In-depth usage example: more control over your benchmark

This section borrows the example from the Snoop tutorial on the blake2b hashing function, but relies on Snoop sub-commands for better control over the benchmark process (corresponding to Step 2 in the tutorial). The objectives and the output files are the same as in the tutorial: benchmarking, inferring gas parameter values and generating the corresponding OCaml code, but sub-commands help to understand each sub-step, especially in case of unexpected results.

Step 1: Checking the timer

Before we perform the benchmarks, we need to ensure that the system timer is sufficiently precise. This data is also useful to subtract the latency of the timer for benchmarks of very small duration (which is not required here). We invoke the tool on the built-in benchmark TIMER_LATENCY and specify (through --bench-num) that we want only one closure to benchmark (since all closures are identical for this benchmark) but to execute this closure 100000 times (through --nsamples).

mavkit-snoop benchmark TIMER_LATENCY and save to timer.workload --bench-num 1 --nsamples 100000

The tool returns the following on standard output:

Benchmarking with the following options:
{ options = { flush_cache=false;
              stabilize_gc=false;
              seed=self-init;
              bench #=1;
              nsamples/bench=100000;
              determinizer=percentile 50;
              cpu_affinity=none;
              minor_heap_size=262144 words;
              config directory=None };
   save_file = timer.workload;
   storage = Mem }
Using default configuration for benchmark TIMER_LATENCY
{}
benchmarking 1/1
stats over all benchmarks: { max_time = 25.000000 ; min_time = 25.000000 ; mean_time = 25.000000 ; sigma = 0.000000 }

This commands measures 100000 times the latency of the timer, that is the minimum time between two timing measurements. This yields an empirical distribution on timings. The tool takes the 50th percentile (i.e. the median) of the empirical distribution and returns the result: 25ns latency. This is reasonable. Since there’s only one benchmark (with many samples), the standard deviation is by definition zero. One could also run many benchmarks with fewer samples per benchmark:

mavkit-snoop benchmark TIMER_LATENCY and save to timer.workload --bench-num 1000 --nsamples 100

This yields on standard output:

Benchmarking with the following options:
{ options = { flush_cache=false;
              stabilize_gc=false;
              seed=self-init;
              bench #=1000;
              nsamples/bench=100;
              determinizer=percentile 50;
              cpu_affinity=none;
              minor_heap_size=262144 words;
              config directory=None };
   save_file = timer.workload;
   storage = Mem }
Using default configuration for benchmark TIMER_LATENCY
{}
benchmarking 1000/1000
stats over all benchmarks: { max_time = 40.000000 ; min_time = 23.000000 ; mean_time = 24.130000 ; sigma = 0.653529 }

This is consistent with the previous results.

A reliable timer should have a latency of the order of 20 to 30 nanoseconds, with a very small standard deviation. It can happen on some hardware or software configurations that the timer latency is of the order of microseconds or worse: this makes benchmarking short-lived computations impossible.

Step 2: Benchmarking

If the results obtained in the previous section are reasonable, we can proceed to the generation of raw timing data. We want to invoke the Blake2b_example benchmark and save the resulting data to ./blake2b.workload. We want 500 distinct random inputs, and for each input we will perform the timing measurement 3000 times. The --determinizer option specifies how the empirical timing distribution corresponding to the per-input 3000 samples will be converted to a fixed value: here we pick the 50th percentile, i.e. the median (which happens to also be the default, so this option could have been omitted). We also use an explicit random seed in case we want to reproduce the exact same benchmarks. If not specified, the PRNG will self-initialize using an unknown seed.

mavkit-snoop benchmark Blake2b_example and save to blake2b.workload --bench-num 500 --nsamples 3000 --determinizer percentile@50 --seed 12897

Here’s the output:

Benchmarking with the following options:
{ options = { flush_cache=false;
              stabilize_gc=false;
              seed=12897;
              bench #=500;
              nsamples/bench=3000;
              determinizer=percentile 50;
              cpu_affinity=none;
              minor_heap_size=262144 words;
              config directory=None };
   save_file = blake2b.workload;
   storage = Mem }
Using default configuration for benchmark Blake2b_example
{ "max_bytes": 65536 }
benchmarking 500/500
stats over all benchmarks: { max_time = 71957.000000 ; min_time = 284.000000 ; mean_time = 34750.532000 ; sigma = 20155.604394 }

Since the size of inputs varies a lot, the statistics over all benchmarks are less useful.

