Is it safe to use the ARPACK eigensolver from different threads at the same time from a program written in C? Or, if ARPACK itself is not thread-safe, is there an API-compatible thread-safe implementation out there? A quick Google search didn't turn up anything useful, but given the fact that ARPACK is used heavily in large scientific calculations, I'd find it highly surprising to be the first one who needs a thread-safe sparse eigensolver.
I'm not too familiar with Fortran, so I translated the ARPACK source code to C using f2c, and it seems that there are quite a few static variables. Basically, all the local variables in the translated routines seem to be static, implying that the library itself is not thread-safe.
Fortran 77 does not support recursion, and hence a standard conforming compiler can allocate all variables in the data section of the program; in principle, neither a stack nor a heap is needed [1].
It might be that this is what f2c is doing, and if so, it might be that it's the f2c step that makes the program non thread-safe, rather than the program itself. Of course, as others have mentioned, check out for COMMON blocks as well. EDIT: Also, check for explicit SAVE directives. SAVE means that the value of the variable should be retained between subsequent invocations of the procedure, similar to static in C. Now, allocating all procedure local data in the data section makes all variables implicitly SAVE, and unfortunately, there is a lot of old code that assumes this even though it's not guaranteed by the Fortran standard. Such code, obviously, is not thread-safe. Wrt. ARPACK specifically, I can't promise anything but ARPACK is generally well regarded and widely used so I'd be surprised if it suffered from these kinds of dusty-deck problems.
Most modern Fortran compilers do use stack allocation. You might have better luck compiling ARPACK with, say, gfortran and the -frecursive option.
EDIT:
[1] Not because it's more efficient, but because Fortran was originally designed before stacks and heaps were invented, and for some reason the standards committee wanted to retain the option to implement Fortran on hardware with neither stack nor heap support all the way up to Fortran 90. Actually, I'd guess that stacks are more efficient on todays heavily cache-dependent hardware rather than accessing procedure local data that is spread all over the data section.