List sum too large, throwing overflow exception

Question

I have a list of prime numbers up to 2 000 000. That's a list containing almost 150 000 very large integers. I want a sum of all the numbers in it. Here's a random list of large integers just for demonstration:

List<int> numbers = new List<int>();
for (int i = 0; i < 100; i++)
{
    numbers.Add(1000000000);
}
Console.WriteLine(numbers.Sum().ToString());

I'm getting a "Arithmetic operation resulted in an overflow" exception. I guess the sum is too large, but converting it to Int64 didn't help, it still throws the same exception.

Console.WriteLine(Convert.ToUInt64(numbers.Sum()).ToString());

I even tried saving the sum into Int64 variable and then using it, but this didn't work either.

long sum = numbers.Sum();
Console.WriteLine(sum.ToString());

Is there any data type that can hold this large number, or am I making the mistake somewhere else? Thanks for any help.

Your number may be larger than what `int` can hold. I would try changing it to `long` — Jaskier, Oct 03 '18 at 18:04
This is a common bug pattern. In all your attempts you change the sum to long, but changing the *sum* to `long` doesn't help because that converts *too late*. That converts the *final sum* to long, but by then it has already overflowed! — Eric Lippert, Oct 03 '18 at 18:05
We also see this pattern as: `int x = whatever; double percentage = x / 100;` but `x/100` is *int*, so this converts to double *too late*. What you want is `((double)x)/100` or `x/100.0`, which causes the compiler to insert the conversion for you. There are lots of variations on this bug. — Eric Lippert, Oct 03 '18 at 18:09

Ashkan Mobayen Khiabani · Answer 1 · 2022-10-22T14:49:05.670

14

Try casting to Int64 (long) before getting sum:

Console.WriteLine(numbers.Select(x=> (long)x).Sum().ToString());

edited Oct 22 '22 at 14:49

answered Oct 03 '18 at 18:02

Ashkan Mobayen Khiabani

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150K very large integers probably will overflow even longs. – Steve Oct 03 '18 at 18:13
2

This solution requires to convert `int` to `long` 150 000 times. I doubt that it's an optimal solution – Fabjan Oct 03 '18 at 18:14
@Steve well then he should implement a custom adding system, for example one that works for strings. – Ashkan Mobayen Khiabani Oct 03 '18 at 18:15
I was thinking about BigInteger, however I should rethink my comment. Adding 150K times Int.MaxValue doesn't overflow a long MaxValue – Steve Oct 03 '18 at 18:16
@Fabjan as China Syndrome said its better to choose a `List` instead of `List` but I assumed this is something obvious and OP may already know that. I thought may be this is an example and he can not simply change the type. I have tried to make the least change to OP's code and just correct where it is wrong. – Ashkan Mobayen Khiabani Oct 03 '18 at 18:18
Thank you very much! That was the problem. – Milan Vodák Oct 03 '18 at 18:20
@Steve I'm sorry, from the example it looks like I have 150k integers with 1 billion value. But their values are only up to almost 2 milion. – Milan Vodák Oct 03 '18 at 18:26
Integers are ok to store them but as @Fabjan noted, using Int64 list is probably the way to go, to avoid a lot of converting. – Milan Vodák Oct 03 '18 at 18:46
2

Just as a note you need at least 4.3 billion integers to oveflow long (and they would not fit into single array anyway). – Antonín Lejsek Apr 10 '21 at 17:35
@Steve, Int64.MaxValue / Int32.MaxValue = 4,294,967,298, so no, 150K very large integers are at most 0.00349 % of Int64.MaxValue. – Olivier Jacot-Descombes Oct 22 '22 at 15:02

China Syndrome · Accepted Answer · 2018-10-03T18:07:45.997

7

Problem is your answer is over 2.65 billions. Change the int to Int64

List<Int64> numbers = new List<Int64>();
for (int i = 0; i < 100; i++)
{
    numbers.Add(1000000000);
}
Console.WriteLine(numbers.Sum().ToString());

To Clarify an Int has a max value of 2.65 billion roughly and Int64 is in the trillions

edited Oct 03 '18 at 18:07

answered Oct 03 '18 at 18:04

China Syndrome

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I think this is a better way than doing 150k conversions, even though the integers are alright for the numbers. Thanks! – Milan Vodák Oct 03 '18 at 18:48

score 5 · Answer 3 · answered Oct 03 '18 at 18:06

5

You can use Aggregate method:

Console.WriteLine(numbers.Aggregate(0L, (c, n) => c + n));

This overload of Aggregate take an accumulator as first argument
Literal 0L will be treated as long, not int. This will save you from arithmetic overflow

answered Oct 03 '18 at 18:06

Aleks Andreev

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score 2 · Answer 4 · answered Apr 10 '21 at 18:15

Conversions from int to long are cheap, sometimes even for free. Lets compare five codes

long sum = intArr.Select(x => (long)x).Sum(); // 0.95s

long sum = intArr.Sum(x => (long)x); // 0.95s

long sum = longArr.Sum(); // 0.86s

long sum = 0;
foreach (int x in intArr)
{
    sum += x; // 0.22s
}

long sum = 0;
foreach (long x in longArr)
{
    sum += x; // 0.23s
}

elapsed time is for 100M items. As you see, if you care about performace, the conversion is not an issue

List sum too large, throwing overflow exception

4 Answers4