When 0.99 isn't 0.99

[Thelonius]

If you add these two lines:

     my $x = $final_data{$key};
     printf "x = %.20f  high= %.20f\n", $x, $high;

you will get this output:

x = 0.98999999999999999000  high= 0.99000000000000010000
x = 0.97999999999999998000  high= 0.98000000000000009000
x = 0.96999999999999997000  high= 0.97000000000000008000
x = 0.95999999999999996000  high= 0.96000000000000008000
x = 0.94999999999999996000  high= 0.95000000000000007000
x = 0.93999999999999995000  high= 0.94000000000000006000
x = 0.93000000000000005000  high= 0.94000000000000006000
x = 0.92000000000000004000  high= 0.93000000000000005000
x = 0.91000000000000003000  high= 0.92000000000000004000
x = 0.90000000000000002000  high= 0.91000000000000003000

As you can see, the 0.99 that you get by assigning 0.99 is not the same as the 0.99 you get when you start with 0.90 and add 0.01 nine times. That's the way it is with binary floating point numbers. They're not exactly what you expect. There are several things you could do:

1. Don't worry about it. If these are measurements, e.g., then ones that fall right on the boundaries of the bins are inherently ambiguous.
2. Use an arbitrary-precision math package. There are ones for Perl, but I haven't used them, so I can't comment more.
3. Scale everything so that they are all integers.