[eigen] Help on solving a race condition

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I'm looking for some help on understanding how the following piece of
code in Eigen can lead to a race condition when the function
manage_caching_sizes is called from different threads:

inline std::ptrdiff_t manage_caching_sizes_helper(std::ptrdiff_t a,
std::ptrdiff_t b)
  return a<=0 ? b : a;

inline void manage_caching_sizes(Action action, std::ptrdiff_t* l1=0,
std::ptrdiff_t* l2=0)
  static std::ptrdiff_t m_l1CacheSize =
manage_caching_sizes_helper(queryL1CacheSize(),8 * 1024);
  static std::ptrdiff_t m_l2CacheSize =

During it's first call, this function computes and store the cache sizes.

I would like to find a solution that avoids making the static variable
"thread private" as suggested there:
The problem with this approach, is that the cache-sizes are recomputed
for every thread.



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