#define y2in(off)  (32*0 + 8 + off)(RSP)
#define s2(off)    (32*1 + 8 + off)(RSP)
#define z1sqr(off) (32*2 + 8 + off)(RSP)
#define h(off)	   (32*3 + 8 + off)(RSP)
#define r(off)	   (32*4 + 8 + off)(RSP)
#define hsqr(off)  (32*5 + 8 + off)(RSP)
#define rsqr(off)  (32*6 + 8 + off)(RSP)
#define hcub(off)  (32*7 + 8 + off)(RSP)

#define z2sqr(off) (32*8 + 8 + off)(RSP)
#define s1(off) (32*9 + 8 + off)(RSP)

#undef s2
#undef u1
#undef u2
#undef z1sqr
#undef z2sqr
#undef h
#undef r
#undef hsqr
#undef rsqr
#undef hcub
#undef rptr
/* ---------------------------------------*/
#define x(off) (32*0 + off)(SP)
#define y(off) (32*1 + off)(SP)
#define z(off) (32*2 + off)(SP)

#define s(off)	(32*3 + off)(SP)
#define m(off)	(32*4 + off)(SP)
#define zsqr(off) (32*5 + off)(SP)

		BPtr:         &zBool,
		Bs:           []bool{zBool},
		BPtrs:        []*bool{&zBool},
		Bytes:        []byte{},
		BytesPtr:     &zBytes,
		SPtr:         &zStr,
		Ss:           []string{zStr},
		SPtrs:        []*string{&zStr},
		Children:     []Child{{}},
		ChildPtr:     new(Child),
		ChildToEmbed: ChildToEmbed{},
	}
	if !reflect.DeepEqual(v, want) {

			// V(k'+1) = V(2k+2) = V(k+1)² - 2.
			t1 = t1.sqr(vk1)
			t1 = t1.add(t1, nm2)
			t2, vk1 = t2.div(vk1, t1, n)
		} else {
			// k' = 2k
			// V(k'+1) = V(2k+1) = V(k) V(k+1) - P.
			t1 = t1.mul(vk, vk1)
			t1 = t1.add(t1, n)
			t1 = t1.sub(t1, natP)
			t2, vk1 = t2.div(vk1, t1, n)
			// V(k') = V(2k) = V(k)² - 2
			t1 = t1.sqr(vk)
			t1 = t1.add(t1, nm2)
			t2, vk = t2.div(vk, t1, n)
		}

				// to check performance before making changes.
				zz = zz.sqr(z)
				zz, z = z, zz
				z = z.trunc(z, logM)

				zz = zz.sqr(z)
				zz, z = z, zz
				z = z.trunc(z, logM)

				zz = zz.sqr(z)
				zz, z = z, zz
				z = z.trunc(z, logM)

				zz = zz.sqr(z)
				zz, z = z, zz
				z = z.trunc(z, logM)
			}

	x2sq.Square(&x)

	if x2 != x2sq {
		t.Fatalf("all ones failed\nmul: %x\nsqr: %x\n", x2, x2sq)
	}

	var bytes [32]byte

	_, err := io.ReadFull(rand.Reader, bytes[:])
	if err != nil {
		t.Fatal(err)
	}
	x.SetBytes(bytes[:])

	x2.Multiply(&x, &x)
	x2sq.Square(&x)

	if x2 != x2sq {
		t.Fatalf("all ones failed\nmul: %x\nsqr: %x\n", x2, x2sq)
	}
}

func TestEqual(t *testing.T) {

				}
			}
		}
	}
}

func testSqr(t *testing.T, x nat) {
	got := make(nat, 2*len(x))
	want := make(nat, 2*len(x))
	got = got.sqr(x)
	want = want.mul(x, x)
	if got.cmp(want) != 0 {
		t.Errorf("basicSqr(%v), got %v, want %v", x, got, want)
	}
}

func TestSqr(t *testing.T) {
	for _, a := range prodNN {
		if a.x != nil {

func (z *Rat) Mul(x, y *Rat) *Rat {
	if x == y {
		// a squared Rat is positive and can't be reduced (no need to call norm())
		z.a.neg = false
		z.a.abs = z.a.abs.sqr(x.a.abs)
		if len(x.b.abs) == 0 {
			z.b.abs = z.b.abs.setWord(1)
		} else {
			z.b.abs = z.b.abs.sqr(x.b.abs)
		}
		return z
	}
	z.a.Mul(&x.a, &y.a)
	z.b.abs = mulDenom(z.b.abs, x.b.abs, y.b.abs)
	return z.norm()
}

	"​":                  "\u200b",
	"Ζ":                            "\u0396",
	"ℨ":                             "\u2128",
	"ℤ":                            "\u2124",
	"𝒵":                            "\U0001d4b5",
	"á":                          "\u00e1",
	"ă":                          "\u0103",
	"∾":                              "\u223e",

	var t, r nat         // temporaries
	for {
		if _, r = t.div(r, q, f); len(r) != 0 {
			break // f doesn't divide q evenly
		}
		tab = append(tab, f)
		f = nat(nil).sqr(f) // nat(nil) to ensure a new f for each table entry
	}

	// Factor q using the table entries, if any.
	// We start with the largest factor f = tab[len(tab)-1]
	// that evenly divides q. It does so at most once because