No matter what "precision" or "epsilon" I set, the result I get from "sqrt" is not rounded up

[PaulRBerg]

This is potentially related to #2608.

I have the following configuration:

{
    number: "BigNumber",
    precision: 60 + 18 + 2,
    epsilon: 1e-80,
}

I am then trying to run sqrt(x.mul(y)) over the following two numbers:

const x = math.bignumber!("115792089237316195423570985008687907853269984665640564039457584007913129639935");
const y = math.bignumber!("0.000000000000000001");
const result = math.sqrt!(x.mul(y));

This produces the result 340282366920938463463.374607431768211455.

But, as per the result I get on Wolfram, I was expecting the result to be 340282366920938463463.374607431768211456 (with a 6 at the end) instead. More specifically, I was expecting the .99999... decimals to cause the result to be rounded up.

Why is the result not rounded up, and how can I make it be so?

Note: this started to happen after I upgraded mathjs to v10.6.4. When I was using v10.4.0, the value I was getting was 340282366920938463463.374607431768211456.

[josdejong]

Executing your expression, I get:

340282366920938463463.37460743176821145599999999999999999999999999999999999999853

Which is indeed the correct answer but contains a rounding error.

The BigNumber data type (powered by Decimal.js) has a higher precision but is still a floating point number type, and hence can have round-off errors.

You can use math.format or math.round to round the result if you want to get rid of the round-off errors:

math.config({precision: 60+18+2})
const x = math.bignumber("115792089237316195423570985008687907853269984665640564039457.584007913129639935")
const y = math.bignumber("0.000000000000000001")
const result = math.sqrt(x.mul(y))
// "340282366920938463463.37460743176821145599999999999999999999999999999999999999853"

const decimals = 18
const roundedResult = math.round(result, decimals)
// "340282366920938463463.374607431768211456" 

[PaulRBerg]

Thanks for the tip to use math.round!