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# Different Results When Summing a double[]

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How do you break a Monolith into Microservices at Scale? This ebook shows strategies and techniques for building scalable and resilient microservices.

The order you add double values can give you different results. This gets worse as the sum approaches 0 as the error is large compared with the result. Something I found interesting recently is seeing how many possible results you can get depending on the order you sum the values.

## Looking at variations on the sum

In the following code, the program creates random numbers around zero, adding a value to the list which ensures the sum is almost zero. It lists the different sums it finds.

```List doubles = new ArrayList();
Random rand = new Random();
double sum0 = 0;
for (int i = 0; i < 1000; i++) {
sum0 += doubles.get(doubles.size() - 1);
}

SortedSet sums = new TreeSet();
for (int i = 0; i < 10 * 1000 * 1000; i++) {
Collections.shuffle(doubles, rand);
double sum = 0;
for (double d : doubles)
sum += d;
System.out.println(sum);
}
System.out.printf("Found %,d different sums from %g to %g%n", sums.size(), sums.first(), sums.last());
```

prints

```-1.0891287871572786E-13
5.184741524999481E-14
-1.0469403122215226E-13
-1.1235457009206584E-13
3.985700658404312E-14
... many snipped ...
-1.042499420123022E-13
7.37188088351104E-14
-1.1379786002407855E-13
-1.084687895058778E-13
-1.0591527654923993E-13
Found 1,411 different sums from -1.39000e-13 to 7.37188e-14
```
For an array of 100, it found 156 possible sums. For 10,000 values you can get
```Found 12,701 different sums from -8.01137e-13 to 1.59517e-12
```

To get an exact answer you can use BigDecimal. This will give you same result regardless of order.

```BigDecimal bd = BigDecimal.ZERO;
for (double d : doubles)
Collections.shuffle(doubles, rand);
BigDecimal bd2 = BigDecimal.ZERO;
for (double d : doubles)
if (!bd.equals(bd2))
throw new AssertionError();
System.out.println("The actual sum is exactly "+bd);
```

and prints something like

```The actual sum is exactly 4.77395900588817312382161617279052734375E-15
```

How do you break a Monolith into Microservices at Scale? This ebook shows strategies and techniques for building scalable and resilient microservices.

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