1 \section[GHC.Base]{Module @GHC.Base@}
3 The overall structure of the GHC Prelude is a bit tricky.
5 a) We want to avoid "orphan modules", i.e. ones with instance
6 decls that don't belong either to a tycon or a class
7 defined in the same module
9 b) We want to avoid giant modules
11 So the rough structure is as follows, in (linearised) dependency order
14 GHC.Prim Has no implementation. It defines built-in things, and
15 by importing it you bring them into scope.
16 The source file is GHC.Prim.hi-boot, which is just
17 copied to make GHC.Prim.hi
19 GHC.Base Classes: Eq, Ord, Functor, Monad
20 Types: list, (), Int, Bool, Ordering, Char, String
22 Data.Tuple Types: tuples, plus instances for GHC.Base classes
24 GHC.Show Class: Show, plus instances for GHC.Base/GHC.Tup types
26 GHC.Enum Class: Enum, plus instances for GHC.Base/GHC.Tup types
28 Data.Maybe Type: Maybe, plus instances for GHC.Base classes
30 GHC.List List functions
32 GHC.Num Class: Num, plus instances for Int
33 Type: Integer, plus instances for all classes so far (Eq, Ord, Num, Show)
35 Integer is needed here because it is mentioned in the signature
36 of 'fromInteger' in class Num
38 GHC.Real Classes: Real, Integral, Fractional, RealFrac
39 plus instances for Int, Integer
40 Types: Ratio, Rational
41 plus intances for classes so far
43 Rational is needed here because it is mentioned in the signature
44 of 'toRational' in class Real
46 GHC.ST The ST monad, instances and a few helper functions
48 Ix Classes: Ix, plus instances for Int, Bool, Char, Integer, Ordering, tuples
50 GHC.Arr Types: Array, MutableArray, MutableVar
52 Arrays are used by a function in GHC.Float
54 GHC.Float Classes: Floating, RealFloat
55 Types: Float, Double, plus instances of all classes so far
57 This module contains everything to do with floating point.
58 It is a big module (900 lines)
59 With a bit of luck, many modules can be compiled without ever reading GHC.Float.hi
62 Other Prelude modules are much easier with fewer complex dependencies.
65 {-# OPTIONS_GHC -XNoImplicitPrelude #-}
66 {-# OPTIONS_HADDOCK hide #-}
67 -----------------------------------------------------------------------------
70 -- Copyright : (c) The University of Glasgow, 1992-2002
71 -- License : see libraries/base/LICENSE
73 -- Maintainer : cvs-ghc@haskell.org
74 -- Stability : internal
75 -- Portability : non-portable (GHC extensions)
77 -- Basic data types and classes.
79 -----------------------------------------------------------------------------
91 module GHC.Prim, -- Re-export GHC.Prim and GHC.Err, to avoid lots
92 module GHC.Err -- of people having to import it explicitly
101 import {-# SOURCE #-} GHC.Err
105 infix 4 ==, /=, <, <=, >=, >
111 default () -- Double isn't available yet
115 %*********************************************************
117 \subsection{DEBUGGING STUFF}
118 %* (for use when compiling GHC.Base itself doesn't work)
120 %*********************************************************
124 data Bool = False | True
125 data Ordering = LT | EQ | GT
133 (&&) True True = True
139 unpackCString# :: Addr# -> [Char]
140 unpackFoldrCString# :: Addr# -> (Char -> a -> a) -> a -> a
141 unpackAppendCString# :: Addr# -> [Char] -> [Char]
142 unpackCStringUtf8# :: Addr# -> [Char]
143 unpackCString# a = error "urk"
144 unpackFoldrCString# a = error "urk"
145 unpackAppendCString# a = error "urk"
146 unpackCStringUtf8# a = error "urk"
151 %*********************************************************
153 \subsection{Standard classes @Eq@, @Ord@}
155 %*********************************************************
159 -- | The 'Eq' class defines equality ('==') and inequality ('/=').
160 -- All the basic datatypes exported by the "Prelude" are instances of 'Eq',
161 -- and 'Eq' may be derived for any datatype whose constituents are also
162 -- instances of 'Eq'.
164 -- Minimal complete definition: either '==' or '/='.
167 (==), (/=) :: a -> a -> Bool
169 x /= y = not (x == y)
170 x == y = not (x /= y)
172 -- | The 'Ord' class is used for totally ordered datatypes.
