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All elementary functions from a single binary operator

arxiv.org

11–20 of 317 posts

Re: All elementary functions from a single binary operator

#11

How would an architecture with a highly-optimized hardware implementation of EML compare with a traditional math coprocessor?

Dreadfully slow for integer math but probably some similar performance to something like a CORDIC for specific operations. If you can build an FPU that does exp() and ln() really fast, it's simple binary tree traversal to find the solution.

Re: All elementary functions from a single binary operator

#13
post #4

Reminds me a bit of the coolest talk I ever got to see in person: https://youtu.be/FITJMJjASUs?si=Fx4hmo77A62zHqzy It’s a derivation of the Y combinator from ruby lambdas

If you've never worked through a derivation/explanation of the Y combinator, definitely find one (there are many across the internet) and work through it until the light bulb goes off. It's pretty incredible, it almost seems like "matter ex nihilo" which shouldn't work, and yet does.

It's one of those facts that tends to blow minds when it's first encountered, I can see why one would name a company after it.

Re: All elementary functions from a single binary operator

#16
post #9
post #5

So, like brainf*ck (the esoteric programming language), but for maths?

But even tighter. With eml and 1 you could encode a funtion in rpn as bits. Although you also need to encode where to put the input. The real question is what emoji to use for eml when written out.

> The real question is what emoji to use for eml when written out.

Some Emil or another, I suppose. Maybe the one from Ratatouille, or maybe this one: https://en.wikipedia.org/wiki/Emil_i_L%C3%B6nneberga

Re: All elementary functions from a single binary operator

#18

How does one actually add with this?

Don't know adding, but multiplication has diagram on the last page of the PDF.

xy = eml(eml(1, eml(eml(eml(eml(1, eml(eml(1, eml(1, x)), 1)), eml(1, eml(eml(1, eml(y, 1)), 1))), 1), 1)), 1)

From Table 4, I think addition is slightly more complicated?

Re: All elementary functions from a single binary operator

#19
post #16
post #9

Earlier quoted context omitted.

But even tighter. With eml and 1 you could encode a funtion in rpn as bits. Although you also need to encode where to put the input. The real question is what emoji to use for eml when written out.

> The real question is what emoji to use for eml when written out. Some Emil or another, I suppose. Maybe the one from Ratatouille, or maybe this one: https://en.wikipedia.org/wiki/Emil_i_L%C3%B6nneberga

Not brainf*ck. This is the SUBLEQ equivalent of math https://en.wikipedia.org/wiki/One-instruction_set_computer#S...
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