damn this is good

Mathematics did.

damn i wish i thought of this... stack overflow helps a lot, i suppose.

What a good solution, good job!

Can someone explain this solution???

why is this so small. my code was 8 lines with same logic. :(

S-tier solution. You have brought shame upon my crappy submission -- nice job!

I think page_count use python not useful for math, but I don't no what is right between math and python?

IEEE 754 1985

...each of the operations shall be performed as if it first produced an intermediate result correct to infinite precision and with unbounded range, and then coerced this intermediate result to fit in the destination’s format...

The square root operation shall be provided in all supported formats. The result is defined and has a positive sign for all operands ≥ 0, except that √ –0 shall be −0. The destination format shall be at least as wide as the operand’s. The result shall be rounded as specified in Section 4.

IEEE 754 2008 seems to say that pow is also a reccomended "correctly rounded function", I wonder if that was implemented in the C library...

It's not so much about C or the function itself as that you should be extremely suspicious when it comes to expecting exact results from a float. Unless you have some way of reasoning about why this would be correct to do, you're better off avoiding it. And maybe even if you can reason about it. In most cases it is incorrect to use == with floats, that is imo the relevant knowledge here.

to do some lazy research, looking at https://en.cppreference.com/w/c/numeric/math/sqrt

sqrt is required by the IEEE standard to be correctly rounded from the infinitely precise result. In particular, the exact result is produced if it can be represented in the floating-point type.

That would seem to promise the desired behaviour here. I would still prefer an integer-only solution.

that actual standard, to my understandaing, is paywalled. quite obnoxious.

This one times out for me. I had to add a test to break the loop when the new term equals 0.0

Dunno, personally i prefere to handle tests for preconditions and assumptions on parameters (valid values) transparently and seperately