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Published: Apr 23, 2021 License: Apache-2.0 Imports: 11 Imported by: 0


pa - Performance (Change) Analysis

pa is an efficient tool for analyzing performance data based on statistical simulation, i.e., bootstrap. The performance data can come from measurements such as performance tests or benchmarks.

There are two main ways how to analyze performance data with pa:

  1. Single version analysis: statistic (e.g., mean) + variability (confidence interval of the statistic)
  2. Analysis between two versions: confidence interval ratio of a statistic (e.g., mean)

Inspired by [1], pa employs a Monte-Carlo technique called bootstrap [2] to estimate the population confidence interval from a given sample. It uses hierarchical random re-sampling with replacement [3]. In the context of performance analysis, these hierarchical levels correspond to levels where measurement repetition happens to have reliable results. These hierarchical levels are:

  1. invocation
  2. iteration
  3. fork
  4. trial
  5. instance

Higher levels are composed of multiple occurrences of lower levels, i.e., an iteration (level 2) consists of many invocations (level 1), and so on.

Requirements and Installations

pa requires only Go with version 1.14 or higher (Install Page).

Install pa by running go get


Command Line Interface

pa comes with a simple command line interface (optional flags in [...] with their defaults):

pa  [-bs 10000] [-is 0] [-sl 0.01] [-st mean] [-os] [-m 1] [-tra id:id] \
    file_1 \
    [file_2 ... file_n] 

If 1 file (file_1) is provided, the single version analysis is performed, i.e., the confidence intervals of a single performance experiment is computed.

If multiple files are provided, the two version analysis is performed: the confidence intervals for both versions and the confidence interval ratio between the two versions is computed. In the simple case, 2 files are provided, file_1 for version 1 and file_2 for version 2. It is also possible to provide multiple files per version (of equal number) by setting the flag -m.

Note that the files MUST be sorted alphabetically by their benchmarks (see section "Input Files").


  • -bs defines the number of bootstrap simulations, i.e., how many random samples are taken to estimate the population distribution
  • -is defines how many invocation samples are used (0 takes the mean across all invocations of an iteration, -1 takes all invocations, and > 0 for number of samples).
  • -sl defines the significance level. The confidence level for the confidence intervals is then 1-sl. The default is 0.01 which corresponds to a 99% confidence level.
  • -st defines the statistic for which a confidence interval is computed. The default is mean. Another option is median.
  • -os defines whether the statistic, as set by -st, is included in the output file.
  • -m sets the number of files per version (control and test group). For example, if -m 3 pa expects 6 files, where file_1, file_2, and file_3 belong to version 1, and file_4, file_5, and file_6 belong to version two.
  • -tra defines the transformation(s) applied to the benchmark results (i.e., the file(s)), in the form of transformer1:transformer2, where transformer1 is applied to the first (control) group and transformer2 is applied to the second (test) group (if it exists). Transformers can be one of id (identity, no transformation) or f0.0 ('f' for factor followed by a user-specified float64 value)
Input Files

pa expects CSV input files of the following form. For JMH benchmark results, the tool bencher can transform JMH JSON output to this CSV file format.


The columns represent the following values:

  1. project is the project name
  2. commit is the project version, e.g., a commit hash
  3. benchmark is the name of the fully-qualified benchmark method
  4. params are the performance parameters (not the function/method parameters) of the benchmark in comma-separated form. Every parameter consists of a name and a value, separated by an equal sign (name=value). For example JMH supports performance parameters through its @Param annotation
  5. instance is the name of the instance or machine (level 5)
  6. trial is the number of the trial (level 4)
  7. fork is the fork number (level 3). For example JMH supports forks through their @Fork annotation
  8. iteration is the iteration number within a fork (level 2)
  9. mode is the benchmark mode. For exmaple JMH supports average time avgt, throughput thrpt, or sample time sample
  10. unit is the measurement unit of the benchmark value. Depending on the mode, the measurement unit can be ns/op for average time or op/s for throughput
  11. value_count is the number of invocations (level 1) the value occurred in this iteration. Every iteration can have multiple values (i.e., invocations), which are presented as a histogram. Each histogram value corresponds to one CSV row, and the occurrences of this value is defined by value_count.
  12. value is the performance metric with a certain unit

IMPORTANT: the input files must be sorted by benchmark and params, otherwise the tool will not work correctly. This is because input files can be large and, therefore, pa works on file input streams.


pa writes the results in CSV form to stdout. The output can contain 3 types of CSV rows:

  • rows starting with # are comments
  • empty rows
  • all other rows are CSV rows

The columns are:

  1. benchmark is the name of the benchmark
  2. params are the function/method parameters of the benchmark. pa does not populate this column, because the input format does not provide the function/method parameters
  3. perf_params is a comma-separated list of performance parameters. See column params of the input files for comparison
  4. st is the statistic the confidence interval is for. Can be "mean" or "median"
  5. ci_l is the lower bound of the confidence interval
  6. ci_u is the upper bound of the confidence interval
  7. cl is the confidence level of the confidence interval
Single Version Analysis

The output file is a CSV with the following columns (without -os):


And with the statistic, as set by -os, it has the following columns:

Two Version Analysis

The output file is a CSV with the following columns (without -os):


And with the statistic, as set by -os, it has the following columns:


Compared to the single version analysis, the two version analysis has three or four (with or without -os) columns, for both versions (v1 and v2) and the confidence interval for the ratio between the two versions (ratio).


[1] T. Kalibera and R. Jones, “Quantifying performance changes with effect size confidence intervals”, University of Kent, Technical Report 4–12, June 2012. Available: URL

[2] A. C. Davison and D. V. Hinkley, “Bootstrap methods and their application”

[3] S. Ren, H. Lai, W. Tong, M. Aminzadeh, X. Hou, and S. Lai, “Nonparametric bootstrapping for hierarchical data”, Journal of Applied Statistics, vol. 37, no. 9, pp. 1487–1498, 2010. Available: DOI


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