The Exponent Zero Case

This fast-exponentiation routine is supposed to return $x^y$ for $y \ge 0$:

int f(int x, int y) {
  int r = 1;
  int b = x;   /* base     */
  int e = y;   /* exponent */
  while (e > 1) {
    if (e % 2 == 1) { r = b * r; }
    b = b * b;
    e = e / 2;
  }
  return r * b;
}

Tracing f(2, 7) shows the quantity $r \cdot b^{e}$ never moves:

iteration	b	e	r	$b^{e}$	$r \cdot b^{e}$
0	2	7	1	128	128
1	4	3	2	64	128
2	16	1	8	16	128

The loop exits with e == 1, and return r * b reads off $8 \cdot 16 = 128 = 2^7$. Which call still returns the wrong answer?