This edge case is only possible with the new optimal encoding selector,
since before zstd would always choose `set_basic` for small numbers of
sequences.
Fix `FSE_readNCount()` to support buffers < 4 bytes.
Credit to OSS-Fuzz
Estimate the cost for using FSE modes `set_basic`, `set_compressed`, and
`set_repeat`, and select the one with the lowest cost.
* The cost of `set_basic` is computed using the cross-entropy cost
function `ZSTD_crossEntropyCost()`, using the normalized default count
and the count.
* The cost of `set_repeat` is computed using `FSE_bitCost()`. We check the
previous table to see if it is able to represent the distribution.
* The cost of `set_compressed` is computed with the entropy cost function
`ZSTD_entropyCost()`, together with the cost of writing the normalized
count `ZSTD_NCountCost()`.
The cover algorithm selects one segment per epoch, and it selects the epoch
size such that `epochs * segmentSize ~= dictSize`. Selecting less epochs
gives the algorithm more candidates to choose from for each segment it
selects, and then it will loop back to the first epoch when it hits the
last one.
The trade off is that now it takes longer to select each segment, since it
has to look at more data before making a choice.
I benchmarked on the following data sets using this command:
```sh
$ZSTD -T0 -3 --train-cover=d=8,steps=256 $DIR -r -o dict && $ZSTD -3 -D dict -rc $DIR | wc -c
```
| Data set | k (approx) | Before | After | % difference |
|--------------|------------|----------|----------|--------------|
| GitHub | ~1000 | 738138 | 746610 | +1.14% |
| hg-changelog | ~90 | 4295156 | 4285336 | -0.23% |
| hg-commands | ~500 | 1095580 | 1079814 | -1.44% |
| hg-manifest | ~400 | 16559892 | 16504346 | -0.34% |
There is some noise in the measurements, since small changes to `k` can
have large differences, which is why I'm using `steps=256`, to try to
minimize the noise. However, the GitHub data set still has some noise.
If I run the GitHub data set on my Mac, which presumably lists directory
entries in a different order, so the dictionary builder sees the files in
a different order, or I use `steps=1024` I see these results.
| Run | Before | After | % difference |
|------------|--------|--------|--------------|
| steps=1024 | 738138 | 734470 | -0.50% |
| MacBook | 738451 | 737132 | -0.18% |
Question: Should we expose this as a parameter? I don't think it is
necessary. Someone might want to turn it up to exchange a much longer
dictionary building time in exchange for a slightly better dictionary.
I tested `2`, `4`, and `16`, and `4` got most of the benefit of `16`
with a faster running time.
this patch makes btultra do 2 passes on the first block,
the first one being dedicated to collecting statistics
so that the 2nd pass is more accurate.
It translates into a very small compression ratio gain :
enwik7, level 20:
blocks 4K : 2.142 -> 2.153
blocks 16K : 2.447 -> 2.457
blocks 64K : 2.716 -> 2.726
On the other hand, the cpu cost is doubled.
The trade off looks bad.
Though, that's ultimately a price to pay to reach better compression ratio.
So it's only enabled when setting btultra.
this improves compression ratio by a *tiny* amount.
It also reduces speed by a small amount.
Consequently, bit-fractional evaluation is only turned on for btultra.
