{-# LANGUAGE Trustworthy #-} {-# LANGUAGE NoImplicitPrelude, MagicHash, StandaloneDeriving, BangPatterns, KindSignatures, DataKinds, ConstraintKinds, MultiParamTypeClasses, FunctionalDependencies #-} {-# LANGUAGE UnboxedTuples #-} {-# LANGUAGE AllowAmbiguousTypes #-} -- ip :: IP x a => a is strictly speaking ambiguous, but IP is magic {-# LANGUAGE UndecidableSuperClasses #-} -- Because of the type-variable superclasses for tuples {-# OPTIONS_GHC -Wno-unused-imports #-} -- -Wno-unused-imports needed for the GHC.Tuple import below. Sigh. {-# OPTIONS_GHC -Wno-unused-top-binds #-} -- -Wno-unused-top-binds is there (I hope) to stop Haddock complaining -- about the constraint tuples being defined but not used {-# OPTIONS_HADDOCK not-home #-} ----------------------------------------------------------------------------- -- | -- Module : GHC.Classes -- Copyright : (c) The University of Glasgow, 1992-2002 -- License : see libraries/base/LICENSE -- -- Maintainer : cvs-ghc@haskell.org -- Stability : internal -- Portability : non-portable (GHC extensions) -- -- Basic classes. -- ----------------------------------------------------------------------------- module GHC.Classes( -- * Implicit paramaters IP(..), -- * Equality and ordering Eq(..), Ord(..), -- ** Monomorphic equality operators -- $matching_overloaded_methods_in_rules eqInt, neInt, eqWord, neWord, eqChar, neChar, eqFloat, eqDouble, -- ** Monomorphic comparison operators gtInt, geInt, leInt, ltInt, compareInt, compareInt#, gtWord, geWord, leWord, ltWord, compareWord, compareWord#, -- * Functions over Bool (&&), (||), not, -- * Integer arithmetic divInt#, divInt8#, divInt16#, divInt32#, modInt#, modInt8#, modInt16#, modInt32#, divModInt#, divModInt8#, divModInt16#, divModInt32# ) where -- GHC.Magic is used in some derived instances import GHC.Magic () import GHC.Prim import GHC.Tuple import GHC.CString (unpackCString#) import GHC.Types infix 4 ==, /=, <, <=, >=, > infixr 3 && infixr 2 || default () -- Double isn't available yet -- | The syntax @?x :: a@ is desugared into @IP "x" a@ -- IP is declared very early, so that libraries can take -- advantage of the implicit-call-stack feature class IP (x :: Symbol) a | x -> a where ip :: a {- $matching_overloaded_methods_in_rules Matching on class methods (e.g. @(==)@) in rewrite rules tends to be a bit fragile. For instance, consider this motivating example from the @bytestring@ library, @ break :: (Word8 -> Bool) -> ByteString -> (ByteString, ByteString) breakByte :: Word8 -> ByteString -> (ByteString, ByteString) \{\-\# RULES "break -> breakByte" forall a. break (== x) = breakByte x \#\-\} @ Here we have two functions, with @breakByte@ providing an optimized implementation of @break@ where the predicate is merely testing for equality with a known @Word8@. As written, however, this rule will be quite fragile as the @(==)@ class operation rule may rewrite the predicate before our @break@ rule has a chance to fire. For this reason, most of the primitive types in @base@ have 'Eq' and 'Ord' instances defined in terms of helper functions with inlinings delayed to phase 1. For instance, @Word8@\'s @Eq@ instance looks like, @ instance Eq Word8 where (==) = eqWord8 (/=) = neWord8 eqWord8, neWord8 :: Word8 -> Word8 -> Bool eqWord8 (W8# x) (W8# y) = ... neWord8 (W8# x) (W8# y) = ... \{\-\# INLINE [1] eqWord8 \#\-\} \{\-\# INLINE [1] neWord8 \#\-\} @ This allows us to save our @break@ rule above by rewriting it to instead match against @eqWord8@, @ \{\-\# RULES "break -> breakByte" forall a. break (`eqWord8` x) = breakByte x \#\-\} @ Currently this is only done for @('==')@, @('/=')@, @('<')@, @('<=')@, @('>')@, and @('>=')@ for the types in "GHC.Word" and "GHC.Int". -} -- | The 'Eq' class defines equality ('==') and inequality ('/='). -- All the basic datatypes exported by the "Prelude" are instances of 'Eq', -- and 'Eq' may be derived for any datatype whose constituents are also -- instances of 'Eq'. -- -- The Haskell Report defines no laws for 'Eq'. However, instances are -- encouraged to follow these properties: -- -- [__Reflexivity__]: @x == x@ = 'True' -- [__Symmetry__]: @x == y@ = @y == x@ -- [__Transitivity__]: if @x == y && y == z@ = 'True', then @x == z@ = 'True' -- [__Extensionality__]: if @x == y@ = 'True' and @f@ is a function -- whose return type is an instance of 'Eq', then @f x == f y@ = 'True' -- [__Negation__]: @x /= y@ = @not (x == y)@ -- -- Minimal complete definition: either '==' or '/='. -- class Eq a where (==), (/=) :: a -> a -> Bool {-# INLINE (/=) #-} {-# INLINE (==) #-} x /= y = not (x == y) x == y = not (x /= y) {-# MINIMAL (==) | (/=) #-} deriving instance Eq () deriving instance Eq a => Eq (Solo a) deriving instance (Eq a, Eq b) => Eq (a, b) deriving instance (Eq a, Eq b, Eq c) => Eq (a, b, c) deriving instance (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) deriving instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) instance (Eq a) => Eq [a] where {-# SPECIALISE instance Eq [[Char]] #-} {-# SPECIALISE instance Eq [Char] #-} {-# SPECIALISE instance Eq [Int] #-} [] == [] = True (x:xs) == (y:ys) = x == y && xs == ys _xs == _ys = False deriving instance Eq Module instance Eq TrName where TrNameS a == TrNameS b = isTrue# (a `eqAddr#` b) a == b = toString a == toString b where toString (TrNameS s) = unpackCString# s toString (TrNameD s) = s deriving instance Eq Bool deriving instance Eq Ordering instance Eq Word where (==) = eqWord (/=) = neWord -- See GHC.Classes#matching_overloaded_methods_in_rules {-# INLINE [1] eqWord #-} {-# INLINE [1] neWord #-} eqWord, neWord :: Word -> Word -> Bool (W# x) `eqWord` (W# y) = isTrue# (x `eqWord#` y) (W# x) `neWord` (W# y) = isTrue# (x `neWord#` y) -- See GHC.Classes#matching_overloaded_methods_in_rules instance Eq Char where (==) = eqChar (/=) = neChar -- See GHC.Classes#matching_overloaded_methods_in_rules {-# INLINE [1] eqChar #-} {-# INLINE [1] neChar #-} eqChar, neChar :: Char -> Char -> Bool (C# x) `eqChar` (C# y) = isTrue# (x `eqChar#` y) (C# x) `neChar` (C# y) = isTrue# (x `neChar#` y) -- | Note that due to the presence of @NaN@, `Float`'s 'Eq' instance does not -- satisfy reflexivity. -- -- >>> 0/0 == (0/0 :: Float) -- False -- -- Also note that `Float`'s 'Eq' instance does not satisfy extensionality: -- -- >>> 0 == (-0 :: Float) -- True -- >>> recip 0 == recip (-0 :: Float) -- False instance Eq Float where (==) = eqFloat -- See GHC.Classes#matching_overloaded_methods_in_rules {-# INLINE [1] eqFloat #-} eqFloat :: Float -> Float -> Bool (F# x) `eqFloat` (F# y) = isTrue# (x `eqFloat#` y) -- | Note that due to the presence of @NaN@, `Double`'s 'Eq' instance does not -- satisfy reflexivity. -- -- >>> 0/0 == (0/0 :: Double) -- False -- -- Also note that `Double`'s 'Eq' instance does not satisfy substitutivity: -- -- >>> 0 == (-0 :: Double) -- True -- >>> recip 0 == recip (-0 :: Double) -- False instance Eq Double where (==) = eqDouble -- See GHC.Classes#matching_overloaded_methods_in_rules {-# INLINE [1] eqDouble #-} eqDouble :: Double -> Double -> Bool (D# x) `eqDouble` (D# y) = isTrue# (x ==## y) instance Eq Int where (==) = eqInt (/=) = neInt -- See GHC.Classes#matching_overloaded_methods_in_rules {-# INLINE [1] eqInt #-} {-# INLINE [1] neInt #-} eqInt, neInt :: Int -> Int -> Bool (I# x) `eqInt` (I# y) = isTrue# (x ==# y) (I# x) `neInt` (I# y) = isTrue# (x /=# y) instance Eq TyCon where (==) (TyCon hi1 lo1 _ _ _ _) (TyCon hi2 lo2 _ _ _ _) = isTrue# (hi1 `eqWord64#` hi2) && isTrue# (lo1 `eqWord64#` lo2) instance Ord TyCon where compare (TyCon hi1 lo1 _ _ _ _) (TyCon hi2 lo2 _ _ _ _) | isTrue# (hi1 `gtWord64#` hi2) = GT | isTrue# (hi1 `ltWord64#` hi2) = LT | isTrue# (lo1 `gtWord64#` lo2) = GT | isTrue# (lo1 `ltWord64#` lo2) = LT | True = EQ -- | The 'Ord' class is used for totally ordered datatypes. -- -- Instances of 'Ord' can be derived for any user-defined datatype whose -- constituent types are in 'Ord'. The declared order of the constructors in -- the data declaration determines the ordering in derived 'Ord' instances. The -- 'Ordering' datatype allows a single comparison to determine the precise -- ordering of two objects. -- -- 'Ord', as defined by the Haskell report, implements a total order and has the -- following properties: -- -- [__Comparability__]: @x <= y || y <= x@ = 'True' -- [__Transitivity__]: if @x <= y && y <= z@ = 'True', then @x <= z@ = 'True' -- [__Reflexivity__]: @x <= x@ = 'True' -- [__Antisymmetry__]: if @x <= y && y <= x@ = 'True', then @x == y@ = 'True' -- -- The following operator interactions are expected to hold: -- -- 1. @x >= y@ = @y <= x@ -- 2. @x < y@ = @x <= y && x /= y@ -- 3. @x > y@ = @y < x@ -- 4. @x < y@ = @compare x y == LT@ -- 5. @x > y@ = @compare x y == GT@ -- 6. @x == y@ = @compare x y == EQ@ -- 7. @min x y == if x <= y then x else y@ = 'True' -- 8. @max x y == if x >= y then x else y@ = 'True' -- -- Note that (7.) and (8.) do /not/ require 'min' and 'max' to return either of -- their arguments. The result is merely required to /equal/ one of the -- arguments in terms of '(==)'. -- -- Minimal complete definition: either 'compare' or '<='. -- Using 'compare' can be more efficient for complex types. -- class (Eq a) => Ord a where compare :: a -> a -> Ordering (<), (<=), (>), (>=) :: a -> a -> Bool max, min :: a -> a -> a compare x y = if x == y then EQ -- NB: must be '<=' not '<' to validate the -- above claim about the minimal things that -- can be defined for an instance of Ord: else if x <= y then LT else GT x < y = case compare x y of { LT -> True; _ -> False } x <= y = case compare x y of { GT -> False; _ -> True } x > y = case compare x y of { GT -> True; _ -> False } x >= y = case compare x y of { LT -> False; _ -> True } -- These two default methods use '<=' rather than 'compare' -- because the latter is often more expensive max x y = if x <= y then y else x min x y = if x <= y then x else y {-# MINIMAL compare | (<=) #-} deriving instance Ord () deriving instance Ord a => Ord (Solo a) deriving instance (Ord a, Ord b) => Ord (a, b) deriving instance (Ord a, Ord b, Ord c) => Ord (a, b, c) deriving instance (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) deriving instance (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) instance (Ord a) => Ord [a] where {-# SPECIALISE instance Ord [[Char]] #-} {-# SPECIALISE instance Ord [Char] #-} {-# SPECIALISE instance Ord [Int] #-} compare [] [] = EQ compare [] (_:_) = LT compare (_:_) [] = GT compare (x:xs) (y:ys) = case compare x y of EQ -> compare xs ys other -> other deriving instance Ord Bool deriving instance Ord Ordering -- We don't use deriving for Ord Char, because for Ord the derived -- instance defines only compare, which takes two primops. Then -- '>' uses compare, and therefore takes two primops instead of one. instance Ord Char where (C# c1) > (C# c2) = isTrue# (c1 `gtChar#` c2) (C# c1) >= (C# c2) = isTrue# (c1 `geChar#` c2) (C# c1) <= (C# c2) = isTrue# (c1 `leChar#` c2) (C# c1) < (C# c2) = isTrue# (c1 `ltChar#` c2) -- | Note that due to the presence of @NaN@, `Float`'s 'Ord' instance does not -- satisfy reflexivity. -- -- >>> 0/0 <= (0/0 :: Float) -- False -- -- Also note that, due to the same, `Ord`'s operator interactions are not -- respected by `Float`'s instance: -- -- >>> (0/0 :: Float) > 1 -- False -- >>> compare (0/0 :: Float) 1 -- GT instance Ord Float where (F# x) `compare` (F# y) = if isTrue# (x `ltFloat#` y) then LT else if isTrue# (x `eqFloat#` y) then EQ else GT (F# x) < (F# y) = isTrue# (x `ltFloat#` y) (F# x) <= (F# y) = isTrue# (x `leFloat#` y) (F# x) >= (F# y) = isTrue# (x `geFloat#` y) (F# x) > (F# y) = isTrue# (x `gtFloat#` y) -- | Note that due to the presence of @NaN@, `Double`'s 'Ord' instance does not -- satisfy reflexivity. -- -- >>> 0/0 <= (0/0 :: Double) -- False -- -- Also note that, due to the same, `Ord`'s operator interactions are not -- respected by `Double`'s instance: -- -- >>> (0/0 :: Double) > 1 -- False -- >>> compare (0/0 :: Double) 1 -- GT instance Ord Double where (D# x) `compare` (D# y) = if isTrue# (x <## y) then LT else if isTrue# (x ==## y) then EQ else GT (D# x) < (D# y) = isTrue# (x <## y) (D# x) <= (D# y) = isTrue# (x <=## y) (D# x) >= (D# y) = isTrue# (x >=## y) (D# x) > (D# y) = isTrue# (x >## y) instance Ord Int where compare = compareInt (<) = ltInt (<=) = leInt (>=) = geInt (>) = gtInt -- See GHC.Classes#matching_overloaded_methods_in_rules {-# INLINE [1] gtInt #-} {-# INLINE [1] geInt #-} {-# INLINE [1] ltInt #-} {-# INLINE [1] leInt #-} gtInt, geInt, ltInt, leInt :: Int -> Int -> Bool (I# x) `gtInt` (I# y) = isTrue# (x ># y) (I# x) `geInt` (I# y) = isTrue# (x >=# y) (I# x) `ltInt` (I# y) = isTrue# (x <# y) (I# x) `leInt` (I# y) = isTrue# (x <=# y) compareInt :: Int -> Int -> Ordering (I# x#) `compareInt` (I# y#) = compareInt# x# y# compareInt# :: Int# -> Int# -> Ordering compareInt# x# y# | isTrue# (x# <# y#) = LT | isTrue# (x# ==# y#) = EQ | True = GT instance Ord Word where compare = compareWord (<) = ltWord (<=) = leWord (>=) = geWord (>) = gtWord -- See GHC.Classes#matching_overloaded_methods_in_rules {-# INLINE [1] gtWord #-} {-# INLINE [1] geWord #-} {-# INLINE [1] ltWord #-} {-# INLINE [1] leWord #-} gtWord, geWord, ltWord, leWord :: Word -> Word -> Bool (W# x) `gtWord` (W# y) = isTrue# (x `gtWord#` y) (W# x) `geWord` (W# y) = isTrue# (x `geWord#` y) (W# x) `ltWord` (W# y) = isTrue# (x `ltWord#` y) (W# x) `leWord` (W# y) = isTrue# (x `leWord#` y) compareWord :: Word -> Word -> Ordering (W# x#) `compareWord` (W# y#) = compareWord# x# y# compareWord# :: Word# -> Word# -> Ordering compareWord# x# y# | isTrue# (x# `ltWord#` y#) = LT | isTrue# (x# `eqWord#` y#) = EQ | True = GT -- OK, so they're technically not part of a class...: -- Boolean functions -- | Boolean \"and\", lazy in the second argument (&&) :: Bool -> Bool -> Bool True && x = x False && _ = False -- | Boolean \"or\", lazy in the second argument (||) :: Bool -> Bool -> Bool True || _ = True False || x = x -- | Boolean \"not\" not :: Bool -> Bool not True = False not False = True ------------------------------------------------------------------------ -- These don't really belong here, but we don't have a better place to -- put them -- These functions have built-in rules. {-# INLINE [0] divInt# #-} divInt# :: Int# -> Int# -> Int# x# `divInt#` y# = ((x# +# bias#) `quotInt#` y#) -# hard# where -- See Note [divInt# implementation] !yn# = y# <# 0# !c0# = (x# <# 0#) `andI#` (notI# yn#) !c1# = (x# ># 0#) `andI#` yn# !bias# = c0# -# c1# !hard# = c0# `orI#` c1# {-# INLINE [0] divInt8# #-} divInt8# :: Int8# -> Int8# -> Int8# x# `divInt8#` y# = ((x# `plusInt8#` bias#) `quotInt8#` y#) `subInt8#` hard# where zero# = intToInt8# 0# x `andInt8#` y = word8ToInt8# (int8ToWord8# x `andWord8#` int8ToWord8# y) x `orInt8#` y = word8ToInt8# (int8ToWord8# x `orWord8#` int8ToWord8# y) notInt8# x = word8ToInt8# (notWord8# (int8ToWord8# x)) -- See Note [divInt# implementation] !yn# = intToInt8# (y# `ltInt8#` zero#) !c0# = intToInt8# (x# `ltInt8#` zero#) `andInt8#` (notInt8# yn#) !c1# = intToInt8# (x# `gtInt8#` zero#) `andInt8#` yn# !bias# = c0# `subInt8#` c1# !hard# = c0# `orInt8#` c1# {-# INLINE [0] divInt16# #-} divInt16# :: Int16# -> Int16# -> Int16# x# `divInt16#` y# = ((x# `plusInt16#` bias#) `quotInt16#` y#) `subInt16#` hard# where zero# = intToInt16# 0# x `andInt16#` y = word16ToInt16# (int16ToWord16# x `andWord16#` int16ToWord16# y) x `orInt16#` y = word16ToInt16# (int16ToWord16# x `orWord16#` int16ToWord16# y) notInt16# x = word16ToInt16# (notWord16# (int16ToWord16# x)) -- See Note [divInt# implementation] !yn# = intToInt16# (y# `ltInt16#` zero#) !c0# = intToInt16# (x# `ltInt16#` zero#) `andInt16#` (notInt16# yn#) !c1# = intToInt16# (x# `gtInt16#` zero#) `andInt16#` yn# !bias# = c0# `subInt16#` c1# !hard# = c0# `orInt16#` c1# {-# INLINE [0] divInt32# #-} divInt32# :: Int32# -> Int32# -> Int32# x# `divInt32#` y# = ((x# `plusInt32#` bias#) `quotInt32#` y#) `subInt32#` hard# where zero# = intToInt32# 0# x `andInt32#` y = word32ToInt32# (int32ToWord32# x `andWord32#` int32ToWord32# y) x `orInt32#` y = word32ToInt32# (int32ToWord32# x `orWord32#` int32ToWord32# y) notInt32# x = word32ToInt32# (notWord32# (int32ToWord32# x)) -- See Note [divInt# implementation] !yn# = intToInt32# (y# `ltInt32#` zero#) !c0# = intToInt32# (x# `ltInt32#` zero#) `andInt32#` (notInt32# yn#) !c1# = intToInt32# (x# `gtInt32#` zero#) `andInt32#` yn# !bias# = c0# `subInt32#` c1# !hard# = c0# `orInt32#` c1# -- Note [divInt# implementation] -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- divInt# (truncated toward zero) is implemented with quotInt# (truncated -- toward negative infinity). They differ when inputs x and y have different signs: -- - x `rem` y has the sign of x and (x `quot` y)*y + (x `rem` y) == x -- - x `mod` y has the sign of y and (x `div` y)*y + (x `mod` y) == x -- -- So we bias the input and the result of quotInt as follows: -- -- if isTrue# (x# ># 0#) && isTrue# (y# <# 0#) then ((x# -# 1#) `quotInt#` y#) -# 1# -- else if isTrue# (x# <# 0#) && isTrue# (y# ># 0#) then ((x# +# 