i of { res# ->
296 if res# ># 0# then LT else
297 if res# <# 0# then GT else EQ
299 compare (J# s1 d1) (J# s2 d2)
300 = case cmpInteger# s1 d1 s2 d2 of { res# ->
301 if res# <# 0# then LT else
302 if res# ># 0# then GT else EQ
307 %*********************************************************
309 \subsection{The @Integer@ instances for @Num@}
311 %*********************************************************
314 instance Num Integer where
318 negate = negateInteger
321 -- ORIG: abs n = if n >= 0 then n else -n
322 abs (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
323 abs (S# i) = case abs (I# i) of I# j -> S# j
324 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
326 signum (S# i) = case signum (I# i) of I# j -> S# j
329 cmp = cmpIntegerInt# s d 0#
331 if cmp ># 0# then S# 1#
332 else if cmp ==# 0# then S# 0#
333 else S# (negateInt# 1#)
335 plusInteger i1@(S# i) i2@(S# j) = case addIntC# i j of { (# r, c #) ->
336 if c ==# 0# then S# r
337 else toBig i1 + toBig i2 }
338 plusInteger i1@(J# _ _) i2@(S# _) = i1 + toBig i2
339 plusInteger i1@(S# _) i2@(J# _ _) = toBig i1 + i2
340 plusInteger (J# s1 d1) (J# s2 d2) = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
342 minusInteger i1@(S# i) i2@(S# j) = case subIntC# i j of { (# r, c #) ->
343 if c ==# 0# then S# r
344 else toBig i1 - toBig i2 }
345 minusInteger i1@(J# _ _) i2@(S# _) = i1 - toBig i2
346 minusInteger i1@(S# _) i2@(J# _ _) = toBig i1 - i2
347 minusInteger (J# s1 d1) (J# s2 d2) = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
349 timesInteger i1@(S# i) i2@(S# j) = case mulIntC# i j of { (# r, c #) ->
350 if c ==# 0# then S# r
351 else toBig i1 * toBig i2 }
352 timesInteger i1@(J# _ _) i2@(S# _) = i1 * toBig i2
353 timesInteger i1@(S# _) i2@(J# _ _) = toBig i1 * i2
354 timesInteger (J# s1 d1) (J# s2 d2) = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
356 negateInteger (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
357 negateInteger (S# i) = S# (negateInt# i)
358 negateInteger (J# s d) = J# (negateInt# s) d
362 %*********************************************************
364 \subsection{The @Integer@ instance for @Enum@}
366 %*********************************************************
369 instance Enum Integer where
372 toEnum n = int2Integer n
373 fromEnum n = integer2Int n
375 {-# INLINE enumFrom #-}
376 {-# INLINE enumFromThen #-}
377 {-# INLINE enumFromTo #-}
378 {-# INLINE enumFromThenTo #-}
379 enumFrom x = efdInteger x 1
380 enumFromThen x y = efdInteger x (y-x)
381 enumFromTo x lim = efdtInteger x 1 lim
382 enumFromThenTo x y lim = efdtInteger x (y-x) lim
385 efdInteger = enumDeltaIntegerList
386 efdtInteger = enumDeltaToIntegerList
389 "efdInteger" forall x y. efdInteger x y = build (\c _ -> enumDeltaIntegerFB c x y)
390 "efdtInteger" forall x y l.efdtInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
391 "enumDeltaInteger" enumDeltaIntegerFB (:) = enumDeltaIntegerList
392 "enumDeltaToInteger" enumDeltaToIntegerFB (:) [] = enumDeltaToIntegerList
395 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
396 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
398 enumDeltaIntegerList :: Integer -> Integer -> [Integer]
399 enumDeltaIntegerList x d = x : enumDeltaIntegerList (x+d) d
401 enumDeltaToIntegerFB c n x delta lim
402 | delta >= 0 = up_fb c n x delta lim
403 | otherwise = dn_fb c n x delta lim
405 enumDeltaToIntegerList x delta lim
406 | delta >= 0 = up_list x delta lim
407 | otherwise = dn_list x delta lim
409 up_fb c n x delta lim = go (x::Integer)
412 | otherwise = x `c` go (x+delta)
413 dn_fb c n x delta lim = go (x::Integer)
416 | otherwise = x `c` go (x+delta)
418 up_list x delta lim = go (x::Integer)
421 | otherwise = x : go (x+delta)
422 dn_list x delta lim = go (x::Integer)
425 | otherwise = x : go (x+delta)
430 %*********************************************************
432 \subsection{The @Integer@ instances for @Show@}
434 %*********************************************************
437 instance Show Integer where
439 | n < 0 && p > 6 = '(' : jtos n (')' : r)
440 | otherwise = jtos n r
441 showList = showList__ (showsPrec 0)
443 jtos :: Integer -> String -> String
445 | n < 0 = '-' : jtos' (-n) cs
446 | otherwise = jtos' n cs
448 jtos' :: Integer -> String -> String
450 | n' < 10 = case unsafeChr (ord '0' + fromInteger n') of
452 | otherwise = case unsafeChr (ord '0' + fromInteger r) of
453 c@(C# _) -> jtos' q (c:cs')
455 (q,r) = n' `quotRemInteger` 10