What's with this output from a double?

Question

I am getting strange output when I add doubles together. Can someone tell me why I'm getting repeating decimals when I am adding 0.1 every time?

I have worked out the formula for adding these numbers together and I have done this myself on paper up to 3.3...

The sum of all numbers (decreasing by 1 tenth) from 3.3 to 1 equals 51.6

3.3
3.2
3.1 +
3.0
...
1.0
_
51.6

There is an easier way to calculate this using two formulas:

The linear formula for the increasing number: Y = 0.1X + 1
And the sum of increasing numbers formula: [X * (Y + 1)]/2 = total

first solve for Y using any number (in this case 100)

11 = 0.1(100) + 1

Then solve for the total using X and Y

[100 * (11+1)]/2 = 600

The output of the following code should be 600 I believe. There is no question that it should not have a repeating decimal. What am I doing wrong here? There must be something I missed.

public static void main(String[] args) {

      int days = 100;
      double inc = 0.1;
      double init = 1;
      double total = 0;

      for (int i = 1; i <= days; i++) {
          if (i == 1) {
            total = total + init;
          } else {
            init = init + inc;
            total = total + init;
          }
      }
      System.out.println("Total: " + total);
      System.out.println("Daily: " + init);
  }

What is the output you are getting? Is this a simple case of double precision limits (`0.1` cannot be represented exactly…) — Floris, Dec 31 '13 at 20:51
[What Every Computer Scientist Should Know About Floating Point](http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html) — Don Roby, Dec 31 '13 at 20:52
@DonRoby - thanks for finding the link. I was just looking for it myself... — Floris, Dec 31 '13 at 20:52
(You know, you can easily work the problem in integer form, then divide by 10.) — Hot Licks, Dec 31 '13 at 20:54
It looks like my formulas were off by a bit. Should be Y = 0.1X + 0.9 — Dave Hulse, Dec 31 '13 at 22:09

Elliott Frisch · Answer 1 · 2014-01-01T01:59:44.963

2

Double does not have infinite precision (Neither does BigDecimal, but BigDecimal has sufficient precision for this implementation).

Try this,

public static void main(String[] args) {
  int days = 100;
  java.math.BigDecimal init = java.math.BigDecimal.ONE;
  java.math.BigDecimal total = java.math.BigDecimal.ZERO;
  java.math.BigDecimal oneTenth = new java.math.BigDecimal(
      "0.1");
  for (int i = 1; i <= days; i++) {
    if (i != 1) {
      init = init.add(oneTenth);
    }
    total = total.add(init);
  }
  System.out.println("Total: " + total);
  System.out.println("Daily: " + init);
}

Which outputs

Total: 595.0
Daily: 10.9

edited Jan 01 '14 at 01:59

answered Dec 31 '13 at 20:55

Elliott Frisch

198,278
20
158
249

3

Your answer seems to imply that BigDecimal has infinite precision and that this is why it works. BigDecimal does not have infinite precision any more than `double` does. It works here because it happens to be able to represent the intermediate results involved. It wouldn't if `oneTenth` was `oneSeventh`. – Pascal Cuoq Jan 01 '14 at 01:55

Peter Lawrey · Answer 2 · 2013-12-31T21:01:17.070

The formula should be

0.1 * (100 * (100 + 1) / 2)

except you start at 10 * 0.1 so the formula is more complicated.

In any case double precision is not exact esp for numbers like 0.1, so you should expect to get rounding error.

You can work around this by using numbers which can be represented accurately like 1 instead of 0.1 (or rounding the result)

public static void main(String... ignored) {
    int days = 100;
    double inc = 1;
    double init = 10;
    double total = 0;

    for (int i = 1; i <= days; i++) {
        if (i == 1) {
            total = total + init;
        } else {
            init = init + inc;
            total = total + init;
        }
    }
    total /= 10;
    init /= 10;
    System.out.println("Total: " + total);
    System.out.println("Daily: " + init);
}

or round the result.

public static void main(String... ignored) {
    int days = 100;
    double inc = 0.1;
    double init = 1;
    double total = 0;

    for (int i = 1; i <= days; i++) {
        if (i == 1) {
            total = total + init;
        } else {
            init = init + inc;
            total = total + init;
        }
    }
    System.out.printf("Total: %.1f%n", total);
    System.out.printf("Daily: %.1f%n", init);
}

both print

Total: 595.0
Daily: 10.9

score 1 · Accepted Answer · edited May 23 '17 at 10:25

Please read the link that Don Roby posted. In essence, double precision is not a good way to represent fractions. A number like 0.1 does not have an exact representation in binary float notation - because floating point numbers are written as "something times two to the power something else". And you cannot solve that exactly for 0.1. Thus, you are really getting a slightly smaller number - actually

0.0999999999999998

And that missing amount is enough to mess up the math…

See Jon Skeet's very excellent answer on this topic: https://stackoverflow.com/a/1089026/1967396

What's with this output from a double?

3 Answers3