HN Debrief

A faster way to calculate the day of the week

  • Programming
  • Performance
  • Developer Tools
  • Mathematics

The post is a deep dive into a low-level algorithm for calculating the day of the week faster on modern CPUs. It focuses on turning date arithmetic into cheaper multiply, add, shift, and modulo tricks, with special handling for language quirks around signed remainder. This is not a general calendar explainer. It is a performance and implementation piece aimed at programmers who care about how weekday calculation is compiled and executed.

If you own date-heavy code paths, this is worth benchmarking instead of assuming weekday calculation is trivial or already optimal. Separately, the strong reaction to the presentation is a reminder that clear interactive explanations can make niche technical work far more reusable inside teams and codebases.

Discussion mood

Strongly positive. People liked the algorithm, but even more they liked the presentation and the fact that it made a niche bit-twiddling optimization feel understandable and trustworthy.

Key insights

  1. 01

    Weekday math does hit hot paths

    This pushes back on the instinct that weekday calculation is too small to matter. If you are formatting huge numbers of RFC 822 timestamps or running yield curve and settlement logic in finance, date arithmetic can sit directly in hot loops. In those contexts, a faster weekday primitive is not a curiosity. It is one more place to shave latency without changing behavior.

    Check profiling data before dismissing calendar code as overhead. If your system emits lots of dated text or prices instruments over large schedules, benchmark weekday computation alongside parsing and formatting.

      Attribution:
    • cowl #1
    • Joker_vD #1
    • userbinator #1
  2. 02

    The trick is really constant division

    This reframes the post as an application of a broader compiler and arithmetic pattern, not a one-off calendar stunt. The interesting part is using division-by-constant techniques and pairing them with the right modulo behavior for negative dates and language-specific remainder semantics. That makes the result easier to trust and port, because you can reason about it as standard integer machinery plus calendar-specific offsets.

    Treat this as a reusable implementation pattern, not just a date hack. When you port it across languages, verify remainder semantics first, especially for negative values and signed `%` behavior.

      Attribution:
    • masklinn #1
    • gblargg #1
    • nk_kolja #1
  3. 03

    Doomsday is the human version

    For mental calculation, Conway’s Doomsday rule completely outclassed the machine-focused article for everyday usefulness. The key idea is to memorize a handful of anchor dates that share a weekday each year, then derive nearby dates with tiny offsets. One commenter also supplied the Odd+11 rule from an arXiv paper to compute the year’s anchor day faster, which fills in the piece that many people find hardest to remember.

    If you want a practical head-only method, learn Doomsday instead of adapting the CPU algorithm. Memorize the anchor dates and keep one year-anchor shortcut handy if you expect to use it more than as a party trick.

      Attribution:
    • rmunn #1
    • elfly #1
    • phpdave11 #1
  4. 04

    Presentation determines whether clever code survives

    The useful point here is not just that the page looks nice. Several comments argued that strong visual explanation is what keeps compact algorithms from being dismissed as opaque hacks in reviews and maintenance. The author even said the visual aid and function explorer took more effort than the algorithm itself because otherwise the functions were too hard to understand or customize. That is exactly why the polish matters.

    When you introduce a dense optimization, budget time for an explainer, not just code comments. A small interactive proof or design note can be what gets an optimization accepted and kept.

      Attribution:
    • eru #1
    • honr #1
    • benjoffe #1
  5. 05

    Calendars are harder socially than mathematically

    The most grounded calendar discussion was not about formulas at all. It was about how many people juggle multiple active calendar systems at once, from Gregorian to Islamic lunar to Solar Hijri, plus fiscal and accounting calendars like 4-4-5. The pain is remembering which calendar governs which interaction. Conversion is the easy part. Social context is the actual complexity.

    If your product touches scheduling, travel, commerce, or regional workflows, do not assume one calendar model is enough. Model the relevant business and cultural calendars explicitly, then surface which one is in effect at each step.

      Attribution:
    • walrus01 #1
    • BrtByte #1
    • tacostakohashi #1

Against the grain

  1. 01

    Most people do not need this at all

    The skeptical view is that fast mental weekday calculation is mostly recreational math. For actual scheduling, people need their event calendar, not the weekday label, and they will open a calendar app anyway. Even the strongest defender of the mnemonic described it as occasionally handy and mostly fun. That sharply limits the practical value of the mental side discussion.

    Do not overinvest in head-calculation tricks unless you genuinely enjoy them or need them in conversation. For product work, optimize the software path first because that is where repeated utility actually shows up.

      Attribution:
    • embedding-shape #1
    • rmunn #1
    • mananaysiempre #1
  2. 02

    A lookup table might be enough

    This undercuts the whole optimization journey for some workloads. If your date range is bounded, you do not need a table for all 4 billion possible values. A much smaller precomputed range could cover the application lifetime or supported years. That can be simpler than carrying a subtle arithmetic routine, especially in systems where clarity beats squeezing a few instructions.

    Match the solution to the date range you actually support. For a fixed product horizon, a compact precomputed table may be easier to audit and maintain than a highly tuned general formula.

      Attribution:
    • xiaodai #1
    • masklinn #1
    • jjk166 #1

In plain english

arXiv ↩
An online repository where researchers post scientific papers, especially in physics, mathematics, and computer science.
CPU ↩
Central processing unit, the main processor that executes program instructions.
Doomsday rule ↩
A mental algorithm, devised by John Conway, for finding the weekday of any date using memorable anchor dates.
hot path ↩
A part of a program that runs very often or dominates execution time, so small optimizations there can matter.
modulo ↩
The arithmetic operation that gives the remainder after division and is often used to wrap values around a fixed range like 0 through 6 for weekdays.
Odd+11 rule ↩
A shortcut used within some Doomsday calculations to find a year’s anchor weekday from its last two digits.
RFC 822 ↩
An older Internet standard for message formats whose date strings include a weekday name, still referenced by later email and timestamp formats.
signed remainder ↩
The result of the `%` operator when negative numbers are involved, which differs across languages and can produce negative outputs.
yield curve ↩
A finance model showing interest rates across different maturities, often involving a lot of date and day-count calculations.

Reference links

Mental weekday calculation references

Presentation and explainer design

  • Red Blob Games
    Suggested as a model for interactive technical explanations similar to the post’s style.

Calendar systems and history

Calendar tools and related resources