0g-chain/x/auction/keeper/math.go

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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
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// 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 {
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// Limit input to +ve numbers as algorithm hasn't been scoped to work with -ve numbers.
if amount.IsNegative() {
panic("negative amount")
}
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if len(buckets) < 1 {
panic("no buckets")
}
for _, bucket := range buckets {
if bucket.IsNegative() {
panic("negative bucket")
}
}
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// 1) Split the amount by weights, recording whole number part and remainder
totalWeights := totalInts(buckets...)
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if !totalWeights.IsPositive() {
panic("total weights must sum to > 0")
}
quotients := make([]quoRem, len(buckets))
for i := range buckets {
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// 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}
}
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// 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 {
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return quotients[i].rem.GT(quotients[j].rem)
})
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// calculate total left over from remainders
allocated := sdk.ZeroInt()
for _, qr := range quotients {
allocated = allocated.Add(qr.quo)
}
leftToAllocate := amount.Sub(allocated)
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// 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
}