BigNumber Rounding Error

[omurovec]

Ethers Version

5.5.2

Search Terms

rounding, round, remainder, cut off

Describe the Problem

When using BigNumber.div(), decimals are always cut off instead of rounded. This leads to rounding errors in many cases and when using libraries like https://github.com/paulrberg/prb-math that use proper rounding it causes conflicting results.

Ethers.js relies on BN.js for BigNumber math and there have been issues created regarding this:
indutny/bn.js#290

However, there has been very little activity around it, and the only other similar issue has been stale for 4+ years. Alternatively this could be solved within the BigNumber implementation by checking for the number in the first decimal place and rounding accordingly, similar to the code example I have provided.

Code Snippet

10 / -6 // = -1.6666
BigNumber.from(10).div(-6).toString() // -1

10 / 6 // = 1.6666
BigNumber.from(10).div(6).toString() // 1

// Solution
const safeDiv = (a, b) => {
  const quotient = a.div(b)
  if (a.mul(10).div(b).abs().mod(10).gte(5)) {
    if (quotient.lt(0)) {
      return quotient.sub(1)
    }
    return quotient.add(1)
  }
  return quotient
}

safeDiv(BigNumber.from(10), BigNumber.from(-6)) // -2

### Contract ABI

_No response_

### Errors

_No response_

### Environment

node.js (v12 or newer)

### Environment (Other)

_No response_

[ricmoo]

The BigNumber class implements integer maths, which implies truncation. There are many ways to round, depending on the goal.

The FixedNumber class offers the round-to-infinity operation (via .round), which looks like you are after. This is the rounding most people are familiar with in display logic or thresholds, but is often inappropriate for analytical purposes as errors compound very quickly. Rounding fixed numbers is of course dependent on the fractional width specified; by default it is 18 decimals places, but if you require rounding at this depth, you would require a higher depth represented internally.

For other rounding strategies, such as round-to-parity, you will need to implement that yourself. For blockchain purposes, you almost always want truncation (which is what BigNumber implements), as that is what the EVM performs.