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Here's BLIS's object API:
https://github.com/flame/blis/blob/master/docs/BLISObjectAPI...
Searching "object" in BLIS's README (https://github.com/flame/blis) to see what they think of it:
"Objects are relatively lightweight structs and passed by address, which helps tame function calling overhead."
"This is API abstracts away properties of vectors and matrices within obj_t structs that can be queried with accessor functions. Many developers and experts prefer this API over the typed API."
In my opinion, this API is a strict improvement over BLAS. I do not think there is any reason to prefer the old BLAS-style API over an improvement like this.
Regarding your own experience, it's great that using BLAS proved to be a valuable learning experience for you. But your argument that the BLAS API is somehow uniquely helpful in terms of learning how to program numerical algorithms efficiently, or that it will help you avoid performance problems, is not true. It is possible to replace the BLAS API with a more modern and intuitive API with the same benefits. To be clear, the benefits here are direct memory management and control of striding and matrix layout, which create opportunities for optimization. There is nothing unique about BLAS in this regard---it's possible to learn these lessons using any of the other listed options if you're paying attention and being systematic.