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Groups > comp.lang.c > #60055

Re: SAFEcode

From Keith Thompson <kst-u@mib.org>
Newsgroups comp.lang.c
Subject Re: SAFEcode
Date 2015-04-14 13:08 -0700
Organization None to speak of
Message-ID <871tjmtqur.fsf@kst-u.example.com> (permalink)
References (7 earlier) <4964f920-9e9b-44d1-a8c5-125462c8192e@googlegroups.com> <87egnmu3lj.fsf@kst-u.example.com> <0ce60a7d-2fc9-47b0-9897-9bbe5f6857c6@googlegroups.com> <87a8yatusw.fsf@kst-u.example.com> <36e7f907-f6bb-4213-bbe6-7e44f7b48cb0@googlegroups.com>

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Malcolm McLean <malcolm.mclean5@btinternet.com> writes:
> On Tuesday, April 14, 2015 at 7:43:38 PM UTC+1, Keith Thompson wrote:
>> Malcolm McLean <malcolm.mclean5@btinternet.com> writes:
>>
>>The "optimal strategy" for determining the argument value for which a 
>>function returns 0 (or perhaps "close enough" to 0) depends critically 
>>on what information we have about the function.  Is it continuous 
>>(subject to the fact that floating-point representations are discrete)? 
>>Is it monotone?  Is its first derivative continuous? 
>>
> The real issues that that you don't know much about the function,
> you're probing it. If it's pathological, such as a golf course function,
> then there's nothing you can do. But you know that it represents a physical
>  process, so that's unlikely - not impossible, but there probably
> isn't a demon setting things up so you can't work out what is
> going on.
> It's not continuous, it consists of three sections, one which returns
> -1, one which returns 1, and a very small one (limited by machine precision)
> which returns 0. You know the machine precision, so if it so happens
> that one value returns 1 and the next representable value returns -1,
> then you've bracketed zero.
> That's a bit unrealistic. The idea that you can't take derivatives isn't
> unrealistic at all. 

Ok, so the fact that the function is monotonic increasing is enough to
let us search for the argument value for which it returns 0, or at least
where it transitions from negative to positive.  A binary search would
work.  A biased binary search might be preferable, but we can't
implement it without more specific information about how we *expect* the
function to behave.  (I'm making a general point, not asking for more
details about this particular function.)

[...]

>> The big problem is that ln(x) is undefined for x <= 0.0.  A secondary
>> problem is that there might not a value of x such that ln(x) - n == 0
>> (mathematically there is, but floating-point is not so well behaved).
>>
> That's not a big problem, since I've told you that n is under 100
> and all runs have produced values over 1, and n represents the
> number of steps in a physical process, with a bit of fuzziness to 
> make the problem continuous. 
> Clearly we can't pass x < 0.0. We've got one limit, but not the other
> one. 

The second version of your function computes ln(x), which is undefined
for x <= 0.0.  In your original description, you said the function is
defined over the range -99 .. +99.  If you were computing ln(n) and we
know that n >= 1, that would be ok -- but you're computing ln(x).

Your description is inconsistent.

This probably isn't relevant to the general problem, except that we
can't work with the function unless we have a consistent description of
its behavior.

>> Ignoring those problems (assuming a similar function that's actually
>> defined over -99..+99), and given information about the probability
>> distribution of the value of n and of the choice of which of the two
>> functions is being used, I have little doubt that an optimal strategy
>> could be devised, probably some kind of biased binary search.  I'm
>> skeptical that it would be worth the effort over a simple unbiased
>> binary search, but perhaps in some applications it would be.
>> 
> It is, yes. Obviously for the problem as I have defined it you can
> get the result in under just noticeable time on a modern machine,
> so it wouldn't really be worth the effort. But in reality f(x) 
> might represent a physical measurement and be quite costly.
> Another common situation is that you spend several days of processor
> time minimising a function that takes several parameters.

Sure, all that seems plausible.

Your original claim was something about a "golden section search".
Perhaps later I'll read up on that.  But I think we've gone rather far
afield from that claim.

-- 
Keith Thompson (The_Other_Keith) kst-u@mib.org  <http://www.ghoti.net/~kst>
Working, but not speaking, for JetHead Development, Inc.
"We must do something.  This is something.  Therefore, we must do this."
    -- Antony Jay and Jonathan Lynn, "Yes Minister"

