This topic continues a discussion started in another topic here on discourse . The goal here is to assemble a list of potential issues which may arise if you assume floating-point rounding errors are random rather than deterministic. Additions and corrections are welcome! It may make you overlook …

If you are trying to do low level stuff, knowing exactly when operations are exact can be really powerful. In general for things like trig or other transcendental functions, assuming random error is pretty correct since you are truncating a transcendental number. However, for arithmatic (+,-,*, fma)…

Thanks for opening this topic, it was a good idea. The issues you raise are very important and go beyond Julia language. Since we are gathered here as Julia programmers, you might add a bullet or two on how these considerations reflect Julia packages, at least those from the General registry. Cou…

The problem is when doing high level stuff, and specifically for applications such as accounting, or finance in general, where the norm is to have rounded numbers. Improvements to Fixed Point numbers would be for these tasks, and fitting with the style of Julia programming, vs a lower level languag…

Thanks for doing this thread! [image] ettersi: It may make you overlook bugs in your code, e.g. race conditions or uninitialised memory which may have a similar effect as rounding errors. That’s a good point but is still pretty unlikely (although certainly possible) that a race of invalid me…

Said differently : would life be very different if, instead of rounding to nearest, arithmetic would round randomly up or down?

Machine Hardware (CPU and GPU) The IEEE-754 standard [this is the 2008 version; see changes for the 2019 version ; also short comment here ] defines five rounding rules –2 are “round to nearest rules”, and 3 are “directed rounding” rules: Roundings to Nearest Round to nearest, ties to even – round…

[image] Niceno: Thanks for opening this topic, it was a good idea. [image] antoine-levitt: Thanks for doing this thread! Thanks for the kind words, much appreciated! :blush: [image] Niceno: The issues you raise are very important and go beyond Julia language. Since we are gathere…

[image] ettersi: I vaguely remember some friends of mine doing semester projects with the Swiss weather forecasting agency, and I think their task was to parallelise some given codes under the constraint that the results had to be exactly the same. This is fairly hearsay, though, and I would be …

Hello, thank everyone for this insightful discussion. From the abrupt end of the thread, I infer that this is going to stay, in Julia. However, I want to make the argument that random approximation of rounding errors causes very weird computations. I hereby present an example: julia> for x in 1:1…

[image] alequa: Can someone explain to me the deep meaning of it? Thanks [image] PSA: floating-point arithmetic Offtopic Sometimes people are surprised by the results of floating-point calculations such as julia> 5/6 0.8333333333333334 …

Why assuming floating-point rounding errors are random is bad

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Sukera March 29, 2022, 12:00pm 11

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Why assuming floating-point rounding errors are random is bad

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