`IsCollinear`: detect and handle integer multiplication wrapping #832

reunanen · 2024-05-09T05:51:07Z

Resolves #831.

reunanen · 2024-05-09T07:10:43Z

CPP/Clipper2Lib/include/clipper2/clipper.core.h

+
+ if (MultiplyWrap::IsDifferentForSure(ab, cd))
+ {
+ return false;


If plain integer multiplication gives a different result, then the true result is different, even if there's wrapping.

Assuming these comments are to explain what's going on for the review, perhaps it's an indication that they should be code comments instead to make them more permanent?

Yeah, I was thinking of that too. Maybe. Or even better: the code should be obvious even without the comments. Not sure if the comments are needed as it is now – thought that if they are not necessary, then they are that much less harmful and less noisy when they are here and not in the source file. What do you think? Genuine question.

I think a play by play isn't necessarily required, but a high-level explanation is probably worth having. Looking at MultiplyWrap takes a bit of parsing through the interface and reasoning through the math to figure out what it's intended to do. Similarly, checks and operations in this function require that baseline knowledge to understand what's going on.

If there's a top-level commenting explaining what MultiplyWrap does at a conceptual level and how it's used in combination with the overflow computation that follows, then the specifics of the code will probably become self-evident.

Thank you for your feedback, much appreciated.

Honestly I don't really love the name MultiplyWrap. Think that just renaming it to something better might already help a bit.

Maybe SignedMultiply?

Edit: Something like OverflowMultiply may also be a good choice if you move CalculateCarry() into this class and have it be more self-contained.

Something like OverflowMultiply may also be a good choice if you move CalculateCarry() into this class and have it be more self-contained.

The main reason I didn't move CalculateCarry() there just yet is that it's kind of uint64_t specific, when MultiplyWrap is more naturally uintmax_t. Yea I know in practice they are the same...

reunanen · 2024-05-09T07:10:58Z

CPP/Clipper2Lib/include/clipper2/clipper.core.h

+
+ if (!ab.IsWrap() && !cd.IsWrap())
+ {
+ return true;


If there isn't wrapping, then we can take a shortcut.

reunanen · 2024-05-09T07:11:44Z

CPP/Clipper2Lib/include/clipper2/clipper.core.h

+ }
+
+ const auto carry_ab = CalculateCarry(a, b);
+ const auto carry_cd = CalculateCarry(c, d);


Calculate carry only if really needed (at least one result wrapped, and the potentially wrapped multiplication results are equal).

here-abarany · 2024-05-09T20:16:08Z

CPP/Clipper2Lib/include/clipper2/clipper.core.h

+ private:
+ void Init(intmax_t value, uintmax_t& abs_value)
+ {
+ if (value >= 0)


Perhaps bit math could be used here to avoid conditionals that may degrade performance?

Yeah, was thinking of that too, but wasn't sure if it'd be premature optimization at this point.

here-abarany · 2024-05-09T20:21:24Z

CPP/Clipper2Lib/include/clipper2/clipper.core.h

+
+ static bool IsDifferentForSure(const MultiplyWrap& a, const MultiplyWrap& b)
+ {
+ if (a.abs_result != b.abs_result) return true;


Might be worth looking at the disassembly to verify that these multiple if statements get optimized out, otherwise they could be combined into a single return value. For example, the following return statement should be equivalent:

return a.abs_result != b.abs_result || (a.abs_result != 0 && a.sign != b.sign);

(I only check a.abs_result != 0 since that portion would only get executed if a.abs_result == b.abs_result)

Correct. Noticed that as well, but decided for the time being to leave the redundant b.abs_result != 0 part for clarity and symmetricity.

Might try to improve on these fronts in the near future. Thanks again for the feedback!

Hi again Juha, and thank you for your help with this tricky issue.

bool IsWrap() const { return abs_a != 0 && abs_result / abs_a != abs_b; }

I'm trying without success to get my head around the code logic above, though I am just waking up 🤣.
Could you explain how this tests for presumably overflow wrap?
And ISTM that there's a potential divide by zero and, if so, how this is handled in C++?

