2 {-# OPTIONS_GHC -fno-implicit-prelude #-}
3 -----------------------------------------------------------------------------
6 -- Copyright : (c) The University of Glasgow 1994-2002
7 -- License : see libraries/base/LICENSE
9 -- Maintainer : cvs-ghc@haskell.org
10 -- Stability : internal
11 -- Portability : non-portable (GHC Extensions)
13 -- The 'Num' class and the 'Integer' type.
15 -----------------------------------------------------------------------------
18 #if SIZEOF_HSWORD == 4
19 #define LEFTMOST_BIT 2147483648
20 #elif SIZEOF_HSWORD == 8
21 #define LEFTMOST_BIT 9223372036854775808
23 #error Please define LEFTMOST_BIT to be 2^(SIZEOF_HSWORD*8-1)
29 import {-# SOURCE #-} GHC.Err
37 default () -- Double isn't available yet,
38 -- and we shouldn't be using defaults anyway
41 %*********************************************************
43 \subsection{Standard numeric class}
45 %*********************************************************
48 -- | Basic numeric class.
50 -- Minimal complete definition: all except 'negate' or @(-)@
51 class (Eq a, Show a) => Num a where
52 (+), (-), (*) :: a -> a -> a
57 -- | Sign of a number.
58 -- The functions 'abs' and 'signum' should satisfy the law:
60 -- > abs x * signum x == x
62 -- For real numbers, the 'signum' is either @-1@ (negative), @0@ (zero)
65 -- | Conversion from an 'Integer'.
66 -- An integer literal represents the application of the function
67 -- 'fromInteger' to the appropriate value of type 'Integer',
68 -- so such literals have type @('Num' a) => a@.
69 fromInteger :: Integer -> a
74 -- | the same as @'flip' ('-')@.
76 -- Because @-@ is treated specially in the Haskell grammar,
77 -- @(-@ /e/@)@ is not a section, but an application of prefix negation.
78 -- However, @('subtract'@ /exp/@)@ is equivalent to the disallowed section.
79 {-# INLINE subtract #-}
80 subtract :: (Num a) => a -> a -> a
85 %*********************************************************
87 \subsection{Instances for @Int@}
89 %*********************************************************
92 instance Num Int where
97 abs n = if n `geInt` 0 then n else negateInt n
99 signum n | n `ltInt` 0 = negateInt 1
103 fromInteger = integer2Int
105 quotRemInt :: Int -> Int -> (Int, Int)
106 quotRemInt a@(I# _) b@(I# _) = (a `quotInt` b, a `remInt` b)
107 -- OK, so I made it a little stricter. Shoot me. (WDP 94/10)
109 divModInt :: Int -> Int -> (Int, Int)
110 divModInt x@(I# _) y@(I# _) = (x `divInt` y, x `modInt` y)
111 -- Stricter. Sorry if you don't like it. (WDP 94/10)
114 %*********************************************************
116 \subsection{The @Integer@ type}
118 %*********************************************************
121 -- | Arbitrary-precision integers.
