Technically, none of the random number generators in C++ are O(1). This means there is a small (infinitesimal?) probability that it may cause real-time problems (for some of the implementation it may be near impossible). To ensure absolute safety at the cost of slightly non-uniform random number generation, cactus-rt implements a O(1) random number generator with the Xorshift algorithm. This example shows how to use it.
WARNING: DO NOT USE THIS RNG IN SECURE CRYPTOGRAPHIC CONTEXT AS IT IS NOT PERFECTLY RANDOM.