The linear interpolation (assuming that observations are uniformly
distributed within a bucket) is a solid and simple assumption in lack
of any other information. However, the exponential bucketing used by
standard schemas of native histograms has been chosen to cover the
whole range of observations in a way that bucket populations are
spread out over buckets in a reasonably way for typical distributions
encountered in real-world scenarios.
This is the origin of the idea implemented here: If we divide a given
bucket into two (or more) smaller exponential buckets, we "most
naturally" expect that the samples in the original buckets will split
among those smaller buckets in a more or less uniform fashion. With
this assumption, we end up with an "exponential interpolation", which
therefore appears to be a better match for histograms with exponential
bucketing.
This commit leaves the linear interpolation in place for NHCB, but
changes the interpolation for exponential native histograms to
exponential. This affects `histogram_quantile` and
`histogram_fraction` (because the latter is more or less the inverse
of the former).
The zero bucket has to be treated specially because the assumption
above would lead to an "interpolation to zero" (the bucket density
approaches infinity around zero, and with the postulated uniform usage
of buckets, we would end up with an estimate of zero for all quantiles
ending up in the zero bucket). We simply fall back to linear
interpolation within the zero bucket.
At the same time, this commit makes the call to stick with the
assumption that the zero bucket only contains positive observations
for native histograms without negative buckets (and vice versa). (This
is an assumption relevant for interpolation. It is a mostly academic
point, as the zero bucket is supposed to be very small anyway.
However, in cases where it _is_ relevantly broad, the assumption helps
a lot in practice.)
This commit also updates and completes the documentation to match both
details about interpolation.
As a more high level note: The approach here attempts to strike a
balance between a more simplistic approach without any assumption, and
a more involved approach with more sophisticated assumptions. I will
shortly describe both for reference:
The "zero assumption" approach would be to not interpolate at all, but
_always_ return the harmonic mean of the bucket boundaries of the
bucket the quantile ends up in. This has the advantage of minimizing
the maximum possible relative error of the quantile estimation.
(Depending on the exact definition of the relative error of an
estimation, there is also an argument to return the arithmetic mean of
the bucket boundaries.) While limiting the maximum possible relative
error is a good property, this approach would throw away the
information if a quantile is closer to the upper or lower end of the
population within a bucket. This can be valuable trending information
in a dashboard. With any kind of interpolation, the maximum possible
error of a quantile estimation increases to the full width of a bucket
(i.e. it more than doubles for the harmonic mean approach, and
precisely doubles for the arithmetic mean approach). However, in
return the _expectation value_ of the error decreases. The increase of
the theoretical maximum only has practical relevance for pathologic
distributions. For example, if there are thousand observations within
a bucket, they could _all_ be at the upper bound of the bucket. If the
quantile calculation picks the 1st observation in the bucket as the
relevant one, an interpolation will yield a value close to the lower
bucket boundary, while the true quantile value is close to the upper
boundary.
The "fancy interpolation" approach would be one that analyses the
_actual_ distribution of samples in the histogram. A lot of statistics
could be applied based on the information we have available in the
histogram. This would include the population of neighboring (or even
all) buckets in the histogram. In general, the resolution of a native
histogram should be quite high, and therefore, those "fancy"
approaches would increase the computational cost quite a bit with very
little practical benefits (i.e. just tiny corrections of the estimated
quantile value). The results are also much harder to reason with.
Signed-off-by: beorn7 <beorn@grafana.com>
* modify unit test framework to automatically generate native histograms with custom buckets from classic histogram series
* add very basic tests for classic histogram converted into native histogram with custom bounds
* fix histogram_quantile for native histograms with custom buckets
* make loading with nhcb explicit
* evaluate native histograms with custom buckets on queries with explicit keyword
* use regex replacer
* use temp histogram struct for automatically loading converted nhcb
Signed-off-by: Jeanette Tan <jeanette.tan@grafana.com>
Signed-off-by: George Krajcsovits <krajorama@users.noreply.github.com>
promql: Improve histogram_quantile calculation for classic buckets
Tiny differences between classic buckets are most likely caused by floating point precision issues. With this commit, relative changes below a certain threshold are ignored. This makes the result of histogram_quantile more meaningful, and also avoids triggering the _input to histogram_quantile needed to be fixed for monotonicity_ annotations in unactionable cases.
