BigDecimal:金额计算为什么会出现 0.1 + 0.2

  double:0.1 + 0.2 = 0.30000000000000004;0.1 + 0.2 == 0.3 是 false;0.1f + 0.2f == 0.3f 是 true
  BigDecimal 的三种构造:
    new BigDecimal(0.1)        = 0.1000000000000000055511151231257827021181583404541015625
    BigDecimal.valueOf(0.1)    = 0.1(用 Double.toString)
    new BigDecimal("0.1")      = 0.1
  new BigDecimal("0.1").add(new BigDecimal("0.2")) = 0.3,compareTo(0.3) = 0

  x = 12.50(unscaled=1250,scale=2,precision=4),y = 0.125(unscaled=125,scale=3,precision=3)
  x + y = 12.625(unscaled=12625,scale=3,precision=5)(scale 取较大的)
  x - y = 12.375(unscaled=12375,scale=3,precision=5)
  x × y = 1.56250(unscaled=156250,scale=5,precision=6)(scale 相加:2 + 3)
  1 / 3 → ArithmeticException: Non-terminating decimal expansion; no exact representable decimal result.
  1 / 8 = 0.125(unscaled=125,scale=3,precision=3)(能除尽就精确);1 / 3,scale=5,HALF_UP = 0.33333;MathContext(5) = 0.33333

  2.0 equals 2.00 = false;compareTo = 0(equals 连 scale 一起比较)
  HashSet 里放 2.0,contains(2.00) = false;TreeSet(用 compareTo)放 2.0,contains(2.00) = true
  hashCode:2.0 → 621,2.00 → 6202
  stripTrailingZeros:2.00 → 2;100 → 1E+2(toString 变成科学计数法),toPlainString = 100

  把 2.5、3.5、-2.5、2.51 setScale(0,…),各种舍入模式的结果:
                  2.5    3.5   -2.5   2.51   2.49
    HALF_UP         3      4     -3      3      2
    HALF_EVEN       2      4     -2      3      2
    HALF_DOWN       2      3     -2      3      2
    UP              3      4     -3      3      3
    DOWN            2      3     -2      2      2
    CEILING         3      4     -2      3      3
    FLOOR           2      3     -3      2      2
  RoundingMode.UNNECESSARY 在需要舍入时抛 ArithmeticException: Rounding necessary
  先把每个 0.333 舍入到 2 位再累加 3 次 = 0.99;先累加再舍入 = 1.00(舍入的时机会影响结果)