Step 2.5: (optional) Removing outliers

It is possible to remove outliers from the raw benchmark data. The command is the following:

mavkit-snoop remove outliers from data ./blake2b.workload above 3 sigmas and save to blake2b-cleaned.workload

In this particular example, the data seems clean though:

Measure.load: loaded ./blake2b.workload
Removing outliers.
Stats: { max_time = 71925.000000 ; min_time = 289.000000 ; mean_time = 34988.436000 ; sigma = 20766.341788 }
Validity interval: [-27310.589365, 97287.461365].
Removed 0 outliers out of 500 elements.

The best defense against outliers is to have clean data in the first place: use a stable environment for benchmarking.

Step 3: Fitting the model

We can now proceed to inferring the free parameters from the model using the data. At the time of writing, the tool offloads the regression problem to the scikit-learn (aka sklearn) and the statmodels Python libraries: install them before proceeding.

pip install scikit-learn statsmodels

Let’s execute the following command:

mavkit-snoop infer parameters for model blake2b on data blake2b.workload using lasso --lasso-positive --dump-csv blake2b.csv --save-solution blake2b.sol --plot

Initializing python... Done.
Measure.load: loaded blake2b.workload
Applying model to workload data 500/500
Initializing matrices 500/500
Importing blake2b.csv
Exporting to blake2b.csv
Saved solution to blake2b.sol

The command performed the following tasks:

  • load the workload data from blake2b.workload;

  • construct a linear regression problem using the chosen model: here, the Blake2b_example benchmark only provides the blake2b model;

  • solve this problem using the specified lasso algorithm, with the constraint that the inferred coefficients must be positive;

  • dump the result of inference to a csv file named blake2b.csv;

  • save a structured solution (useful for code generation) to blake2b.sol;

  • plot the result of inference.

Let’s first have a look at the contents of the CSV solution blake2b.csv.

Inference results

blake2b_const

blake2b_ns_p_byte

129.279086813

1.09627036127

The columns correspond to the inferred values for the free variables of the blake2b cost model. The units are respectively ns/bytes for blake2b_ns_p_byte and ns for blake2b_const.

The tool also produces a plot:

../_images/inference.png

The leftmost figure plots the empirical data, i.e. the raw execution time (in nanoseconds) as a function of the input size (here, in bytes – other data structures might use different notions of sizes). The rightmost figure plots the empirical data along the predicted execution time. If the model is good and the parameters were correctly fitted, these should match. The central plot is useful when using complex nonlinearities to model the execution time of some piece of code: the tool will project back the raw data in the linear space spanned by the chosen nonlinearities and if the model is good, one should observe that the empirical data lies along a linear subspace. Here, the model is trivial so the central plot is less interesting.

Step 4: Generating code

As a final step, we demonstrate how to generate code corresponding to the model. This is typically used to generate gas consumption functions for Michelson instructions and not for raw functions like blake2b but the principle is similar.

mavkit-snoop generate code using solution blake2b.sol and model blake2b_codegen

By default, the tool produces integer code by casting floating point constant to integers. The tool produces the following code on stdout:

let model_blake2b_codegen size =
    (int_of_float 144.753899773) + (int_of_float 1.17988921492) * size

It is also possible to generate code implementing the cost function using fixed-point arithmetic. This requires specifying some codegen parameters in a JSON file. For instance, we can require to consider 5 bits of precision and use rounding to nearest to convert constants, failing if we make more than 10% relative error when casting. The inverse_scaling and resolution parameters respectively specify the fraction of digits considered to be not significant, and the resolution of the grid used when prettifying constants (in nanoseconds).

{ "precision": 6, "max_relative_error": 0.1, "cast_mode": "Round", "inverse_scaling": 10, "resolution": 5 }

Calling the tool:

mavkit-snoop generate code using solution blake2b.sol and model blake2b_codegen --fixed-point codegen_params.json

We get:

let model_blake2b_codegen size =
    let v0 = size in
    150 + ((v0 + (v0 lsr 3)) + (v0 lsr 5))