// -1 << 63, which is still negative.
				return nil, false
			}
		}
		if n > 1e6 {
			return nil, false // avoid excessively large exponents
		}
		pow5 := z.b.abs.expNN(natFive, nat(nil).setWord(Word(n)), nil, false) // use underlying array of z.b.abs
		if exp5 > 0 {
			z.a.abs = z.a.abs.mul(z.a.abs, pow5)
			z.b.abs = z.b.abs.setWord(1)
		} else {
			z.b.abs = pow5
		}

		}
		z[len(limit)-1] &= mask
		if z.cmp(limit) < 0 {
			break
		}
	}

	return z.norm()
}

// If m != 0 (i.e., len(m) != 0), expNN sets z to x**y mod m;
// otherwise it sets z to x**y. The result is the value of z.
func (z nat) expNN(x, y, m nat, slow bool) nat {
	if alias(z, x) || alias(z, y) {
		// We cannot allow in-place modification of x or y.
		z = nil
	}

	// x**y mod 1 == 0

	nm3Len := nm3.bitLen()

NextRandom:
	for i := 0; i < reps; i++ {
		if i == reps-1 && force2 {
			x = x.set(natTwo)
		} else {
			x = x.random(rand, nm3, nm3Len)
			x = x.add(x, natTwo)
		}
		y = y.expNN(x, q, n, false)
		if y.cmp(natOne) == 0 || y.cmp(nm1) == 0 {
			continue
		}
		for j := uint(1); j < k; j++ {
			y = y.sqr(y)
			quotient, y = quotient.div(y, y, n)
			if y.cmp(nm1) == 0 {

}

var cacheBase10 struct {
	sync.Mutex
	table [64]divisor // cached divisors for base 10
}

// expWW computes x**y
func (z nat) expWW(x, y Word) nat {
	return z.expNN(nat(nil).setWord(x), nat(nil).setWord(y), nil, false)
}

// construct table of powers of bb*leafSize to use in subdivisions.
func divisors(m int, b Word, ndigits int, bb Word) []divisor {

		x := natFromString(test.x)
		y := natFromString(test.y)
		out := natFromString(test.out)

		var m nat
		if len(test.m) > 0 {
			m = natFromString(test.m)
		}

		z := nat(nil).expNN(x, y, m, false)
		if z.cmp(out) != 0 {
			t.Errorf("#%d got %s want %s", i, z.utoa(10), out.utoa(10))
		}
	}
}

func FuzzExpMont(f *testing.F) {

	}

	for _, a := range argshrVU {
		arg := a
		testShiftFunc(t, shrVU, arg)
	}
}

func TestIssue31084(t *testing.T) {
	// compute 10^n via 5^n << n.
	const n = 165
	p := nat(nil).expNN(nat{5}, nat{n}, nil, false)
	p = p.shl(p, n)
	got := string(p.utoa(10))
	want := "1" + strings.Repeat("0", n)
	if got != want {
		t.Errorf("shl(%v, %v)\n\tgot  %s\n\twant %s", p, n, got, want)
	}
}

	}
	yWords := y.abs

	var mWords nat
	if m != nil {
		if z == m || alias(z.abs, m.abs) {
			m = new(Int).Set(m)
		}
		mWords = m.abs // m.abs may be nil for m == 0
	}

	z.abs = z.abs.expNN(xWords, yWords, mWords, slow)
	z.neg = len(z.abs) > 0 && x.neg && len(yWords) > 0 && yWords[0]&1 == 1 // 0 has no sign
	if z.neg && len(mWords) > 0 {
		// make modulus result positive