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From: Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups: comp.lang.javascript
Subject: Re: Best search algorithm to find a condition within a range.
Date: Fri, 10 Apr 2015 00:02:27 +0100
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Dr J R Stockton <reply1500@merlyn.demon.co.uk.invalid> writes:

> In comp.lang.javascript message <878ue3zrws.fsf@bsb.me.uk>, Tue, 7 Apr
> 2015 19:58:59, Ben Bacarisse <ben.usenet@bsb.me.uk> posted:
>
>>If, however, you only want to find the leading digit, there may be a
>>better way, but it's likely to use logarithms:
>>
>>  log(3243787...54395)/log(4294967295) = 8.15..
>>  floor(3243787...54395 / 4294967295^8) = 28
>
>
> It seems probable that, with real rather than integer arithmetic, there
> will be at least one case in which the small errors in the division and
> logarithms will put the value on the wrong side of an integer, in the
> opinion of float.
>
> So either one must test all possible cases or do some rather difficult
> reasoning to prove that it always works correctly, or accept the risk of
> occasional error.

Yes, it's not hard to test both possible powers so the occasional error
hardly matters.  In fact, one might even use a very crude log function
(maybe just take the digit length?), accept the ensuing errors, and test
the possible powers.

BTW, I make not claim that this is of any value (I can't see how it
could be, really) just that it's a way to do what the OP (incorrectly,
in my option) claimed to want.

<snip>
-- 
Ben.