Markdown footnotes added in 2000/bmeyer

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Cody Boone Ferguson committed 2023-12-03 11:34:43 -08:00
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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
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
what is actually going on....\[0\]
what is actually going on....[^0]
### 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
pixels. However, the contribution of each pixel is weighted according to its
[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
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
accordingly, the arithmetic coder/decoder updated, and the
interval halving repeated until the precise value has been
en/decoded\[4\].
en/decoded[^4].
[0] Yes, this could be seen as a challenge....
[1] Actually, the weight is `pow(0.8,D)/s`, where `s` is the sigma
[^0]: Yes, this could be seen as a challenge....
[^1]: Actually, the weight is `pow(0.8,D)/s`, where `s` is the sigma
used for encoding/decoding the particular previous pixel. Dividing
by `s` is a rather arbitrary action justified only by the
improvement in results. Mathematically, I can only justify
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
results allows `O(1)` calculation, rather than the
`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
associated with them. So `glicbawls` adds a bias towards an
averaging predictor to the equation system the least squares
predictor is calculated from. The weight that is given to
this bias is constantly adjusted throughout coding/decoding,
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
(the split points are chosen in such a way as to minimise the
expected number of bits needed for coding). Also, the