Hack-a-day 2026

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+---
+author: admin
+categories:
+- technical
+date: 2026-11-05
+tags:
+- hack-a-day
+title: "Hack-a-Day, Day 05: Assembly Coding"
+---
+
+Whew, hey everyone. Yes, hack-a-day is happening this year! I was a few days late starting (out of state), and then I did an assembly programming project! But then I promptly got a nasty bug and was laid up in bed for four days. Not a fast start! But that's okay, I'm feeling good.
+
+I'm thinking this year will be AI-light to AI-none. Last year it was novel for me, this year I want a break from it. And really, hack-a-day is about learning and flow for me, as much as shiny demos.
+
+On day 5, I decided to learn some X86-64 assembly coding. AI help was limited to an assembly cheatsheet (I didn't know assembly), and some final bugfix help after I got sick, since I was over my 1-day budget.
+
+The problem is to solve the following equation using positive integers. As far as I know it doesn't have a specific name, although it has a short [lineage](https://en.wikipedia.org/wiki/Diophantine_equation): Euler conjectured no solutions, Elkies found infinitely many solutions, and Frye found the smallest by computer search.
+
+    x^4 + y^4 + z^4 = w^4
+
+We're given the hint that there is exactly one solution with all numbers less than 1 million. I'll avoid posting the answer here, but you can find it if you follow the wikipedia link above.
+
+The algorithm I'm using was worked out by me and Kragen Javier Sittaker (mostly Kragen), although it's been long enough I had to reinvent it. It turns out it's the same one that Frye used to solve it originally, in 1988 -- although he used a parallel implementation I don't know the details of.
+
+Brute force search doesn't work -- one million times one million, times one million, times one million, is too many possibilities to try (10^24). So instead we make two lists, one of numbers x^4 + y^4 (in sorted order), and one of numbers w^4 - z^4 (in sorted order). And then it's easy to see if they're ever equal. Of course, those would be lists of a trillion things, so we can't make them either. We use a priority heap of a million elements, instead.
+
+For fast testing, we hint the solver has to the right bounds for X, Y, etc. For me it takes about 4 hours for the full run.
+
+I'm happy I got this to work! I'm sure my assembly isn't the best, since it's about my second assembly program, but I learned a little about x86 and about the intel syntax and nasm macros.
+
+Python and x86-64 assembly versions both [on github](https://github.com/za3k/hack2026-asm).
+
+Next project will be something a little more chill.
+
+Happy hacking!

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 author: admin
 categories:
 - Uncategorized
-date: 2026-??-??
+date: 2026-11-??
 tags:
-- untagged
-title: TITLE
+- hack-a-day
+title: "Hack-a-Day, Day XX: TITLE"
 ---