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Merge pull request #1613 from xexyl/2000-bmeyer-footnotes

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Landon Curt Noll authored and GitHub committed 2023-12-03 13:22:39 -07:00
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@@ -215,7 +215,7 @@ In short --- running it through the preprocessor and the
pretty-printer will give you something that looks slightly less pretty-printer will give you something that looks slightly less
like line noise and slightly more like a C program, but unless you like line noise and slightly more like a C program, but unless you
are a true wizard, it is unlikely to gain you any insights into are a true wizard, it is unlikely to gain you any insights into
what is actually going on....\[0\] what is actually going on....[^0]
### Bugs, Assumptions and TODO ### Bugs, Assumptions and TODO
@@ -269,7 +269,7 @@ ordering. For each pixel, an expected value is calculated by creating a least
squares predictor of order 12 based on all of the previously encoded/decoded squares predictor of order 12 based on all of the previously encoded/decoded
pixels. However, the contribution of each pixel is weighted according to its pixels. However, the contribution of each pixel is weighted according to its
[Manhattan-distance](https://en.wikipedia.org/wiki/Taxicab_geometry) from the [Manhattan-distance](https://en.wikipedia.org/wiki/Taxicab_geometry) from the
current pixel, `D`. That weight used is `pow(0.8,D)`. \[1\] \[2\] \[3\] current pixel, `D`. That weight used is `pow(0.8,D)`. [^1] [^2] [^3]
In a similar way, the prediction *errors* for all previous pixels In a similar way, the prediction *errors* for all previous pixels
are combined --- a weighted average (with weight `pow(0.7,D)`) of are combined --- a weighted average (with weight `pow(0.7,D)`) of
@@ -293,27 +293,27 @@ arithmetic decoder provides the information which half the actual
value is in. In both cases, the interval borders are adjusted value is in. In both cases, the interval borders are adjusted
accordingly, the arithmetic coder/decoder updated, and the accordingly, the arithmetic coder/decoder updated, and the
interval halving repeated until the precise value has been interval halving repeated until the precise value has been
en/decoded\[4\]. en/decoded[^4].
[0] Yes, this could be seen as a challenge.... [^0]: Yes, this could be seen as a challenge....
[1] Actually, the weight is `pow(0.8,D)/s`, where `s` is the sigma [^1]: Actually, the weight is `pow(0.8,D)/s`, where `s` is the sigma
used for encoding/decoding the particular previous pixel. Dividing used for encoding/decoding the particular previous pixel. Dividing
by `s` is a rather arbitrary action justified only by the by `s` is a rather arbitrary action justified only by the
improvement in results. Mathematically, I can only justify improvement in results. Mathematically, I can only justify
dividing by `s^2`, or not dividing at all.... dividing by `s^2`, or not dividing at all....
[2] Obviously, these least squares predictors are not calculated [^2]: Obviously, these least squares predictors are not calculated
from scratch for each pixel. Some clever reuse of earlier from scratch for each pixel. Some clever reuse of earlier
results allows `O(1)` calculation, rather than the results allows `O(1)` calculation, rather than the
`O(previous_rows*columns)` this description would suggest. `O(previous_rows*columns)` this description would suggest.
[3] As anyone who has ever tried local least squares knows from [^3]: As anyone who has ever tried local least squares knows from
bitter experience, there is a lot of numerical instability bitter experience, there is a lot of numerical instability
associated with them. So `glicbawls` adds a bias towards an associated with them. So `glicbawls` adds a bias towards an
averaging predictor to the equation system the least squares averaging predictor to the equation system the least squares
predictor is calculated from. The weight that is given to predictor is calculated from. The weight that is given to
this bias is constantly adjusted throughout coding/decoding, this bias is constantly adjusted throughout coding/decoding,
thus justifying the 'a' in `glicbawls`. thus justifying the 'a' in `glicbawls`.
[4] In the case of near-lossless coding, the interval is not [^4]: In the case of near-lossless coding, the interval is not
necessarily *halved*, but rather split at a convenient point necessarily *halved*, but rather split at a convenient point
(the split points are chosen in such a way as to minimise the (the split points are chosen in such a way as to minimise the
expected number of bits needed for coding). Also, the expected number of bits needed for coding). Also, the