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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 GCP c2-standard-4 (Intel Cascade) and 2017 Macbook (2.8GHz, quad-core).

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.

Operation Latency Throughput 1 MiB 1 GiB
Sequential Memory R/W (64 bytes) 5 ns 50 GiB/s 20 μs 20 ms
Hashing, not crypto-safe (64 bytes) 25 ns 2 GiB/s 500 μs 500 ms
Random Memory R/W (64 bytes) 50 ns 1 GiB/s 1 ms 1s
Fast Serialization [8] [9] N/A 1 GiB/s 1 ms 1s
Fast Deserialization [8] [9] N/A 1 GiB/s 1 ms 1s
System Call 500 ns N/A N/A N/A
Hashing, crypto-safe (64 bytes) 500 ns 200 MiB/s 10 ms 10s
Sequential SSD read (8 KiB) 1 μs 4 GiB/s 200 μs 200 ms
Context Switch [1] [2] 10 μs N/A N/A N/A
Sequential SSD write, -fsync (8KiB) 10 μs 1 GiB/s 1 ms 1s
TCP Echo Server (32 KiB) 10 μs 4 GiB/s 200 μs 200 ms
Decompression [11] N/A 1 GiB/s 1 ms 1s
Compression [11] N/A 500 MiB/s 2 ms 2s
Sequential SSD write, +fsync (8KiB) 1 ms 10 MiB/s 100 ms 2 min
Sorting (64-bit integers) N/A 200 MiB/s 5 ms 5s
Random SSD Seek (8 KiB) 100 μs 70 MiB/s 15 ms 15s
Serialization [8] [9] N/A 100 MiB/s 10 ms 10s
Deserialization [8] [9] N/A 100 MiB/s 10 ms 10s
Proxy: Envoy/ProxySQL/Nginx/HAProxy 50 μs ? ? ?
Network within same region [6] 250 μs 100 MiB/s 10 ms 10s
{MySQL, Memcached, Redis, ..} Query 500 μs ? ? ?
Random HDD Seek (8 KiB) 10 ms 70 MiB/s 15 ms 15 s
Network between regions [6] Varies 25 MiB/s 40 ms 40s
Network NA East <-> West 60 ms 25 MiB/s 40 ms 40s
Network EU West <-> NA East 80 ms 25 MiB/s 40 ms 40s
Network NA West <-> Singapore 180 ms 25 MiB/s 40 ms 40s
Network EU West <-> Singapore 160 ms 25 MiB/s 40 ms 40s

†: "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.

What Amount $ / Month $ / Hour
CPU 1 $10 $0.02
Memory 1 GB $1
SSD 1 GB $0.1
Disk 1 GB $0.01
S3, GCS, .. 1 GB $0.01
Network 1 GB $0.01

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.

What Compression Ratio
HTML 2-3x
English 2-4x
Source Code 2-4x
Executables 2-3x
RPC 5-10x
SSL -2% [10]

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.

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