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Thread

SAFEcode G G <gdotone@gmail.com> - 2015-04-13 21:19 -0700
  Re: SAFEcode Ian Collins <ian-news@hotmail.com> - 2015-04-14 17:12 +1200
    Re: SAFEcode Ian Collins <ian-news@hotmail.com> - 2015-04-14 17:19 +1200
  Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-14 00:24 -0500
    Re: SAFEcode G G <gdotone@gmail.com> - 2015-04-13 23:45 -0700
  SAFEcode asetofsymbols@gmail.com - 2015-04-13 22:30 -0700
  Re: SAFEcode Robbie Hatley <see.my.sig@for.my.address> - 2015-04-14 00:14 -0700
    Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-14 10:33 +0200
      Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 02:01 -0700
        Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-14 10:23 +0100
        Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-14 11:49 +0200
          Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 04:31 -0700
            Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-14 14:54 +0200
              Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 06:39 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-14 16:10 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 08:11 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-14 23:58 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 01:25 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-15 11:11 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 02:35 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-15 13:52 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 06:04 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-15 08:08 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 08:57 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-15 18:24 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 09:45 -0700
                Re: SAFEcode Johannes Bauer <dfnsonfsduifb@gmx.de> - 2015-04-15 19:09 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 22:29 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-16 08:23 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-16 10:44 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-16 11:22 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-19 15:33 +0000
                Re: SAFEcode Steve Thompson <stevet810@gmail.com> - 2015-04-16 04:38 +0000
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-16 14:12 -0500
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-17 09:28 +0200
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-17 09:33 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-17 02:08 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-17 09:43 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-17 08:04 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-17 17:08 -0500
                Re: SAFEcode Tim Rentsch <txr@alumni.caltech.edu> - 2015-04-17 08:07 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-15 12:29 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 22:56 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-16 10:29 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-16 04:46 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-16 13:08 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-16 08:42 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-16 16:47 +0100
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-16 16:53 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-16 10:52 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-16 22:11 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-17 10:22 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-17 02:17 -0700
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-17 05:56 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-17 04:37 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-17 10:04 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-17 08:38 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-17 20:52 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-18 13:16 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-18 04:22 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-18 14:08 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-18 06:00 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-18 21:42 +0200
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-18 17:47 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 00:11 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-19 12:52 +0000
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-19 09:10 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 07:21 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-19 12:54 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 11:18 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-20 09:58 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 08:09 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-20 13:06 -0500
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-19 07:32 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 09:03 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-19 16:30 +0100
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-19 12:58 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 05:37 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-18 08:00 -0500
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-18 19:28 +0100
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-18 09:37 -0500
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-19 11:37 +0100
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-19 09:56 -0500
                Re: SAFEcode Tim Rentsch <txr@alumni.caltech.edu> - 2015-04-22 15:49 -0700
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 18:13 -0500
                Re: SAFEcode Tim Rentsch <txr@alumni.caltech.edu> - 2015-04-28 12:46 -0700
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-20 16:50 -0500
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-17 10:31 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-17 21:09 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-17 19:01 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-18 15:18 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-18 09:00 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-18 21:52 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 00:02 -0700
                Re: SAFEcode asetofsymbols@gmail.com - 2015-04-19 00:40 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 03:52 -0700
                Re: SAFEcode asetofsymbols@gmail.com - 2015-04-21 09:02 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-19 12:58 +0000
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 07:25 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-19 15:51 +0000
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-19 23:22 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 16:26 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-20 00:48 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 09:15 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 00:39 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 10:33 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 01:55 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 11:28 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 02:39 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 12:35 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 03:58 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 13:37 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 06:04 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 15:37 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 06:52 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 16:23 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 07:32 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 22:42 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 21:56 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-21 09:21 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 01:00 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-21 10:37 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 01:59 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-21 12:21 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 03:45 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-21 10:05 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-21 12:14 +0200
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-21 08:18 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 08:51 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-22 09:44 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 01:38 -0700
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 03:45 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 02:13 -0700
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 04:29 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 03:29 -0700
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 10:30 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 09:13 -0700
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 13:03 -0500
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-22 11:38 -0700
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 15:25 -0500
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-22 21:49 +0100
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 16:17 -0500
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-22 22:33 +0100
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 16:56 -0500
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-23 09:24 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-23 02:25 -0700
                Re: SAFEcode Richard Damon <Richard@Damon-Family.org> - 2015-04-23 08:24 -0400
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-23 06:18 -0700
                Re: SAFEcode Ben Bacarisse <ben.lists@bsb.me.uk> - 2015-04-23 14:47 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-23 07:16 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-23 17:20 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-23 08:44 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-25 10:14 +0000
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-25 04:04 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-25 12:22 +0000
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-25 10:53 -0700
