The OpenTK libraries, and with them, MonoTouch and MonoDroid, contain the method LengthFast, which should calculate an approximation of a vector's length without the use of Math.Sqrt (which seems to be known as slow). LengthFast uses MathHelper.InverseSqrtFast, a quite interesting method which should give a fast approximation of the square root (see lines 172 and 196 of http://www.opentk.com/files/doc/_math_helper_8cs_source.html).
I created a small benchmark which invokes both calculations 100'000'000 times, with vector lengths between about 1 and 100.
On Windows 7 / Intel i7-2600 3.40 GHz, I got:
Length: 2947 ms
LengthFast: 4754 ms
On an iPad 3 with MonoTouch, I got:
Length: 51575 ms
LengthFast: 41252 ms
So, LengthFast is much slower on the Intel CPU, on the iPad's ARM it is slightly faster.
Any explanation for this? Is that the result of the Intel CPU being able to calculate the square root 'natively' (without the use of software approximation)? Shouldn't LengthFast be always faster, at least a little bit?
All Math members are really fast. Don't try to speed up .NET math code. On a ARM processor it may be faster because there are some missing X86/X86_64 commands which are required for the same implementation on a ARM processor, so the code is different.