When you have a dynamically allocated buffer that varies its size at runtime in unpredictable ways (for example a vector or a string) one way to optimize its allocation is to only resize its backing store on powers of 2 (or some other set of boundaries/thresholds), and leave the extra space unused. This helps to amortize the cost of searching for new free memory and copying the data across, at the expense of a little extra memory use. For example the interface specification (reserve vs resize vs trim) of many C++ stl containers have such a scheme in mind.
My question is does the default implementation of the malloc/realloc/free memory manager on Linux 3.0 x86_64, GLIBC 2.13, GCC 4.6 (Ubuntu 11.10) have such an optimization?
void* p = malloc(N);
... // time passes, stuff happens
void* q = realloc(p,M);
Put another way, for what values of N and M (or in what other circumstances) will p == q?