Example #1
0
// number = int_lit [ "p" int_lit ] .
//
func (p *gcParser) parseNumber() Const {
	// mantissa
	sign, val := p.parseInt()
	mant, ok := new(big.Int).SetString(sign+val, 10)
	assert(ok)

	if p.lit == "p" {
		// exponent (base 2)
		p.next()
		sign, val = p.parseInt()
		exp, err := strconv.Atoui(val)
		if err != nil {
			p.error(err)
		}
		if sign == "-" {
			denom := big.NewInt(1)
			denom.Lsh(denom, exp)
			return Const{new(big.Rat).SetFrac(mant, denom)}
		}
		if exp > 0 {
			mant.Lsh(mant, exp)
		}
		return Const{new(big.Rat).SetInt(mant)}
	}

	return Const{mant}
}
Example #2
0
func bitwise_arithmetic_shift_left(x, y Obj) Obj {
	xfx := (uintptr(unsafe.Pointer(x)) & fixnum_mask) == fixnum_tag
	yfx := (uintptr(unsafe.Pointer(y)) & fixnum_mask) == fixnum_tag
	if !yfx {
		panic("bad shift amount")
	}
	amount := uint(uintptr(unsafe.Pointer(y)) >> fixnum_shift)
	if xfx && amount < 32-fixnum_shift {
		i := int64(int(uintptr(unsafe.Pointer(x)) >> fixnum_shift))
		r := i << amount
		if r >= int64(fixnum_min) && r <= int64(fixnum_max) {
			return Obj(unsafe.Pointer(uintptr((r << fixnum_shift) | fixnum_tag)))
		} else {
			return wrap(big.NewInt(r))
		}
	} else if xfx {
		x = wrap(big.NewInt(int64(fixnum_to_int(x))))
	} else if (uintptr(unsafe.Pointer(x)) & heap_mask) != heap_tag {
		panic("bad type")
	}

	switch vx := (*x).(type) {
	case *big.Int:
		var z *big.Int = big.NewInt(0)
		return wrap(z.Lsh(vx, amount))
	}
	panic("bad type")
}
Example #3
0
// 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
}
Example #4
0
// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
// (x2, y2, z2) and returns their sum, also in Jacobian form.
func (curve *Curve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
	// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
	z1z1 := new(big.Int).Mul(z1, z1)
	z1z1.Mod(z1z1, curve.P)
	z2z2 := new(big.Int).Mul(z2, z2)
	z2z2.Mod(z2z2, curve.P)

	u1 := new(big.Int).Mul(x1, z2z2)
	u1.Mod(u1, curve.P)
	u2 := new(big.Int).Mul(x2, z1z1)
	u2.Mod(u2, curve.P)
	h := new(big.Int).Sub(u2, u1)
	if h.Sign() == -1 {
		h.Add(h, curve.P)
	}
	i := new(big.Int).Lsh(h, 1)
	i.Mul(i, i)
	j := new(big.Int).Mul(h, i)

	s1 := new(big.Int).Mul(y1, z2)
	s1.Mul(s1, z2z2)
	s1.Mod(s1, curve.P)
	s2 := new(big.Int).Mul(y2, z1)
	s2.Mul(s2, z1z1)
	s2.Mod(s2, curve.P)
	r := new(big.Int).Sub(s2, s1)
	if r.Sign() == -1 {
		r.Add(r, curve.P)
	}
	r.Lsh(r, 1)
	v := new(big.Int).Mul(u1, i)

	x3 := new(big.Int).Set(r)
	x3.Mul(x3, x3)
	x3.Sub(x3, j)
	x3.Sub(x3, v)
	x3.Sub(x3, v)
	x3.Mod(x3, curve.P)

	y3 := new(big.Int).Set(r)
	v.Sub(v, x3)
	y3.Mul(y3, v)
	s1.Mul(s1, j)
	s1.Lsh(s1, 1)
	y3.Sub(y3, s1)
	y3.Mod(y3, curve.P)

	z3 := new(big.Int).Add(z1, z2)
	z3.Mul(z3, z3)
	z3.Sub(z3, z1z1)
	if z3.Sign() == -1 {
		z3.Add(z3, curve.P)
	}
	z3.Sub(z3, z2z2)
	if z3.Sign() == -1 {
		z3.Add(z3, curve.P)
	}
	z3.Mul(z3, h)
	z3.Mod(z3, curve.P)

	return x3, y3, z3
}