+% -----------------------------------------------------------------------------
+% $Id: Ix.lhs,v 1.19 2001/08/29 09:34:05 simonmar Exp $
%
-% (c) The AQUA Project, Glasgow University, 1994-1999
+% (c) The University of Glasgow, 1994-2000
%
\section[Ix]{Module @Ix@}
\begin{code}
-{-# OPTIONS -fno-implicit-prelude #-}
-
module Ix
(
Ix
( range -- :: (Ix a) => (a,a) -> [a]
, index -- :: (Ix a) => (a,a) -> a -> Int
, inRange -- :: (Ix a) => (a,a) -> a -> Bool
+ , rangeSize -- :: (Ix a) => (a,a) -> Int
)
- , rangeSize -- :: (Ix a) => (a,a) -> Int
-- Ix instances:
--
-- Ix Char
-- Implementation checked wrt. Haskell 98 lib report, 1/99.
) where
+import Prelude
#ifndef __HUGS__
-import {-# SOURCE #-} PrelErr ( error )
-import PrelTup
-import PrelBase
-import PrelList( null )
-import PrelEnum
-import PrelShow
-import PrelNum
-\end{code}
-
-%*********************************************************
-%* *
-\subsection{The @Ix@ class}
-%* *
-%*********************************************************
-
-\begin{code}
-class (Ord a) => Ix a where
- range :: (a,a) -> [a]
- index, unsafeIndex :: (a,a) -> a -> Int
- inRange :: (a,a) -> a -> Bool
-
- -- Must specify one of index, unsafeIndex
- index b i | inRange b i = unsafeIndex b i
- | otherwise = error "Error in array index"
- unsafeIndex b i = index b i
-\end{code}
-
-%*********************************************************
-%* *
-\subsection{Instances of @Ix@}
-%* *
-%*********************************************************
-
-\begin{code}
--- abstract these errors from the relevant index functions so that
--- the guts of the function will be small enough to inline.
-
-{-# NOINLINE indexError #-}
-indexError :: Show a => (a,a) -> a -> String -> b
-indexError rng i tp
- = error (showString "Ix{" . showString tp . showString "}.index: Index " .
- showParen True (showsPrec 0 i) .
- showString " out of range " $
- showParen True (showsPrec 0 rng) "")
-
-----------------------------------------------------------------------
-instance Ix Char where
- {-# INLINE range #-}
- range (m,n) = [m..n]
-
- {-# INLINE unsafeIndex #-}
- unsafeIndex (m,_n) i = fromEnum i - fromEnum m
-
- index b i | inRange b i = unsafeIndex b i
- | otherwise = indexError b i "Char"
-
- inRange (m,n) i = m <= i && i <= n
-
-----------------------------------------------------------------------
-instance Ix Int where
- {-# INLINE range #-}
- -- The INLINE stops the build in the RHS from getting inlined,
- -- so that callers can fuse with the result of range
- range (m,n) = [m..n]
-
- {-# INLINE unsafeIndex #-}
- unsafeIndex (m,_n) i = i - m
-
- index b i | inRange b i = unsafeIndex b i
- | otherwise = indexError b i "Int"
-
- {-# INLINE inRange #-}
- inRange (I# m,I# n) (I# i) = m <=# i && i <=# n
-
-----------------------------------------------------------------------
-instance Ix Integer where
- {-# INLINE range #-}
- range (m,n) = [m..n]
-
- {-# INLINE unsafeIndex #-}
- unsafeIndex (m,_n) i = fromInteger (i - m)
-
- index b i | inRange b i = unsafeIndex b i
- | otherwise = indexError b i "Integer"
-
- inRange (m,n) i = m <= i && i <= n
-
-
-----------------------------------------------------------------------
-instance Ix Bool where -- as derived
- {-# INLINE range #-}
- range (m,n) = [m..n]
-
- {-# INLINE unsafeIndex #-}
- unsafeIndex (l,_) i = fromEnum i - fromEnum l
-
- index b i | inRange b i = unsafeIndex b i
- | otherwise = indexError b i "Bool"
-
- inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u
-
-----------------------------------------------------------------------
-instance Ix Ordering where -- as derived
- {-# INLINE range #-}
- range (m,n) = [m..n]
-
- {-# INLINE unsafeIndex #-}
- unsafeIndex (l,_) i = fromEnum i - fromEnum l
-
- index b i | inRange b i = unsafeIndex b i
- | otherwise = indexError b i "Ordering"
-
- inRange (l,u) i = fromEnum i >= fromEnum l && fromEnum i <= fromEnum u
-
-----------------------------------------------------------------------
-instance Ix () where
- {-# INLINE range #-}
- range ((), ()) = [()]
- {-# INLINE unsafeIndex #-}
- unsafeIndex ((), ()) () = 0
- {-# INLINE inRange #-}
- inRange ((), ()) () = True
- {-# INLINE index #-}
- index b i = unsafeIndex b i
-
-
-----------------------------------------------------------------------