123 = S# Int# -- small integers
125 | J# Int# ByteArray# -- large integers
127 | J# Void BigInteger -- .NET big ints
129 foreign type dotnet "BigInteger" BigInteger
133 Convenient boxed Integer PrimOps.
136 zeroInteger :: Integer
139 int2Integer :: Int -> Integer
140 {-# INLINE int2Integer #-}
141 int2Integer (I# i) = S# i
143 integer2Int :: Integer -> Int
144 integer2Int (S# i) = I# i
145 integer2Int (J# s d) = case (integer2Int# s d) of { n# -> I# n# }
147 toBig (S# i) = case int2Integer# i of { (# s, d #) -> J# s d }
152 %*********************************************************
154 \subsection{Dividing @Integers@}
156 %*********************************************************
159 quotRemInteger :: Integer -> Integer -> (Integer, Integer)
160 quotRemInteger a@(S# (-LEFTMOST_BIT#)) b = quotRemInteger (toBig a) b
161 quotRemInteger (S# i) (S# j)
162 = case quotRemInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j )
163 quotRemInteger i1@(J# _ _) i2@(S# _) = quotRemInteger i1 (toBig i2)
164 quotRemInteger i1@(S# _) i2@(J# _ _) = quotRemInteger (toBig i1) i2
165 quotRemInteger (J# s1 d1) (J# s2 d2)
166 = case (quotRemInteger# s1 d1 s2 d2) of
168 -> (J# s3 d3, J# s4 d4)
170 divModInteger a@(S# (-LEFTMOST_BIT#)) b = divModInteger (toBig a) b
171 divModInteger (S# i) (S# j)
172 = case divModInt (I# i) (I# j) of ( I# i, I# j ) -> ( S# i, S# j)
173 divModInteger i1@(J# _ _) i2@(S# _) = divModInteger i1 (toBig i2)
174 divModInteger i1@(S# _) i2@(J# _ _) = divModInteger (toBig i1) i2
175 divModInteger (J# s1 d1) (J# s2 d2)
176 = case (divModInteger# s1 d1 s2 d2) of
178 -> (J# s3 d3, J# s4 d4)
180 remInteger :: Integer -> Integer -> Integer
182 = error "Prelude.Integral.rem{Integer}: divide by 0"
183 remInteger a@(S# (-LEFTMOST_BIT#)) b = remInteger (toBig a) b
184 remInteger (S# a) (S# b) = S# (remInt# a b)
185 {- Special case doesn't work, because a 1-element J# has the range
186 -(2^32-1) -- 2^32-1, whereas S# has the range -2^31 -- (2^31-1)
187 remInteger ia@(S# a) (J# sb b)
188 | sb ==# 1# = S# (remInt# a (word2Int# (integer2Word# sb b)))
189 | sb ==# -1# = S# (remInt# a (0# -# (word2Int# (integer2Word# sb b))))
191 | otherwise = S# (0# -# a)
193 remInteger ia@(S# _) ib@(J# _ _) = remInteger (toBig ia) ib
194 remInteger (J# sa a) (S# b)
195 = case int2Integer# b of { (# sb, b #) ->
196 case remInteger# sa a sb b of { (# sr, r #) ->
197 S# (integer2Int# sr r) }}
198 remInteger (J# sa a) (J# sb b)
199 = case remInteger# sa a sb b of (# sr, r #) -> J# sr r
201 quotInteger :: Integer -> Integer -> Integer
203 = error "Prelude.Integral.quot{Integer}: divide by 0"
204 quotInteger a@(S# (-LEFTMOST_BIT#)) b = quotInteger (toBig a) b
205 quotInteger (S# a) (S# b) = S# (quotInt# a b)
206 {- Special case disabled, see remInteger above
207 quotInteger (S# a) (J# sb b)
208 | sb ==# 1# = S# (quotInt# a (word2Int# (integer2Word# sb b)))
209 | sb ==# -1# = S# (quotInt# a (0# -# (word2Int# (integer2Word# sb b))))
210 | otherwise = zeroInteger
212 quotInteger ia@(S# _) ib@(J# _ _) = quotInteger (toBig ia) ib
213 quotInteger (J# sa a) (S# b)
214 = case int2Integer# b of { (# sb, b #) ->
215 case quotInteger# sa a sb b of (# sq, q #) -> J# sq q }
216 quotInteger (J# sa a) (J# sb b)
217 = case quotInteger# sa a sb b of (# sg, g #) -> J# sg g
223 gcdInteger :: Integer -> Integer -> Integer
224 -- SUP: Do we really need the first two cases?
