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%
% (c) The AQUA Project, Glasgow University, 1994-1999
%
\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
-- Ix instances:
--
-- Ix Char
-- Ix Int
-- Ix Integer
-- Ix Bool
-- Ix Ordering
-- Ix ()
-- (Ix a, Ix b) => Ix (a, b)
-- ...
-- Implementation checked wrt. Haskell 98 lib report, 1/99.
) where
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"
inRange (m,n) 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
-- 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}
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