This commit also adds explanation of the new adjustment and of the monotonicity annotation to the documentation of `histogram_quantile`.
---------
Signed-off-by: Jeanette Tan <jeanette.tan@grafana.com>
Wiser coders than myself have come to the conclusion that a `switch`
statement is almost always superior to a statement that includes any
`else if`.
The exceptions that I have found in our codebase are just these two:
* The `if else` is followed by an additional statement before the next
condition (separated by a `;`).
* The whole thing is within a `for` loop and `break` statements are
used. In this case, using `switch` would require tagging the `for`
loop, which probably tips the balance.
Why are `switch` statements more readable?
For one, fewer curly braces. But more importantly, the conditions all
have the same alignment, so the whole thing follows the natural flow
of going down a list of conditions. With `else if`, in contrast, all
conditions but the first are "hidden" behind `} else if `, harder to
spot and (for no good reason) presented differently from the first
condition.
I'm sure the aforemention wise coders can list even more reasons.
In any case, I like it so much that I have found myself recommending
it in code reviews. I would like to make it a habit in our code base,
without making it a hard requirement that we would test on the CI. But
for that, there has to be a role model, so this commit eliminates all
`if else` occurrences, unless it is autogenerated code or fits one of
the exceptions above.
Signed-off-by: beorn7 <beorn@grafana.com>
In other words: Instead of having a “polymorphous” `Point` that can
either contain a float value or a histogram value, use an `FPoint` for
floats and an `HPoint` for histograms.
This seemingly small change has a _lot_ of repercussions throughout
the codebase.
The idea here is to avoid the increase in size of `Point` arrays that
happened after native histograms had been added.
The higher-level data structures (`Sample`, `Series`, etc.) are still
“polymorphous”. The same idea could be applied to them, but at each
step the trade-offs needed to be evaluated.
The idea with this change is to do the minimum necessary to get back
to pre-histogram performance for functions that do not touch
histograms. Here are comparisons for the `changes` function. The test
data doesn't include histograms yet. Ideally, there would be no change
in the benchmark result at all.
First runtime v2.39 compared to directly prior to this commit:
```
name old time/op new time/op delta
RangeQuery/expr=changes(a_one[1d]),steps=1-16 391µs ± 2% 542µs ± 1% +38.58% (p=0.000 n=9+8)
RangeQuery/expr=changes(a_one[1d]),steps=10-16 452µs ± 2% 617µs ± 2% +36.48% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_one[1d]),steps=100-16 1.12ms ± 1% 1.36ms ± 2% +21.58% (p=0.000 n=8+10)
RangeQuery/expr=changes(a_one[1d]),steps=1000-16 7.83ms ± 1% 8.94ms ± 1% +14.21% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_ten[1d]),steps=1-16 2.98ms ± 0% 3.30ms ± 1% +10.67% (p=0.000 n=9+10)
RangeQuery/expr=changes(a_ten[1d]),steps=10-16 3.66ms ± 1% 4.10ms ± 1% +11.82% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_ten[1d]),steps=100-16 10.5ms ± 0% 11.8ms ± 1% +12.50% (p=0.000 n=8+10)
RangeQuery/expr=changes(a_ten[1d]),steps=1000-16 77.6ms ± 1% 87.4ms ± 1% +12.63% (p=0.000 n=9+9)
RangeQuery/expr=changes(a_hundred[1d]),steps=1-16 30.4ms ± 2% 32.8ms ± 1% +8.01% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_hundred[1d]),steps=10-16 37.1ms ± 2% 40.6ms ± 2% +9.64% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_hundred[1d]),steps=100-16 105ms ± 1% 117ms ± 1% +11.69% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_hundred[1d]),steps=1000-16 783ms ± 3% 876ms ± 1% +11.83% (p=0.000 n=9+10)
```
And then runtime v2.39 compared to after this commit:
```
name old time/op new time/op delta
RangeQuery/expr=changes(a_one[1d]),steps=1-16 391µs ± 2% 547µs ± 1% +39.84% (p=0.000 n=9+8)
