# Benchmark Tools
## compare.py
The `compare.py` can be used to compare the result of benchmarks.
### Dependencies
The utility relies on the [scipy](https://www.scipy.org) package which can be installed using pip:
```bash
pip3 install -r requirements.txt
```
### Displaying aggregates only
The switch `-a` / `--display_aggregates_only` can be used to control the
displayment of the normal iterations vs the aggregates. When passed, it will
be passthrough to the benchmark binaries to be run, and will be accounted for
in the tool itself; only the aggregates will be displayed, but not normal runs.
It only affects the display, the separate runs will still be used to calculate
the U test.
### Modes of operation
There are three modes of operation:
1. Just compare two benchmarks
The program is invoked like:
``` bash
$ compare.py benchmarks <benchmark_baseline> <benchmark_contender> [benchmark options]...
```
Where `<benchmark_baseline>` and `<benchmark_contender>` either specify a benchmark executable file, or a JSON output file. The type of the input file is automatically detected. If a benchmark executable is specified then the benchmark is run to obtain the results. Otherwise the results are simply loaded from the output file.
`[benchmark options]` will be passed to the benchmarks invocations. They can be anything that binary accepts, be it either normal `--benchmark_*` parameters, or some custom parameters your binary takes.
Example output:
```
$ ./compare.py benchmarks ./a.out ./a.out
RUNNING: ./a.out --benchmark_out=/tmp/tmprBT5nW
Run on (8 X 4000 MHz CPU s)
2017-11-07 21:16:44
------------------------------------------------------
Benchmark Time CPU Iterations
------------------------------------------------------
BM_memcpy/8 36 ns 36 ns 19101577 211.669MB/s
BM_memcpy/64 76 ns 76 ns 9412571 800.199MB/s
BM_memcpy/512 84 ns 84 ns 8249070 5.64771GB/s
BM_memcpy/1024 116 ns 116 ns 6181763 8.19505GB/s
BM_memcpy/8192 643 ns 643 ns 1062855 11.8636GB/s
BM_copy/8 222 ns 222 ns 3137987 34.3772MB/s
BM_copy/64 1608 ns 1608 ns 432758 37.9501MB/s
BM_copy/512 12589 ns 12589 ns 54806 38.7867MB/s
BM_copy/1024 25169 ns 25169 ns 27713 38.8003MB/s
BM_copy/8192 201165 ns 201112 ns 3486 38.8466MB/s
RUNNING: ./a.out --benchmark_out=/tmp/tmpt1wwG_
Run on (8 X 4000 MHz CPU s)
2017-11-07 21:16:53
------------------------------------------------------
Benchmark Time CPU Iterations
------------------------------------------------------
BM_memcpy/8 36 ns 36 ns 19397903 211.255MB/s
BM_memcpy/64 73 ns 73 ns 9691174 839.635MB/s
BM_memcpy/512 85 ns 85 ns 8312329 5.60101GB/s
BM_memcpy/1024 118 ns 118 ns 6438774 8.11608GB/s
BM_memcpy/8192 656 ns 656 ns 1068644 11.6277GB/s
BM_copy/8 223 ns 223 ns 3146977 34.2338MB/s
BM_copy/64 1611 ns 1611 ns 435340 37.8751MB/s
BM_copy/512 12622 ns 12622 ns 54818 38.6844MB/s
BM_copy/1024 25257 ns 25239 ns 27779 38.6927MB/s
BM_copy/8192 205013 ns 205010 ns 3479 38.108MB/s
Comparing ./a.out to ./a.out
Benchmark Time CPU Time Old Time New CPU Old CPU New
------------------------------------------------------------------------------------------------------
BM_memcpy/8 +0.0020 +0.0020 36 36 36 36
BM_memcpy/64 -0.0468 -0.0470 76 73 76 73
BM_memcpy/512 +0.0081 +0.0083 84 85 84 85
BM_memcpy/1024 +0.0098 +0.0097 116 118 116 118
BM_memcpy/8192 +0.0200 +0.0203 643 656 643 656
BM_copy/8 +0.0046 +0.0042 222 223 222 223
BM_copy/64 +0.0020 +0.0020 1608 1611 1608 1611
BM_copy/512 +0.0027 +0.0026 12589 12622 12589 12622
BM_copy/1024 +0.0035 +0.0028 25169 25257 25169 25239
BM_copy/8192 +0.0191 +0.0194 201165 205013 201112 205010
```
What it does is for the every benchmark from the first run it looks for the benchmark with exactly the same name in the second run, and then compares the results. If the names differ, the benchmark is omitted from the diff.
