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main.go
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main.go
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// Package price implements functions to ease working with aiblocks price values.
// At present, prices are only used within the offer system, and are represented
// by a fraction whose numberator and denominator are both 32-bit signed
// integers.
package price
import (
"errors"
"fmt"
"math"
"math/big"
"math/bits"
"regexp"
"strconv"
"github.com/aiblocks/go/xdr"
)
var (
// validAmountSimple is a simple regular expression checking if a string looks like
// a number, more or less. The details will be checked in `math/big` internally.
// What we want to prevent is passing very big numbers like `1e9223372036854775807`
// to `big.Rat.SetString` triggering long calculations.
// Note: {1,20} because the biggest amount you can use in AiBlocks is:
// len("922337203685.4775807") = 20.
validAmountSimple = regexp.MustCompile("^-?[.0-9]{1,20}$")
// ErrDivisionByZero is returned when a price operation would result in a division by 0
ErrDivisionByZero = errors.New("division by 0")
// ErrOverflow is returned when a price operation would result in an integer overflow
ErrOverflow = errors.New("overflow")
)
// Parse calculates and returns the best rational approximation of the given
// real number price while still keeping both the numerator and the denominator
// of the resulting value within the precision limits of a 32-bit signed
// integer..
func Parse(v string) (xdr.Price, error) {
return continuedFraction(v)
}
// continuedFraction calculates and returns the best rational approximation of
// the given real number.
func continuedFraction(price string) (xdrPrice xdr.Price, err error) {
if !validAmountSimple.MatchString(price) {
return xdrPrice, fmt.Errorf("invalid price format: %s", price)
}
number := &big.Rat{}
maxInt32 := &big.Rat{}
zero := &big.Rat{}
one := &big.Rat{}
_, ok := number.SetString(price)
if !ok {
return xdrPrice, fmt.Errorf("cannot parse price: %s", price)
}
maxInt32.SetInt64(int64(math.MaxInt32))
zero.SetInt64(int64(0))
one.SetInt64(int64(1))
fractions := [][2]*big.Rat{
{zero, one},
{one, zero},
}
i := 2
for {
if number.Cmp(maxInt32) == 1 {
break
}
f := &big.Rat{}
h := &big.Rat{}
k := &big.Rat{}
a := floor(number)
f.Sub(number, a)
h.Mul(a, fractions[i-1][0])
h.Add(h, fractions[i-2][0])
k.Mul(a, fractions[i-1][1])
k.Add(k, fractions[i-2][1])
if h.Cmp(maxInt32) == 1 || k.Cmp(maxInt32) == 1 {
break
}
fractions = append(fractions, [2]*big.Rat{h, k})
if f.Cmp(zero) == 0 {
break
}
number.Quo(one, f)
i++
}
n, d := fractions[len(fractions)-1][0], fractions[len(fractions)-1][1]
if n.Cmp(zero) == 0 || d.Cmp(zero) == 0 {
return xdrPrice, errors.New("Couldn't find approximation")
}
return xdr.Price{
N: xdr.Int32(n.Num().Int64()),
D: xdr.Int32(d.Num().Int64()),
}, nil
}
func floor(n *big.Rat) *big.Rat {
f := &big.Rat{}
z := new(big.Int)
z.Div(n.Num(), n.Denom())
f.SetInt(z)
return f
}
//StringFromFloat64 will format a float64 to decimal representation with 7 digits after the decimal point
func StringFromFloat64(v float64) string {
return strconv.FormatFloat(v, 'f', 7, 64)
}
// ConvertToBuyingUnits uses special rounding logic to multiply the amount by the price and returns (buyingUnits, sellingUnits) that can be taken from the offer
//
// offerSellingBound = (offer.price.n > offer.price.d)
// ? offer.amount : ceil(floor(offer.amount * offer.price) / offer.price)
// pathPaymentAmountBought = min(offerSellingBound, pathPaymentBuyingBound)
// pathPaymentAmountSold = ceil(pathPaymentAmountBought * offer.price)
//
// offer.amount = amount selling
// offerSellingBound = roundingCorrectedOffer
// pathPaymentBuyingBound = needed
// pathPaymentAmountBought = what we are consuming from offer
// pathPaymentAmountSold = amount we are giving to the buyer
// Sell units = pathPaymentAmountSold and buy units = pathPaymentAmountBought
//
// this is how we do floor and ceiling in aiblocks-core:
// https://github.com/aiblocks/aiblocks-core/blob/9af27ef4e20b66f38ab148d52ba7904e74fe502f/src/util/types.cpp#L201
func ConvertToBuyingUnits(sellingOfferAmount int64, sellingUnitsNeeded int64, pricen int64, priced int64) (int64, int64, error) {
var e error
// offerSellingBound
result := sellingOfferAmount
if pricen <= priced {
result, e = MulFractionRoundDown(sellingOfferAmount, pricen, priced)
if e != nil {
return 0, 0, e
}
result, e = mulFractionRoundUp(result, priced, pricen)
if e != nil {
return 0, 0, e
}
}
// pathPaymentAmountBought
result = min(result, sellingUnitsNeeded)
sellingUnitsExtracted := result
// pathPaymentAmountSold
result, e = mulFractionRoundUp(result, pricen, priced)
if e != nil {
return 0, 0, e
}
return result, sellingUnitsExtracted, nil
}
// MulFractionRoundDown sets x = (x * n) / d, which is a round-down operation
// see https://github.com/aiblocks/aiblocks-core/blob/9af27ef4e20b66f38ab148d52ba7904e74fe502f/src/util/types.cpp#L201
func MulFractionRoundDown(x int64, n int64, d int64) (int64, error) {
if d == 0 {
return 0, ErrDivisionByZero
}
hi, lo := bits.Mul64(uint64(x), uint64(n))
denominator := uint64(d)
if denominator <= hi {
return 0, ErrOverflow
}
q, _ := bits.Div64(hi, lo, denominator)
if q > math.MaxInt64 {
return 0, ErrOverflow
}
return int64(q), nil
}
// mulFractionRoundUp sets x = ((x * n) + d - 1) / d, which is a round-up operation
// see https://github.com/aiblocks/aiblocks-core/blob/9af27ef4e20b66f38ab148d52ba7904e74fe502f/src/util/types.cpp#L201
func mulFractionRoundUp(x int64, n int64, d int64) (int64, error) {
if d == 0 {
return 0, ErrDivisionByZero
}
hi, lo := bits.Mul64(uint64(x), uint64(n))
lo, carry := bits.Add64(lo, uint64(d-1), 0)
hi += carry
denominator := uint64(d)
if denominator <= hi {
return 0, ErrOverflow
}
q, _ := bits.Div64(hi, lo, denominator)
if q > math.MaxInt64 {
return 0, ErrOverflow
}
return int64(q), nil
}
// min impl for int64
func min(x int64, y int64) int64 {
if x <= y {
return x
}
return y
}