A problem:  On some systems, the timing function gives times in multiples of .01 seconds.  On others, the timing coarseness may be significantly smaller or larger.  (You should determine the timing coarseness for your machine.)  Thus, for example, on a system with .01 second timing coarseness, timing anything which takes less than one fiftieth of a second could result in more than a 50% error.  Your programs, for small values of n, should be easily this fast.

A solution:  When the algorithm to be timed is too fast to obtain an accurate measurement, the algorithm can be run many times in succession, with the cumulative time being measured.  This time can then be divided by the number of runs to obtain a more accurate measurement of the time required by an individual run.  As little as possible, other then the successive calls, should occur while the timing is taking place.  In fact, for particularly speedy code, the time spent updating the loop variable may be of the same order of magnitude as the time you are attempting to measure.  To account for this, you can subsequently time the loop with a (nearly) empty body and subtract this measure from your first measure, the net result reflecting more accurately the time spent within the code of interest. One should note that some optimizing compilers will optimize loops that contain an empty body by discarding them.

Timer package

• user_time()
  returns the total amount of user cpu time used by the current process
  
• start_timer()
  starts the timer [actually, it only records the current value of user_time()]
  
• elapsed_time()
  returns the amount of cpu time that has been used since the last call to start_timer()

Header file timer.h declares the routines that are defined in timer.c and it should be included in all program files that invoke any of those routines.

Timing coarseness and computer speed

gcc -O9 timex2.c timer.o -o timex2 
gcc     timex2.c timer.o -o timexu2

You should write your own version of timex, but the executable of my version is available for downloading:

The results of running this program are summarized in the following table.  Running such a program several times on the same machine might sometimes give slightly different results.  (Why is that?)  Send me your results for other machines.  Specify whether you used my or another timer package.