As you can note, the values in `Time` and `CPU` columns are calculated as `(new - old) / |old|`.
2. Compare two different filters of one benchmark
The program is invoked like:
``` bash
$ compare.py filters <benchmark> <filter_baseline> <filter_contender> [benchmark options]...
```
Where `<benchmark>` either specify a benchmark executable file, or a JSON output file. The type of the input file is automatically detected. If a benchmark executable is specified then the benchmark is run to obtain the results. Otherwise the results are simply loaded from the output file.
Where `<filter_baseline>` and `<filter_contender>` are the same regex filters that you would pass to the `[--benchmark_filter=<regex>]` parameter of the benchmark binary.
`[benchmark options]` will be passed to the benchmarks invocations. They can be anything that binary accepts, be it either normal `--benchmark_*` parameters, or some custom parameters your binary takes.
Example output:
```
$ ./compare.py filters ./a.out BM_memcpy BM_copy
RUNNING: ./a.out --benchmark_filter=BM_memcpy --benchmark_out=/tmp/tmpBWKk0k
Run on (8 X 4000 MHz CPU s)
2017-11-07 21:37:28
------------------------------------------------------
Benchmark Time CPU Iterations
------------------------------------------------------
BM_memcpy/8 36 ns 36 ns 17891491 211.215MB/s
BM_memcpy/64 74 ns 74 ns 9400999 825.646MB/s
BM_memcpy/512 87 ns 87 ns 8027453 5.46126GB/s
BM_memcpy/1024 111 ns 111 ns 6116853 8.5648GB/s
BM_memcpy/8192 657 ns 656 ns 1064679 11.6247GB/s
RUNNING: ./a.out --benchmark_filter=BM_copy --benchmark_out=/tmp/tmpAvWcOM
Run on (8 X 4000 MHz CPU s)
2017-11-07 21:37:33
----------------------------------------------------
Benchmark Time CPU Iterations
----------------------------------------------------
BM_copy/8 227 ns 227 ns 3038700 33.6264MB/s
BM_copy/64 1640 ns 1640 ns 426893 37.2154MB/s
BM_copy/512 12804 ns 12801 ns 55417 38.1444MB/s
BM_copy/1024 25409 ns 25407 ns 27516 38.4365MB/s
BM_copy/8192 202986 ns 202990 ns 3454 38.4871MB/s
Comparing BM_memcpy to BM_copy (from ./a.out)
Benchmark Time CPU Time Old Time New CPU Old CPU New
--------------------------------------------------------------------------------------------------------------------
[BM_memcpy vs. BM_copy]/8 +5.2829 +5.2812 36 227 36 227
[BM_memcpy vs. BM_copy]/64 +21.1719 +21.1856 74 1640 74 1640
[BM_memcpy vs. BM_copy]/512 +145.6487 +145.6097 87 12804 87 12801
[BM_memcpy vs. BM_copy]/1024 +227.1860 +227.1776 111 25409 111 25407
[BM_memcpy vs. BM_copy]/8192 +308.1664 +308.2898 657 202986 656 202990
```
As you can see, it applies filter to the benchmarks, both when running the benchmark, and before doing the diff. And to make the diff work, the matches are replaced with some common string. Thus, you can compare two different benchmark families within one benchmark binary.
As you can note, the values in `Time` and `CPU` columns are calculated as `(new - old) / |old|`.
3. Compare filter one from benchmark one to filter two from benchmark two:
The program is invoked like:
``` bash
$ compare.py filters <benchmark_baseline> <filter_baseline> <benchmark_contender> <filter_contender> [benchmark options]...
```
Where `<benchmark_baseline>` and `<benchmark_contender>` either specify a benchmark executable file, or a JSON output file. The type of the input file is automatically detected. If a benchmark executable is specified then the benchmark is run to obtain the results. Otherwise the results are simply loaded from the output file.
Where `<filter_baseline>` and `<filter_contender>` are the same regex filters that you would pass to the `[--benchmark_filter=<regex>]` parameter of the benchmark binary.
`[benchmark options]` will be passed to the benchmarks invocations. They can be anything that binary accepts, be it either normal `--benchmark_*` parameters, or some custom parameters your binary takes.
Example output:
```
$ ./compare.py benchmarksfiltered ./a.out BM_memcpy ./a.out BM_copy
RUNNING: ./a.out --benchmark_filter=BM_memcpy --benchmark_out=/tmp/tmp_FvbYg
Run on (8 X 4000 MHz CPU s)
2017-11-07 21:38:27
------------------------------------------------------
Benchmark Time CPU Iterations
------------------------------------------------------
BM_memcpy/8 37 ns 37 ns 18953482 204.118MB/s
BM_memcpy/64 74 ns 74 ns 9206578 828.245MB/s
BM_memcpy/512 91 ns 91 ns 8086195 5.25476GB/s
BM_memcpy/1024 120 ns 120 ns 5804513 7.95662GB/s
BM_memcpy/8192 664 ns 664 ns 1028363 11.4948GB/s
RUNNING: ./a.out --benchmark_filter=BM_copy --benchmark_out=/tmp/tmpDfL5iE
Run on (8 X 4000 MHz CPU s)
2017-11-07 21:38:32
----------------------------------------------------
Benchmark Time CPU Iterations
----------------------------------------------------
BM_copy/8 230 ns 230 ns 2985909 33.1161MB/s
BM_copy/64 1654 ns 1653 ns 419408 36.9137MB/s
BM_copy/512 13122 ns 13120 ns 53403 37.2156MB/s
BM_copy/1024 26679 ns 26666 ns 26575 36.6218MB/s
BM_copy/8192 215068 ns 215053 ns 3221 36.3283MB/s
Comparing BM_memcpy (from ./a.out) to BM_copy (from ./a.out)
Benchmark Time CPU Time Old Time New CPU Old CPU New
--------------------------------------------------------------------------------------------------------------------
[BM_memcpy vs. BM_copy]/8 +5.1649 +5.1637 37 230 37 230
[BM_memcpy vs. BM_copy]/64 +21.4352 +21.4374 74 1654 74 1653
[BM_memcpy vs. BM_copy]/512 +143.6022 +143.5865 91 13122 91 13120
[BM_memcpy vs. BM_copy]/1024 +221.5903 +221.4790 120 26679 120 26666
[BM_memcpy vs. BM_copy]/8192 +322.9059 +323.0096 664 215068 664 215053
```
This is a mix of the previous two modes, two (potentially different) benchmark binaries are run, and a different filter is applied to each one.
As you can note, the values in `Time` and `CPU` columns are calculated as `(new - old) / |old|`.
### Note: Interpreting the output
Performance measurements are an art, and performance comparisons are doubly so.
Results are often noisy and don't necessarily have large absolute differences to
them, so just by visual inspection, it is not at all apparent if two
measurements are actually showing a performance change or not. It is even more
confusing with multiple benchmark repetitions.
Thankfully, what we can do, is use statistical tests on the results to determine
whether the performance has statistically-significantly changed. `compare.py`
uses [Mann–Whitney U
test](https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test), with a null
hypothesis being that there's no difference in performance.
**The below output is a summary of a benchmark comparison with statistics
provided for a multi-threaded process.**
```
Benchmark Time CPU Time Old Time New CPU Old CPU New
-----------------------------------------------------------------------------------------------------------------------------
benchmark/threads:1/process_time/real_time_pvalue 0.0000 0.0000 U Test, Repetitions: 27 vs 27
benchmark/threads:1/process_time/real_time_mean -0.1442 -0.1442 90 77 90 77
benchmark/threads:1/process_time/real_time_median -0.1444 -0.1444 90 77 90 77
benchmark/threads:1/process_time/real_time_stddev +0.3974 +0.3933 0 0 0 0
benchmark/threads:1/process_time/real_time_cv +0.6329 +0.6280 0 0 0 0
OVERALL_GEOMEAN -0.1442 -0.1442 0 0 0 0
```
--------------------------------------------
Here's a breakdown of each row:
**benchmark/threads:1/process_time/real_time_pvalue**: This shows the _p-value_ for
the statistical test comparing the performance of the process running with one
thread. A value of 0.0000 suggests a statistically significant difference in
performance. The comparison was conducted using the U Test (Mann-Whitney
U Test) with 27 repetitions for each case.