RangeQuery/expr=changes(a_one[1d]),steps=10-16 452µs ± 2% 616µs ± 2% +36.15% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_one[1d]),steps=100-16 1.12ms ± 1% 1.26ms ± 1% +12.20% (p=0.000 n=8+10)
RangeQuery/expr=changes(a_one[1d]),steps=1000-16 7.83ms ± 1% 7.95ms ± 1% +1.59% (p=0.000 n=10+8)
RangeQuery/expr=changes(a_ten[1d]),steps=1-16 2.98ms ± 0% 3.38ms ± 2% +13.49% (p=0.000 n=9+10)
RangeQuery/expr=changes(a_ten[1d]),steps=10-16 3.66ms ± 1% 4.02ms ± 1% +9.80% (p=0.000 n=10+9)
RangeQuery/expr=changes(a_ten[1d]),steps=100-16 10.5ms ± 0% 10.8ms ± 1% +3.08% (p=0.000 n=8+10)
RangeQuery/expr=changes(a_ten[1d]),steps=1000-16 77.6ms ± 1% 78.1ms ± 1% +0.58% (p=0.035 n=9+10)
RangeQuery/expr=changes(a_hundred[1d]),steps=1-16 30.4ms ± 2% 33.5ms ± 4% +10.18% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_hundred[1d]),steps=10-16 37.1ms ± 2% 40.0ms ± 1% +7.98% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_hundred[1d]),steps=100-16 105ms ± 1% 107ms ± 1% +1.92% (p=0.000 n=10+10)
RangeQuery/expr=changes(a_hundred[1d]),steps=1000-16 783ms ± 3% 775ms ± 1% -1.02% (p=0.019 n=9+9)
```
In summary, the runtime doesn't really improve with this change for
queries with just a few steps. For queries with many steps, this
commit essentially reinstates the old performance. This is good
because the many-step queries are the one that matter most (longest
absolute runtime).
In terms of allocations, though, this commit doesn't make a dent at
all (numbers not shown). The reason is that most of the allocations
happen in the sampleRingIterator (in the storage package), which has
to be addressed in a separate commit.
Signed-off-by: beorn7 <beorn@grafana.com>
The bucket receiving math.MaxFloat64 observations now has
math.MaxFloat64 as upper bound, while the bucket after it (the last
possible bucket) has +Inf.
This also adds a test for getBound and moves the getBound code to
generic.go (where it should have been in the first place).
Signed-off-by: beorn7 <beorn@grafana.com>
* histogram: Simplify iterators
We don't really need currLower and currUpper and can calculate it when
needed (as already done for the floatBucketIterator). The calculation
is cheap, while keeping those extra variables around costs RAM
(potentially a lot with many iterators).
* histogram: Convert Bucket/FloatBucket to one generic type
* histogram: Move some bucket iterator code into generic base iterator
* histogram: Remove cumulative iterator for FloatHistogram
We added it in the past for completeness (Histogram has one), but it
has never been used. Plus, even the cumulative iterator for Histogram
is only there for test reasons.
We can always add it back, and then maybe even using generics.
Signed-off-by: beorn7 <beorn@grafana.com>
Essentially, this mirrors the existing behavior for negative buckets:
If a histogram has only negative buckets, the upper bound of the zero
bucket is assumed to be zero.
Furthermore, it makes sure that the zero bucket boundaries are not
modified if a histogram that has no buckets at all but samples in the
zero bucket.
Also, add an TODO to vet if we really want this behavior.
Signed-off-by: beorn7 <beorn@grafana.com>
For conventional histograms, we need to gather all the individual
bucket timeseries at a data point to do the quantile calculation. The
code so far mirrored this behavior for the new native
histograms. However, since a single data point contains all the
buckets alreade, that's actually not needed. This PR simplifies the
code while still detecting a mix of conventional and native
histograms.
The weird signature calculation for the conventional histograms is
getting even weirder because of that. If this PR turns out to do the
right thing, I will implement a proper fix for the signature
calculation upstream.
Signed-off-by: beorn7 <beorn@grafana.com>
- Simplify the code a bit.
- Cover more corner cases.
