// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
// returns its double, also in Jacobian form.
func (curve *Curve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
delta := new(big.Int).Mul(z, z)
delta.Mod(delta, curve.P)
gamma := new(big.Int).Mul(y, y)
gamma.Mod(gamma, curve.P)
alpha := new(big.Int).Sub(x, delta)
if alpha.Sign() == -1 {
alpha.Add(alpha, curve.P)
}
alpha2 := new(big.Int).Add(x, delta)
alpha.Mul(alpha, alpha2)
alpha2.Set(alpha)
alpha.Lsh(alpha, 1)
alpha.Add(alpha, alpha2)
beta := alpha2.Mul(x, gamma)
x3 := new(big.Int).Mul(alpha, alpha)
beta8 := new(big.Int).Lsh(beta, 3)
x3.Sub(x3, beta8)
for x3.Sign() == -1 {
x3.Add(x3, curve.P)
}
x3.Mod(x3, curve.P)
z3 := new(big.Int).Add(y, z)
z3.Mul(z3, z3)
z3.Sub(z3, gamma)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Sub(z3, delta)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Mod(z3, curve.P)
beta.Lsh(beta, 2)
beta.Sub(beta, x3)
if beta.Sign() == -1 {
beta.Add(beta, curve.P)
}
y3 := alpha.Mul(alpha, beta)
gamma.Mul(gamma, gamma)
gamma.Lsh(gamma, 3)
gamma.Mod(gamma, curve.P)
y3.Sub(y3, gamma)
if y3.Sign() == -1 {
y3.Add(y3, curve.P)
}
y3.Mod(y3, curve.P)
return x3, y3, z3
}
func Factorial(n uint64) (r *big.Int) {
var oddFactNDiv2, oddFactNDiv4 big.Int
// closes on oddFactNDiv2, oddFactNDiv4
oddSwing := func(n uint64) (r *big.Int) {
if n < uint64(len(smallOddSwing)) {
return big.NewInt(smallOddSwing[n])
}
length := (n - 1) / 4
if n%4 != 2 {
length++
}
high := n - (n+1)&1
ndiv4 := n / 4
var oddFact big.Int
if ndiv4 < uint64(len(smallOddFactorial)) {
oddFact.SetInt64(smallOddFactorial[ndiv4])
r = &oddFact
} else {
r = &oddFactNDiv4
}
return oddFact.Quo(oddProduct(high, length), r)
}
// closes on oddFactNDiv2, oddFactNDiv4, oddSwing, and itself
var oddFactorial func(uint64) *big.Int
oddFactorial = func(n uint64) (oddFact *big.Int) {
if n < uint64(len(smallOddFactorial)) {
oddFact = big.NewInt(smallOddFactorial[n])
} else {
oddFact = oddFactorial(n / 2)
oddFact.Mul(oddFact.Mul(oddFact, oddFact), oddSwing(n))
}
oddFactNDiv4.Set(&oddFactNDiv2)
oddFactNDiv2.Set(oddFact)
return oddFact
}
oddFactNDiv2.SetInt64(1)
oddFactNDiv4.SetInt64(1)
r = oddFactorial(n)
exp := uint(n - uint64(xmath.BitCount64(n)))
return r.Lsh(r, exp)
}
func recursive(in int64, value *big.Int, v vector.IntVector, primeIndex int, primes []*big.Int, winner *big.Int, winner2 *vector.IntVector) {
if in > 4000000 {
if value.Cmp(winner) < 0 || winner.Cmp(big.NewInt(-1)) == 0 {
winner.Set(value)
*winner2 = v
fmt.Println(in, winner, *winner2)
//fmt.Print(in, winner, *winner2, " (")
//for k, v := range *winner2 {
// fmt.Print(primes[k], "**", v, " * ")
//}
//fmt.Println(")")
}
return
}
for i := int64(15); i >= 1; i -= 1 {
var factor big.Int
factor.Exp(primes[primeIndex], big.NewInt(i), nil)
//fmt.Println(factor, i, primes[primeIndex])
newV := v.Copy()
newV.Push(int(i))
var newValue big.Int
newValue.Mul(value, &factor)
recursive(in*(2*i+1)-i, &newValue, newV, primeIndex+1, primes, winner, winner2)
}
}