code: def optimized_binary_search(tab, logsize):
      
      hi = (1 << logsize) - 1
      intervalsize = (1 << logsize) >> 1
      while intervalsize > 0:
          if tab[hi ^ intervalsize]:
              hi ^= intervalsize
          intervalsize >>= 1
      return hi
docs: Binary search in a table using bit operations
  
      :param tab: boolean monotone table
         of size :math:`2^\\textrm{logsize}`
         with tab[hi] = True
      :param int logsize:
      :returns: first i such that tab[i]
      :complexity: O(logsize)