174 -- Instances of 'Ord' can be derived for any user-defined
175 -- datatype whose constituent types are in 'Ord'. The declared order
176 -- of the constructors in the data declaration determines the ordering
177 -- in derived 'Ord' instances. The 'Ordering' datatype allows a single
178 -- comparison to determine the precise ordering of two objects.
180 -- Minimal complete definition: either 'compare' or '<='.
181 -- Using 'compare' can be more efficient for complex types.
183 class (Eq a) => Ord a where
184 compare :: a -> a -> Ordering
185 (<), (<=), (>), (>=) :: a -> a -> Bool
186 max, min :: a -> a -> a
190 | x <= y = LT -- NB: must be '<=' not '<' to validate the
191 -- above claim about the minimal things that
192 -- can be defined for an instance of Ord
195 x < y = case compare x y of { LT -> True; _other -> False }
196 x <= y = case compare x y of { GT -> False; _other -> True }
197 x > y = case compare x y of { GT -> True; _other -> False }
198 x >= y = case compare x y of { LT -> False; _other -> True }
200 -- These two default methods use '<=' rather than 'compare'
201 -- because the latter is often more expensive
202 max x y = if x <= y then y else x
203 min x y = if x <= y then x else y
206 %*********************************************************
208 \subsection{Monadic classes @Functor@, @Monad@ }
210 %*********************************************************
213 {- | The 'Functor' class is used for types that can be mapped over.
214 Instances of 'Functor' should satisfy the following laws:
217 > fmap (f . g) == fmap f . fmap g
219 The instances of 'Functor' for lists, 'Data.Maybe.Maybe' and 'System.IO.IO'
220 defined in the "Prelude" satisfy these laws.
223 class Functor f where
224 fmap :: (a -> b) -> f a -> f b
226 {- | The 'Monad' class defines the basic operations over a /monad/,
227 a concept from a branch of mathematics known as /category theory/.
228 From the perspective of a Haskell programmer, however, it is best to
229 think of a monad as an /abstract datatype/ of actions.
230 Haskell's @do@ expressions provide a convenient syntax for writing
233 Minimal complete definition: '>>=' and 'return'.
235 Instances of 'Monad' should satisfy the following laws:
237 > return a >>= k == k a
239 > m >>= (\x -> k x >>= h) == (m >>= k) >>= h
241 Instances of both 'Monad' and 'Functor' should additionally satisfy the law:
243 > fmap f xs == xs >>= return . f
245 The instances of 'Monad' for lists, 'Data.Maybe.Maybe' and 'System.IO.IO'
246 defined in the "Prelude" satisfy these laws.
250 -- | Sequentially compose two actions, passing any value produced
251 -- by the first as an argument to the second.
252 (>>=) :: forall a b. m a -> (a -> m b) -> m b
253 -- | Sequentially compose two actions, discarding any value produced
254 -- by the first, like sequencing operators (such as the semicolon)
255 -- in imperative languages.
256 (>>) :: forall a b. m a -> m b -> m b
257 -- Explicit for-alls so that we know what order to
258 -- give type arguments when desugaring
260 -- | Inject a value into the monadic type.
262 -- | Fail with a message. This operation is not part of the
263 -- mathematical definition of a monad, but is invoked on pattern-match
264 -- failure in a @do@ expression.
265 fail :: String -> m a
267 m >> k = m >>= \_ -> k
272 %*********************************************************
274 \subsection{The list type}
276 %*********************************************************
279 -- do explicitly: deriving (Eq, Ord)
280 -- to avoid weird names like con2tag_[]#
282 instance (Eq a) => Eq [a] where
283 {-# SPECIALISE instance Eq [Char] #-}
285 (x:xs) == (y:ys) = x == y && xs == ys
288 instance (Ord a) => Ord [a] where
289 {-# SPECIALISE instance Ord [Char] #-}
291 compare [] (_:_) = LT
292 compare (_:_) [] = GT
293 compare (x:xs) (y:ys) = case compare x y of
297 instance Functor [] where
300 instance Monad [] where
301 m >>= k = foldr ((++) . k) [] m
302 m >> k = foldr ((++) . (\ _ -> k)) [] m
307 A few list functions that appear here because they are used here.
308 The rest of the prelude list functions are in GHC.List.
310 ----------------------------------------------
311 -- foldr/build/augment
312 ----------------------------------------------
315 -- | 'foldr', applied to a binary operator, a starting value (typically
316 -- the right-identity of the operator), and a list, reduces the list
317 -- using the binary operator, from right to left:
319 -- > foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
321 foldr :: (a -> b -> b) -> b -> [a] -> b
323 -- foldr f z (x:xs) = f x (foldr f z xs)
324 {-# INLINE [0] foldr #-}
325 -- Inline only in the final stage, after the foldr/cons rule has had a chance
329 go (y:ys) = y `k` go ys
331 -- | A list producer that can be fused with 'foldr'.
