Rounding errors?

["Ian Latham" <ilatham@...>]

Hi, I was wondering if someone could enlighten me as to why the
following script does not produce the output I would expect:

x=0
upper_bound = 1
while x<upper_bound do
x=x+.01
print(x)
end

I would expect to see all the values in the interval (0,.5] listed out
at .01 increments to a precision of .01, but instead I get this:

0.01
0.02
0.03
0.04
0.05
0.06000000000000001
0.07000000000000001
0.08
0.09
0.09999999999999999
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.2100000000000001
0.2200000000000001
0.2300000000000001
0.2400000000000001
0.2500000000000001
0.2600000000000001
0.2700000000000001
0.2800000000000001
0.2900000000000001
0.3000000000000001
0.3100000000000001
0.3200000000000001
0.3300000000000001
0.3400000000000001
0.3500000000000001
0.3600000000000002
0.3700000000000002
0.3800000000000002
0.3900000000000002
0.4000000000000002
0.4100000000000002
0.4200000000000002
0.4300000000000002
0.4400000000000002
0.4500000000000002
0.4600000000000002
0.4700000000000003
0.4800000000000003
0.4900000000000003
0.5000000000000002

Can someone explain the extra decimals? Is this a rounding error? An
error in the internal representation of the float? A bug in the tostring
function? A bug in the addition code? Try changing upper_bound to 50 and
the errors get even more severe.


Thanks,

Ian Latham