ruby issue with float point iteration

Question

When I run the code

count = 0

while count < 1
  count += 0.1
  puts count
end

I would expect

0.1 
0.2 
0.3 
. . .

I have however been getting

0.1
0.2
0.30000000000000004
0.4
0.5
0.6
0.7
0.7999999999999999
0.8999999999999999
0.9999999999999999
1.0999999999999999

can anyone help explain this?

Search Stack Overflow for questions about floating point precision. There are lots of answers already. Here’s one that I wrote: http://stackoverflow.com/questions/28512650/strange-output-when-using-float-instead-of-double/28512770#28512770 — yellowantphil, May 03 '15 at 00:28
I STRONGLY encourage you to read [What Every Computer Scientist Should Know About Floating-Point Arithmetic](http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html) — Amxx, May 03 '15 at 00:41
Hint: don't repeatedly add 0.1 - instead, increment an *integer* by 1 then at each step, multiply by 0.1. You will still have a similar problem, but you'll get *less* rounding error. Have a look at "[*Is floating point math broken?*](https://stackoverflow.com/q/588004/1364007)" for a **very** detailed discussion of your problem. — Wai Ha Lee, May 03 '15 at 00:47

Martin Konecny · Accepted Answer · 2015-05-03T00:35:43.013

1

Think of it this way:

Your computer only has 32 or 64 bits to represent a number. That means it can only represent a finite amount of numbers.

Now consider all the decimal values between 0 and 1. There is an infinite amount of them. How can you possibly represent all Real Numbers if your machine can't even represent all the numbers between 0 and 1?

The answer is that your machine needs to approximate decimal numbers. This is what you are seeing.

Of course there are libraries that try to overcome these limitations and make it so that you can still accurately represent decimal numbers. One such library is BigDecimal:

require 'bigdecimal'

count = BigDecimal.new("0")
while count < 1
  count += 0.1
  puts count.to_s('F')
end

The downfall is that these libraries are generally slower at arithmetic, because they are a software layer above the CPU doing these calculations.

edited May 03 '15 at 00:35

answered May 03 '15 at 00:29

Martin Konecny

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Using `Rational` would be easier. – sawa May 03 '15 at 00:37
Doesn't `BigDecimal` have the same problem as `Float` (but just causes the problem to appear later)? – sawa May 03 '15 at 00:40
1

Yes, I agree with you. It cannot represent all values exactly. However you can set the precision you require, and then use it for specific calculations within that precision level with confidence - that's what makes it much more useful than working with simply floating point values. – Martin Konecny May 03 '15 at 00:56
@sawa: In short, no. – Mike Sherrill 'Cat Recall' May 03 '15 at 01:11

score 0 · Answer 2 · answered May 03 '15 at 00:28

Floating-point numbers cannot precisely represent all real numbers, and floating-point operations cannot precisely represent true arithmetic operations, this leads to many surprising situations.

I advise to read: https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems

You may want to use BigDecimal to avoid such problems.

score 0 · Answer 3 · edited May 23 '17 at 12:06

This is one of the many consequences of the representation of floating point number in memory !

To explain what exactly is is happening would be very long, and has other people have already done it better before, the best thing for you would be to read about go read about it elsewhere :

The very good What Every Computer Scientist Should Know About Floating-Point Arithmetic (article from 1991, reprint on oracle)
Wikipedia pages Floating point and IEEE floating point
IEEE 754 References

You can also have a look at those previous questions on SO:

ruby issue with float point iteration

3 Answers3