332 -- This function is merely
334 -- > build g = g (:) []
336 -- but GHC's simplifier will transform an expression of the form
337 -- @'foldr' k z ('build' g)@, which may arise after inlining, to @g k z@,
338 -- which avoids producing an intermediate list.
340 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
341 {-# INLINE [1] build #-}
342 -- The INLINE is important, even though build is tiny,
343 -- because it prevents [] getting inlined in the version that
344 -- appears in the interface file. If [] *is* inlined, it
345 -- won't match with [] appearing in rules in an importing module.
347 -- The "1" says to inline in phase 1
351 -- | A list producer that can be fused with 'foldr'.
352 -- This function is merely
354 -- > augment g xs = g (:) xs
356 -- but GHC's simplifier will transform an expression of the form
357 -- @'foldr' k z ('augment' g xs)@, which may arise after inlining, to
358 -- @g k ('foldr' k z xs)@, which avoids producing an intermediate list.
360 augment :: forall a. (forall b. (a->b->b) -> b -> b) -> [a] -> [a]
361 {-# INLINE [1] augment #-}
362 augment g xs = g (:) xs
365 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
366 foldr k z (build g) = g k z
368 "foldr/augment" forall k z xs (g::forall b. (a->b->b) -> b -> b) .
369 foldr k z (augment g xs) = g k (foldr k z xs)
371 "foldr/id" foldr (:) [] = \x -> x
372 "foldr/app" [1] forall ys. foldr (:) ys = \xs -> xs ++ ys
373 -- Only activate this from phase 1, because that's
374 -- when we disable the rule that expands (++) into foldr
376 -- The foldr/cons rule looks nice, but it can give disastrously
377 -- bloated code when commpiling
378 -- array (a,b) [(1,2), (2,2), (3,2), ...very long list... ]
379 -- i.e. when there are very very long literal lists
380 -- So I've disabled it for now. We could have special cases
381 -- for short lists, I suppose.
382 -- "foldr/cons" forall k z x xs. foldr k z (x:xs) = k x (foldr k z xs)
384 "foldr/single" forall k z x. foldr k z [x] = k x z
385 "foldr/nil" forall k z. foldr k z [] = z
387 "augment/build" forall (g::forall b. (a->b->b) -> b -> b)
388 (h::forall b. (a->b->b) -> b -> b) .
389 augment g (build h) = build (\c n -> g c (h c n))
390 "augment/nil" forall (g::forall b. (a->b->b) -> b -> b) .
391 augment g [] = build g
394 -- This rule is true, but not (I think) useful:
395 -- augment g (augment h t) = augment (\cn -> g c (h c n)) t
399 ----------------------------------------------
401 ----------------------------------------------
404 -- | 'map' @f xs@ is the list obtained by applying @f@ to each element
407 -- > map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
408 -- > map f [x1, x2, ...] == [f x1, f x2, ...]
410 map :: (a -> b) -> [a] -> [b]
412 map f (x:xs) = f x : map f xs
415 mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst
416 {-# INLINE [0] mapFB #-}
417 mapFB c f x ys = c (f x) ys
419 -- The rules for map work like this.
421 -- Up to (but not including) phase 1, we use the "map" rule to
422 -- rewrite all saturated applications of map with its build/fold
423 -- form, hoping for fusion to happen.
424 -- In phase 1 and 0, we switch off that rule, inline build, and
425 -- switch on the "mapList" rule, which rewrites the foldr/mapFB
426 -- thing back into plain map.
428 -- It's important that these two rules aren't both active at once
429 -- (along with build's unfolding) else we'd get an infinite loop
430 -- in the rules. Hence the activation control below.
432 -- The "mapFB" rule optimises compositions of map.
434 -- This same pattern is followed by many other functions:
435 -- e.g. append, filter, iterate, repeat, etc.
