func sieveInterval(n *big.Int) (min, max *big.Int) {
lnn := float64(n.BitLen()) * math.Log(2)
if lnn < 1.0 {
/* if this is not done. if n is 1 everything explodes sqrt(<0) = NaN */
lnn = 1.0
}
lnlnn := math.Log(lnn)
exp := int64(math.Ceil(math.Sqrt(lnn*lnlnn) * math.Log2(math.E)))
L := big.NewInt(0)
L.Exp(misc.Two, big.NewInt(exp), nil) // magic parameter (wikipedia)
sqrtN := misc.SquareRootCeil(n)
sieveMin := big.NewInt(0)
sieveMin.Sub(sqrtN, L)
sieveMax := big.NewInt(0)
sieveMax.Add(sqrtN, L)
return sieveMin, sieveMax
}
func findXandY(n *big.Int, cis, dis []*big.Int, exponents [][]int) (*big.Int, *big.Int) {
ls := linearSystemFromExponents(exponents)
ls.GaussianElimination(ls)
ls = ls.EliminateEmptyRows()
ls = ls.Transpose()
usedCombinations := ls.MakeEmptyRows()
if len(usedCombinations) == 0 {
return nil, nil
}
aAndBSquaredList := []AandBSquared{}
for _, indexSet := range usedCombinations {
a := big.NewInt(1)
bb := big.NewInt(1)
for _, i := range indexSet {
a.Mul(a, cis[i])
bb.Mul(bb, dis[i])
}
aAndBSquaredList = append(aAndBSquaredList, AandBSquared{a, bb})
}
x := big.NewInt(0)
y := big.NewInt(0)
xTimesY := big.NewInt(0)
multiplicity := big.NewInt(0)
testMod := big.NewInt(0)
gcd := big.NewInt(0)
abbChannel := make(chan AandBSquared, 100000)
doneChannel := make(chan bool)
cancelChannel := make(chan bool, 1)
var abb AandBSquared
go createPowerSetRecursively(0, AandBSquared{big.NewInt(1), big.NewInt(1)},
aAndBSquaredList, abbChannel, cancelChannel, doneChannel)
numberOfIndexSetsToGo := -1
for attempts := 0; ; /*attempts < 100*/ attempts += 1 {
if numberOfIndexSetsToGo == 0 {
break
}
select {
case <-doneChannel:
numberOfIndexSetsToGo = len(abbChannel)
continue
case abb = <-abbChannel:
if numberOfIndexSetsToGo > -1 {
numberOfIndexSetsToGo -= 1
}
}
x.SetInt64(0)
y.SetInt64(0)
abb.b = misc.SquareRootCeil(abb.b)
x.Add(abb.a, abb.b)
x.Mod(x, n)
y.Sub(abb.a, abb.b)
y.Mod(y, n)
if x.Cmp(misc.Zero) == 0 || x.Cmp(misc.One) == 0 || y.Cmp(misc.Zero) == 0 || y.Cmp(misc.One) == 0 {
/* discard trivial solutions */
continue
}
xTimesY.Mul(x, y)
multiplicity.DivMod(xTimesY, n, testMod)
if testMod.Cmp(misc.Zero) != 0 {
continue
}
if multiplicity.Cmp(misc.One) == 1 {
gcd.GCD(nil, nil, x, multiplicity)
if x.Cmp(gcd) != 0 {
x.Div(x, gcd)
}
multiplicity.Div(multiplicity, gcd)
gcd.GCD(nil, nil, y, multiplicity)
if y.Cmp(gcd) != 0 {
y.Div(y, gcd)
}
}
cancelChannel <- true
return x, y
}
cancelChannel <- true
return nil, nil
}