1 % ------------------------------------------------------------------------------
2 % $Id: Num.lhs,v 1.4 2002/02/05 17:32:26 simonmar Exp $
4 % (c) The University of Glasgow, 1994-2000
7 \section[GHC.Num]{Module @GHC.Num@}
19 {-# OPTIONS -fno-implicit-prelude #-}
22 #if SIZEOF_HSWORD == 4
23 #define LEFTMOST_BIT 2147483648
24 #elif SIZEOF_HSWORD == 8
25 #define LEFTMOST_BIT 9223372036854775808
27 #error Please define LEFTMOST_BIT to be 2^(SIZEOF_HSWORD*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
113 | J# Int# ByteArray# -- large integers
115 | J# Void BigInteger -- .NET big ints
117 foreign type dotnet "BigInteger" BigInteger
121 Convenient boxed Integer PrimOps.
124 zeroInteger :: Integer
127 int2Integer :: Int -> Integer
128 {-# INLINE int2Integer #-}
129 int2Integer (I# i) = S# i
131 integer2Int :: Integer -> Int
132 integer2Int (S# i) = I# i
133 integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
135 toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
140 %*********************************************************
142 \subsection{Dividing @Integers@}
144 %*********************************************************
147 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
148 quotRemInteger a@(S# (-LEFTMOST_BIT#)) b = quotRemInteger (toBig a) b
149 quotRemInteger (S# i) (S# j)
150 = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j )
151 quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
152 quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
153 quotRemInteger (J# s1 d1) (J# s2 d2)
154 = case (quotRemInteger# s1 d1 s2 d2) of
156 -> (J# s3 d3, J# s4 d4)
158 divModInteger a@(S# (-LEFTMOST_BIT#)) b = divModInteger (toBig a) b
159 divModInteger (S# i) (S# j)
160 = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
161 divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
162 divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
163 divModInteger (J# s1 d1) (J# s2 d2)
164 = case (divModInteger# s1 d1 s2 d2) of
166 -> (J# s3 d3, J# s4 d4)
168 remInteger :: Integer -> Integer -> Integer
170 = error "Prelude.Integral.rem{Integer}: divide by 0"
171 remInteger a@(S# (-LEFTMOST_BIT#)) b = remInteger (toBig a) b
172 remInteger (S# a) (S# b) = S# (remInt# a b)
173 {- Special case doesn't work, because a 1-element J# has the range
174 -(2^32-1) -- 2^32-1, whereas S# has the range -2^31 -- (2^31-1)
175 remInteger ia@(S# a) (J# sb b)
176 | sb ==# 1# = S# (remInt# a (word2Int# (integer2Word# sb b)))
177 | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
179 | otherwise = S# (0# -# a)
181 remInteger ia@(S# _) ib@(J# _ _) = remInteger (toBig ia) ib
182 remInteger (J# sa a) (S# b)
183 = case int2Integer# b of { (# sb, b #) ->
184 case remInteger# sa a sb b of { (# sr, r #) ->
185 S# (integer2Int# sr r) }}
186 remInteger (J# sa a) (J# sb b)
187 = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
189 quotInteger :: Integer -> Integer -> Integer
191 = error "Prelude.Integral.quot{Integer}: divide by 0"
192 quotInteger a@(S# (-LEFTMOST_BIT#)) b = quotInteger (toBig a) b
193 quotInteger (S# a) (S# b) = S# (quotInt# a b)
194 {- Special case disabled, see remInteger above
195 quotInteger (S# a) (J# sb b)
196 | sb ==# 1# = S# (quotInt# a (word2Int# (integer2Word# sb b)))
197 | sb ==# -1# = S# (quotInt# a (0# -# (word2Int# (integer2Word# sb b))))
198 | otherwise = zeroInteger
200 quotInteger ia@(S# _) ib@(J# _ _) = quotInteger (toBig ia) ib
201 quotInteger (J# sa a) (S# b)
202 = case int2Integer# b of { (# sb, b #) ->
203 case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
204 quotInteger (J# sa a) (J# sb b)
205 = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
211 gcdInteger :: Integer -> Integer -> Integer
212 -- SUP: Do we really need the first two cases?
