"Centrist" in practice means "more or less content with the status quo." That is fundamentally a conservative position orthogonal to any notion of "facts".
The work discussed in this post shipped in the OS last year (fall 2025), so nothing here is dependent on very recent changes.
Field hockey is almost exclusively a girls sport in the US, while boys have (American) football in the fall. Both draw from the potential pool of soccer players in US middle and high schools.
“in a real race we have no actual chance of winning” is an absolutely wild thing to say in response to a link to a real race in which the human has won the last few years in a row.
What sort of engineering standards are these Cybertrucks built to? Oh, very rigorous engineering standards. The wheels aren't supposed to fall off for a start.
We have a ground-source heat pump for our ADU. We did it because we were curious about just how efficient we could make the house, but I don't expect that it will ever break even financially vs a modern air-source…
Prior to the current generation Intel designs, Apple’s branch predictor tables were a good deal larger than Intel’s IIRC, so depending on benchmarking details it’s plausible that Apple Silicon was predicting every…
Must be the water.
The CORE-MATH project authors, most of whom are French academics (including the author of the linked paper). I don’t know of any interesting work in this space that came out of Red Hat, why do you suggest them?
"I'd like to thank my mother, Ayn Rand, and God" is the usual example. Yes, you can reorder the list to remove the ambiguity, but sometimes the order of the list matters. The serial comma should be used when necessary…
That would fall under "more constrained", due to process limits.
Enlarging a branch predictor requires area and timing tradeoffs. CPU designers have to balance branch predictor improvements against other improvements they could make with the same area and timing resources. What this…
Your students should be able to figure out if a computation is exact or not, because they should understand binary representation of numbers.
You can often eke something out for order-four, depending on uArch details. But basically yeah.
For throughput-dominated contexts, evaluation via Horner's rule does very well because it minimizes register pressure and the number of operations required. But the latency can be relatively high, as you note. There are…
When Intel specced the rsqrt[ps]s and rcp[ps]s instructions ~30 years ago, they didn't fully specify their behavior. They just said their relative error is "smaller than 1.5 * 2⁻¹²," which someone thought was very…
For the asinf libcall on macOS/x86, my former colleague Eric Postpischil invented the novel (at least at the time, I believe) technique of using a Remez-optimized refinement polynomial following rsqrtss instead of the…
Ideally either one is just a library call to generate the coefficients. Remez can get into trouble near the endpoints of the interval for asin and require a little bit of manual intervention, however.
Newer rsqrt approximations (ARM NEON and SVE, and the AVX512F approximations on x86) make the behavior architectural so this is somewhat less of a problem (it still varies between _architectures_, however).
These sorts of approximations (and more sophisticated methods) are fairly widely used in systems programming, as seen by the fact that Apple's asin is only a couple percent slower and sub-ulp accurate…
Yann is definitely more well-known outside of academia. Inside academia, it's going to depend a lot on your specific background and how old you are.
Mechanically, you're probably right, but the screen-centric controls of the newer generation are _awful_ by comparison to the F generation's physical buttons and dials (this isn't BMW though, it's the whole industry).…
Our (~2015) 3-series controls are just about perfect. Where they differ from Honda/Toyota's controls that I am also very familiar with, they're noticeably better now that I'm familiar with them. Everything is really…
Schubfach's table is quite large compared to some alternatives with similar performance characteristics. swiftDtoa's code and tables combined are smaller than just Schubfach's table in the linked implementation. Ryu and…
IEEE 754 is a floating point standard. It has a few warts that would be nice to fix if we had tabula rasa, but on the whole is one of the most successful standards anywhere. It defines a set of binary and decimal types…
"Centrist" in practice means "more or less content with the status quo." That is fundamentally a conservative position orthogonal to any notion of "facts".
The work discussed in this post shipped in the OS last year (fall 2025), so nothing here is dependent on very recent changes.
Field hockey is almost exclusively a girls sport in the US, while boys have (American) football in the fall. Both draw from the potential pool of soccer players in US middle and high schools.
“in a real race we have no actual chance of winning” is an absolutely wild thing to say in response to a link to a real race in which the human has won the last few years in a row.
What sort of engineering standards are these Cybertrucks built to? Oh, very rigorous engineering standards. The wheels aren't supposed to fall off for a start.
We have a ground-source heat pump for our ADU. We did it because we were curious about just how efficient we could make the house, but I don't expect that it will ever break even financially vs a modern air-source…
Prior to the current generation Intel designs, Apple’s branch predictor tables were a good deal larger than Intel’s IIRC, so depending on benchmarking details it’s plausible that Apple Silicon was predicting every…
Must be the water.
The CORE-MATH project authors, most of whom are French academics (including the author of the linked paper). I don’t know of any interesting work in this space that came out of Red Hat, why do you suggest them?
"I'd like to thank my mother, Ayn Rand, and God" is the usual example. Yes, you can reorder the list to remove the ambiguity, but sometimes the order of the list matters. The serial comma should be used when necessary…
That would fall under "more constrained", due to process limits.
Enlarging a branch predictor requires area and timing tradeoffs. CPU designers have to balance branch predictor improvements against other improvements they could make with the same area and timing resources. What this…
Your students should be able to figure out if a computation is exact or not, because they should understand binary representation of numbers.
You can often eke something out for order-four, depending on uArch details. But basically yeah.
For throughput-dominated contexts, evaluation via Horner's rule does very well because it minimizes register pressure and the number of operations required. But the latency can be relatively high, as you note. There are…
When Intel specced the rsqrt[ps]s and rcp[ps]s instructions ~30 years ago, they didn't fully specify their behavior. They just said their relative error is "smaller than 1.5 * 2⁻¹²," which someone thought was very…
For the asinf libcall on macOS/x86, my former colleague Eric Postpischil invented the novel (at least at the time, I believe) technique of using a Remez-optimized refinement polynomial following rsqrtss instead of the…
Ideally either one is just a library call to generate the coefficients. Remez can get into trouble near the endpoints of the interval for asin and require a little bit of manual intervention, however.
Newer rsqrt approximations (ARM NEON and SVE, and the AVX512F approximations on x86) make the behavior architectural so this is somewhat less of a problem (it still varies between _architectures_, however).
These sorts of approximations (and more sophisticated methods) are fairly widely used in systems programming, as seen by the fact that Apple's asin is only a couple percent slower and sub-ulp accurate…
Yann is definitely more well-known outside of academia. Inside academia, it's going to depend a lot on your specific background and how old you are.
Mechanically, you're probably right, but the screen-centric controls of the newer generation are _awful_ by comparison to the F generation's physical buttons and dials (this isn't BMW though, it's the whole industry).…
Our (~2015) 3-series controls are just about perfect. Where they differ from Honda/Toyota's controls that I am also very familiar with, they're noticeably better now that I'm familiar with them. Everything is really…
Schubfach's table is quite large compared to some alternatives with similar performance characteristics. swiftDtoa's code and tables combined are smaller than just Schubfach's table in the linked implementation. Ryu and…
IEEE 754 is a floating point standard. It has a few warts that would be nice to fix if we had tabula rasa, but on the whole is one of the most successful standards anywhere. It defines a set of binary and decimal types…