rounding_errors

Rounding errors

Application developers must take care of correct rounding of numbers, especially if the rounding impacts tokens amounts.

Cosmos-sdk offers two custom types for dealing with numbers:

• sdk.Int (sdk.UInt) type for integral numbers
• sdk.Dec type for decimal arithmetic

The sdk.Dec type has problems with precision and does not guarantee associativity, so it must be used carefully. But even if a more robust library for decimal numbers is deployed in the cosmos-sdk, rounding may be unavoidable.

Example

Below we see a simple example demonstrating sdk.Dec type's precision problems.

func TestDec() {
    a := sdk.MustNewDecFromStr("10")
    b := sdk.MustNewDecFromStr("1000000010")
    x := a.Quo(b).Mul(b)
    fmt.Println(x)  // 9.999999999999999000

    q := float32(10)
    w := float32(1000000010)
    y := (q / w) * w
    fmt.Println(y)  // 10
}

Mitigations

• Ensure that all tokens operations that must round results always benefit the system (application) and not users. In other words, always decide on the correct rounding direction. See Appendix G in the Umee audit report

• Apply "multiplication before division" pattern. That is, instead of computing (x / y) * z do (x * z) / y

• Observe issue #11783 for a replacement of the sdk.Dec type

External examples

• Umee had vulnerability caused by incorrect rounding direction