however, we are talking about a fraction of a second, over a million iterations to see such differences, and at the cost of a minor bit of accuracy. i still think overall 1/sqrt is much simplier than this other method.
Yeah, that's not enough to matter for my purposes. It's more that I was wondering if there was some completely alternate way of doing it that I might be missing out on-- you know, like all those nice tricks you can do with dot and cross products.
For my specific purposes-- direction toward/away from infinite line from a particular point, I hoped their might be some common equation that I was ignorant of, rather than "find closest point, normalize vector." That WORKS, but again, sometimes there's cute tricks, and that's what I was hoping for.