438 "map" [~1] forall f xs. map f xs = build (\c n -> foldr (mapFB c f) n xs)
439 "mapList" [1] forall f. foldr (mapFB (:) f) [] = map f
440 "mapFB" forall c f g. mapFB (mapFB c f) g = mapFB c (f.g)
445 ----------------------------------------------
447 ----------------------------------------------
449 -- | Append two lists, i.e.,
451 -- > [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
452 -- > [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
454 -- If the first list is not finite, the result is the first list.
456 (++) :: [a] -> [a] -> [a]
458 (++) (x:xs) ys = x : xs ++ ys
461 "++" [~1] forall xs ys. xs ++ ys = augment (\c n -> foldr c n xs) ys
467 %*********************************************************
469 \subsection{Type @Bool@}
471 %*********************************************************
474 -- |The 'Bool' type is an enumeration. It is defined with 'False'
475 -- first so that the corresponding 'Prelude.Enum' instance will give
476 -- 'Prelude.fromEnum' 'False' the value zero, and
477 -- 'Prelude.fromEnum' 'True' the value 1.
478 -- The actual definition is in the ghc-prim package.
480 -- XXX These don't work:
481 -- deriving instance Eq Bool
482 -- deriving instance Ord Bool
483 -- <wired into compiler>:
484 -- Illegal binding of built-in syntax: con2tag_Bool#
486 instance Eq Bool where
488 False == False = True
491 instance Ord Bool where
492 compare False True = LT
493 compare True False = GT
496 -- Read is in GHC.Read, Show in GHC.Show
501 (&&) :: Bool -> Bool -> Bool
506 (||) :: Bool -> Bool -> Bool
515 -- |'otherwise' is defined as the value 'True'. It helps to make
516 -- guards more readable. eg.
518 -- > f x | x < 0 = ...
519 -- > | otherwise = ...
524 %*********************************************************
526 \subsection{Type @Ordering@}
528 %*********************************************************
531 -- | Represents an ordering relationship between two values: less
532 -- than, equal to, or greater than. An 'Ordering' is returned by
534 -- XXX These don't work:
535 -- deriving instance Eq Ordering
536 -- deriving instance Ord Ordering
537 -- Illegal binding of built-in syntax: con2tag_Ordering#
538 instance Eq Ordering where
543 -- Read in GHC.Read, Show in GHC.Show
545 instance Ord Ordering where
554 %*********************************************************
556 \subsection{Type @Char@ and @String@}
558 %*********************************************************
561 -- | A 'String' is a list of characters. String constants in Haskell are values
566 {-| The character type 'Char' is an enumeration whose values represent
567 Unicode (or equivalently ISO\/IEC 10646) characters
568 (see <http://www.unicode.org/> for details).
569 This set extends the ISO 8859-1 (Latin-1) character set
570 (the first 256 charachers), which is itself an extension of the ASCII
571 character set (the first 128 characters).
572 A character literal in Haskell has type 'Char'.
574 To convert a 'Char' to or from the corresponding 'Int' value defined
575 by Unicode, use 'Prelude.toEnum' and 'Prelude.fromEnum' from the
576 'Prelude.Enum' class respectively (or equivalently 'ord' and 'chr').
579 -- We don't use deriving for Eq and Ord, because for Ord the derived
580 -- instance defines only compare, which takes two primops. Then
581 -- '>' uses compare, and therefore takes two primops instead of one.
583 instance Eq Char where
584 (C# c1) == (C# c2) = c1 `eqChar#` c2
585 (C# c1) /= (C# c2) = c1 `neChar#` c2
587 instance Ord Char where
588 (C# c1) > (C# c2) = c1 `gtChar#` c2
589 (C# c1) >= (C# c2) = c1 `geChar#` c2
590 (C# c1) <= (C# c2) = c1 `leChar#` c2
591 (C# c1) < (C# c2) = c1 `ltChar#` c2
594 "x# `eqChar#` x#" forall x#. x# `eqChar#` x# = True
595 "x# `neChar#` x#" forall x#. x# `neChar#` x# = False
596 "x# `gtChar#` x#" forall x#. x# `gtChar#` x# = False
597 "x# `geChar#` x#" forall x#. x# `geChar#` x# = True
598 "x# `leChar#` x#" forall x#. x# `leChar#` x# = True
599 "x# `ltChar#` x#" forall x#. x# `ltChar#` x# = False
602 -- | The 'Prelude.toEnum' method restricted to the type 'Data.Char.Char'.
604 chr (I# i#) | int2Word# i# `leWord#` int2Word# 0x10FFFF# = C# (chr# i#)
605 | otherwise = error "Prelude.chr: bad argument"
607 unsafeChr :: Int -> Char
608 unsafeChr (I# i#) = C# (chr# i#)
610 -- | The 'Prelude.fromEnum' method restricted to the type 'Data.Char.Char'.
