The Toolchefs’ Soft IK is an advanced solution for two-bone setups and is now open source.
The Toolchefs are Daniele Federico and Alan Stanzione, a team making plugins for Autodesk Maya. The group recently released their Soft IK solver plugin for Maya as open source. The solver fixes the joint popping problem that happens with Maya’s default IK solver. The soft IK tool also implements a controllable stretch algorithm and an “elbow slide” and “elbow lock” system needed by modern rigs.
Toolchefs note that the advantage of their solver is that no extra nodes are needed and for this reason is faster than some other solutions out there. While the Soft IK Solver was always free, it is now under an Open Source license. Visit the page at Toolchefs to learn more, and the Github page for the source.