With some changes to your code I got the difference down to two microseconds:
#!/usr/bin/perl
use Time::HiRes qw(gettimeofday);
my ($secs1,$sec2,$micro1,$micro2);
#discard once
gettimeofday();
($secs1, $micro1) = gettimeofday();
($secs2, $micro2) = gettimeofday();
print "$secs1$micro1\n";
print "$secs2$micro2\n";
__OUTPUT__
1133355471176848
1133355471176850
This is on a dual-2.8GHz Xeon, so I suspect you'll have trouble getting it to display identical values on a "normal" current system.
As for whether it's theoretically possible, I am pretty sure it'd be possible on SMP machines.
Update: after thinking about this some more, I'm pretty sure this is also possible on uniprocessor machines if you're running an operating system with a preemptible kernel.
Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it. -- Brian W. Kernighan
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