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Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value
From: |
Charles Levert |
Subject: |
Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value |
Date: |
Fri, 8 Jul 2005 12:45:37 -0400 |
User-agent: |
Mutt/1.4.1i |
* On Friday 2005-07-08 at 08:21:10 -0400, Charles Levert wrote:
> So it suffices to show that
>
> 3 > a * (log_2(2^(b + 2) + 2) - log_2(2^b + 2))
>
> for a given value of b, for my upper bound
> to get even looser compared to Knuth's when
> that b is increased to b + 2. By taking the
> power of 2 on each side, this inequality can be
> transformed into
>
> 8 + phi > (2^(b + 2) + 2) / (2^b + 2)
>
> 8 + phi > (4 * 2^b + 2) / (2^b + 2)
>
> (8 + phi) * (2^b + 2) > (4 * 2^b + 2)
>
> (8 + phi) * 2^b + (8 + phi) * 2 > 4 * 2^b + 2
>
> (8 + phi) * 2^b + (16 + 2 * phi) > 4 * 2^b + 2
>
> ((8 + phi) - 4) * 2^b > 2 - (16 + 2 * phi)
>
> (4 + phi) * 2^b > -14 - 2 * phi
>
> positive > negative
Before anyone else points out my mistake with
"8 + phi", here's the corrected development.
The conclusion still holds.
3 > a * (log_2(2^(b + 2) + 2) - log_2(2^b + 2))
3/a > log_2(2^(b + 2) + 2) - log_2(2^b + 2)
2^(3/a) > (2^(b + 2) + 2) / (2^b + 2)
2^(3/a) * (2^b + 2) > (2^(b + 2) + 2)
2^(3/a) * 2^b + 2^(3/a) * 2 > 4 * 2^b + 2
(2^(3/a) - 4) * 2^b > (1 - 2^(3/a)) * 2
0.236067977499791 * 2^b > -6.47213595499958
positive > negative
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, (continued)
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Julian Foad, 2005/07/04
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Paul Eggert, 2005/07/05
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Charles Levert, 2005/07/05
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Paul Eggert, 2005/07/05
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Charles Levert, 2005/07/05
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Paul Eggert, 2005/07/05
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Charles Levert, 2005/07/07
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Paul Eggert, 2005/07/07
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Charles Levert, 2005/07/08
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value,
Charles Levert <=
- Re: src/kwset.c (kwsincr): Replace arbitrary array size by proper value, Paul Eggert, 2005/07/08