func TestIssue820(t *testing.T) {
	x := NewRat(3, 1)
	y := NewRat(2, 1)
	z := y.Quo(x, y)
	q := NewRat(3, 2)
	if z.Cmp(q) != 0 {
		t.Errorf("got %s want %s", z, q)
	}

	y = NewRat(3, 1)
	x = NewRat(2, 1)
	z = y.Quo(x, y)
	q = NewRat(2, 3)
	if z.Cmp(q) != 0 {
		t.Errorf("got %s want %s", z, q)
	}

	x = NewRat(3, 1)
	z = x.Quo(x, x)
	q = NewRat(3, 3)
	if z.Cmp(q) != 0 {

			if !is63bit(a) || !is63bit(b) {
				return makeInt(newInt().Add(big.NewInt(a), big.NewInt(b)))
			}
			c = a + b
		case token.SUB:
			if !is63bit(a) || !is63bit(b) {
				return makeInt(newInt().Sub(big.NewInt(a), big.NewInt(b)))
			}
			c = a - b
		case token.MUL:
			if !is32bit(a) || !is32bit(b) {
				return makeInt(newInt().Mul(big.NewInt(a), big.NewInt(b)))
			}
			c = a * b
		case token.QUO:

}

func TestZetas(t *testing.T) {
	ζ := big.NewInt(17)
	q := big.NewInt(q)
	for k, zeta := range zetas {
		// ζ^BitRev7(k) mod q
		exp := new(big.Int).Exp(ζ, big.NewInt(int64(BitRev7(uint8(k)))), q)
		if big.NewInt(int64(zeta)).Cmp(exp) != 0 {
			t.Errorf("zetas[%d] = %v, expected %v", k, zeta, exp)
		}
	}
}

func TestGammas(t *testing.T) {
	ζ := big.NewInt(17)
	q := big.NewInt(q)

	// is made), such uninitialized denominators are set to 1.
	// a.neg determines the sign of the Rat, b.neg is ignored.
	a, b Int
}

// NewRat creates a new [Rat] with numerator a and denominator b.
func NewRat(a, b int64) *Rat {
	return new(Rat).SetFrac64(a, b)
}

// SetFloat64 sets z to exactly f and returns z.
// If f is not finite, SetFloat returns nil.

		{Bool, false, false},
		{String, "hello", "hello"},

		{Int, int64(1), int64(1)},
		{Int, big.NewInt(10), int64(10)},
		{Int, new(big.Int).Lsh(big.NewInt(1), 62), int64(1 << 62)},
		dup(Int, new(big.Int).Lsh(big.NewInt(1), 63)),

		{Float, big.NewFloat(0), floatVal0.val},
		dup(Float, big.NewFloat(2.0)),
		dup(Float, big.NewRat(1, 3)),
	} {
		val := Make(test.arg)
		got := Val(val)

		Qinv, err := bigmod.NewNat().SetBytes(priv.Precomputed.Qinv.Bytes(), P)
		if err != nil {
			return nil, ErrDecryption
		}
		c, err = bigmod.NewNat().SetBytes(ciphertext, N)
		if err != nil {
			return nil, ErrDecryption
		}

		// m = c ^ Dp mod p
		m = bigmod.NewNat().Exp(t0.Mod(c, P), priv.Precomputed.Dp.Bytes(), P)
		// m2 = c ^ Dq mod q

	}

	// SEC 1, Version 2.0, Section 4.1.4

	r, err := bigmod.NewNat().SetBytes(rBytes, c.N)
	if err != nil || r.IsZero() == 1 {
		return false
	}
	s, err := bigmod.NewNat().SetBytes(sBytes, c.N)
	if err != nil || s.IsZero() == 1 {
		return false
	}

	e := bigmod.NewNat()
	hashToNat(c, e, hash)

	// w = s⁻¹
	w := bigmod.NewNat()
	inverse(c, w, s)

	// p₁ = [e * s⁻¹]G

	// are likely to be more efficient if necessary.

	table := [(1 << 4) - 1]*Nat{ // table[i] = x ^ (i+1)
		// newNat calls are unrolled so they are allocated on the stack.
		NewNat(), NewNat(), NewNat(), NewNat(), NewNat(),
		NewNat(), NewNat(), NewNat(), NewNat(), NewNat(),
		NewNat(), NewNat(), NewNat(), NewNat(), NewNat(),
	}
	table[0].set(x).montgomeryRepresentation(m)
	for i := 1; i < len(table); i++ {

	N, _ := NewModulusFromBig(n)
	A := NewNat().setBig(a).ExpandFor(N)
	B := NewNat().setBig(b).ExpandFor(N)

	if A.Mul(B, N).IsZero() != 1 {
		t.Error("a * b mod (a * b) != 0")
	}

	i := new(big.Int).ModInverse(a, b)
	N, _ = NewModulusFromBig(b)
	A = NewNat().setBig(a).ExpandFor(N)
	I := NewNat().setBig(i).ExpandFor(N)
	one := NewNat().setBig(big.NewInt(1)).ExpandFor(N)

	if A.Mul(I, N).Equal(one) != 1 {

		// gives a smooth-ish transition between the two.
		newcap += (newcap + 3*threshold) >> 2

		// We need to check `newcap >= newLen` and whether `newcap` overflowed.
		// newLen is guaranteed to be larger than zero, hence
		// when newcap overflows then `uint(newcap) > uint(newLen)`.
		// This allows to check for both with the same comparison.
		if uint(newcap) >= uint(newLen) {
			break
		}
	}