#1517: Ratio Int is not well ordered
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Reporter: [EMAIL PROTECTED] | Owner:
Type: bug | Status: new
Priority: normal | Milestone:
Component: libraries/base | Version: 6.6.1
Severity: normal | Keywords:
Difficulty: Easy (1 hr) | Os: Multiple
Testcase: | Architecture: Multiple
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Ratio Int is declared to be in class Ord, which means (according to
http://haskell.org/ghc/docs/latest/html/libraries/base/Data-
Ord.html#t%3AOrd) that < should be a total ordering. Yet consider the
following interactive session in GHCI (on a 32 bit computer!):
{{{
Prelude> :m + Ratio
Prelude Ratio> let a = 1 % (2 :: Int)
Prelude Ratio> let b = 883177231 % (662415279 :: Int)
Prelude Ratio> let c = 1616076535 % (430549561 :: Int)
Prelude Ratio> a < b && b < c
True
Prelude Ratio> a < c
False
}}}
The problem is that overflow occurs in Real.lhs (from the GHC source
code), in the definition
{{{
(x:%y) < (x':%y') = x * y' < x' * y
}}}
That works for unbounded types (such as Integer). But to define a total
order on bounded types, a more complicated method is necessary.
See
http://boost.cvs.sourceforge.net/boost/boost/boost/rational.hpp?revision=1.21&view=markup,
line 374, for a correct implementation in C++.
--
Ticket URL: <http://hackage.haskell.org/trac/ghc/ticket/1517>
GHC <http://www.haskell.org/ghc/>
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