Napkin Math

The goal of this project is to collect software, numbers, and techniques to
quickly estimate the expected performance of systems from first-principles. For
example, how quickly can you read 1 GB of memory? By composing these resources
you should be able to answer interesting questions like: how much storage cost
should you expect to pay for logging for an application with 100,000 RPS?

The best introduction to this skill is through my talk at
SRECON.

The best way to practise napkin math in the grand domain of computers is to work
on your own problems. The second-best is to subscribe to this
newsletter where you'll get a problem every few
weeks to practise on. It should only take you a few minutes to solve each one as your
facility with these techniques improve.

The archive of problems to practise with are
here. The solution will be in the following
newsletter.

Numbers

Below are numbers that are rounded from runs on a metal Intel Xeon E-2236 3.4GHz
with 12 (virtual) cores.

Note 1: Some throughput and latency numbers don't line up, this is
intentional for ease of calculations.

Note 2: Take the numbers with a grain of salt. E.g. for I/O, fio is
the state-of-the-art. I am continuously updating these numbers as I learn more
to improve accuracy and as hardware improves.

†: "Fast serialization/deserialization" is typically a simple wire-protocol
that just dumps bytes, or a very efficient environment. Typically standard
serialization such as e.g. JSON will be of the slower kind. We include both here
as serialization/deserialization is a very, very broad topic with extremely
different performance characteristics depending on data and implementation.

You can run this with ./run to run with the right optimization levels. You
won't get the right numbers when you're compiling in debug mode. You can help
this project by adding new suites and filling out the blanks.

Note: I'm currently porting the benchmarks over to Criterion.rs, so some are
in bench/ now. You can run those by uncommenting the relevant line in ./run.

I am aware of some inefficiencies in this suite. I intend to improve my skills
in this area, in order to ensure the numbers are the upper-bound of performance
you may be able to squeeze out in production. I find it highly unlikely any of
them will be more than 2-3x off, which shouldn't be a problem for most users.

Cost Numbers

Approximate numbers that should be consistent between Cloud providers.

† This refers to network leaving your cloud provider, e.g. sending data to S3
from GCP or egress network for sending HTML from AWS to a client.

‡ An additional per cache-fill fee is incurred that costs close to blob storage
write costs (see just below).

Furthermore, for blob storage (S3/GCS/R2/...), you're charged per read/write
operation (fewer, large files is cheaper):

Compression Ratios

This is sourced from a few sources. [3] [4] [5] Note that compression speeds (but
generally not ratios) vary by an order of magnitude depending on the algorithm
and the level of compression (which trades speed for compression).

I typically ballpark that another x in compression ratio decreases performance
by 10x. E.g. we can get a 2x ratio on English
Wikipedia at ~200
MiB/s, and 3x at ~20MiB/s, and 4x at 1MB/s.

Techniques

• Don't overcomplicate. If you are basing your calculation on more than 6
  assumptions, you're likely making it harder than it should be.
• Keep the units. They're good checksumming.
  Wolframalpha has terrific support if you need a
  hand in converting e.g. KiB to TiB.
• Calculate with exponents. A lot of back-of-the-envelope calculations are
  done with just coefficients and exponents, e.g. c * 10^e. Your goal is to
  get within an order of magnitude right--that's just e. c matters a lot
  less. Only worrying about single-digit coefficients and exponents makes it
  much easier on a napkin (not to speak of all the zeros you avoid writing).
• Perform Fermi decomposition. Write down things you can guess at until you
  can start to hint at an answer. When you want to know the cost of storage
  for logging, you're going to want to know how big a log line is, how many of
  those you have per second, what that costs, and so on.

Resources

• [1]: https://eli.thegreenplace.net/2018/measuring-context-switching-and-memory-overheads-for-linux-threads/
• [2]: https://blog.tsunanet.net/2010/11/how-long-does-it-take-to-make-context.html
• [3]: https://cran.r-project.org/web/packages/brotli/vignettes/brotli-2015-09-22.pdf
• [4]: https://github.com/google/snappy
• [5]: https://quixdb.github.io/squash-benchmark/
• [6]: https://dl.acm.org/doi/10.1145/1879141.1879143
• [7]: https://en.wikipedia.org/wiki/Hard_disk_drive_performance_characteristics#Seek_times_&_characteristics
• [8]: https://github.com/simdjson/simdjson#performance-results
• [9]: https://github.com/protocolbuffers/protobuf/blob/master/docs/performance.md
• [10]: https://www.imperialviolet.org/2010/06/25/overclocking-ssl.html
• [11]: https://github.com/inikep/lzbench
• "How to get consistent results when benchmarking on
  Linux?".
  Great compilation of various Kernel and CPU features to toggle for reliable
  bench-marking, e.g. CPU affinity, disabling turbo boost, etc. It also has
  resources on proper statistical methods for benchmarking.
• LLVM benchmarking tips. Similar
  to the above in terms of dedicating CPUs, disabling address space
  randomization, etc.
• Top-Down performance analysis
  methodology.
  Useful post about using toplev to find the bottlenecks. This is particularly
  useful for the benchmarking suite we have here, to ensure the programs are
  correctly written (I have not taken them through this yet, but plan to).
• Godbolt's compiler explorer. Fantastic resource
  for comparing assembly between Rust and e.g. C with Clang/GCC.
• cargo-show-asm. Cargo extension to allow
  disassembling functions. Unfortunately the support for closure is a bit
  lacking, which requires some refactoring.
• Agner's Assembly
  Guide. An excellent
  resource on writing optimum assembly, which will be useful to inspect the
  various functions for inefficiencies in our suite.
• Agner's Instruction
  Tables. Thorough
  resource on the expected throughput for various instructions which is helpful
  to inspect the assembly.
• halobates.de. Useful resource for low-level
  performance by the author of toplev.
• Systems Performance (book). Fantastic book about analyzing system performance, finding bottlenecks, and understanding operating systems.
• io_uring. Best summary, it links to many
  resources.
• How Long Does It Takes To Make a Context Switch
• Integer Compression Comparisons
• Files are hard