225 gcdInteger a@(S# (-LEFTMOST_BIT#)) b = gcdInteger (toBig a) b
226 gcdInteger a b@(S# (-LEFTMOST_BIT#)) = gcdInteger a (toBig b)
227 gcdInteger (S# a) (S# b) = case gcdInt (I# a) (I# b) of { I# c -> S# c }
228 gcdInteger ia@(S# 0#) ib@(J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
229 gcdInteger ia@(S# a) ib@(J# sb b)
232 | otherwise = S# (gcdIntegerInt# absSb b absA)
233 where absA = if a <# 0# then negateInt# a else a
234 absSb = if sb <# 0# then negateInt# sb else sb
235 gcdInteger ia@(J# _ _) ib@(S# _) = gcdInteger ib ia
236 gcdInteger (J# 0# _) (J# 0# _) = error "GHC.Num.gcdInteger: gcd 0 0 is undefined"
237 gcdInteger (J# sa a) (J# sb b)
238 = case gcdInteger# sa a sb b of (# sg, g #) -> J# sg g
240 lcmInteger :: Integer -> Integer -> Integer
246 = (divExact aa (gcdInteger aa ab)) * ab
250 divExact :: Integer -> Integer -> Integer
251 divExact a@(S# (-LEFTMOST_BIT#)) b = divExact (toBig a) b
252 divExact (S# a) (S# b) = S# (quotInt# a b)
253 divExact (S# a) (J# sb b)
254 = S# (quotInt# a (integer2Int# sb b))
255 divExact (J# sa a) (S# b)
256 = case int2Integer# b of
257 (# sb, b #) -> case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
258 divExact (J# sa a) (J# sb b)
259 = case divExactInteger# sa a sb b of (# sd, d #) -> J# sd d
263 %*********************************************************
265 \subsection{The @Integer@ instances for @Eq@, @Ord@}
267 %*********************************************************
270 instance Eq Integer where
271 (S# i) == (S# j) = i ==# j
272 (S# i) == (J# s d) = cmpIntegerInt# s d i ==# 0#
273 (J# s d) == (S# i) = 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 (S# i) /= (J# s d) = cmpIntegerInt# s d i /=# 0#
278 (J# s d) /= (S# i) = cmpIntegerInt# s d i /=# 0#
279 (J# s1 d1) /= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) /=# 0#
281 ------------------------------------------------------------------------
282 instance Ord Integer where
283 (S# i) <= (S# j) = i <=# j
284 (J# s d) <= (S# i) = cmpIntegerInt# s d i <=# 0#
285 (S# i) <= (J# s d) = cmpIntegerInt# s d i >=# 0#
286 (J# s1 d1) <= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <=# 0#
288 (S# i) > (S# j) = i ># j
289 (J# s d) > (S# i) = cmpIntegerInt# s d i ># 0#
290 (S# i) > (J# s d) = cmpIntegerInt# s d i <# 0#
291 (J# s1 d1) > (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) ># 0#
293 (S# i) < (S# j) = i <# j
294 (J# s d) < (S# i) = cmpIntegerInt# s d i <# 0#
295 (S# i) < (J# s d) = cmpIntegerInt# s d i ># 0#
296 (J# s1 d1) < (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) <# 0#
298 (S# i) >= (S# j) = i >=# j
299 (J# s d) >= (S# i) = cmpIntegerInt# s d i >=# 0#
300 (S# i) >= (J# s d) = cmpIntegerInt# s d i <=# 0#
301 (J# s1 d1) >= (J# s2 d2) = (cmpInteger# s1 d1 s2 d2) >=# 0#
303 compare (S# i) (S# j)
307 compare (J# s d) (S# i)
308 = case cmpIntegerInt# s d i of { res# ->
309 if res# <# 0# then LT else
310 if res# ># 0# then GT else EQ
312 compare (S# i) (J# s d)
313 = case cmpIntegerInt# s d i of { res# ->
314 if res# ># 0# then LT else
315 if res# <# 0# then GT else EQ
317 compare (J# s1 d1) (J# s2 d2)
318 = case cmpInteger# s1 d1 s2 d2 of { res# ->
319 if res# <# 0# then LT else
320 if res# ># 0# then GT else EQ
325 %*********************************************************
327 \subsection{The @Integer@ instances for @Num@}
329 %*********************************************************
332 instance Num Integer where
336 negate = negateInteger
339 -- ORIG: abs n = if n >= 0 then n else -n
340 abs (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
341 abs (S# i) = case abs (I# i) of I# j -> S# j
342 abs n@(J# s d) = if (s >=# 0#) then n else J# (negateInt# s) d
344 signum (S# i) = case signum (I# i) of I# j -> S# j
347 cmp = cmpIntegerInt# s d 0#
