Question

I’m not sure if this is a bug or not, so I thought that maybe you folks might want to take a look.

The problem lies with this code:

for i=0,1,.05 do
    print(i)
end

The output should be:

0
.05
.1
--snip--
.95
1

Instead, the output is:

0
.05
.1
--snip--
.95

This same problem happened with a while loop:

w = 0
while w <= 1 do
    print(w)
    w = w + .05
end
--output:
0
.05
.1
--snip--
.95

The value of w is 1, which can be verified by a print statement after the loop.

I have verified as much as possible that any step that is less than or equal .05 will produce this error. Any step above .05 should be fine. I verified that 1/19 (0.052631579) does print a 1. (Obviously, a decimal denominator like 19.9 or 10.5 will not produce output from [0,1] inclusive.) Is there a possibility that this is not an error of the language? Both the interpreter and a regular Lua file produce this error.

Answer 1

This is a rounding problem. The issue is that 0.05 is represented as a floating point binary number, and it does not have an exact representation in binary. In base 2 (binary), it is a repeating decimal similar to numbers like 1/3 in base 10. When added repeatedly, the rounding results in a number which is slightly more than 1. It is only very, very slightly more than 1, so if you print it out, it shows 1 as the output, but it is not exactly 1.

> x=0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05+0.05
> print(x)
1
> print(1==x)
false
> print(x-1)
2.2204460492503e-16

So, as you can see, although really close to 1, it is actually slightly more.

A similar situation can come up in decimal when we have repeating fractions. If we were to add together 1/3 + 1/3 + 1/3, but we had to round to six digits to work with, we would add 0.333333 + 0.333333 + 0.333333 and get 0.999999 which is not actually 1. This is an analogous case for binary math. 1/20 cannot be precisely represented in binary.

Note that the rounding is slightly different for multiplication so

> print(0.05*20-1)
0
> print(0.05*20==1)
true

As a result, you could rewrite your code to say

for i=0,20,1 do
    print(i*0.05)
end

And it would work correctly. In general, it’s advisable not to use floating point numbers (that is, numbers with decimal points) for controlling loops when it can be avoided.