I am the author of an open-source package for mathematical optimization and automatic differentiation called CasADi (www.casadi.org) and have recently started realize the potential of the LLVM project. At the core of CasADi are two fast interpretors for mathematical expressions and I’m now planning to complement these with JIT-compilation using LLVM.
Does anyone know if there is someone using LLVM for either automatic differentiation or (sparse) linear algebra (two of the things CasADi is capable of doing)? One thing particularly interesting would be direct sparse linear algebra. The only thing I could find was a blog entry from 2009: http://justindomke.wordpress.com/2009/11/30/automatic-differentiation-without-compromises/