Fastest stable algorithm for solving dense symmetric linear system $Ax = b$

Question

I am trying to find the fastest algorithm for solving a linear system:

$$ Ax = b. $$

I know that $A$ will always be symmetric and dense, and will sometimes be positive definite. And $b$ will always be dense as well. So far, I have thought of two algorithms:

1. If not positive definite => use LDL decomposition
2. If positive definite => use Cholesky decomposition

My question is: is there any practical (one that can be implemented quite easily) algorithm that is faster than the two that I currently have. The algorithm must be stable in terms of its floating point operation. I am using this as part of a physics engine that I am building, so the matrix will be of quite large dimensions, thus I would like the asymptotic time to be as small as possible. Thank you very much.