“非平凡的旋转”一词是什么意思？

Question

论文“Gimli:跨平台置换”包含以下信息：

偶尔(在24、20、16等回合之后)Gimli在第一行的条目0中添加一个不对称常量。这个常数有许多位集(它本质上是在TEA中使用的黄金比率0x9e3779b9 )，并且不接近于它的任何非平凡的旋转(从来不少于12位不同)。

“非平凡的旋转”一词是什么意思？如何区分“非平凡”旋转与“平凡”旋转？

Answer 1

平凡的旋转是指旋转的输入等于输出(因此旋转等于恒等函数)。按n的倍数旋转对于所有n位值来说都是微不足道的旋转。请注意，对于某些值，可能存在其他琐碎的旋转。有关0x9e3779b9 (n = 32)的(右)旋转值和每一位的不同位数，请参见下面的内容：

0:  0x9e3779b9 (0  bits different)
1:  0xcf1bbcdc (14 bits different)
2:  0x678dde6e (22 bits different)
3:  0x33c6ef37 (18 bits different)
4:  0x99e3779b (12 bits different)
5:  0xccf1bbcd (14 bits different)
6:  0xe678dde6 (18 bits different)
7:  0x733c6ef3 (16 bits different)
8:  0xb99e3779 (14 bits different)
9:  0xdccf1bbc (12 bits different)
10: 0x6e678dde (16 bits different)
11: 0x3733c6ef (16 bits different)
12: 0x9b99e377 (16 bits different)
13: 0xcdccf1bb (14 bits different)
14: 0xe6e678dd (12 bits different)
15: 0xf3733c6e (16 bits different)
16: 0x79b99e37 (20 bits different)
17: 0xbcdccf1b (16 bits different)
18: 0xde6e678d (12 bits different)
19: 0xef3733c6 (14 bits different)
20: 0x779b99e3 (16 bits different)
21: 0xbbcdccf1 (16 bits different)
22: 0xdde6e678 (16 bits different)
23: 0x6ef3733c (12 bits different)
24: 0x3779b99e (14 bits different)
25: 0x1bbcdccf (16 bits different)
26: 0x8dde6e67 (18 bits different)
27: 0xc6ef3733 (14 bits different)
28: 0xe3779b99 (12 bits different)
29: 0xf1bbcdcc (18 bits different)
30: 0x78dde6e6 (22 bits different)
31: 0x3c6ef373 (14 bits different)

Answer 2

简单地说，旋转是指对图形进行旋转，使图形本身映射回原来的位置，使旋转大于0°，但小于360°。