Matrix Operation Program Cache Block Segmentation
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Solution Overview
Problem
The computational complexity of pattern mining processing increases exponentially with the number of products to be combined, leading to significant slowdowns in large-scale data analysis, as evident in the need to investigate numerous combinations of product pairs and their purchase patterns.
Innovation Solution
A matrix operation program and method that divides the matrix into column groups based on data size and storage capacity, allowing for parallel processing within the L2 cache before accessing the main memory, thereby reducing cache misses and enhancing processing speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the matrix operation processes all column combinations sequentially by accessing the main memory, then the processing is simple to implement, but the processing time increases significantly due to frequent cache misses
Solution Approach 1:
The patent divides the matrix columns into multiple blocks, where each block can be independently processed. By segmenting the column combinations into blocks that fit within L2 cache capacity, the system reduces the frequency of main memory accesses while maintaining processing completeness. This segmentation allows hot data to remain in faster cache memory during processing.
Solution Approach 2:
The patent pre-loads column blocks into the L2 cache before processing begins. By anticipating which columns will be needed and loading them into cache memory in advance, the system minimizes runtime memory access delays. This preliminary action ensures that frequently accessed column data is already in fast cache memory when processing starts.
2Loss of time
If the entire matrix is loaded into L2 cache, then memory access time is reduced, but the storage capacity requirement increases beyond practical limits
Solution Approach 1:
The patent segments the matrix columns into multiple manageable blocks that individually fit within L2 cache capacity. Instead of loading the entire matrix at once, only the necessary column blocks are loaded into cache for each processing stage. This segmentation makes it feasible to work with large matrices that would otherwise exceed cache memory limits.
Solution Approach 2:
The patent processes column combinations in partial batches rather than all at once. By processing a subset of column combinations using only the necessary column blocks currently in cache, the system achieves sufficient processing without requiring the entire matrix to reside in cache simultaneously. This partial action approach balances cache usage with processing needs.
Data Source
AI summary
A computer-readable recording medium stores a matrix operation program for a computer. In a matrix operation in which an arithmetic circuit executes processing that combines at least two columns included in a matrix, obtains a product of each of rows of the combined columns, and calculates a sum of the product of each of the rows for all combinations of columns in the matrix, the program causes the computer to divide the matrix into blocks of a column group based on a data size of the column and storage capacity of a second storage to be accessed by the arithmetic circuit prior to accessing a first storage that stores information related to the matrix such that the column group to be combined is contained in the second storage, and to execute the calculation processing for each block of the divided column group.