213 gcdInteger a@(S# (-LEFTMOST_BIT#)) b = gcdInteger (toBig a) b
214 gcdInteger a b@(S# (-LEFTMOST_BIT#)) = gcdInteger a (toBig b)
215 gcdInteger (S# a) (S# b) = case gcdInt (I# a) (I# b) of { I# c -> S# c }
216 gcdInteger ia@(S# 0#) ib@(J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
217 gcdInteger ia@(S# a) ib@(J# sb b)
220 | otherwise = S# (gcdIntegerInt# absSb b absA)
221 where absA = if a <# 0# then negateInt# a else a
222 absSb = if sb <# 0# then negateInt# sb else sb
223 gcdInteger ia@(J# _ _) ib@(S# _) = gcdInteger ib ia
224 gcdInteger (J# 0# _) (J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
225 gcdInteger (J# sa a) (J# sb b)
226 = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
228 lcmInteger :: Integer -> Integer -> Integer
234 = (divExact aa (gcdInteger aa ab)) * ab
238 divExact :: Integer -> Integer -> Integer
239 divExact a@(S# (-LEFTMOST_BIT#)) b = divExact (toBig a) b
240 divExact (S# a) (S# b) = S# (quotInt# a b)
241 divExact (S# a) (J# sb b)
242 = S# (quotInt# a (integer2Int# sb b))
243 divExact (J# sa a) (S# b)
244 = case int2Integer# b of
245 (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
246 divExact (J# sa a) (J# sb b)
247 = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
251 %*********************************************************
253 \subsection{The @Integer@ instances for @Eq@, @Ord@}
255 %*********************************************************
258 instance Eq Integer where
259 (S# i) == (S# j) = i ==# j
260 (S# i) == (J# s d) = cmpIntegerInt# s d i ==# 0#
261 (J# s d) == (S# i) = cmpIntegerInt# s d i ==# 0#
262 (J# s1 d1) == (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ==# 0#
264 (S# i) /= (S# j) = i /=# j
265 (S# i) /= (J# s d) = cmpIntegerInt# s d i /=# 0#
266 (J# s d) /= (S# i) = cmpIntegerInt# s d i /=# 0#
267 (J# s1 d1) /= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) /=# 0#
269 ------------------------------------------------------------------------
270 instance Ord Integer where
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 (S# i) < (S# j) = i <# j
282 (J# s d) < (S# i) = cmpIntegerInt# s d i <# 0#
283 (S# i) < (J# s d) = cmpIntegerInt# s d i ># 0#
284 (J# s1 d1) < (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
286 (S# i) >= (S# j) = i >=# j
287 (J# s d) >= (S# i) = cmpIntegerInt# s d i >=# 0#
288 (S# i) >= (J# s d) = cmpIntegerInt# s d i <=# 0#
289 (J# s1 d1) >= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
291 compare (S# i) (S# j)
295 compare (J# s d) (S# i)
296 = case cmpIntegerInt# s d i of { res# ->
297 if res# <# 0# then LT else
298 if res# ># 0# then GT else EQ
300 compare (S# i) (J# s d)
301 = case cmpIntegerInt# s d i of { res# ->
302 if res# ># 0# then LT else
303 if res# <# 0# then GT else EQ
305 compare (J# s1 d1) (J# s2 d2)
306 = case cmpInteger# s1 d1 s2 d2 of { res# ->
307 if res# <# 0# then LT else
308 if res# ># 0# then GT else EQ
313 %*********************************************************
315 \subsection{The @Integer@ instances for @Num@}
317 %*********************************************************
320 instance Num Integer where
324 negate = negateInteger
327 -- ORIG: abs n = if n >= 0 then n else -n
328 abs (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
329 abs (S# i) = case abs (I# i) of I# j -> S# j
330 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
332 signum (S# i) = case signum (I# i) of I# j -> S# j
335 cmp = cmpIntegerInt# s d 0#
337 if cmp ># 0# then S# 1#
338 else if cmp ==# 0# then S# 0#
339 else S# (negateInt# 1#)
341 plusInteger i1@(S# i) i2@(S# j) = case addIntC# i j of { (# r, c #) ->