**benchmark/threads:1/process_time/real_time_mean**: This shows the relative
difference in mean execution time between two different cases. The negative
value (-0.1442) implies that the new process is faster by about 14.42%. The old
time was 90 units, while the new time is 77 units.
**benchmark/threads:1/process_time/real_time_median**: Similarly, this shows the
relative difference in the median execution time. Again, the new process is
faster by 14.44%.
**benchmark/threads:1/process_time/real_time_stddev**: This is the relative
difference in the standard deviation of the execution time, which is a measure
of how much variation or dispersion there is from the mean. A positive value
(+0.3974) implies there is more variance in the execution time in the new
process.
**benchmark/threads:1/process_time/real_time_cv**: CV stands for Coefficient of
Variation. It is the ratio of the standard deviation to the mean. It provides a
standardized measure of dispersion. An increase (+0.6329) indicates more
relative variability in the new process.
**OVERALL_GEOMEAN**: Geomean stands for geometric mean, a type of average that is
less influenced by outliers. The negative value indicates a general improvement
in the new process. However, given the values are all zero for the old and new
times, this seems to be a mistake or placeholder in the output.
-----------------------------------------
Let's first try to see what the different columns represent in the above
`compare.py` benchmarking output:
1. **Benchmark:** The name of the function being benchmarked, along with the
size of the input (after the slash).
2. **Time:** The average time per operation, across all iterations.
3. **CPU:** The average CPU time per operation, across all iterations.
4. **Iterations:** The number of iterations the benchmark was run to get a
stable estimate.
5. **Time Old and Time New:** These represent the average time it takes for a
function to run in two different scenarios or versions. For example, you
might be comparing how fast a function runs before and after you make some
changes to it.
6. **CPU Old and CPU New:** These show the average amount of CPU time that the
function uses in two different scenarios or versions. This is similar to
Time Old and Time New, but focuses on CPU usage instead of overall time.
In the comparison section, the relative differences in both time and CPU time
are displayed for each input size.
A statistically-significant difference is determined by a **p-value**, which is
a measure of the probability that the observed difference could have occurred
just by random chance. A smaller p-value indicates stronger evidence against the
null hypothesis.
**Therefore:**
1. If the p-value is less than the chosen significance level (alpha), we
reject the null hypothesis and conclude the benchmarks are significantly
different.
2. If the p-value is greater than or equal to alpha, we fail to reject the
null hypothesis and treat the two benchmarks as similar.
The result of said the statistical test is additionally communicated through color coding:
```diff
+ Green:
```
The benchmarks are _**statistically different**_. This could mean the
performance has either **significantly improved** or **significantly
deteriorated**. You should look at the actual performance numbers to see which
is the case.
```diff
- Red:
```
The benchmarks are _**statistically similar**_. This means the performance
**hasn't significantly changed**.
In statistical terms, **'green'** means we reject the null hypothesis that
there's no difference in performance, and **'red'** means we fail to reject the
null hypothesis. This might seem counter-intuitive if you're expecting 'green'
to mean 'improved performance' and 'red' to mean 'worsened performance'.
```bash
But remember, in this context:
'Success' means 'successfully finding a difference'.
'Failure' means 'failing to find a difference'.
```
Also, please note that **even if** we determine that there **is** a
statistically-significant difference between the two measurements, it does not
_necessarily_ mean that the actual benchmarks that were measured **are**
different, or vice versa, even if we determine that there is **no**
statistically-significant difference between the two measurements, it does not
necessarily mean that the actual benchmarks that were measured **are not**
different.
### U test
If there is a sufficient repetition count of the benchmarks, the tool can do
a [U Test](https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test), of the
null hypothesis that it is equally likely that a randomly selected value from
one sample will be less than or greater than a randomly selected value from a
second sample.
If the calculated p-value is below this value is lower than the significance
level alpha, then the result is said to be statistically significant and the
null hypothesis is rejected. Which in other words means that the two benchmarks
aren't identical.
**WARNING**: requires **LARGE** (no less than 9) number of repetitions to be
meaningful!
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