如何用少量汇编指令生成半对数序列？含直方图分箱优化需求
2026-7-31
分箱索引序列的浮点优化需求
需要生成如下数值序列，用于分箱大小递增的直方图中确定数据所属分箱：
- 第(1)列是对数序列，直方图分箱大小以2的幂次递增；
- 第(2)至(7)列是对前一列的细分，每个大分箱拆分为两个子分箱。
已有离散实现，希望通过浮点技巧进一步减少执行周期。
对应的数值序列如下：
| 索引 | (1) | (2) | (3) | (4) | (5) | (6) | (7) |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| 3 | 2 | 3 | 3 | 3 | 3 | 3 | 3 |
| 4 | 3 | 4 | 4 | 4 | 4 | 4 | 4 |
| 5 | 3 | 4 | 5 | 5 | 5 | 5 | 5 |
| 6 | 3 | 5 | 6 | 6 | 6 | 6 | 6 |
| 7 | 3 | 5 | 7 | 7 | 7 | 7 | 7 |
| 8 | 4 | 6 | 8 | 8 | 8 | 8 | 8 |
| 9 | 4 | 6 | 8 | 9 | 9 | 9 | 9 |
| 10 | 4 | 6 | 9 | 10 | 10 | 10 | 10 |
| 11 | 4 | 6 | 9 | 11 | 11 | 11 | 11 |
| 12 | 4 | 7 | 10 | 12 | 12 | 12 | 12 |
| 13 | 4 | 7 | 10 | 13 | 13 | 13 | 13 |
| 14 | 4 | 7 | 11 | 14 | 14 | 14 | 14 |
| 15 | 4 | 7 | 11 | 15 | 15 | 15 | 15 |
| 16 | 5 | 8 | 12 | 16 | 16 | 16 | 16 |
| 17 | 5 | 8 | 12 | 16 | 17 | 17 | 17 |
| 18 | 5 | 8 | 12 | 17 | 18 | 18 | 18 |
| 19 | 5 | 8 | 12 | 17 | 19 | 19 | 19 |
| 20 | 5 | 8 | 13 | 18 | 20 | 20 | 20 |
| 21 | 5 | 8 | 13 | 18 | 21 | 21 | 21 |
| 22 | 5 | 8 | 13 | 19 | 22 | 22 | 22 |
| 23 | 5 | 8 | 13 | 19 | 23 | 23 | 23 |
| 24 | 5 | 9 | 14 | 20 | 24 | 24 | 24 |
| 25 | 5 | 9 | 14 | 20 | 25 | 25 | 25 |
| 26 | 5 | 9 | 14 | 21 | 26 | 26 | 26 |
| 27 | 5 | 9 | 14 | 21 | 27 | 27 | 27 |
| 28 | 5 | 9 | 15 | 22 | 28 | 28 | 28 |
| 29 | 5 | 9 | 15 | 22 | 29 | 29 | 29 |
| 30 | 5 | 9 | 15 | 23 | 30 | 30 | 30 |
| 31 | 5 | 9 | 15 | 23 | 31 | 31 | 31 |
| 32 | 6 | 10 | 16 | 24 | 32 | 32 | 32 |
| 33 | 6 | 10 | 16 | 24 | 32 | 33 | 33 |
| 34 | 6 | 10 | 16 | 24 | 33 | 34 | 34 |
| 35 | 6 | 10 | 16 | 24 | 33 | 35 | 35 |
| 36 | 6 | 10 | 16 | 25 | 34 | 36 | 36 |
| 37 | 6 | 10 | 16 | 25 | 34 | 37 | 37 |
| 38 | 6 | 10 | 16 | 25 | 35 | 38 | 38 |
| 39 | 6 | 10 | 16 | 25 | 35 | 39 | 39 |
| 40 | 6 | 10 | 17 | 26 | 36 | 40 | 40 |
| 41 | 6 | 10 | 17 | 26 | 36 | 41 | 41 |
| 42 | 6 | 10 | 17 | 26 | 37 | 42 | 42 |
| 43 | 6 | 10 | 17 | 26 | 37 | 43 | 43 |
| 44 | 6 | 10 | 17 | 27 | 38 | 44 | 44 |
| 45 | 6 | 10 | 17 | 27 | 38 | 45 | 45 |
| 46 | 6 | 10 | 17 | 27 | 39 | 46 | 46 |
| 47 | 6 | 10 | 17 | 27 | 39 | 47 | 47 |
| 48 | 6 | 11 | 18 | 28 | 40 | 48 | 48 |
| 49 | 6 | 11 | 18 | 28 | 40 | 49 | 49 |
| 50 | 6 | 11 | 18 | 28 | 41 | 50 | 50 |
| 51 | 6 | 11 | 18 | 28 | 41 | 51 | 51 |
| 52 | 6 | 11 | 18 | 29 | 42 | 52 | 52 |
| 53 | 6 | 11 | 18 | 29 | 42 | 53 | 53 |
| 54 | 6 | 11 | 18 | 29 | 43 | 54 | 54 |
| 55 | 6 | 11 | 18 | 29 | 43 | 55 | 55 |
| 56 | 6 | 11 | 19 | 30 | 44 | 56 | 56 |
| 57 | 6 | 11 | 19 | 30 | 44 | 57 | 57 |
| 58 | 6 | 11 | 19 | 30 | 45 | 58 | 58 |
| 59 | 6 | 11 | 19 | 30 | 45 | 59 | 59 |
| 60 | 6 | 11 | 19 | 31 | 46 | 60 | 60 |
| 61 | 6 | 11 | 19 | 31 | 46 | 61 | 61 |
| 62 | 6 | 11 | 19 | 31 | 47 | 62 | 62 |
| 63 | 6 | 11 | 19 | 31 | 47 | 63 | 63 |
内容的提问来源于stack exchange，提问作者Henrique Bucher
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