Using aggregation group `$sum` accumulator on large and small doubles

Working with Data
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1

I would like to understand how aggregation $sum accumulator works for big numbers and small numbers. In this example, I’m using neg-big, neg-bigger, pos-big and pos-bigger for doubles that are big enough to lose precision, a very small number small and a standard double number.

test> db.test.insertMany(
[
  { _id: 'number', val: 41.13 },
  { _id: 'small', val: 5e-324 },
  { _id: 'pos-big', val: 9223372036854776000 },
  { _id: 'neg-big', val: -9223372036854776000 },
  { _id: 'pos-bigger', val: 9223372036854778000 },
  { _id: 'neg-bigger', val: -9223372036854778000 }
]
)

Below shows $sort responses for applying ascending sort and descending sort on _id.

test> db.test.aggregate([ {$sort: {_id: 1} } ])
[
  { _id: 'neg-big', val: -9223372036854776000 },
  { _id: 'neg-bigger', val: -9223372036854778000 },
  { _id: 'number', val: 41.13 },
  { _id: 'pos-big', val: 9223372036854776000 },
  { _id: 'pos-bigger', val: 9223372036854778000 },
  { _id: 'small', val: 5e-324 }
]

test> db.test.aggregate([{$sort: {_id: -1} } ])
[
  { _id: 'small', val: 5e-324 },
  { _id: 'pos-bigger', val: 9223372036854778000 },
  { _id: 'pos-big', val: 9223372036854776000 },
  { _id: 'number', val: 41.13 },
  { _id: 'neg-bigger', val: -9223372036854778000 },
  { _id: 'neg-big', val: -9223372036854776000 }
]

When I apply $group’s $sum accumulator after ascending sort, it returns 41.13000000000011.

test> db.test.aggregate([ {$sort: {_id: 1} }, { $group: { _id: null, total: { $sum: "$val" } } } ])
[ { _id: null, total: 41.13000000000011 } ]

While if I apply it after descending sort, it returns 0.

test> db.test.aggregate([{$sort: {_id: -1} }, { $group: { _id: null, total: { $sum: "$val" } } } ])
[ { _id: null, total: 0 } ]

How does ascending sort sums up to41.13000000000011. I think number contributes to 41.13 but where does the rest of it comes from? I would understand if there is lost precision resulting in such as 41.1300000000001, but double 11 at the end is mystery to me.

Also how does the descending sort result sums up to 0?

I would like to understand them so I know how I could handle large numbers.

2

Is anyone able to help me on this?

I would love to figure out how I can handle big numbers.