612 ord (C# c#) = I# (ord# c#)
615 String equality is used when desugaring pattern-matches against strings.
618 eqString :: String -> String -> Bool
619 eqString [] [] = True
620 eqString (c1:cs1) (c2:cs2) = c1 == c2 && cs1 `eqString` cs2
623 {-# RULES "eqString" (==) = eqString #-}
624 -- eqString also has a BuiltInRule in PrelRules.lhs:
625 -- eqString (unpackCString# (Lit s1)) (unpackCString# (Lit s2) = s1==s2
629 %*********************************************************
631 \subsection{Type @Int@}
633 %*********************************************************
636 zeroInt, oneInt, twoInt, maxInt, minInt :: Int
641 {- Seems clumsy. Should perhaps put minInt and MaxInt directly into MachDeps.h -}
642 #if WORD_SIZE_IN_BITS == 31
643 minInt = I# (-0x40000000#)
644 maxInt = I# 0x3FFFFFFF#
645 #elif WORD_SIZE_IN_BITS == 32
646 minInt = I# (-0x80000000#)
647 maxInt = I# 0x7FFFFFFF#
649 minInt = I# (-0x8000000000000000#)
650 maxInt = I# 0x7FFFFFFFFFFFFFFF#
653 instance Eq Int where
657 instance Ord Int where
664 compareInt :: Int -> Int -> Ordering
665 (I# x#) `compareInt` (I# y#) = compareInt# x# y#
667 compareInt# :: Int# -> Int# -> Ordering
675 %*********************************************************
677 \subsection{The function type}
679 %*********************************************************
682 -- | Identity function.
686 -- | The call '(lazy e)' means the same as 'e', but 'lazy' has a
687 -- magical strictness property: it is lazy in its first argument,
688 -- even though its semantics is strict.
691 -- Implementation note: its strictness and unfolding are over-ridden
692 -- by the definition in MkId.lhs; in both cases to nothing at all.
693 -- That way, 'lazy' does not get inlined, and the strictness analyser
694 -- sees it as lazy. Then the worker/wrapper phase inlines it.
698 -- | The call '(inline f)' reduces to 'f', but 'inline' has a BuiltInRule
699 -- that tries to inline 'f' (if it has an unfolding) unconditionally
700 -- The 'NOINLINE' pragma arranges that inline only gets inlined (and
701 -- hence eliminated) late in compilation, after the rule has had
702 -- a god chance to fire.
704 {-# NOINLINE[0] inline #-}
707 -- Assertion function. This simply ignores its boolean argument.
708 -- The compiler may rewrite it to @('assertError' line)@.
710 -- | If the first argument evaluates to 'True', then the result is the
711 -- second argument. Otherwise an 'AssertionFailed' exception is raised,
712 -- containing a 'String' with the source file and line number of the
715 -- Assertions can normally be turned on or off with a compiler flag
716 -- (for GHC, assertions are normally on unless optimisation is turned on
717 -- with @-O@ or the @-fignore-asserts@
718 -- option is given). When assertions are turned off, the first
719 -- argument to 'assert' is ignored, and the second argument is
720 -- returned as the result.
722 -- SLPJ: in 5.04 etc 'assert' is in GHC.Prim,
723 -- but from Template Haskell onwards it's simply
724 -- defined here in Base.lhs
725 assert :: Bool -> a -> a
731 breakpointCond :: Bool -> a -> a
732 breakpointCond _ r = r
734 data Opaque = forall a. O a
736 -- | Constant function.
740 -- | Function composition.
742 (.) :: (b -> c) -> (a -> b) -> a -> c
745 -- | @'flip' f@ takes its (first) two arguments in the reverse order of @f@.
746 flip :: (a -> b -> c) -> b -> a -> c
749 -- | Application operator. This operator is redundant, since ordinary
750 -- application @(f x)@ means the same as @(f '$' x)@. However, '$' has
751 -- low, right-associative binding precedence, so it sometimes allows
752 -- parentheses to be omitted; for example:
754 -- > f $ g $ h x = f (g (h x))
756 -- It is also useful in higher-order situations, such as @'map' ('$' 0) xs@,
757 -- or @'Data.List.zipWith' ('$') fs xs@.
759 ($) :: (a -> b) -> a -> b
762 -- | @'until' p f@ yields the result of applying @f@ until @p@ holds.