1#) `quotInt#` y#) -# 1# -- else x# `quotInt#` y# -- -- However this leads to assembly code with lots of branches (#19636) while we -- would like simpler code that we could inline (#18067). So we use some -- branchless code instead as derived below: -- -- if isTrue# (x# ># 0#) && isTrue# (y# <# 0#) then ((x# -# 1#) `quotInt#` y#) -# 1# -- else if isTrue# (x# <# 0#) && isTrue# (y# ># 0#) then ((x# +# 1#) `quotInt#` y#) -# 1# -- else x# `quotInt#` y# -- -- ===> { Give names to constants and always use them } -- -- ((x# +# bias#) `quotInt#` y#) -# hard# -- where -- (bias#,hard#) -- | isTrue# (x# ># 0#) && isTrue# (y# <# 0#) = (-1#, 1#) -- | isTrue# (x# <# 0#) && isTrue# (y# ># 0#) = ( 1#, 1#) -- | otherwise = ( 0#, 0#) -- -- ===> { Compute bias# and hard# independently using Bool# (0#,1#) } -- -- ((x# +# bias#) `quotInt#` y#) -# hard# -- where -- c0# = (x# <# 0#) &&# (y# ># 0#) -- c1# = (x# ># 0#) &&# (y# <# 0#) -- bias# = c0# -# c1# -- both cases are mutually exclusive so we can subtract them -- hard# = c0# ||# c1# -- (we could add them too here but OR is slightly better) -- -- ===> { Use yn# variable for "y# <# 0#" } -- -- ((x# +# bias#) `quotInt#` y#) -# hard# -- where -- -- y# ==# 0# throws an exception so we don't need to consider it -- yn# = y# <# 0# -- c0# = (x# <# 0#) &&# (notI# yn#) -- c1# = (x# ># 0#) &&# yn# -- bias# = c0# -# c1# -- hard# = c0# ||# c1# -- -- -- Note that we need to be careful NOT to overflow if we do any additional -- arithmetic on the arguments... the following previous version of this code -- had problems with overflow: -- | (x# ># 0#) && (y# <# 0#) = ((x# -# y#) -# 1#) `quotInt#` y# -- | (x# <# 0#) && (y# ># 0#) = ((x# -# y#) +# 1#) `quotInt#` y# {-# INLINE [0] modInt# #-} modInt# :: Int# -> Int# -> Int# x# `modInt#` y# = r# +# k# where -- See Note [modInt# implementation] !yn# = y# <# 0# !c0# = (x# <# 0#) `andI#` (notI# yn#) !c1# = (x# ># 0#) `andI#` yn# !s# = 0# -# ((c0# `orI#` c1#) `andI#` (r# /=# 0#)) !k# = s# `andI#` y# !r# = x# `remInt#` y# {-# INLINE [0] modInt8# #-} modInt8# :: Int8# -> Int8# -> Int8# x# `modInt8#` y# = r# `plusInt8#` k# where zero# = intToInt8# 0# x `andInt8#` y = word8ToInt8# (int8ToWord8# x `andWord8#` int8ToWord8# y) x `orInt8#` y = word8ToInt8# (int8ToWord8# x `orWord8#` int8ToWord8# y) notInt8# x = word8ToInt8# (notWord8# (int8ToWord8# x)) -- See Note [modInt# implementation] !yn# = intToInt8# (y# `ltInt8#` zero#) !c0# = intToInt8# (x# `ltInt8#` zero#) `andInt8#` (notInt8# yn#) !c1# = intToInt8# (x# `gtInt8#` zero#) `andInt8#` yn# !s# = zero# `subInt8#` ((c0# `orInt8#` c1#) `andInt8#` (intToInt8# (r# `neInt8#` zero#))) !k# = s# `andInt8#` y# !r# = x# `remInt8#` y# {-# INLINE [0] modInt16# #-} modInt16# :: Int16# -> Int16# -> Int16# x# `modInt16#` y# = r# `plusInt16#` k# where zero# = intToInt16# 0# x `andInt16#` y = word16ToInt16# (int16ToWord16# x `andWord16#` int16ToWord16# y) x `orInt16#` y = word16ToInt16# (int16ToWord16# x `orWord16#` int16ToWord16# y) notInt16# x = word16ToInt16# (notWord16# (int16ToWord16# x)) -- See Note [modInt# implementation] !yn# = intToInt16# (y# `ltInt16#` zero#) !c0# = intToInt16# (x# `ltInt16#` zero#) `andInt16#` (notInt16# yn#) !c1# = intToInt16# (x# `gtInt16#` zero#) `andInt16#` yn# !s# = zero# `subInt16#` ((c0# `orInt16#` c1#) `andInt16#` (intToInt16# (r# `neInt16#` zero#))) !k# = s# `andInt16#` y# !r# = x# `remInt16#` y# {-# INLINE [0] modInt32# #-} modInt32# :: Int32# -> Int32# -> Int32# x# `modInt32#` y# = r# `plusInt32#` k# where zero# = intToInt32# 0# x `andInt32#` y = word32ToInt32# (int32ToWord32# x `andWord32#` int32ToWord32# y) x `orInt32#` y = word32ToInt32# (int32ToWord32# x `orWord32#` int32ToWord32# y) notInt32# x = word32ToInt32# (notWord32# (int32ToWord32# x)) -- See Note [modInt# implementation] !yn# = intToInt32# (y# `ltInt32#` zero#) !c0# = intToInt32# (x# `ltInt32#` zero#) `andInt32#` (notInt32# yn#) !c1# = intToInt32# (x# `gtInt32#` zero#) `andInt32#` yn# !s# = zero# `subInt32#` ((c0# `orInt32#` c1#) `andInt32#` (intToInt32# (r# `neInt32#` zero#))) !k# = s# `andInt32#` y# !r# = x# `remInt32#` y# -- Note [modInt# implementation] -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- Similarly to divInt# (see Note [divInt# implementation]), we can derive the -- branchless implementation of modInt# as follows: -- -- = if isTrue# (x# ># 0#) && isTrue# (y# <# 0#) || -- isTrue# (x# <# 0#) && isTrue# (y# ># 0#) -- then if isTrue# (r# /=# 0#) then r# +# y# else 0# -- else r# -- where -- r# = x# `remInt#` y# -- -- ===> { Introduce constant k# } -- -- r# +# k# -- where -- k# = if isTrue# (x# ># 0#) && isTrue# (y# <# 0#) || -- isTrue# (x# <# 0#) && isTrue# (y# ># 0#) -- then if isTrue# (r# /=# 0#) then y# else 0# -- else 0# -- r# = x# `remInt#` y# -- -- ===> { Compute using Bool# } -- -- r# +# k# -- where -- yn# = y# <# 0# -- we don't need to consider y# ==# 0# -- c0# = (x# <# 0#) &&# (notI# yn#) -- c1# = (x# ># 0#) &&# yn# -- k# = if isTrue# ((c0# ||# c1#) &&# (r# /=# 0#)) -- then y# -- else 0# -- r# = x# `remInt#` y# -- -- ===> { Select y# or 0# in branchless way } -- -- r# +# k# -- where -- yn# = y# <# 0# -- c0# = (x# <# 0#) &&# (notI# yn#) -- c1# = (x# ># 0#) &&# yn# -- -- s# is either equal to: -- -- 0# (00..00b) -- -- -1# (11..11b) -- -- So we can AND s# with y# -- s# = 0# -# ((c0# ||# c1#) &&# (r# /=# 0#)) -- k# = s# &&# y# -- r# = x# `remInt#` y# {-# INLINE [0] divModInt# #-} divModInt# :: Int# -> Int# -> (# Int#, Int# #) x# `divModInt#` y# = case (x# +# bias#) `quotRemInt#` y# of (# q#, r# #) -> (# q# -# hard#, r# +# k# #) where -- See Note [divModInt# implementation] !yn# = y# <# 0# !c0# = (x# <# 0#) `andI#` (notI# yn#) !c1# = (x# ># 0#) `andI#` yn# !bias# = c0# -# c1# !hard# = c0# `orI#` c1# !s# = 0# -# hard# !k# = (s# `andI#` y#) -# bias# {-# INLINE [0] divModInt8# #-} divModInt8# :: Int8# -> Int8# -> (# Int8#, Int8# #) x# `divModInt8#` y# = case (x# `plusInt8#` bias#) `quotRemInt8#` y# of (# q#, r# #) -> (# q# `subInt8#` hard#, r# `plusInt8#` k# #) where zero# = intToInt8# 0# x `andInt8#` y = word8ToInt8# (int8ToWord8# x `andWord8#` int8ToWord8# y) x `orInt8#` y = word8ToInt8# (int8ToWord8# x `orWord8#` int8ToWord8# y) notInt8# x = word8ToInt8# (notWord8# (int8ToWord8# x)) -- See Note [divModInt# implementation] !yn# = intToInt8# (y# `ltInt8#` zero#) !c0# = intToInt8# (x# `ltInt8#` zero#) `andInt8#` (notInt8# yn#) !c1# = intToInt8# (x# `gtInt8#` zero#) `andInt8#` yn# !bias# = c0# `subInt8#` c1# !hard# = c0# `orInt8#` c1# !s# = zero# `subInt8#` hard# !k# = (s# `andInt8#` y#) `subInt8#` bias# {-# INLINE [0] divModInt16# #-} divModInt16# :: Int16# -> Int16# -> (# Int16#, Int16# #) x# `divModInt16#` y# = case (x# `plusInt16#` bias#) `quotRemInt16#` y# of (# q#, r# #) -> (# q# `subInt16#` hard#, r# `plusInt16#` k# #) where zero# = intToInt16# 0# x `andInt16#` y = word16ToInt16# (int16ToWord16# x `andWord16#` int16ToWord16# y) x `orInt16#` y = word16ToInt16# (int16ToWord16# x `orWord16#` int16ToWord16# y) notInt16# x = word16ToInt16# (notWord16# (int16ToWord16# x)) -- See Note [divModInt# implementation] !yn# = intToInt16# (y# `ltInt16#` zero#) !c0# = intToInt16# (x# `ltInt16#` zero#) `andInt16#` (notInt16# yn#) !c1# = intToInt16# (x# `gtInt16#` zero#) `andInt16#` yn# !bias# = c0# `subInt16#` c1# !hard# = c0# `orInt16#` c1# !s# = zero# `subInt16#` hard# !k# = (s# `andInt16#` y#) `subInt16#` bias# {-# INLINE [0] divModInt32# #-} divModInt32# :: Int32# -> Int32# -> (# Int32#, Int32# #) x# `divModInt32#` y# = case (x# `plusInt32#` bias#) `quotRemInt32#` y# of (# q#, r# #) -> (# q# `subInt32#` hard#, r# `plusInt32#` k# #) where zero# = intToInt32# 0# x `andInt32#` y = word32ToInt32# (int32ToWord32# x `andWord32#` int32ToWord32# y) x `orInt32#` y = word32ToInt32# (int32ToWord32# x `orWord32#` int32ToWord32# y) notInt32# x = word32ToInt32# (notWord32# (int32ToWord32# x)) -- See Note [divModInt# implementation] !yn# = intToInt32# (y# `ltInt32#` zero#) !c0# = intToInt32# (x# `ltInt32#` zero#) `andInt32#` (notInt32# yn#) !c1# = intToInt32# (x# `gtInt32#` zero#) `andInt32#` yn# !bias# = c0# `subInt32#` c1# !hard# = c0# `orInt32#` c1# !s# = zero# `subInt32#` hard# !k# = (s# `andInt32#` y#) `subInt32#` bias# -- Note [divModInt# implementation] -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- divModInt# is written by deriving the following code similarly to divInt# and -- modInt# (see Note [divInt# implementation] and Note [modInt# -- implementation]). -- -- x# `divModInt#` y# -- | isTrue# (x# ># 0#) && isTrue# (y# <# 0#) = -- case (x# -# 1#) `quotRemInt#` y# of -- (# q, r #) -> (# q -# 1#, r +# y# +# 1# #) -- | isTrue# (x# <# 0#) && isTrue# (y# ># 0#) = -- case (x# +# 1#) `quotRemInt#` y# of -- (# q, r #) -> (# q -# 1#, r +# y# -# 1# #) -- | otherwise = -- x# `quotRemInt#` y# -- -- ===> { Introduce constants } -- -- case (x# +# bias#) `quotRemInt#` y# of -- (# q#, r# #) -> (# q# -# hard#, r# +# k# #) -- where -- (bias#,hard#,k#) -- | isTrue# (x# ># 0#) && isTrue# (y# <# 0#) = (-1#, 1#, y#+1#) -- | isTrue# (x# <# 0#) && isTrue# (y# ># 0#) = ( 1#, 1#, y#-1#) -- | otherwise = ( 0#, 0#, 0#-0#) -- -- ===> { Compute using Bool# } -- -- case (x# +# bias#) `quotRemInt#` y# of -- (# q#, r# #) -> (# q# -# hard#, r# +# k# #) -- where -- yn# = y# <# 0# -- c0# = (x# <# 0#) `andI#` (notI# yn#) -- c1# = (x# ># 0#) `andI#` yn# -- bias# = c0# -# c1# -- hard# = c0# `orI#` c1# -- s# = 0# -# hard# -- k# = (s# `andI#` y#) -# bias# -- {- ************************************************************* * * * Constraint tuples * * * ************************************************************* -} class () class (c1, c2) => (c1, c2) class (c1, c2, c3) => (c1, c2, c3) class (c1, c2, c3, c4) => (c1, c2, c3, c4) class (c1, c2, c3, c4, c5) => (c1, c2, c3, c4, c5) class (c1, c2, c3, c4, c5, c6) => (c1, c2, c3, c4, c5, c6) class (c1, c2, c3, c4, c5, c6, c7) => (c1, c2, c3, c4, c5, c6, c7) class (c1, c2, c3, c4, c5, c6, c7, c8) => (c1, c2, c3, c4, c5, c6, c7, c8) class (c1, c2, c3, c4, c5, c6, c7, c8, c9) => (c1, c2, c3, c4, c5, c6, c7, c8, c9) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17,c18) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63) class (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64) => (c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64)