Why Are the FixedNumber Methods Unsafe

[mudgen]

https://docs.ethers.io/v5/api/utils/fixednumber/

The math methods for FixedNumber have "Unsafe" appended to them. Why are they unsafe?
How can I do safe math with FixedNumber values?

When should and when should I not use the Unsafe methods?

These are immediate questions I have right now, so any quick answer is much appreciated.

[tkporter]

I came across this comment this a while back when I had the same question, you may find it helpful: #1322 (comment)

[mudgen]

I am thinking that if I use large enough precision, for example "fixed182x18" then I don't have to worry about the underflow for my calculations.

[ricmoo]

Keep in mind underflow compounds; if you do many operations, the lower bits become more and more corrupt with each operation. Which is why floating point use techniques like round-to-even to reduce the rate of corruption, probabilistically.

[mudgen]

Thanks. But is there any other alternative other than using floating point? Because using Integer or FixedNumber, I would get the same rounding/trunction behavior, right? FixedNumber is Integer math behind the scenes, correct?

[ricmoo]

Yupp, it’s integer math under the hood.

It depends on your purposes. If you need to match solidity, make sure you use the correct operations.

If you are doing a simple calculation, perform all numerator operations first before doing any division.

If you are computing running or alpha weighted values, you need to take much against compounded errors.

• a = (( 1 + 1 + 1 + 1 + 1) / 2) = 2
• b = (1/2) + (1/2) + (1/2) + (1/2) + (1/2) = 0

In that example, a is much closer to the actual value than b. Outside of symbolic computation, order of operations plays a large role in accuracy, so just make sure you are taking that into account. :)

[mudgen]

Why is addition and multiplication unsafe? Because it can overflow?