floorMod 与 floorDiv

Python 翻译 Java 经典错误：

取模/余

print(4 % -3)  # -2
print(-4 % 3)  # 2

System.out.println(4 % -3); // 1
System.out.println(-4 % 3); // -1


System.out.println(Math.floorMod(4, -3)); // -2
System.out.println(Math.floorMod(-4, 3)); // 2

除法

print(-4 // 3)  # -2

System.out.println(-4 / 3); // -1

System.out.println(Math.floorDiv(-4, 3)); // -2

floorMod

    /**
     * Returns the floor modulus of the {@code int} arguments.
     * <p>
     * The floor modulus is {@code x - (floorDiv(x, y) * y)},
     * has the same sign as the divisor {@code y}, and
     * is in the range of {@code -abs(y) < r < +abs(y)}.
     *
     * <p>
     * The relationship between {@code floorDiv} and {@code floorMod} is such that:
     * <ul>
     *   <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
     * </ul>
     * <p>
     * The difference in values between {@code floorMod} and
     * the {@code %} operator is due to the difference between
     * {@code floorDiv} that returns the integer less than or equal to the quotient
     * and the {@code /} operator that returns the integer closest to zero.
     * <p>
     * Examples:
     * <ul>
     *   <li>If the signs of the arguments are the same, the results
     *       of {@code floorMod} and the {@code %} operator are the same.<br>
     *       <ul>
     *       <li>{@code floorMod(+4, +3) == +1}; &nbsp; and {@code (+4 % +3) == +1}</li>
     *       <li>{@code floorMod(-4, -3) == -1}; &nbsp; and {@code (-4 % -3) == -1}</li>
     *       </ul>
     *   <li>If the signs of the arguments are different, the results
     *       differ from the {@code %} operator.<br>
     *       <ul>
     *       <li>{@code floorMod(+4, -3) == -2}; &nbsp; and {@code (+4 % -3) == +1}</li>
     *       <li>{@code floorMod(-4, +3) == +2}; &nbsp; and {@code (-4 % +3) == -1}</li>
     *       </ul>
     *   </li>
     * </ul>
     * <p>
     * If the signs of arguments are unknown and a positive modulus
     * is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}.
     *
     * @param x the dividend
     * @param y the divisor
     * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
     * @throws ArithmeticException if the divisor {@code y} is zero
     * @see #floorDiv(int, int)
     * @since 1.8
     */
    public static int floorMod(int x, int y) {
        int mod = x % y;
        // if the signs are different and modulo not zero, adjust result
        if ((mod ^ y) < 0 && mod != 0) {
            mod += y;
        }
        return mod;
    }

floorDiv

    /**
     * Returns the largest (closest to positive infinity)
     * {@code int} value that is less than or equal to the algebraic quotient.
     * There is one special case, if the dividend is the
     * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
     * then integer overflow occurs and
     * the result is equal to {@code Integer.MIN_VALUE}.
     * <p>
     * Normal integer division operates under the round to zero rounding mode
     * (truncation).  This operation instead acts under the round toward
     * negative infinity (floor) rounding mode.
     * The floor rounding mode gives different results from truncation
     * when the exact result is negative.
     * <ul>
     *   <li>If the signs of the arguments are the same, the results of
     *       {@code floorDiv} and the {@code /} operator are the same.  <br>
     *       For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li>
     *   <li>If the signs of the arguments are different,  the quotient is negative and
     *       {@code floorDiv} returns the integer less than or equal to the quotient
     *       and the {@code /} operator returns the integer closest to zero.<br>
     *       For example, {@code floorDiv(-4, 3) == -2},
     *       whereas {@code (-4 / 3) == -1}.
     *   </li>
     * </ul>
     *
     * @param x the dividend
     * @param y the divisor
     * @return the largest (closest to positive infinity)
     * {@code int} value that is less than or equal to the algebraic quotient.
     * @throws ArithmeticException if the divisor {@code y} is zero
     * @see #floorMod(int, int)
     * @see #floor(double)
     * @since 1.8
     */
    public static int floorDiv(int x, int y) {
        int r = x / y;
        // if the signs are different and modulo not zero, round down
        if ((x ^ y) < 0 && (r * y != x)) {
            r--;
        }
        return r;
    }

（全文完）