4 ms·

Modern computers can calculate with a very large finite precision using decimal types. We have so much machine to waste today that if calculations of that sort

Modern computers can calculate with a very large finite precision using decimal types. We have so much machine to waste today that if calculations of that sort are relevant, just throw more iron at it.

wiz21c 4y ago
Nope! More precision sure helps but not in all cases. For example, having more precision will not help in boundary problems where you have to decide if something (for example an amount of money) is above or below a threshold. Moreover, many problems related to money) must compute with limited accuracy. For example, all intermediary results must be in 1/1000th of euros. You can use floats (yeah, I know, everybody say it's a no go) or fixed point, but in the end, you absolutely can't avoid thinking about rounding.
- MaxBarraclough 4y ago
  See also catastrophic cancellation, [0] although I'm unsure of the impact of using very large floating point types. [0] https://en.wikipedia.org/wiki/Catastrophic_cancellation https://en.wikipedia.org/wiki/Catastrophic_cancellation
vlovich123 4y ago
As someone who worked on indoor positioning at Apple, I’ll disagree with this. We were doing some basic probability estimation of WiFi signals (ML techniques but not AI). First, you still need the computation to compute within a reasonable time/power envelope. Secondly you need it to be numerically stable (adding a large number of very large and very small floating point together). Doing this using infinite precision libraries would be infeasible because while fast they aren’t as fast as regular floating point. Additionally using regular floating point meant that we could utilize BLAS and Lapack which had SIMD HW acceleration. At the end we managed to fit this within the power envelope of GPS with minimal CPU utilization (after many rounds of optimizing the CPU and WiFi scanning). Additionally, the runtime performance of the core numerical algorithm determined how long the training (building the maps was similar to locating yourself) and -validation tools (checking if a commit changed runtime performance) ran. Now sometimes you don’t need this level of effort but don’t underestimate just how much CPU you might be leaving on the floor. Sometimes it can mean what seems like an impractically slow algorithm actually runs fine. Even if you ran an infinite precision version of the ML code on a modern desktop CPU you might struggle to get perf to get the system to run in real-time (we needed to run the simulation within 5-10 ms and then do a bunch of even more complicated math to compute the blue dot location every 250ms)
llamajams 4y ago
Some of us have to write SW that can run on a potato.

wiz21c 4y ago

Nope! More precision sure helps but not in all cases. For example, having more precision will not help in boundary problems where you have to decide if something (for example an amount of money) is above or below a threshold. Moreover, many problems related to money) must compute with limited accuracy. For example, all intermediary results must be in 1/1000th of euros. You can use floats (yeah, I know, everybody say it's a no go) or fixed point, but in the end, you absolutely can't avoid thinking about rounding.

MaxBarraclough 4y ago
See also catastrophic cancellation, [0] although I'm unsure of the impact of using very large floating point types. [0] https://en.wikipedia.org/wiki/Catastrophic_cancellation https://en.wikipedia.org/wiki/Catastrophic_cancellation

vlovich123 4y ago

As someone who worked on indoor positioning at Apple, I’ll disagree with this. We were doing some basic probability estimation of WiFi signals (ML techniques but not AI). First, you still need the computation to compute within a reasonable time/power envelope. Secondly you need it to be numerically stable (adding a large number of very large and very small floating point together). Doing this using infinite precision libraries would be infeasible because while fast they aren’t as fast as regular floating point. Additionally using regular floating point meant that we could utilize BLAS and Lapack which had SIMD HW acceleration. At the end we managed to fit this within the power envelope of GPS with minimal CPU utilization (after many rounds of optimizing the CPU and WiFi scanning). Additionally, the runtime performance of the core numerical algorithm determined how long the training (building the maps was similar to locating yourself) and -validation tools (checking if a commit changed runtime performance) ran. Now sometimes you don’t need this level of effort but don’t underestimate just how much CPU you might be leaving on the floor. Sometimes it can mean what seems like an impractically slow algorithm actually runs fine. Even if you ran an infinite precision version of the ML code on a modern desktop CPU you might struggle to get perf to get the system to run in real-time (we needed to run the simulation within 5-10 ms and then do a bunch of even more complicated math to compute the blue dot location every 250ms)

llamajams 4y ago

Some of us have to write SW that can run on a potato.