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let mid = (lo + hi) / 2; Overflows #2

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kaltu opened this issue Dec 22, 2023 · 2 comments · May be fixed by #5
Open

let mid = (lo + hi) / 2; Overflows #2

kaltu opened this issue Dec 22, 2023 · 2 comments · May be fixed by #5

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@kaltu
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kaltu commented Dec 22, 2023

bisection/src/lib.rs

Line 140 in 14c9562

let mid = (lo + hi) / 2;

Overflow may happen in (lo + hi) where (lo, hi): (usize, usize)

consider changing it to lo + (hi - lo) / 2

This is not an issue in the original Python implementation because Python handles overflow to large numbers automatically
But that is not the case for Rust
@musicinmybrain
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https://research.google/blog/extra-extra-read-all-about-it-nearly-all-binary-searches-and-mergesorts-are-broken/

@kaltu
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kaltu commented May 7, 2024 •
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https://research.google/blog/extra-extra-read-all-about-it-nearly-all-binary-searches-and-mergesorts-are-broken/

Thanks for the added context.
But please be aware that the bit shift trick demonstrated without detailed elaboration in the post is taking advantage of signed int. In Rust where unsigned integer type usize is used, the trick won't work.

As for why bit shift works for singed integers, when signed integers overflow in addition, the sign bit is incorrectly flipped, but this error can be salvaged by blindly shifting every bit to the right, including the flipped sign bit. I.e. the unsigned bit shift right >>> in Java, or temporarily cast to unsigned integer before bit shift right >> in C/C++. But when unsigned integers overflow, the carry is lost, using a shift right will fill the most significant bit with 0 instead of the correct 1.

@kaltu kaltu closed this as completed May 7, 2024
@kaltu kaltu reopened this May 7, 2024
musicinmybrain added a commit to musicinmybrain/bisection that referenced this issue May 8, 2024
@musicinmybrain
Fix integer overflow in midpoint calculation
e8acfd4 
Fixes SteadBytes#2 as suggested by @kaltu (Yulin Liu) in the issue.

See also:

https://research.google/blog/extra-extra-read-all-about-it-nearly-all-binary-searches-and-mergesorts-are-broken/
@musicinmybrain musicinmybrain linked a pull request May 8, 2024 that will close this issue
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Fix integer overflow in midpoint calculation musicinmybrain/bisection
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@musicinmybrain @kaltu