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"
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 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.
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.
>Bruce helped the young athlete understand his movements in a way that seemed to decelerate time. “Bruce showed me how to harness some of what was raging inside me and summon it completely at my will. The Chinese call it chi; the Japanese, ki; the Indians, prana—it is the life force,” he said. “I was quite amazed to find, after working with Bruce, that when I really had my presence of mind, when I did control my life force, that’s what I saw, things coming at me in slow motion with plenty of time to get out of the way.
Seemingly we are learning here something new about Bruce Lee, that outside observers can't understand, most notably western ones. This decelaration of time also happened to me two times spontaneously, when I was attacked on surprise, hence I believe this verbatim. In both cases, that got me plenty of time, to decide what to do and was able to save myself without a scratch. However it never occurred to me,that that had something to do with my Chi force...
The explanation is, that the number is _not_ the infinite string of characters, but the sum of the scaled digits of the string. This sum is defined as the limit of the partial sums.
In Germany, you can understand this in high school.