Computing Singular Value Decomposition of small ($4times 4$) matrices

I need to compute the Singular Value Decomposition (SVD) of many $4 times 4$ matrices. I’m looking for SVD algorithms specialized for small matrices. I’ve read that the std::vector sorting algorithm in the C++ STL is often hardcoded for short vectors for optimal performance. I want to hard code the SVD for the case $4 times 4$ matrices.

What information is there about optimally solving small cases of SVD?