763 until :: (a -> Bool) -> (a -> a) -> a -> a
764 until p f x | p x = x
765 | otherwise = until p f (f x)
767 -- | 'asTypeOf' is a type-restricted version of 'const'. It is usually
768 -- used as an infix operator, and its typing forces its first argument
769 -- (which is usually overloaded) to have the same type as the second.
770 asTypeOf :: a -> a -> a
774 %*********************************************************
776 \subsection{@getTag@}
778 %*********************************************************
780 Returns the 'tag' of a constructor application; this function is used
781 by the deriving code for Eq, Ord and Enum.
783 The primitive dataToTag# requires an evaluated constructor application
784 as its argument, so we provide getTag as a wrapper that performs the
785 evaluation before calling dataToTag#. We could have dataToTag#
786 evaluate its argument, but we prefer to do it this way because (a)
787 dataToTag# can be an inline primop if it doesn't need to do any
788 evaluation, and (b) we want to expose the evaluation to the
789 simplifier, because it might be possible to eliminate the evaluation
790 in the case when the argument is already known to be evaluated.
793 {-# INLINE getTag #-}
795 getTag x = x `seq` dataToTag# x
798 %*********************************************************
800 \subsection{Numeric primops}
802 %*********************************************************
805 divInt# :: Int# -> Int# -> Int#
807 -- Be careful NOT to overflow if we do any additional arithmetic
808 -- on the arguments... the following previous version of this
809 -- code has problems with overflow:
810 -- | (x# ># 0#) && (y# <# 0#) = ((x# -# y#) -# 1#) `quotInt#` y#
811 -- | (x# <# 0#) && (y# ># 0#) = ((x# -# y#) +# 1#) `quotInt#` y#
812 | (x# ># 0#) && (y# <# 0#) = ((x# -# 1#) `quotInt#` y#) -# 1#
813 | (x# <# 0#) && (y# ># 0#) = ((x# +# 1#) `quotInt#` y#) -# 1#
814 | otherwise = x# `quotInt#` y#
816 modInt# :: Int# -> Int# -> Int#
818 | (x# ># 0#) && (y# <# 0#) ||
819 (x# <# 0#) && (y# ># 0#) = if r# /=# 0# then r# +# y# else 0#
825 Definitions of the boxed PrimOps; these will be
826 used in the case of partial applications, etc.
835 {-# INLINE plusInt #-}
836 {-# INLINE minusInt #-}
837 {-# INLINE timesInt #-}
838 {-# INLINE quotInt #-}
839 {-# INLINE remInt #-}
840 {-# INLINE negateInt #-}
842 plusInt, minusInt, timesInt, quotInt, remInt, divInt, modInt, gcdInt :: Int -> Int -> Int
843 (I# x) `plusInt` (I# y) = I# (x +# y)
844 (I# x) `minusInt` (I# y) = I# (x -# y)
845 (I# x) `timesInt` (I# y) = I# (x *# y)
846 (I# x) `quotInt` (I# y) = I# (x `quotInt#` y)
847 (I# x) `remInt` (I# y) = I# (x `remInt#` y)
848 (I# x) `divInt` (I# y) = I# (x `divInt#` y)
849 (I# x) `modInt` (I# y) = I# (x `modInt#` y)
852 "x# +# 0#" forall x#. x# +# 0# = x#
853 "0# +# x#" forall x#. 0# +# x# = x#
854 "x# -# 0#" forall x#. x# -# 0# = x#
855 "x# -# x#" forall x#. x# -# x# = 0#
856 "x# *# 0#" forall x#. x# *# 0# = 0#
857 "0# *# x#" forall x#. 0# *# x# = 0#
858 "x# *# 1#" forall x#. x# *# 1# = x#
859 "1# *# x#" forall x#. 1# *# x# = x#
862 gcdInt (I# a) (I# b) = g a b
863 where g 0# 0# = error "GHC.Base.gcdInt: gcd 0 0 is undefined"
866 g _ _ = I# (gcdInt# absA absB)
868 absInt x = if x <# 0# then negateInt# x else x
873 negateInt :: Int -> Int
874 negateInt (I# x) = I# (negateInt# x)
