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Full Discussion: Interpolation using awk
Top Forums Shell Programming and Scripting Interpolation using awk Post 302619093 by Scrutinizer on Thursday 5th of April 2012 12:07:11 AM
Old 04-05-2012
j is used for the (known) x coordinates, i is used for all (inter/extrpolated) coordinates, the left x-coordinate is called s and the right x-coordinate is t.

so this checks to see if a shift to use the next pair of coordinates is necessary and this is the case if i>t ( which means i>I[j+1] ) unless the coordinates we then would need to shift to (from I[j] and I[j+1] to I[j+1] and I[j+2]), do not exist. This will not be the case for I[j+1], but if I[j+2] does not exist, then we have reached the end of the array I.

If this is the case (then n lies to the right of the range of coordinates) then in fact we are switching automatically from interpolation to extrapolation. The same formula is used for extrapolation as for interpolation.
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bup-margin(1)						      General Commands Manual						     bup-margin(1)

NAME
bup-margin - figure out your deduplication safety margin SYNOPSIS
bup margin [options...] DESCRIPTION
bup margin iterates through all objects in your bup repository, calculating the largest number of prefix bits shared between any two entries. This number, n, identifies the longest subset of SHA-1 you could use and still encounter a collision between your object ids. For example, one system that was tested had a collection of 11 million objects (70 GB), and bup margin returned 45. That means a 46-bit hash would be sufficient to avoid all collisions among that set of objects; each object in that repository could be uniquely identified by its first 46 bits. The number of bits needed seems to increase by about 1 or 2 for every doubling of the number of objects. Since SHA-1 hashes have 160 bits, that leaves 115 bits of margin. Of course, because SHA-1 hashes are essentially random, it's theoretically possible to use many more bits with far fewer objects. If you're paranoid about the possibility of SHA-1 collisions, you can monitor your repository by running bup margin occasionally to see if you're getting dangerously close to 160 bits. OPTIONS
--predict Guess the offset into each index file where a particular object will appear, and report the maximum deviation of the correct answer from the guess. This is potentially useful for tuning an interpolation search algorithm. --ignore-midx don't use .midx files, use only .idx files. This is only really useful when used with --predict. EXAMPLE
$ bup margin Reading indexes: 100.00% (1612581/1612581), done. 40 40 matching prefix bits 1.94 bits per doubling 120 bits (61.86 doublings) remaining 4.19338e+18 times larger is possible Everyone on earth could have 625878182 data sets like yours, all in one repository, and we would expect 1 object collision. $ bup margin --predict PackIdxList: using 1 index. Reading indexes: 100.00% (1612581/1612581), done. 915 of 1612581 (0.057%) SEE ALSO
bup-midx(1), bup-save(1) BUP
Part of the bup(1) suite. AUTHORS
Avery Pennarun <apenwarr@gmail.com>. Bup unknown- bup-margin(1)
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