Two questions, related:

1) Pretty much all modern desktop processors have some of the basic higher level math approximation functions built-in, right? In particular, square root, and three basic trig functions (sine, cosine, tangent)? (Also, e^x and ln(x) would be good ones.) Are these contained in SSE*, or some other extended instruction set? I read some online material that seemed to indicate that functions were hardwired into the chips now.

2) If you are coding on a typical Gnu/Linux system, is your glibc using the built-in versions of these basic functions? Or do you have to use special calls / libraries to make use of them? I poked around a little in some glibc source code I have (2.14), and I couldn't tell for sure. The README.libm seemed to indicate that for sqrt, glibc uses a "(slow but portable) bit by bit method using integer arithmetic" which sounded kind of scary.

1) That is the case with x86 processors.

2) That depends on which processor the program is intended to be run on. See glibc/wiki/FAQ for more details. The short answer is, "You only need to say --without-fp, and configure your compiler accordingly, if your machine has no way to execute floating-point instructions."

I'm not quite clear yet: So, if I am compiling of x86, then glibc is using all the above mentioned functions through hardware?

I wish to clear be on this, especially as far as the trigonometric functions are concerned. README.libm in glibc documentation indicates that glibc uses a 14th degree polynomial to approximate cos(x), which would seem like a rather slow operation if this was not replaced by a call to some hardware function.