-instance (Ix a, Ix b) => Ix (a, b) where -- as derived
- {-# SPECIALISE instance Ix (Int,Int) #-}
-
- {- INLINE range #-}
- range ((l1,l2),(u1,u2)) =
- [ (i1,i2) | i1 <- range (l1,u1), i2 <- range (l2,u2) ]
-
- {- INLINE unsafeIndex #-}
- unsafeIndex ((l1,l2),(u1,u2)) (i1,i2) =
- unsafeIndex (l1,u1) i1 * unsafeRangeSize (l2,u2) + unsafeIndex (l2,u2) i2
-
- {- INLINE inRange #-}
- inRange ((l1,l2),(u1,u2)) (i1,i2) =
- inRange (l1,u1) i1 && inRange (l2,u2) i2
-
- -- Default method for index
-
-----------------------------------------------------------------------
-instance (Ix a1, Ix a2, Ix a3) => Ix (a1,a2,a3) where
- {-# SPECIALISE instance Ix (Int,Int,Int) #-}
-
- range ((l1,l2,l3),(u1,u2,u3)) =
- [(i1,i2,i3) | i1 <- range (l1,u1),
- i2 <- range (l2,u2),
- i3 <- range (l3,u3)]
-
- unsafeIndex ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) =
- unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
- unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
- unsafeIndex (l1,u1) i1))
-
- inRange ((l1,l2,l3),(u1,u2,u3)) (i1,i2,i3) =
- inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
- inRange (l3,u3) i3
-
- -- Default method for index
-
-----------------------------------------------------------------------
-instance (Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1,a2,a3,a4) where
- range ((l1,l2,l3,l4),(u1,u2,u3,u4)) =
- [(i1,i2,i3,i4) | i1 <- range (l1,u1),
- i2 <- range (l2,u2),
- i3 <- range (l3,u3),
- i4 <- range (l4,u4)]
-
- unsafeIndex ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) =
- unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * (
- unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
- unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
- unsafeIndex (l1,u1) i1)))
-
- inRange ((l1,l2,l3,l4),(u1,u2,u3,u4)) (i1,i2,i3,i4) =
- inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
- inRange (l3,u3) i3 && inRange (l4,u4) i4
-
- -- Default method for index
-
-instance (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix (a1,a2,a3,a4,a5) where
- range ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) =
- [(i1,i2,i3,i4,i5) | i1 <- range (l1,u1),
- i2 <- range (l2,u2),
- i3 <- range (l3,u3),
- i4 <- range (l4,u4),
- i5 <- range (l5,u5)]
-
- unsafeIndex ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) =
- unsafeIndex (l5,u5) i5 + unsafeRangeSize (l5,u5) * (
- unsafeIndex (l4,u4) i4 + unsafeRangeSize (l4,u4) * (
- unsafeIndex (l3,u3) i3 + unsafeRangeSize (l3,u3) * (
- unsafeIndex (l2,u2) i2 + unsafeRangeSize (l2,u2) * (
- unsafeIndex (l1,u1) i1))))
-
- inRange ((l1,l2,l3,l4,l5),(u1,u2,u3,u4,u5)) (i1,i2,i3,i4,i5) =
- inRange (l1,u1) i1 && inRange (l2,u2) i2 &&
- inRange (l3,u3) i3 && inRange (l4,u4) i4 &&
- inRange (l5,u5) i5
-
- -- Default method for index
-\end{code}
-
-%********************************************************
-%* *
-\subsection{Size of @Ix@ interval}
-%* *
-%********************************************************
-
-The @rangeSize@ operator returns the number of elements
-in the range for an @Ix@ pair.
-
-\begin{code}
-{-# SPECIALISE unsafeRangeSize :: (Int,Int) -> Int #-}
-{-# SPECIALISE unsafeRangeSize :: ((Int,Int),(Int,Int)) -> Int #-}
-unsafeRangeSize :: (Ix a) => (a,a) -> Int
-unsafeRangeSize b@(_l,h) = unsafeIndex b h + 1
-
-{-# SPECIALISE rangeSize :: (Int,Int) -> Int #-}
-{-# SPECIALISE rangeSize :: ((Int,Int),(Int,Int)) -> Int #-}
-rangeSize :: (Ix a) => (a,a) -> Int
-rangeSize b@(_l,h) | inRange b h = unsafeIndex b h + 1
- | otherwise = 0
+import PrelArr
+#endif
+-- This module is empty, because Ix is defined in PrelArr.
+-- Reason: it's needed internally in the Prelude.
+-- This module serves solely to export it to the user.
--- Note that the following is NOT right
--- rangeSize (l,h) | l <= h = index b h + 1
--- | otherwise = 0
---
--- Because it might be the case that l<h, but the range
--- is nevertheless empty. Consider
--- ((1,2),(2,1))
--- Here l<h, but the second index ranges from 2..1 and
--- hence is empty
\end{code}
-\begin{code}
-#else
--- This module is empty; Ix is currently defined in the prelude, but should
--- eventually be moved to this library file instead.
-#endif
-\end{code}
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