Strange contour issue

Question

I'm not sure if this is a mistake or not, so I thought that you might want to take a look.

The problem is 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 

The same problem occurred with the 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 checked by the print statement after the loop.

I have verified as much as possible that any step that is less than or equal to .05 will lead to this error. Any step above 0.05 should be perfect. I checked that 1/19 (0.052631579) actually prints 1. (Obviously, a decimal denominator such as 19.9 or 10.5 will not output the output from [0,1] inclusive.) Is there a chance that this is not language mistake? Both the interpreter and the regular Lua file generate this error.

Answer 1

This is a rounding issue. The problem is that 0.05 is represented as a binary floating-point number and does not have an exact representation in binary format. In base 2 (binary), this is a repeating decimal number, like digits, like 1/3 in base 10. When added repeatedly, rounding results in a number that is slightly larger than 1. This is very, very slightly larger than 1, so if you print it, 1 will be displayed as output, but it's 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, this is actually a bit more.

A similar situation can occur in decimal when we repeat fractions. If we collected 1/3 + 1/3 + 1/3, but we had to round to six digits for work, we would add 0.333333 + 0.333333 + 0.333333 and get 0.999999, which is actually not 1. This is a similar case for binary mathematics. 1/20 cannot be represented exactly in binary format.

Note that rounding is slightly different for multiplication, so

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

As a result, you can rewrite your code to say

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

And it will work correctly. In general, it is recommended that you avoid using floating point numbers (i.e. decimal point numbers) to control loops when this can be avoided.

Answer 2

This is the result of floating point inaccuracy. The binary64 floating-point number cannot store 0.05, so the result will be rounded to a number that is slightly larger than 0.05. This rounding error remains in the repeated sum, and ultimately the final value will be a little more than 1.0, and therefore will not be displayed.

Answer 3

This is a floating point thing. Computers do not exactly represent floating point numbers. Tiny rounding errors make 20 +0.05 additions not exactly 1.0. Check out this article: “ What Every Programmer Should Know About Floating-Point Arithmetic. ”

To get the desired behavior, you can loop I on 1..20 and set f = i * 0.05

Answer 4

This is not a bug in Lua. The same thing happens in program C below. As others have explained, this is due to floating point inaccuracies, more precisely, the fact that 0.05 is not a binary fraction (i.e., it does not have a finite binary representation).

 #include <stdio.h> int main(void) { double i; for (i=0; i<=1; i+=0.05) printf("%g\n",i); return 0; }