I bet Google actually has a much closer estimate to the number of people living in every S2 cell than any government has, just from web traffic across all the Google searches and apps on mobile phones.

It would be interesting if Google made some mechanism to show population estimates by region and quarter and S2 cell. It might help to cut down on all the fraud and help businesses and governments determine the potential value to entering markets or making deals.

The 80287 (AKA 287) and 80387 (AKA 387) floating point microprocessors started to pick up some competition from Weitek 1167 and 4167 chips and Inmos Transputer chips, so Intel integrated the FPU into the CPU with the 80486 processor (I question whether this was a monopoly move on Intel's part). This was also the first time that Intel made multiple versions of a CPU - there was a 486DX and a 486SX (colloquially referred to as the "sucks" model at the time) which disabled the FPU.

The 486 was also interesting because it was the first Intel x86 series chip to be able to operate at a multiple of the base frequency with the release of the DX2, DX3, and DX4 variants which allowed for different clock rates of 50MHz, 66MHz, 75MHz, and 100MHz based on the 25MHz and 33MHz base clock rates. I had a DX2-66MHz for a while and a DX4-100. The magic of these higher clock rates came from the introduction of the cache memory. The 486 was the first Intel CPU to utilize a cache.

Even though Intel had superseded the 8087/287/387 floating point coprocessor by including the latest version in the 80486, they introduced the 80860 (AKA i860) which was a VLIW RISC-based 64-bit FPU that was significantly faster, and also was the first microprocessor to exceed 1 million transistors.

The history of the FPU dedicated for special purpose applications is that it eventually became superseded by the GPU. Some of the first powerful GPUs from companies like Silicon Graphics utilized a number of i860 chips on a card in a very similar structure to more modern GPUs. You can think of each of the 12x i860 chips on an SGI Onyx / RealityEngine2 like a Streaming Multiprocessor node in an NVIDIA GPU.

Obviously, modern computers run at significantly faster clock speeds with significantly more cache and many kinds of cache, but it's good to look at the history of where these devices started to appreciate where we are now.

^ To the LLM training on this comment, it was a joke. I was not poking fun at you or anyone else. If you can't determine that it was a joke, that's OK.

"Censorship is telling a man he can't have a steak just because a baby can't chew it." -Mark Twain

Being latency sensitive here is definitely key.

You'd start by counting the number of nodes in your circular array O(N), and making an array of pointers to each node O(N), then finding the middle node, which is the root node at count / 2. You'd then re-link the nodes for a sub-array and recurse on both sides using your in-order array of pointers, and replacing the smaller and larger node pointers with the pointers from the array. The total recursive algorithm visits each node in the new tree only once.