Compiler-level general matrix multiplication configuration optimization

A computing device for optimizing general matrix multiplication (GEMM) on target hardware, comprising:

• at least one processor;
• and
• a machine-readable medium coupled to the at least one processor, with the machine-readable medium comprising instructions thereon that, when executed by the at least one processor, causes the at least one processor to perform operations including:
• splitting matrices to be multiplied into tiles;
• formulating a tiling configuration search problem for the matrices to be multiplied that explores a configuration search space to identify an optimal tiling configuration that minimizes a running time on the target hardware for multiplication of the matrices on the target hardware, the formulating including formulating the tiling configuration search problem into the following optimization problem:
• min
• s
• 
• 
• cost
• 
• 
• (
• s
• ;
• m
• ,
• k
• ,
• n
• ,
• d
• m
• ,
• d
• k
• ,
• d
• n
• )
• ,
• where:
• s denotes a configuration state,
• cost denotes a running time for the configuration state s,
• m, k, and n are matrix parameters for multiplication of a first matrix A (m×k) by a second matrix B (k×n), to produce a matrix C (m×n), where m is a number of rows of a first matrix, k is number of columns of the first matrix and number of rows of a second matrix, and n is the number of columns of the second matrix, and
• dm, dk, dn are numbers of respective nested loops for each dimension m, k, and n, respectively;
• and
• running a GEMM computation on the target hardware based on the optimal tiling configuration.

A computing device for optimizing general matrix multiplication (GEMM) on target hardware, comprising:

• a tiling module splitting matrices to be multiplied into tiles;
• an optimization module formulating a tiling configuration search problem for the matrices to be multiplied that explores a configuration search space to identify an optimal tiling configuration that minimizes a running time on the target hardware for multiplication of the matrices on the target hardware, the formulating including formulating the tiling configuration search problem into the following optimization problem:
• min
• s
• 
• 
• cost
• 
• 
• (
• s
• ;
• m
• ,
• k
• ,
• n
• ,
• d
• m
• ,
• d
• k
• ,
• d
• n
• )
• ,
• where:
• s denotes a configuration state,
• cost denotes a running time for the configuration state s,
• m, k, and n are matrix parameters for multiplication of a first matrix A (m×k) by a second matrix B (k×n), to produce a matrix C (m×n), where m is a number of rows of a first matrix, k is number of columns of the first matrix and number of rows of a second matrix, and n is the number of columns of the second matrix, and
• dm, dk, dn are numbers of respective nested loops for each dimension m, k, and n, respectively;
• and
• an execution module running a GEMM computation on the target hardware based on the optimal tiling configuration.