If your code may be compiled, to use the Intel x87 numerical coprocessor, an important issue is the so called "excess precision": Different values on chip can collapse after being rounded and stored to their memory locations, invalidating previous comparisons. Spilling can happen unexpectedly. Note that Intel calls the x87 "legacy"
What is "coder arrogance"? The expectation that the 20-year-old API (SSE) will be used over the deprecated 40-year-old API that is currently losing compiler (and silicon) support? Can you point to a running x86 machine today that does not have SSE?
It is also faster and more precise to use double-double for math over x87 extended precision. There is literally no reason to compile an x87 instruction today aside from a programmer not knowing better.
Statistical clueless amateurs found something they did not like, but of course were unable to convert their suspicions into something sound. They do not even think about it. Nevertheless a big sensation was anounced. I am tired of this.
>However when “few enough” pieces remain on the board (in the endgame), the number of possible game states is small enough that it’s possible to brute force solve the game from each state by enumerating all possible moves and resulting states so as to find the absolute optimal move for any given board position
You can basically never do that, even in the endgame, since you get always exponential blow up! Furthermore with less pieces on the board, they hamper each others movement less, therefore the branching factor really goes down only slightly.
If you want to compute all mate-in-n positions, you discover the theoretical values in tiers, by unmoving each tier twice:
If you know all mate-in-0,...,mate-in-n positions, unmove the mate-in-n set for the defender and filter out results, where he can avoid moving into the union of the known tiers. Then unmove for the attacker, to find mate-in-(n+1). Repeat until convergence. Repeat the whole process for the left over positions, to find more theoretical values.
They are giving their stuff away for free, hence they can do whatever they want.
It goes without saying, that spiritual teachings are not there to create quarrel and division.
It is terrible to lose a relative in young age.
But at least 80% percent of all heart diseases are known to be fully avoidable. The risk factors are known for ages and as matter of fact every adult is fully responsible to care for his own health. The right thing to do, is to watch out for a healthy diet.
For the informed nerd (e.g. read Elizondo first or Greer, Bledsoe) it should by now be established, that we have a serious UAP problem. Hence it's a good thing that all the incidents that were previously ridiculed and downplayed are now one by one reconsidered.
I didn’t know who Elizondo is. I just read a little. It appears he’s been pretty comprehensively debunked?
By serious UAP problem did you mean problem with people claiming everything is a UAP, or did you mean problem in the sense of “there are lots of UAPs and we don’t know why”?
I wonder of we modernized our relationship to phenomena in technology and shift from spectral beings to extraterrestrial beings as a built-in problem of explanations, based in some simplistic reliance of cause and effect.
There are probably 1000s of reports of from people across the globe that are seeing very similar things that remain unexplained. If the evidence went to a courtroom, I think certain UAP “cases” would pass have a positive “verdict” based on overwhelming circumstantial evidence. However, science has a higher bar (as it should) so when we ask our experts what’s happening they have to say “no evidence” or else lose their credibility.
The debunking of each case of UAP I've seen involves a mixture of science and folk science. They're fairly easily debunked if your persepctive changes.
For the records: I'm taking it very seriously and had this book in mind: Elizondo, L. (2024). Imminent: Inside the Pentagon's hunt for UFOs. William Morrow.
The tone is very dark though.
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