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The only real place for quad precision is when you're working with numbers that truly require you to be able span a massive difference in magnitudes without rou

The only real place for quad precision is when you're working with numbers that truly require you to be able span a massive difference in magnitudes without round-off error accumulating. For some context, an electron "has structure" roughly on a length scale of about 10^-15 meters (details here unimportant). If you're representing a quantity in O(1) meters, then doing a handful of floating-point operations in double will likely accumulate error on the order of O(1) electrons. Incredible accuracy! I think the key here is to be mindful of units and make sure you're combining like with like and scaling things appropriately as you go. If you're doing things the wrong way, quad will punish you eventually, too. An underappreciated tool for working more confidently with floats is interval arithmetic. Worth checking out if you actually (truly) need to do things robustly (most people don't).

andrepd 2y ago
That's one of the (many) problems with ieee floats: they "waste" as much bits for mantissa precision in the range of 10^0, 10^1, 10^2, etc, as they do in 10^300 or 10^-300! Proposals like Posits aim to improve on this :)
- nestorD 2y ago
  In practice, Posits grabs very few additional bits and those are mostly felt in low bits (16 and less) regimes. That's a big reason it is mostly seeing adoption in memory constraint regimes. A great thing in the Posit proposal is that they also consider a distinct accumulator type for things like sums and dot product. In my experience (I did a PhD on measuring floating point error in large numerical simulations) those operations are the ones that are most likely to sneak on you and need fixing. But most people don't realize that those accumulator type are actually easy to use with IEEE floats, they are entirely orthogonal to using Posits.
- sfpotter 2y ago
  IEEE floats are an incredible feat of engineering. The people who designed them were geniuses. We should be appreciative of the fact that we have a consistent and portable way to do numerics. I'm glad we've got IEEE 754 and don't have to suffer through the pain of numerous competing standards.

andrepd 2y ago

That's one of the (many) problems with ieee floats: they "waste" as much bits for mantissa precision in the range of 10^0, 10^1, 10^2, etc, as they do in 10^300 or 10^-300! Proposals like Posits aim to improve on this :)

nestorD 2y ago
In practice, Posits grabs very few additional bits and those are mostly felt in low bits (16 and less) regimes. That's a big reason it is mostly seeing adoption in memory constraint regimes. A great thing in the Posit proposal is that they also consider a distinct accumulator type for things like sums and dot product. In my experience (I did a PhD on measuring floating point error in large numerical simulations) those operations are the ones that are most likely to sneak on you and need fixing. But most people don't realize that those accumulator type are actually easy to use with IEEE floats, they are entirely orthogonal to using Posits.
sfpotter 2y ago
IEEE floats are an incredible feat of engineering. The people who designed them were geniuses. We should be appreciative of the fact that we have a consistent and portable way to do numerics. I'm glad we've got IEEE 754 and don't have to suffer through the pain of numerous competing standards.