876 gtInt, geInt, eqInt, neInt, ltInt, leInt :: Int -> Int -> Bool
877 (I# x) `gtInt` (I# y) = x ># y
878 (I# x) `geInt` (I# y) = x >=# y
879 (I# x) `eqInt` (I# y) = x ==# y
880 (I# x) `neInt` (I# y) = x /=# y
881 (I# x) `ltInt` (I# y) = x <# y
882 (I# x) `leInt` (I# y) = x <=# y
885 "x# ># x#" forall x#. x# ># x# = False
886 "x# >=# x#" forall x#. x# >=# x# = True
887 "x# ==# x#" forall x#. x# ==# x# = True
888 "x# /=# x#" forall x#. x# /=# x# = False
889 "x# <# x#" forall x#. x# <# x# = False
890 "x# <=# x#" forall x#. x# <=# x# = True
894 "plusFloat x 0.0" forall x#. plusFloat# x# 0.0# = x#
895 "plusFloat 0.0 x" forall x#. plusFloat# 0.0# x# = x#
896 "minusFloat x 0.0" forall x#. minusFloat# x# 0.0# = x#
897 "minusFloat x x" forall x#. minusFloat# x# x# = 0.0#
898 "timesFloat x 0.0" forall x#. timesFloat# x# 0.0# = 0.0#
899 "timesFloat0.0 x" forall x#. timesFloat# 0.0# x# = 0.0#
900 "timesFloat x 1.0" forall x#. timesFloat# x# 1.0# = x#
901 "timesFloat 1.0 x" forall x#. timesFloat# 1.0# x# = x#
902 "divideFloat x 1.0" forall x#. divideFloat# x# 1.0# = x#
906 "plusDouble x 0.0" forall x#. (+##) x# 0.0## = x#
907 "plusDouble 0.0 x" forall x#. (+##) 0.0## x# = x#
908 "minusDouble x 0.0" forall x#. (-##) x# 0.0## = x#
909 "timesDouble x 1.0" forall x#. (*##) x# 1.0## = x#
910 "timesDouble 1.0 x" forall x#. (*##) 1.0## x# = x#
911 "divideDouble x 1.0" forall x#. (/##) x# 1.0## = x#
915 We'd like to have more rules, but for example:
917 This gives wrong answer (0) for NaN - NaN (should be NaN):
918 "minusDouble x x" forall x#. (-##) x# x# = 0.0##
920 This gives wrong answer (0) for 0 * NaN (should be NaN):
921 "timesDouble 0.0 x" forall x#. (*##) 0.0## x# = 0.0##
923 This gives wrong answer (0) for NaN * 0 (should be NaN):
924 "timesDouble x 0.0" forall x#. (*##) x# 0.0## = 0.0##
926 These are tested by num014.
929 -- Wrappers for the shift operations. The uncheckedShift# family are
930 -- undefined when the amount being shifted by is greater than the size
931 -- in bits of Int#, so these wrappers perform a check and return
932 -- either zero or -1 appropriately.
934 -- Note that these wrappers still produce undefined results when the
935 -- second argument (the shift amount) is negative.
937 -- | Shift the argument left by the specified number of bits
938 -- (which must be non-negative).
939 shiftL# :: Word# -> Int# -> Word#
940 a `shiftL#` b | b >=# WORD_SIZE_IN_BITS# = int2Word# 0#
941 | otherwise = a `uncheckedShiftL#` b
943 -- | Shift the argument right by the specified number of bits
944 -- (which must be non-negative).
945 shiftRL# :: Word# -> Int# -> Word#
946 a `shiftRL#` b | b >=# WORD_SIZE_IN_BITS# = int2Word# 0#
947 | otherwise = a `uncheckedShiftRL#` b
949 -- | Shift the argument left by the specified number of bits
950 -- (which must be non-negative).
951 iShiftL# :: Int# -> Int# -> Int#
952 a `iShiftL#` b | b >=# WORD_SIZE_IN_BITS# = 0#
953 | otherwise = a `uncheckedIShiftL#` b
955 -- | Shift the argument right (signed) by the specified number of bits
956 -- (which must be non-negative).
957 iShiftRA# :: Int# -> Int# -> Int#
958 a `iShiftRA#` b | b >=# WORD_SIZE_IN_BITS# = if a <# 0# then (-1#) else 0#
959 | otherwise = a `uncheckedIShiftRA#` b
961 -- | Shift the argument right (unsigned) by the specified number of bits
962 -- (which must be non-negative).
