Systems and methods for approximation based optimization of data processors

A method for optimizing performance of a processing system, the method comprising:

• in a tiled a loop nest comprising at least one loop, each tile comprising a specified computation based on a first argument, a value of the first argument varying according to a tile index:
• employing an exact procedure implementing the specified computation for a reference tile index;
• determining if a first difference between values of the first argument corresponding to a first non-reference tile index and corresponding to the reference index is greater than a first threshold;
• if the first difference is not greater than the first threshold, employing an approximate procedure implementing the specified computation for the first non-reference tile index, wherein a computation cost according to a cost metric of the approximate procedure is less than a computation cost according to that cost metric of the exact procedure;
• and
• otherwise, employing the exact procedure for the first non-reference tile index.

A compilation system for optimizing performance of a processing system, the compilation system comprising:

• a first processor;
• and
• a first memory in electrical communication with the first processor, the first memory comprising instructions which, when executed by a processing unit comprising at least one of the first processor and a second processor, and in electronic communication with a memory module comprising at least one of the first memory and a second memory, program the processing unit to:
• tile a loop nest comprising at least one loop, each tile comprising a specified computation based on an argument, a value of the argument varying according to a tile index, a tile size being selected such that a difference between a value of the argument corresponding to a final tile index and a value of the argument corresponding to an initial tile index is at most equal to a threshold;
• employ an exact procedure implementing the specified computation for the initial tile index;
• employ an approximate procedure implementing the specified computation for each subsequent tile index, wherein a computation cost according to a cost metric of the approximate procedure is less than a computation cost according to that cost metric of the exact procedure.

A compilation system for optimizing performance of a processing system, the compilation system comprising:

• a first processor;
• and
• a first memory in electrical communication with the first processor, the first memory comprising instructions which, when executed by a processing unit comprising at least one of the first processor and a second processor, and in electronic communication with a memory module comprising at least one of the first memory and a second memory, program the processing unit to:
• employ, in a tiled a loop nest comprising at least one loop, each tile comprising a specified computation based on a first argument, a value of the first argument varying according to a tile index, an exact procedure implementing the specified computation for a reference tile index;
• determine if a first difference between values of the first argument corresponding to first non-reference tile index and corresponding to the reference index is greater than a first threshold;
• if the first difference is not greater than the first threshold, employ an approximate procedure implementing the specified computation for the first non-reference tile index, wherein a computation cost according to a cost metric of the approximate procedure is less than a computation cost according to that cost metric of the exact procedure;
• and
• otherwise, employ the exact procedure for the first non-reference tile index.