342 if c ==# 0# then S# r
343 else toBig i1 + toBig i2 }
344 plusInteger i1@(J# _ _) i2@(S# _) = i1 + toBig i2
345 plusInteger i1@(S# _) i2@(J# _ _) = toBig i1 + i2
346 plusInteger (J# s1 d1) (J# s2 d2) = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
348 minusInteger i1@(S# i) i2@(S# j) = case subIntC# i j of { (# r, c #) ->
349 if c ==# 0# then S# r
350 else toBig i1 - toBig i2 }
351 minusInteger i1@(J# _ _) i2@(S# _) = i1 - toBig i2
352 minusInteger i1@(S# _) i2@(J# _ _) = toBig i1 - i2
353 minusInteger (J# s1 d1) (J# s2 d2) = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
355 timesInteger i1@(S# i) i2@(S# j) = if mulIntMayOflo# i j ==# 0#
357 else toBig i1 * toBig i2
358 timesInteger i1@(J# _ _) i2@(S# _) = i1 * toBig i2
359 timesInteger i1@(S# _) i2@(J# _ _) = toBig i1 * i2
360 timesInteger (J# s1 d1) (J# s2 d2) = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
362 negateInteger (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
363 negateInteger (S# i) = S# (negateInt# i)
364 negateInteger (J# s d) = J# (negateInt# s) d
368 %*********************************************************
370 \subsection{The @Integer@ instance for @Enum@}
372 %*********************************************************
375 instance Enum Integer where
378 toEnum n = int2Integer n
379 fromEnum n = integer2Int n
381 {-# INLINE enumFrom #-}
382 {-# INLINE enumFromThen #-}
383 {-# INLINE enumFromTo #-}
384 {-# INLINE enumFromThenTo #-}
385 enumFrom x = enumDeltaInteger x 1
386 enumFromThen x y = enumDeltaInteger x (y-x)
387 enumFromTo x lim = enumDeltaToInteger x 1 lim
388 enumFromThenTo x y lim = enumDeltaToInteger x (y-x) lim
391 "enumDeltaInteger" [~1] forall x y. enumDeltaInteger x y = build (\c _ -> enumDeltaIntegerFB c x y)
392 "efdtInteger" [~1] forall x y l.enumDeltaToInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
393 "enumDeltaInteger" [1] enumDeltaIntegerFB (:) = enumDeltaInteger
394 "enumDeltaToInteger" [1] enumDeltaToIntegerFB (:) [] = enumDeltaToInteger
397 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
398 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
400 enumDeltaInteger :: Integer -> Integer -> [Integer]
401 enumDeltaInteger x d = x : enumDeltaInteger (x+d) d
403 enumDeltaToIntegerFB c n x delta lim
404 | delta >= 0 = up_fb c n x delta lim
405 | otherwise = dn_fb c n x delta lim
407 enumDeltaToInteger x delta lim
408 | delta >= 0 = up_list x delta lim
409 | otherwise = dn_list x delta lim
411 up_fb c n x delta lim = go (x::Integer)
414 | otherwise = x `c` go (x+delta)
415 dn_fb c n x delta lim = go (x::Integer)
418 | otherwise = x `c` go (x+delta)
420 up_list x delta lim = go (x::Integer)
423 | otherwise = x : go (x+delta)
424 dn_list x delta lim = go (x::Integer)
427 | otherwise = x : go (x+delta)
432 %*********************************************************
434 \subsection{The @Integer@ instances for @Show@}
436 %*********************************************************
439 instance Show Integer where
441 | p > 6 && n < 0 = '(' : jtos n (')' : r)
442 -- Minor point: testing p first gives better code
443 -- in the not-uncommon case where the p argument
445 | otherwise = jtos n r
446 showList = showList__ (showsPrec 0)
448 jtos :: Integer -> String -> String
450 | n < 0 = '-' : jtos' (-n) cs
451 | otherwise = jtos' n cs
453 jtos' :: Integer -> String -> String
455 | n' < 10 = case unsafeChr (ord '0' + fromInteger n') of
457 | otherwise = case unsafeChr (ord '0' + fromInteger r) of
458 c@(C# _) -> jtos' q (c:cs')
460 (q,r) = n' `quotRemInteger` 10