rounding up vs. rounding down

[benibela]

I have run these tests on someone's double parser which discovered thousands of wrongly parsed numbers

But on closer examination, that parser still finds the nearest double number. Just there are two nearest numbers.
E.g. 9008309105029287 has 9008309105029288 (+1) and 9008309105029286 (-1)

Is it really important to return the larger one?

[nigeltao]

If there's a tie then we use standard IEEE 754 round-to-even rules.

https://nigeltao.github.io/blog/2020/eisel-lemire.html#round-to-even has some examples.

At least, that's what I remember doing. Let me know if there's still a discrepancy.

[nigeltao]

Is it really important to return the larger one?

It is important that parsing text-based formats to float64 values is deterministic, across different libraries. As a silly example, it wouldn't work if a message like "send Bob 3.5 million dollars" was rounded by Bob to 4 million but rounded by me to 3 million, even though both are equally distant.

[benibela]

If there's a tie then we use standard IEEE 754 round-to-even rules.

But floats with positive exponent are always even. Either direction would be round-to-even

https://nigeltao.github.io/blog/2020/eisel-lemire.html#round-to-even has some examples.

Guess that explains it. Some numbers are more even than even