One more piece of science! 
Everybody knows that when we calculate "NextPoint = PreviousPoint + JumpPoint", we can also quickly calculate "PreviousPoint - JumpPoint" because the inversion is the same.
Therefore, if the inversion calculation takes a lot of time, this second point is cheap for us, and we can use it to improve K.
I updated Part #1: Added "SOTA+" method with K = 1.02.
Everybody knows that when we calculate "NextPoint = PreviousPoint + JumpPoint", we can also quickly calculate "PreviousPoint - JumpPoint" because the inversion is the same.
Therefore, if the inversion calculation takes a lot of time, this second point is cheap for us, and we can use it to improve K.
I updated Part #1: Added "SOTA+" method with K = 1.02.
I still study your code, especially the gpu part, which gives me a lot to learn.
I think JLP applied this trick in his BSGS/kangaroo.
https://github.com/JeanLucPons/BSGS/blob/master/BSGS.cpp#L347
Yes, he did it for BSGS, and now I’ve figured out how to apply it to Kangaroo.
I took a closer look at JLP's code, and kangaroo's code does not have this.
This PreviousPoint - JumpPoint jump is equivalent to PreviousPoint jumping JumpPoint backwards.
