@misc{OAI:Integer-multiplication-below-n-log-n-September-23-2026, author = {{OpenAI}}, title = {{Integer multiplication below $nlog n$}}, howpublished = {OpenAI Math Release preprint href{https://github.com/openai/math/blob/main/preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf}{OAI:Integer-multiplication-below-n-log-n-September-23-2026}}, year = {2026} }
Integer overflow checking cost Integer overflow checking cost | Patreon How much overhead should we expect from enabling integer overflow checks? Using a compiler flag or built-in intrinsics, we should be able to do the check with a conditional branch … Read more
Abstract:We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new representations … Read more
Here is a rough approximation of float multiplication (source): float rough_float_multiply(float a, float b) { constexpr uint32_t bias = 0x3f76d000; return bit_cast(bit_cast(a) + bit_cast(b) – bias); } We’re casting the floats to ints, adding them, adjusting the exponent, and returning … Read more
After spending a lot of time with language models, I have come to the conclusion that tokenization in general is insane and it is a miracle that language models learn anything at all. To drill down into one specific example … Read more
A long time ago, John Regehr wrote a very nice quiz about C integers. He’s a pretty awesome expert on undefined behavior and this quiz highlights the type of stuff you need to know when auditing C code. A lot … Read more
In real warfare and strategy games, strategists are faced with a common problem: how to allocate their resources to be the most efficient possible? Let’s take an example where we have three resources: 🌾food, 🪵wood, and 🪙gold. We can produce … Read more
Integer overflow in table parsing extension leads to heap memory corruption · Advisory · github/cmark-gfm · GitHub {{ message }} Package cmark-gfm () Affected versions > 0.28.3.gfm.21, Patched versions 0.29.0.gfm.3 0.28.3.gfm.21 Impact An integer overflow in cmark-gfm’s table row parsing … Read more