benjoffe
Joined 16 years ago
Karma
886
Submissions
183
Member since
Sep 12
My site with various personal projects and demos: https://www.benjoffe.com/
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Comment · 2 days ago
Hello, you are correct that part of it is done to death for standard integer division.
The `new` thing is the range-splitting which achieves the floor division for negative inputs (eg. sign-selected for 60% of divisors, and the negative/positive bump for the remaining 20%/20% of cases each).
Comment · 2 months ago
Thanks for sharing that.
I have a mobile-friendly web-app where you can practice this technique, just click the link in the page's nav: "Weekle - Weekday Guessing Game"
Comment · 2 months ago
Thanks! I'm pretty sure with this one I spent more time working on the blog post than I did developing the algorithms.
I would not normally spend such effort, but in this case I felt that the functions were too hard to understand without the visual aid, and too difficult to customise without the Function Explorer.
Then I think I just got a bit carried away with the detail.
Comment · 10 months ago
Correct URL: https://www.benjoffe.com/fast-leap-year
(The link in the submission is incorrect; apologies for the confusion.)
Comment · 10 months ago
In this article I present a new faster full-range function to calculate whether a year is a leap year. This type of calculation is a fundamental date library utility, it is used all over the place: validating and parsing dates, determining the Nth last weekday of a month, handling month overflow/underflow when adjusting the day, etc.
The article outlines the technique, shows related developments before and after its creation, and includes an interactive, human-verifiable "proof".
Comment · 11 months ago
That is an interesting question.
It might also come into play if developing SIMD alternatives for batch date processing, as one can have more lanes with 16-bit. I plan to make a blog post covering SIMD and if 16-bit algorithms have reasonable performance then that will be covered.
Comment · 11 months ago
Thanks, that is a good idea. This was originally a blog post series, and the first article gave a bit of an introduction.
When I started the blog series, I expected the first article to be the most noteworthy, with the 2nd and 3rd being lesser supplementary topics.
Now that the 3rd blog post ended up with a much larger result than I was expecting, it stands on its own and could do with some editing as you suggest.
Comment · 11 months ago
The first article in this blog post series has a little section talking briefly about this history, and there's a representation of this that I think sheds a lot of light on the original design. See the heading "Side-Note on Month / Day Determination" in the below link [1].
Displaying the months like the following helps see the regularity at a glance. Columns 1, 3 and 5 are the long months, others being shorter:
+-----+-----+-----+-----+-----+
| 31 | 30 | 31 | 30 | 31 |
| I | II | III | IV | V |
| MAR | APR | MAY | JUN | JUL |
|-----+-----+-----+-----+-----+
| 31 | 30 | 31 | 30 | 31 |
| VI |VII |VIII | IX | X |
| AUG | SEP | OCT | NOV | DEC |
+-----+-----+-----+-----+-----+
| 31 |28/29|
| XI |XII |
| Jan | FEB |
+-----+-----+
Comment · 11 months ago
Thanks.
I was fortunate enough to be programming on an ARM based device, which meant that the terms (x * 4 + 3) strongly stood out to me as highly inefficient, being 2 cycle prep for the more important division. On x64 computers, those two operations are calculated in only one operation by using the 'LEA' assembly instruction (which I wasn't aware of at the time), and so others using that type of computer might not have felt this step needed any simplification.
I tried everything under the sun to get rid of these steps. The technique noted in the article of using the year 101 BC was for a long time my strongest candidate, you can view the implementation of that attempt at the link below [1].
An epoch of 101 BC still meant that there was extra work required to re-normalise the timeline after the century calculation, but it was only a single addition of 365 in the calculation of `jul`. The explanation of how this works is probably a whole blog post in itself, but now that this algorithm has been discarded it's not worth the time to explain it fully.
I also had the year-modulus-bitshift technique developed at that time, but it couldn't be integrated cleanly with any of my algorithm attempts yet. My plan was to simply document it as an interesting but slower concept.
I don't know what sparked the idea of going backwards other than immersing myself deeply in the problem in my spare time for about a month. It finally came to me one evening, and I thought it was only going to save 1-cycle, but when it also meant the year-modulus-bitshift could be utilised, the entire thing fit together like a glove and the speed collapsed down from 20% time saving to 40%.
[1] https://github.com/benjoffe/fast-date-benchmarks/blob/218356...