Utils BigNumber mul problem

[Sharkoon1]

Hi,

I stumbled upon a weird behavior using the utils bignumber mul function. https://docs.ethers.io/v5/api/utils/bignumber/

From what I saw you can use the mul function to multiply two big numbers. This is exactly what I am trying to do.
I tried to replicate this problem in a simple 4 line of code.

const { ethers } = require("ethers");

let num1 = ethers.utils.parseEther(String(0.03306254672760674));
let num2 = ethers.utils.parseEther(String(6436.466091886065));

console.log(ethers.utils.formatEther(num1.mul(num2)));
// 212805960923639361059.2502060781

This simple multiplication operation logs the following result 212805960923639361059.2502060781 instead of what I expect: 212.80596....

I saw same behaviors using the div function. Am I using the big number math operations wrong ?

[Sharkoon1]

@ricmoo would be very happy, if you could take a quick look at my question 👍 :)

[ricmoo]

You may need to look at your unit analysis to understand what you are trying to do. When you multiple you also multiply the units. Usually you would want something "price ($)" times "quantity (count)" which results in a unit of "$ for count". In your case you are computing a "price ($)" times "price ($)" which gives you a unit of "$ * $". Dollars squared is not generally a useful metric, so I think what you are trying to compute might have gone awry.

But given that, lets look at the example above:

num1 = 0.03306254672760674 * (10 ** 18)
num2 = 6436.466091886065 * (10 ** 18)

v = num1 * num2 = 212.80596092363936 * (10 ** 36)

Then when you use formatEther you are saying to rebase it in (10 ** 18), so you are essentially asking for:

result = v / (10 ** 18) = 212.80596092363936 * (10 ** 36) / (10 ** 18) = 212.80596092363936 * (10 ** 18)

When you multiple or divide in any unit, you must carry the rest of the operations out in that new unit. Usually we use a unit of 1, so things work out fine, but you have expanded the unit by (10 ** 18).

My guess it you want to use FixedPoint Math more than operate on unit-sensitive values, so you can use:

> num1 = FixedNumber.from("0.03306254672760674")
FixedNumber { format: "fixed128x18", value: "0.03306254672760674" }
> num2 = FixedNumber.from("6436.466091886065")
FixedNumber { format: "fixed128x18", value: "6436.466091886065" }
> num1.mulUnsafe(num2)
FixedNumber { format: "fixed128x18", value: "212.805960923639361059" }

The FixedNumber class performs all the unit correction internally for you. Also note to use strings for your values, not cast numbers to strings, otherwise this will happed:

String(1.000000000000000333)
"1.0000000000000002"

Does that make sense?

[Sharkoon1]

In my service, number 1 is a factor and number 2 is an actual price. I am trying to use the BigNumbers, What would be best practice to continue doing calculations with these values?

And these numbers both come from a contract function, so they are BigNumbers , thats why I thought I can just use the mul function and multiple both of them.

This is the thing that I don't really understand. Would I use formatEther to convert them to the unit Ether, and then convert them to a FixedNumber and then do the mathematical operations?

[ricmoo]

You only use parseEther on values which are in ether and formatEther on things which are ether.

I think by “factor” you mean something like quantity? So it sounds to me what you really want is num1.mul(parseEther("6436"). Your value in num1 isn’t a price in ether so you don’t want to convert it to ether, but num2 is ether so you need to convert it.

Does that make sense?

[Sharkoon1]

Okay, then we miss used parseEther. Num1 and num2 are both 10^18. Then I guess we have to write our own function to convert this 10^36 value back to normal "WEI" Unit 10^18.

I was just hoping there is something existing to do operations and convert it back to wei. Because we want to use the product of the calculations to pass it back to another contract function that only accepts wei.

[Sharkoon1]

Thank you for your help!

[ricmoo]

The formatEther converts Wei to a string representation and parseEther converts a string representation of ether to Wei.

The unit Wei² is generally not useful outside the scope of certain scoring systems like quadratic ranking, and often it has its square root taken so that it is normalized back into Wei.

Im not sure of your use case, but it is incredibly rare to need a value whose units are Wei². The article on unit analysis might be of help too. :)

Just a heads up though, let me know if you have any other issues. :)

[Sharkoon1]

Sorry, don't want to keep you too busy ;) , but I still don't really understand how to handle wei units.
I just figured out that the "quantity" was accidently in WEI unit, because I used parseEther on it, but the price is actually coming from a contract function.

So let's say I have a big number "6436466091886065000000" and quantity as a number that is 0.03306254672760674. I still don't really understand how to multiply both values without loosing accuracy. And also how I can use BigNumber.mul that only accepts a string