package keeper import ( "sort" sdk "github.com/cosmos/cosmos-sdk/types" ) // splitIntIntoWeightedBuckets divides an initial +ve integer among several buckets in proportion to the buckets' weights // It uses the largest remainder method: https://en.wikipedia.org/wiki/Largest_remainder_method // See also: https://stackoverflow.com/questions/13483430/how-to-make-rounded-percentages-add-up-to-100 func splitIntIntoWeightedBuckets(amount sdk.Int, buckets []sdk.Int) []sdk.Int { // Limit input to +ve numbers as algorithm hasn't been scoped to work with -ve numbers. if amount.IsNegative() { panic("negative amount") } if len(buckets) < 1 { panic("no buckets") } for _, bucket := range buckets { if bucket.IsNegative() { panic("negative bucket") } } // 1) Split the amount by weights, recording whole number part and remainder totalWeights := totalInts(buckets...) if !totalWeights.IsPositive() { panic("total weights must sum to > 0") } quotients := make([]quoRem, len(buckets)) for i := range buckets { // amount * ( weight/total_weight ) q := amount.Mul(buckets[i]).Quo(totalWeights) r := amount.Mul(buckets[i]).Mod(totalWeights) quotients[i] = quoRem{index: i, quo: q, rem: r} } // 2) Calculate total left over from remainders, and apportion it to buckets with the highest remainder (to minimize error) // sort by decreasing remainder order sort.Slice(quotients, func(i, j int) bool { return quotients[i].rem.GT(quotients[j].rem) }) // calculate total left over from remainders allocated := sdk.ZeroInt() for _, qr := range quotients { allocated = allocated.Add(qr.quo) } leftToAllocate := amount.Sub(allocated) // apportion according to largest remainder results := make([]sdk.Int, len(quotients)) for _, qr := range quotients { results[qr.index] = qr.quo if !leftToAllocate.IsZero() { results[qr.index] = results[qr.index].Add(sdk.OneInt()) leftToAllocate = leftToAllocate.Sub(sdk.OneInt()) } } return results } type quoRem struct { index int quo sdk.Int rem sdk.Int } // totalInts adds together sdk.Ints func totalInts(is ...sdk.Int) sdk.Int { total := sdk.ZeroInt() for _, i := range is { total = total.Add(i) } return total }