ignorance and intolerance in computing communties

[Edward]

On May 2, 8:33 am, Xah Lee <x... at xahlee.org> wrote:

<snip>

> As i have indicated in my post, it is non-trivial to implement a
> function that returns the positive angle of a vector. For example, it
> can be done with sign checking of the coordinate components (in total
> 4 cases, which can be done as 2 levels of nesting if, or simply 4
> if.), and or the evaluation of Min[Abs[ArcCos[x],Abs[ArcSin[x]]], or
> use clever ways with dot product, or ArcTan. It is not a trivial to
> know which algorithm is in general more efficient. (this is important,
> since finding the angle of a vector is a basic function, that may
> needs to be called millions times directly or indirectly) Further,
> consider the inverse trig function, it is likely 99.99% of people with
> a PH D in math wouldn't know how these are actually implemented. So,
> the question of whether calling one of the inverse trig function is
> more robust or efficient than another is a open question. And, besides
> the algorithmic level, the question also entails how the language
> actually implement the inverse trig functions.

<snip>

"We should forget about small efficiencies, say about 97% of the time:
premature optimization is the root of all evil."

The question you are asking depends a great deal on other factors
outside of the coding environment such as the compiler and the
hardware.  If you are coding for a specific language/compiler/hardware
combination,  all you need do is profile different versions of your
code until you're happy with the results.