Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!tut.cis.ohio-state.edu!bloom-beacon!athena.mit.edu!jfc
From: jfc@athena.mit.edu (John F Carr)
Newsgroups: comp.lang.c
Subject: Re: Detecting overflow
Message-ID: <11610@bloom-beacon.MIT.EDU>
Date: 23 May 89 05:36:08 GMT
References: <455@skye.ed.ac.uk> <723@tukki.jyu.fi> <1076@garcon.cso.uiuc.edu> <731@sdrc.UUCP>
Sender: root@bloom-beacon.MIT.EDU
Reply-To: jfc@athena.mit.edu (John F Carr)
Organization: Massachusetts Institute of Technology
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In article <731@sdrc.UUCP> scjones@sdrc.UUCP (Larry Jones) writes:
>If a and b are both integers, then the expression "a"
>does give the same result as "(a*b)/b" except when "(a*b)/b"
>overflows.  If it overflows, the results are undefined and
>getting the "correct" answer without generating an overflow is
>certainly an allowable response to undefined behavior.

If they are unsigned integers, this optimization is not possible,
since overflow is ignored (i.e. given n bit words,

  (2 * (2^n - 1)) / 2 == 2^(n-1) - 1 

is required with unsigned math [becuase the intermediate value,
2*(2^n - 1) must be truncated to 2^n - 2], while the true answer is

  (2 * (2^n - 1)) / 2 ==  2^n - 1

).

    --John Carr (jfc@athena.mit.edu)

   John Carr             "When they turn the pages of history,
   jfc@Athena.mit.edu     When these days have passed long ago,
   bloom-beacon!          Will they read of us with sadness
   athena.mit.edu!jfc     For the seeds that we let grow?"  --Neil Peart