I'd expect a divide by zero to be handled by abs_a != 0 && short-circuiting.

It seems to be detecting overflow by switching around the terms of the formula to make sure it gets the expected result. i.e.

abs_result = abs_a * abs_b

abs_result / abs_a = abs_b

This code assumes that abs_result / abs_a != abs_b would always be true when overflow occurred. On the surface that seems like it would be true, but considering that integer division would throw away the remainder I'm not completely sure at how robust that would be.

I'd expect a divide by zero to be handled by abs_a != 0 && short-circuiting.

Correct.

This code assumes that abs_result / abs_a != abs_b would always be true when overflow occurred. On the surface that seems like it would be true, but considering that integer division would throw away the remainder I'm not completely sure at how robust that would be.

Hmm, I see what you mean (I think). Proving that this (commonly used, I believe) method is correct is discussed e.g. here, but right now I can neither confirm or deny that the proof itself is correct. You didn't have a counterexample in mind, did you? 🙂

I don't have a counter-example, or any proof that it doesn't work, it was mainly a concern I had. After going through the proof you linked many times and comparing to other related posts, I'm pretty sure I understand it and accept it as correct, so I'd say that concern was invalid.

That said, between the divisions, and conditional, and required short-circuit to avoid a CPU exception for divide by zero, it's very possible that in practice performing this early-out may actually be slower than always computing the carry bits.

it's very possible that in practice performing this early-out may actually be slower than always computing the carry bits

Good point. Here, Angus mentioned that using int128 is slow, and I figured calculating the carry like this is probably even slower. But that of course doesn't mean that evaluating the conditionals or the division is fast.

Does anybody have any real-life example(s) where the perf impact of these operations matters? I'm afraid that if I create some benchmark for testing this, I'll be optimizing for some completely irrelevant situation (and pessimizing the real-world scenarios while at it).

Maybe, for simplicity, I could just remove the short-circuits from here? Until it's proven they are beneficial to begin with? Then there's at least no need to document them, or find a better name for MultiplyWrap for that matter.

I would be in favor of removing the short-circuit for overflow. If it's both more complicated and is questionable if it's faster, I think leaving them out unless proven beneficial otherwise is the better option.

Agree. Will look into it.

I'd expect a divide by zero to be handled by abs_a != 0 && short-circuiting.

Indeed. I'll use my "just waking up" as the excuse 🤣.

tomwiel · 2024-05-11T06:49:38Z

About safe multiplication: Starting with C23, C has ckd_mul():
if (ckd_mul(&res, a, b)) { res is wrapped result} else { res is correct result}
Other languages would need the same.

reunanen · 2024-05-11T10:21:14Z

Closed this PR in favor of #834.

reunanen added 6 commits May 9, 2024 08:12

Add test case that fails

b0610d6

IsCollinear: detect and handle integer multiplication wrapping

712657a

Minor simplication: just calculate the carry

85eea82

Fix handling of negative coordinate values

680790c

Fix Linux build

d7db43f

Fix Windows build

ba2a9b7

reunanen marked this pull request as ready for review May 9, 2024 07:07

reunanen commented May 9, 2024

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here-abarany reviewed May 9, 2024

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reunanen mentioned this pull request May 10, 2024

IsCollinear: detect and handle integer multiplication wrapping (version 2) #834

Merged

reunanen closed this May 11, 2024

reunanen deleted the fix-831 branch May 11, 2024 10:40

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`IsCollinear`: detect and handle integer multiplication wrapping #832

`IsCollinear`: detect and handle integer multiplication wrapping #832

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IsCollinear: detect and handle integer multiplication wrapping #832

IsCollinear: detect and handle integer multiplication wrapping #832

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tomwiel commented May 11, 2024

reunanen commented May 11, 2024

`IsCollinear`: detect and handle integer multiplication wrapping #832

`IsCollinear`: detect and handle integer multiplication wrapping #832

reunanen commented May 9, 2024 •

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