349 if cmp ># 0# then S# 1#
350 else if cmp ==# 0# then S# 0#
351 else S# (negateInt# 1#)
353 plusInteger i1@(S# i) i2@(S# j) = case addIntC# i j of { (# r, c #) ->
354 if c ==# 0# then S# r
355 else toBig i1 + toBig i2 }
356 plusInteger i1@(J# _ _) i2@(S# _) = i1 + toBig i2
357 plusInteger i1@(S# _) i2@(J# _ _) = toBig i1 + i2
358 plusInteger (J# s1 d1) (J# s2 d2) = case plusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
360 minusInteger i1@(S# i) i2@(S# j) = case subIntC# i j of { (# r, c #) ->
361 if c ==# 0# then S# r
362 else toBig i1 - toBig i2 }
363 minusInteger i1@(J# _ _) i2@(S# _) = i1 - toBig i2
364 minusInteger i1@(S# _) i2@(J# _ _) = toBig i1 - i2
365 minusInteger (J# s1 d1) (J# s2 d2) = case minusInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
367 timesInteger i1@(S# i) i2@(S# j) = if mulIntMayOflo# i j ==# 0#
369 else toBig i1 * toBig i2
370 timesInteger i1@(J# _ _) i2@(S# _) = i1 * toBig i2
371 timesInteger i1@(S# _) i2@(J# _ _) = toBig i1 * i2
372 timesInteger (J# s1 d1) (J# s2 d2) = case timesInteger# s1 d1 s2 d2 of (# s, d #) -> J# s d
374 negateInteger (S# (-LEFTMOST_BIT#)) = LEFTMOST_BIT
375 negateInteger (S# i) = S# (negateInt# i)
376 negateInteger (J# s d) = J# (negateInt# s) d
380 %*********************************************************
382 \subsection{The @Integer@ instance for @Enum@}
384 %*********************************************************
387 instance Enum Integer where
390 toEnum n = int2Integer n
391 fromEnum n = integer2Int n
393 {-# INLINE enumFrom #-}
394 {-# INLINE enumFromThen #-}
395 {-# INLINE enumFromTo #-}
396 {-# INLINE enumFromThenTo #-}
397 enumFrom x = enumDeltaInteger x 1
398 enumFromThen x y = enumDeltaInteger x (y-x)
399 enumFromTo x lim = enumDeltaToInteger x 1 lim
400 enumFromThenTo x y lim = enumDeltaToInteger x (y-x) lim
403 "enumDeltaInteger" [~1] forall x y. enumDeltaInteger x y = build (\c _ -> enumDeltaIntegerFB c x y)
404 "efdtInteger" [~1] forall x y l.enumDeltaToInteger x y l = build (\c n -> enumDeltaToIntegerFB c n x y l)
405 "enumDeltaInteger" [1] enumDeltaIntegerFB (:) = enumDeltaInteger
406 "enumDeltaToInteger" [1] enumDeltaToIntegerFB (:) [] = enumDeltaToInteger
409 enumDeltaIntegerFB :: (Integer -> b -> b) -> Integer -> Integer -> b
410 enumDeltaIntegerFB c x d = x `c` enumDeltaIntegerFB c (x+d) d
412 enumDeltaInteger :: Integer -> Integer -> [Integer]
413 enumDeltaInteger x d = x : enumDeltaInteger (x+d) d
415 enumDeltaToIntegerFB c n x delta lim
416 | delta >= 0 = up_fb c n x delta lim
417 | otherwise = dn_fb c n x delta lim
419 enumDeltaToInteger x delta lim
420 | delta >= 0 = up_list x delta lim
421 | otherwise = dn_list x delta lim
423 up_fb c n x delta lim = go (x::Integer)
426 | otherwise = x `c` go (x+delta)
427 dn_fb c n x delta lim = go (x::Integer)
430 | otherwise = x `c` go (x+delta)
432 up_list x delta lim = go (x::Integer)
435 | otherwise = x : go (x+delta)
436 dn_list x delta lim = go (x::Integer)
439 | otherwise = x : go (x+delta)
444 %*********************************************************
446 \subsection{The @Integer@ instances for @Show@}
448 %*********************************************************
451 instance Show Integer where
453 | p > 6 && n < 0 = '(' : jtos n (')' : r)
454 -- Minor point: testing p first gives better code
455 -- in the not-uncommon case where the p argument
457 | otherwise = jtos n r
458 showList = showList__ (showsPrec 0)
460 jtos :: Integer -> String -> String
462 | n < 0 = '-' : jtos' (-n) cs
463 | otherwise = jtos' n cs
465 jtos' :: Integer -> String -> String
467 | n' < 10 = case unsafeChr (ord '0' + fromInteger n') of
469 | otherwise = case unsafeChr (ord '0' + fromInteger r) of
470 c@(C# _) -> jtos' q (c:cs')
472 (q,r) = n' `quotRemInteger` 10