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Re: Arithmetic overflow checking

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On 7/25/2011 11:12 AM, Henderson wrote:
> Until some enterprising mathematician thinks up something that can be
> added and multiplied, but has no sensible correspondence to any subset
> of any kind of vectors of real numbers ...

You've never taken abstract algebra, have you? Polynomials are the most 
common counterexample I can think of (although they are treatable as an 
infinite vector space over any finite field). You can also generalize 
functions over the real numbers as a ring, and I'd find it hard pressed 
to come up with a scheme that can sensibly "correspond to any subset of 
any kind of vectors of real numbers" that can handle things as wildly 
varying as f(x) = 1, f(x) = sin x, f(x) = integral from 0 to x of 
exp(-t^2) dt, f(x) = 1 if x is rational and 1/x if x is irrational, or 
f(x) = sum from n = 0 to infinity of 1/2 ^n cos(9^n pi x) (the 
Weierstrass function).

Of course, if you just want addition, I can pull any old group out of a 
hat. Symmetries of an n-gon are a particular favorite example for 
nonabelian groups, as are permutations of sets.

> I think you can cram matrices in there, and complex numbers. Numbers mod
> something, too -- though do you quietly truncate when converting to
> these, or throw an exception? Of course, primitive int is already
> actually an integers-mod-2^32 type so that may be considered already
> settled.

What do you mean by "truncate" in modular arithmetic? Mod 10, 1 and 11 
are the same thing (the set of numbers {..., -9, 1, 11, ... }).

-- 
Beware of bugs in the above code; I have only proved it correct, not 
tried it. -- Donald E. Knuth

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Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-19 20:54 -0400
  Re: Arithmetic overflow checking markspace <-@.> - 2011-07-19 18:07 -0700
    Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-19 21:31 -0400
      Re: Arithmetic overflow checking Arved Sandstrom <asandstrom3minus1@eastlink.ca> - 2011-07-20 07:36 -0300
        Re: Arithmetic overflow checking RedGrittyBrick <RedGrittyBrick@spamweary.invalid> - 2011-07-20 11:58 +0100
          Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-20 09:51 -0700
            Re: Arithmetic overflow checking RedGrittyBrick <RedGrittyBrick@spamweary.invalid> - 2011-07-21 12:11 +0100
              Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-21 12:43 +0000
                Re: Arithmetic overflow checking Tom McGlynn <taqmcglynn@googlemail.com> - 2011-07-21 07:15 -0700
              Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-21 07:35 -0700
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-21 15:38 +0000
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-21 09:03 -0700
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-21 12:00 -0700
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-22 17:16 +0000
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-23 11:28 -0400
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-23 21:03 +0000
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-23 22:55 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 09:16 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-24 10:40 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 10:54 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-24 11:09 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 12:53 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-24 15:15 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 15:41 -0700
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-25 03:21 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-25 00:56 -0700
                Re: Arithmetic overflow checking Arved Sandstrom <asandstrom3minus1@eastlink.ca> - 2011-07-25 07:03 -0300
                Re: Arithmetic overflow checking Thomas Richter <thor@math.tu-berlin.de> - 2011-07-26 09:43 +0200
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-25 11:06 +0000
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-25 11:12 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-25 09:09 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-25 09:30 -0700
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-25 13:33 -0400
                Re: Arithmetic overflow checking "John B. Matthews" <nospam@nospam.invalid> - 2011-07-26 03:04 -0400
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-26 03:28 -0400
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-26 04:53 -0400
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-26 11:35 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-26 10:48 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 17:00 -0400
        Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 19:50 -0400
          Re: Arithmetic overflow checking Arved Sandstrom <asandstrom3minus1@eastlink.ca> - 2011-07-20 23:21 -0300
            Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-21 12:52 +0000
              Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-21 15:58 -0400
            Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 17:06 -0400
      Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-20 14:35 -0700
        Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 18:22 -0400
          Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-21 14:54 -0700

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