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└── H16G.bundle/ ← H16G = M4 ANE target
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Блогеру Арсену Маркаряну дали срок14:50，更多细节参见Feiyi
By carefully choosing Marios position \(p in P\) and velocity \(v in T_p P\), the SM64 community was able to reach a desired positions \(q\) in \(B\) up to collision detection (for reaching some door, collecting a star, etc.). They did this by checking which \(t_1, \dots, t_k\) SM64 actually uses for calculations and then making the right choices, so that \(\rho(\exp_v(t_i)) = q\) for some \(i\) and for all other \(j \neq i\) \(\rho(\exp_v(t_j))\) is not a position that would trigger a collision detection with negative consequences (like resetting \(v\)).
Commutativity and associativity might sound the same, and indeed most commutative operations are also associative. But there are a few math operations that are only one or the other. Matrix multiplication, for example, is associative but not commutative Matrix multiplication - Wikipedia en.wikipedia.org/wiki/Matrix_multiplication#Non-commutativity . And surprisingly, floating point arithmetic — i.e. any math operator in JavaScript — is commutative but not associative Associative property - Wikipedia en.wikipedia.org/wiki/Associative_property#Nonassociativity_of_floating_point_calculation ! ↩