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Regarding the "inexact results", how do we know that the application authors didn't take those into account while analyzing their algorithms? If you know that y

Regarding the "inexact results", how do we know that the application authors didn't take those into account while analyzing their algorithms? If you know that your end result is accurate enough, you don't need to care about those.

steerablesafe 6y ago
Inexact is pretty much meaningless. You will get inexact results in any meaningful calculation you do. And floating point rounding error is only one source of error in these kinds of simulations. Numerically solving complex, non-linear partial differential equations brings its own share of error sources.
- Someone 6y ago
  Also, if I understand the proposed solution correctly, it doesn’t make sense. I think the article says “replace the relatively rare inexact calculations by (more expensive) calls to libraries that produce correct results, then stuff the result in a IEEE float/double, so that the less rare calls can run cheaply. Problems with that approach: - a computation at a given location in the code can be exact zillions of times, only to be inexact on the zillion+1th call, so instrumenting cannot prove a computation to be safe for doing on the hardware. - worse, the “stuff the result in a IEEE float/double” will cause inexact rounding (there may be extremely rare instances where the value of a trig function or something equally complex is exactly representable, but the CPU doesn’t compute that exact number, but those will be extremely rare)
JimTheMan 6y ago
From my memories of classes computation fluid dynamics from almost a decade ago: The whole thing was a balancing act of making sure that solutions were convergent and not unstable. Floating point numbers would fall in that category. Ie its OK to be a little a tiny little bit wrong as long as the final result converges on something reasonable. Especially given the other sources of error are magnitudes higher (for instance, picking a timestep that is way too large, relaxation factors when solving... I don't remember exactly but it felt like a bit of an art within engineering to get the thing to be reasonable. https://www.flow3d.com/resources/cfd-101/numerical-issues/numerical-instability/ https://www.flow3d.com/resources/cfd-101/numerical-issues/nu...

steerablesafe 6y ago

Inexact is pretty much meaningless. You will get inexact results in any meaningful calculation you do. And floating point rounding error is only one source of error in these kinds of simulations. Numerically solving complex, non-linear partial differential equations brings its own share of error sources.

Someone 6y ago
Also, if I understand the proposed solution correctly, it doesn’t make sense. I think the article says “replace the relatively rare inexact calculations by (more expensive) calls to libraries that produce correct results, then stuff the result in a IEEE float/double, so that the less rare calls can run cheaply. Problems with that approach: - a computation at a given location in the code can be exact zillions of times, only to be inexact on the zillion+1th call, so instrumenting cannot prove a computation to be safe for doing on the hardware. - worse, the “stuff the result in a IEEE float/double” will cause inexact rounding (there may be extremely rare instances where the value of a trig function or something equally complex is exactly representable, but the CPU doesn’t compute that exact number, but those will be extremely rare)

JimTheMan 6y ago

From my memories of classes computation fluid dynamics from almost a decade ago: The whole thing was a balancing act of making sure that solutions were convergent and not unstable. Floating point numbers would fall in that category. Ie its OK to be a little a tiny little bit wrong as long as the final result converges on something reasonable. Especially given the other sources of error are magnitudes higher (for instance, picking a timestep that is way too large, relaxation factors when solving... I don't remember exactly but it felt like a bit of an art within engineering to get the thing to be reasonable. https://www.flow3d.com/resources/cfd-101/numerical-issues/numerical-instability/ https://www.flow3d.com/resources/cfd-101/numerical-issues/nu...