func (e *P521Element) Sub(t1, t2 *P521Element) *P521Element {
	p521Sub(&e.x, &t1.x, &t2.x)
	return e
}

// Mul sets e = t1 * t2, and returns e.
func (e *P521Element) Mul(t1, t2 *P521Element) *P521Element {
	p521Mul(&e.x, &t1.x, &t2.x)
	return e
}

// Square sets e = t * t, and returns e.
func (e *P521Element) Square(t *P521Element) *P521Element {
	p521Square(&e.x, &t.x)
	return e

func p521Polynomial(y2, x *fiat.P521Element) *fiat.P521Element {
	y2.Square(x)
	y2.Mul(y2, x)

	threeX := new(fiat.P521Element).Add(x, x)
	threeX.Add(threeX, x)
	y2.Sub(y2, threeX)

	return y2.Add(y2, p521B())
}

func p521CheckOnCurve(x, y *fiat.P521Element) error {
	// y² = x³ - 3x + b
	rhs := p521Polynomial(new(fiat.P521Element), x)
	lhs := new(fiat.P521Element).Square(y)

// license that can be found in the LICENSE file.

// Code generated by addchain. DO NOT EDIT.

package fiat

// Invert sets e = 1/x, and returns e.
//
// If x == 0, Invert returns e = 0.
func (e *P521Element) Invert(x *P521Element) *P521Element {
	// Inversion is implemented as exponentiation with exponent p − 2.
	// The sequence of 13 multiplications and 520 squarings is derived from the

		v := new(fiat.P384Element).One()
		b.ReportAllocs()
		b.ResetTimer()
		for i := 0; i < b.N; i++ {
			v.Mul(v, v)
		}
	})
	b.Run("P521", func(b *testing.B) {
		v := new(fiat.P521Element).One()
		b.ReportAllocs()
		b.ResetTimer()
		for i := 0; i < b.N; i++ {
			v.Mul(v, v)
		}
	})
}

func BenchmarkSquare(b *testing.B) {
	b.Run("P224", func(b *testing.B) {

	// Note that unsaturated_solinas would be about 2x faster than
	// word_by_word_montgomery for P-521, but this curve is used rarely enough
	// that it's not worth carrying unsaturated_solinas support for it.
	{
		Element:  "P521Element",
		Prime:    "2^521 - 1",
		Prefix:   "p521",
		FiatType: "[9]uint64",
		BytesLen: 66,
	},
}

func main() {
	t := template.Must(template.New("montgomery").Parse(tmplWrapper))

		BuildTags: "(!amd64 && !arm64 && !ppc64le && !s390x) || purego",
	},
	{
		P:       "P384",
		Element: "fiat.P384Element",
		Params:  elliptic.P384().Params(),
	},
	{
		P:       "P521",
		Element: "fiat.P521Element",
		Params:  elliptic.P521().Params(),
	},
}

func main() {
	t := template.Must(template.New("tmplNISTEC").Parse(tmplNISTEC))

	tmplAddchainFile, err := os.CreateTemp("", "addchain-template")