New GPU for OpenCL programming

I am currently working on a mathematical problem that requires significant data processing. For brevity, it is a combinatorial optimization problem that my current AMD A8 4-core CPU cannot handle as I am working with billions of data structures. p_threads can speed things up, but not as much as a GPU (*theoretically!)

My plan is to use the on-chip GPU for enumerating the data structures; however, I cannot find anything that states OpenCL runs on the integrated APU GPU. So without further to do:


Est Time of Purchase: Anytime. (*The GPU market still seems too expensive since the crypto-boom. I could wait some time here.)

Price Range: 200 USD. *not including shipping. (I can go above this number for a few bucks if GPU offers better performance.)

Prefered Vendor: newegg.com

Country: USA.

Usage: Combinatorics, specifically enumerative combinatorics for a card game.

Idea GPU?: HERE


If you are also familiar with OpenCL, any pointers as to how I can pick a "good" GPU for the problem at hand?
 
Solution
GPU-Z will tell you if your APU supports OpenCL. I would start by writing the equivalent of "hello world" for OpenCL, because it sounds like you are not very familiar with how to use OpenCL.