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-23 16:48 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-24 12:49 +0200
                Re: SAFEcode Ben Bacarisse <ben.lists@bsb.me.uk> - 2015-04-23 20:40 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-23 13:03 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-23 23:49 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-24 01:07 -0700
                Re: SAFEcode Ben Bacarisse <ben.lists@bsb.me.uk> - 2015-04-24 11:51 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-24 04:29 -0700
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-24 13:20 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-24 06:48 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-25 10:16 +0000
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-24 15:48 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-24 10:05 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-24 22:59 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-26 00:16 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-24 04:39 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-24 22:59 +0100
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-23 08:17 -0500
                Re: SAFEcode Robert Wessel <robertwessel2@yahoo.com> - 2015-04-22 16:49 -0500
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 17:01 -0500
                Re: SAFEcode James Kuyper <jameskuyper@verizon.net> - 2015-04-22 17:51 -0400
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-22 17:35 -0500
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-22 17:45 -0700
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-23 09:29 +0100
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-23 08:29 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-23 08:55 -0700
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-23 21:11 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 06:23 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-22 13:08 -0500
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-22 20:17 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 12:43 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-23 11:52 +0000
                Re: SAFEcode Robert Wessel <robertwessel2@yahoo.com> - 2015-04-23 13:53 -0500
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-25 10:18 +0000
                Re: SAFEcode Morris Dovey <mrdovey@iedu.com> - 2015-04-25 21:37 -0500
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-20 12:05 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 04:28 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 04:38 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-20 12:40 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 14:11 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 06:31 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 16:31 +0200
                Re: SAFEcode jadill33@gmail.com - 2015-04-20 09:38 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-20 22:52 +0200
                Re: SAFEcode asetofsymbols@gmail.com - 2015-04-20 11:10 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-20 22:43 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-20 22:59 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-21 09:27 +0200
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-21 15:12 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 07:31 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-21 16:43 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 08:01 -0700
                Re: SAFEcode raltbos@xs4all.nl (Richard Bos) - 2015-04-21 22:29 +0000
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-21 11:09 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 10:13 -0700
                Re: SAFEcode gwowen <gwowen@gmail.com> - 2015-04-21 10:22 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 16:51 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-22 02:52 +0100
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-21 14:44 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 16:58 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-22 01:11 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-21 17:31 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-22 10:09 +0200
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-22 10:50 +0100
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-22 11:12 +0100
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-22 11:37 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 05:54 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-22 15:31 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 06:48 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-22 16:29 +0200
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-22 16:13 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 08:22 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-22 16:25 +0100
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-22 10:35 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-22 13:24 -0500
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-23 01:18 +0200
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-23 06:11 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-23 09:36 +0200
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-22 08:38 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-22 13:04 +0200
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-22 09:52 -0500
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-22 16:23 +0100
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-22 10:28 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 08:16 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-22 13:53 -0500
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-22 12:45 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-22 16:44 -0500
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-21 22:58 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-22 09:53 +0200
                Re: SAFEcode gwowen <gwowen@gmail.com> - 2015-04-21 10:15 -0700
                Re: SAFEcode Martin Shobe <martin.shobe@yahoo.com> - 2015-04-21 13:57 -0500
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-21 23:01 +0100
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-21 23:46 +0100
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-22 01:49 +0100
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-22 08:32 +0100
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-22 10:02 +0100
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-21 12:06 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-21 20:18 +0100
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-21 12:30 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-21 21:30 +0100
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-21 13:39 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-21 20:21 +0100
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-22 10:24 +0200
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-22 09:46 +0100
                Re: SAFEcode gwowen <gwowen@gmail.com> - 2015-04-22 02:57 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-22 08:42 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-19 16:19 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-19 09:08 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-16 08:55 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-16 11:03 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-16 11:35 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-17 10:28 +0200
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-17 09:51 +0100
                Re: SAFEcode Phil Carmody <pc+usenet@asdf.org> - 2015-04-20 11:28 +0300
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-17 10:32 +0200
                Re: SAFEcode Bartc <bc@freeuk.com> - 2015-04-14 15:24 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 08:03 -0700
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-14 18:48 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 12:43 -0700
                Re: SAFEcode Johannes Bauer <dfnsonfsduifb@gmx.de> - 2015-04-14 21:52 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 13:16 -0700
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-14 21:39 +0100
                Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-15 01:20 +0100
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-15 01:29 +0100
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 01:32 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-15 08:17 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 09:13 -0700
                Re: SAFEcode Johannes Bauer <dfnsonfsduifb@gmx.de> - 2015-04-15 18:33 +0200
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-15 10:02 -0700
                Re: SAFEcode Johannes Bauer <dfnsonfsduifb@gmx.de> - 2015-04-15 20:55 +0200
                Re: SAFEcode Robert Wessel <robertwessel2@yahoo.com> - 2015-04-15 19:27 -0500
                Re: SAFEcode Phil Carmody <pc+usenet@asdf.org> - 2015-04-20 11:53 +0300
                Re: SAFEcode Ian Collins <ian-news@hotmail.com> - 2015-04-16 14:51 +1200
                Re: SAFEcode Tim Rentsch <txr@alumni.caltech.edu> - 2015-04-17 02:13 -0700
                Re: SAFEcode Johannes Bauer <dfnsonfsduifb@gmx.de> - 2015-04-15 08:14 +0200
                Re: SAFEcode Richard Heathfield <rjh@cpax.org.uk> - 2015-04-14 21:02 +0100
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-14 08:33 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 08:54 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-14 11:43 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 12:41 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-14 13:08 -0700
                Re: SAFEcode Malcolm McLean <malcolm.mclean5@btinternet.com> - 2015-04-14 14:02 -0700
                Re: SAFEcode Keith Thompson <kst-u@mib.org> - 2015-04-14 15:29 -0700
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-15 10:03 +0200
                Re: SAFEcode David Brown <david.brown@hesbynett.no> - 2015-04-15 10:02 +0200
        Re: SAFEcode Phil Carmody <pc+usenet@asdf.org> - 2015-04-20 11:13 +0300
    Re: SAFEcode Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-04-14 13:03 +0100

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