Merge pull request giantray#90 from RWBUPT/patch-2

giantray · web-flow · commit b0adca921f8a · 2019-09-14T14:57:35.000+08:00
Create why-does-math.round-(0.49999999999999994)-return-1.md
diff --git a/contents/why-does-math.round-(0.49999999999999994)-return-1.md b/contents/why-does-math.round-(0.49999999999999994)-return-1.md
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+##为什么Math.round(0.49999999999999994)返回1？
+
+###问题描述：
+
+在下面的程序中你可以看到每个稍微比.5小的值都被向下舍入了，除了`0.5`那个。
+
+```
+for (int i = 10; i >= 0; i--) {
+    long l = Double.doubleToLongBits(i + 0.5);
+    double x;
+    do {
+        x = Double.longBitsToDouble(l);
+        System.out.println(x + " rounded is " + Math.round(x));
+        l--;
+    } while (Math.round(x) > i);
+}
+```
+输出
+```
+10.5 rounded is 11
+10.499999999999998 rounded is 10
+9.5 rounded is 10
+9.499999999999998 rounded is 9
+8.5 rounded is 9
+8.499999999999998 rounded is 8
+7.5 rounded is 8
+7.499999999999999 rounded is 7
+6.5 rounded is 7
+6.499999999999999 rounded is 6
+5.5 rounded is 6
+5.499999999999999 rounded is 5
+4.5 rounded is 5
+4.499999999999999 rounded is 4
+3.5 rounded is 4
+3.4999999999999996 rounded is 3
+2.5 rounded is 3
+2.4999999999999996 rounded is 2
+1.5 rounded is 2
+1.4999999999999998 rounded is 1
+0.5 rounded is 1
+0.49999999999999994 rounded is 1
+0.4999999999999999 rounded is 0
+```
+我使用 Java 6 update 31。
+
+###回答：
+
+**总结**
+
+在Java 6中（而且很可能更早），`round x`以`floor(x+0.5)`的方式执行[1]。这是一个规则上的bug，它恰好会导致这样一种不合道理的情况[2]。Java 7不再授权这种分离的执行方式[3]。
+
+**问题**
+
+0.5+0.49999999999999994在双精度数中正好表示1：
+```
+static void print(double d) {
+    System.out.printf("%016x\n", Double.doubleToLongBits(d));
+}
+
+public static void main(String args[]) {
+    double a = 0.5;
+    double b = 0.49999999999999994;
+
+    print(a);      // 3fe0000000000000
+    print(b);      // 3fdfffffffffffff
+    print(a+b);    // 3ff0000000000000
+    print(1.0);    // 3ff0000000000000
+}
+```
+这是因为0.49999999999999994有一个比0.5小的指数，所以它们相加时，它的尾数被移位了，ULP（ULP表示现有数值最后一位代表的最小数值单位，小于ULP的数值将无法累加到现有数值）变的更大。
+
+**解决方法**
+
+从Java 7开始，OpenJDK（如下例）这样执行它（round函数）[4]。
+```
+public static long round(double a) {
+    if (a != 0x1.fffffffffffffp-2) // greatest double value less than 0.5
+        return (long)floor(a + 0.5d);
+    else
+        return 0;
+}
+```
+[1] http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html#round%28double%29
+
+[2] http://bugs.java.com/bugdatabase/view_bug.do?bug_id=6430675 (credits to @SimonNickerson for finding this)
+
+[3] http://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#round%28double%29
+
+[4] http://grepcode.com/file/repository.grepcode.com/java/root/jdk/openjdk/7u40-b43/java/lang/Math.java#Math.round%28double%29
+
+
+[stackoverflow链接：Why does Math.round(0.49999999999999994) return 1?](http://stackoverflow.com/questions/9902968/why-does-math-round0-49999999999999994-return-1)
