}

        boolean dividesEvenly = p.remainder(q).equals(ZERO);

        try {
          BigInteger quotient = BigIntegerMath.divide(p, q, UNNECESSARY);
          BigInteger undone = quotient.multiply(q);
          if (!p.equals(undone)) {
            failFormat("expected %s.multiply(%s) = %s; got %s", quotient, q, p, undone);
          }
          assertTrue(dividesEvenly);
        } catch (ArithmeticException e) {

<pre class="grammar">
+    sum                    integers, floats, complex values, strings
-    difference             integers, floats, complex values
*    product                integers, floats, complex values
/    quotient               integers, floats, complex values
%    remainder              integers

&amp;    bitwise AND            integers
|    bitwise OR             integers
^    bitwise XOR            integers

up (see FIPS 203, Section 2.3). dividend := uint32(y) * q quotient := dividend >> d // (y * q) / 2ᵈ // The d'th least-significant bit of the dividend (the most significant bit // of the remainder) is 1 for the top half of the values that divide to the // same quotient, which are the ones that round up. quotient += dividend >> (d - 1) & 1 // quotient is at most (2¹¹-1) * q / 2¹¹ + 1 = 3328, so it didn't overflow. return fieldElement(quotient) } // ringElement is a polynomial, an element of R_q, represented...

up (see FIPS 203, Section 2.3). dividend := uint32(y) * q quotient := dividend >> d // (y * q) / 2ᵈ // The d'th least-significant bit of the dividend (the most significant bit // of the remainder) is 1 for the top half of the values that divide to the // same quotient, which are the ones that round up. quotient += dividend >> (d - 1) & 1 // quotient is at most (2¹¹-1) * q / 2¹¹ + 1 = 3328, so it didn't overflow. return fieldElement(quotient) } // ringElement is a polynomial, an element of R_q, represented...