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[libc++] Fix sub-overflow in std::gcd implementation #117984

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Merged
merged 2 commits into from
Dec 6, 2024
Merged

[libc++] Fix sub-overflow in std::gcd implementation #117984

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1f04c92
[libc++] Fix sub-overflow in std::gcd implementation
serge-sans-paille Nov 28, 2024
fcaad75
fixup! [libc++] Fix sub-overflow in std::gcd implementation
serge-sans-paille Dec 5, 2024
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22 changes: 9 additions & 13 deletions libcxx/include/__numeric/gcd_lcm.h
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Original file line number Diff line number Diff line change
Expand Up @@ -55,7 +55,7 @@ template <class _Tp>
constexpr _LIBCPP_HIDDEN _Tp __gcd(_Tp __a, _Tp __b) {
static_assert(!is_signed<_Tp>::value, "");

// From: https://lemire.me/blog/2013/12/26/fastest-way-to-compute-the-greatest-common-divisor
// From: https://lemire.me/blog/2024/04/13/greatest-common-divisor-the-extended-euclidean-algorithm-and-speed/
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@hiraditya hiraditya Dec 2, 2024 •
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I believe this is Stein's algorithm (Can't find the link currently but this has a reference on https://aha.stanford.edu/sites/g/files/sbiybj20066/files/media/file/aha_050422_sreedhar_crypto_xgcd_1.pdf#page=14). Maybe we should write that instead of linking to a blogpost? But I'm not sure what the policy is about adding a link in the code. Can we add the blogpost link in a commit message instead? There is a high chance blogpost may be dead in a few years.

//
// If power of two divides both numbers, we can push it out.
// - gcd( 2^x * a, 2^x * b) = 2^x * gcd(a, b)
Expand All @@ -76,21 +76,17 @@ constexpr _LIBCPP_HIDDEN _Tp __gcd(_Tp __a, _Tp __b) {
if (__a == 0)
return __b;

int __az = std::__countr_zero(__a);
int __bz = std::__countr_zero(__b);
int __shift = std::min(__az, __bz);
__a >>= __az;
__b >>= __bz;
_Tp __c = __a | __b;
int __shift = std::__countr_zero(__c);
__a >>= std::__countr_zero(__a);
do {
_Tp __diff = __a - __b;
if (__a > __b) {
__a = __b;
__b = __diff;
_Tp __t = __b >> std::__countr_zero(__b);
if (__a > __t) {
__b = __a - __t;
__a = __t;
} else {
__b = __b - __a;
__b = __t - __a;
}
if (__diff != 0)
__b >>= std::__countr_zero(__diff);
} while (__b != 0);
return __a << __shift;
}
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