963 iShiftRL# :: Int# -> Int# -> Int#
964 a `iShiftRL#` b | b >=# WORD_SIZE_IN_BITS# = 0#
965 | otherwise = a `uncheckedIShiftRL#` b
967 #if WORD_SIZE_IN_BITS == 32
969 "narrow32Int#" forall x#. narrow32Int# x# = x#
970 "narrow32Word#" forall x#. narrow32Word# x# = x#
975 "int2Word2Int" forall x#. int2Word# (word2Int# x#) = x#
976 "word2Int2Word" forall x#. word2Int# (int2Word# x#) = x#
981 %********************************************************
983 \subsection{Unpacking C strings}
985 %********************************************************
987 This code is needed for virtually all programs, since it's used for
988 unpacking the strings of error messages.
991 unpackCString# :: Addr# -> [Char]
992 {-# NOINLINE [1] unpackCString# #-}
997 | ch `eqChar#` '\0'# = []
998 | otherwise = C# ch : unpack (nh +# 1#)
1000 ch = indexCharOffAddr# addr nh
1002 unpackAppendCString# :: Addr# -> [Char] -> [Char]
1003 unpackAppendCString# addr rest
1007 | ch `eqChar#` '\0'# = rest
1008 | otherwise = C# ch : unpack (nh +# 1#)
1010 ch = indexCharOffAddr# addr nh
1012 unpackFoldrCString# :: Addr# -> (Char -> a -> a) -> a -> a
1013 {-# NOINLINE [0] unpackFoldrCString# #-}
1014 -- Don't inline till right at the end;
1015 -- usually the unpack-list rule turns it into unpackCStringList
1016 -- It also has a BuiltInRule in PrelRules.lhs:
1017 -- unpackFoldrCString# "foo" c (unpackFoldrCString# "baz" c n)
1018 -- = unpackFoldrCString# "foobaz" c n
1019 unpackFoldrCString# addr f z
1023 | ch `eqChar#` '\0'# = z
1024 | otherwise = C# ch `f` unpack (nh +# 1#)
1026 ch = indexCharOffAddr# addr nh
1028 unpackCStringUtf8# :: Addr# -> [Char]
1029 unpackCStringUtf8# addr
1033 | ch `eqChar#` '\0'# = []
1034 | ch `leChar#` '\x7F'# = C# ch : unpack (nh +# 1#)
1035 | ch `leChar#` '\xDF'# =
1036 C# (chr# (((ord# ch -# 0xC0#) `uncheckedIShiftL#` 6#) +#
1037 (ord# (indexCharOffAddr# addr (nh +# 1#)) -# 0x80#))) :
1039 | ch `leChar#` '\xEF'# =
1040 C# (chr# (((ord# ch -# 0xE0#) `uncheckedIShiftL#` 12#) +#
1041 ((ord# (indexCharOffAddr# addr (nh +# 1#)) -# 0x80#) `uncheckedIShiftL#` 6#) +#
1042 (ord# (indexCharOffAddr# addr (nh +# 2#)) -# 0x80#))) :
1045 C# (chr# (((ord# ch -# 0xF0#) `uncheckedIShiftL#` 18#) +#
1046 ((ord# (indexCharOffAddr# addr (nh +# 1#)) -# 0x80#) `uncheckedIShiftL#` 12#) +#
1047 ((ord# (indexCharOffAddr# addr (nh +# 2#)) -# 0x80#) `uncheckedIShiftL#` 6#) +#
1048 (ord# (indexCharOffAddr# addr (nh +# 3#)) -# 0x80#))) :
1051 ch = indexCharOffAddr# addr nh
1053 unpackNBytes# :: Addr# -> Int# -> [Char]
1054 unpackNBytes# _addr 0# = []
1055 unpackNBytes# addr len# = unpack [] (len# -# 1#)
1060 case indexCharOffAddr# addr i# of
1061 ch -> unpack (C# ch : acc) (i# -# 1#)
1064 "unpack" [~1] forall a . unpackCString# a = build (unpackFoldrCString# a)
1065 "unpack-list" [1] forall a . unpackFoldrCString# a (:) [] = unpackCString# a
1066 "unpack-append" forall a n . unpackFoldrCString# a (:) n = unpackAppendCString# a n
1068 -- There's a built-in rule (in PrelRules.lhs) for
1069 -- unpackFoldr "foo" c (unpackFoldr "baz" c n) = unpackFoldr "foobaz" c n
1076 -- | A special argument for the 'Control.Monad.ST.ST' type constructor,
1077 -- indexing a state embedded in the 'Prelude.IO' monad by
1078 -- 'Control.Monad.ST.stToIO'.