- Remove TODO for negative buckets. (I think they are handled. Tests
will reveal if not.)
Signed-off-by: beorn7 <beorn@grafana.com>
* MergeFloatBucketIterator for []FloatBucketIterator
Signed-off-by: Ganesh Vernekar <ganeshvern@gmail.com>
* histogram_quantile for histograms
Signed-off-by: Ganesh Vernekar <ganeshvern@gmail.com>
* Fix histogram_quantile
Signed-off-by: Ganesh Vernekar <ganeshvern@gmail.com>
* Unit test and enhancements
Signed-off-by: Ganesh Vernekar <ganeshvern@gmail.com>
* Iterators to iterate buckets in reverse and all buckets together including zero bucket
Signed-off-by: Ganesh Vernekar <ganeshvern@gmail.com>
* Consider all buckets for histogram_quantile and fix the implementation
Signed-off-by: Ganesh Vernekar <ganeshvern@gmail.com>
* Remove unneeded code
Signed-off-by: Ganesh Vernekar <ganeshvern@gmail.com>
* Fix lint
Signed-off-by: Ganesh Vernekar <ganeshvern@gmail.com>
This creates a new `model` directory and moves all data-model related
packages over there:
exemplar labels relabel rulefmt textparse timestamp value
All the others are more or less utilities and have been moved to `util`:
gate logging modetimevfs pool runtime
Signed-off-by: beorn7 <beorn@grafana.com>
This makes things generally more resilient, and will
help with OpenMetrics transitions (and inconsistencies).
Signed-off-by: Brian Brazil <brian.brazil@robustperception.io>
* Force buckets in a histogram to be monotonic for quantile estimation
The assumption that bucket counts increase monotonically with increasing
upperBound may be violated during:
* Recording rule evaluation of histogram_quantile, especially when rate()
has been applied to the underlying bucket timeseries.
* Evaluation of histogram_quantile computed over federated bucket
timeseries, especially when rate() has been applied
This is because scraped data is not made available to RR evalution or
federation atomically, so some buckets are computed with data from the N
most recent scrapes, but the other buckets are missing the most recent
observations.
Monotonicity is usually guaranteed because if a bucket with upper bound
u1 has count c1, then any bucket with a higher upper bound u > u1 must
have counted all c1 observations and perhaps more, so that c >= c1.
Randomly interspersed partial sampling breaks that guarantee, and rate()
exacerbates it. Specifically, suppose bucket le=1000 has a count of 10 from
4 samples but the bucket with le=2000 has a count of 7, from 3 samples. The
monotonicity is broken. It is exacerbated by rate() because under normal
operation, cumulative counting of buckets will cause the bucket counts to
diverge such that small differences from missing samples are not a problem.
rate() removes this divergence.)
bucketQuantile depends on that monotonicity to do a binary search for the
bucket with the qth percentile count, so breaking the monotonicity
guarantee causes bucketQuantile() to return undefined (nonsense) results.
As a somewhat hacky solution until the Prometheus project is ready to
accept the changes required to make scrapes atomic, we calculate the
"envelope" of the histogram buckets, essentially removing any decreases
in the count between successive buckets.
* Fix up comment docs for ensureMonotonic
* ensureMonotonic: Use switch statement
Use switch statement rather than if/else for better readability.
Process the most frequent cases first.
This calculates how much a counter increases over
a given period of time, which is the area under the curve
of it's rate.
increase(x[5m]) is equivilent to rate(x[5m]) * 300.
This copies the evaluation logic from the current rules/ package.
The new engine handles the execution process from query string to final result.
It provides query timeout and cancellation and general flexibility for
future changes.
functions.go: Add evaluation implementation. Slight changes to in/out data but
not to the processing logic.
quantile.go: No changes.
analyzer.go: No changes.
engine.go: Actually new part. Mainly consists of evaluation methods
which were not changed.
setup_test.go: Copy of rules/helpers_test.go to setup test storage.
promql_test.go: Copy of rules/rules_test.go.
Since we are now getting really deep into floating point calculation,
the tests had to take into account the precision loss. Since the rule
tests are based on direct line matching in the output, implementing
the "almost equal" semantics was pretty cumbersome, but here we are.
beorn7