Generalized Orders of Magnitude (GOOMs)

Re:Generalized Orders of Magnitude (GOOMs) by fheinsen on Sunday October 12, 2025 @12:38PM (#45559542)

> GOOMs generalize the concept of "order of magnitude" to incorporate complex numbers that exponentiate to real ones. As with ordinary orders of magnitude, GOOMs are more stable than the real numbers to which they exponentiate.

> This implementation enables you to operate on real numbers far beyond the limits of conventional floating-point formats, for effortless scaling and parallelization of high-dynamic-range computations. You no longer need to scale, clip, or stabilize values to keep magnitudes within those limits.

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Re:Generalized Orders of Magnitude (GOOMs) by zahlman on Sunday October 12, 2025 @02:38PM (#45560599)

Yes, I read all that, but it doesn't communicate clearly. In particular, I don't think they actually mean "complex number" in the sense it's ordinarily understood in mathematics, because in general exponentiating a complex number gives a complex result, even with a real (or even integer) exponent.

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Re:Generalized Orders of Magnitude (GOOMs) by fheinsen on Thursday October 16, 2025 @09:33AM (#45605149)

The paper formally defines GOOMs as the subset of the complex plane that elementwise exponentiates to the real line.

We'll update the README to make that clearer.

Thank you for pointing that out!

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