Lookup Table Floating-Point Computing for Accurate Parallel Math
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing mathematical operations, such as those using the CORDIC algorithm, face challenges in implementing accuracy on multi-core parallel computing systems and are prone to losing precision during recursive approximation.
Innovation Solution
A computing device and method utilizing a look-up table for floating-point operations, comprising a bit arrangement unit, multiple look-up table units, and an operation unit to perform operations on look-up table results, enabling accurate and efficient floating-point calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If CORDIC algorithm or iterative approximation is used for mathematical operations, then the operations can be implemented using only addition/subtraction and shift operations, but accuracy is lost during the recursive approximation process
Solution Approach 1:
The patent pre-calculates and stores mathematical function values in lookup tables before actual computation. By preparing the reference data in advance during table generation, the system avoids iterative approximation errors during runtime while maintaining implementation simplicity through direct table access.
2Measurement precision
If lookup table is used for floating-point operations, then accuracy is maintained and computational costs are reduced, but device complexity increases due to multiple lookup table units and bit arrangement requirements
Solution Approach 1:
The patent divides the lookup table into multiple segmented tables, each handling specific ranges or types of floating-point operations. This segmentation allows parallel access to different table units, maintaining high accuracy while reducing the complexity of any single table unit and enabling modular device architecture.
Solution Approach 2:
The patent transforms the single-dimension lookup approach into multi-dimensional indexing by using multiple index blocks derived from different parts of the input data. This dimensional transformation enables efficient access to large lookup tables through parallel index generation, maintaining accuracy without proportionally increasing device complexity.
3Productivity
If unique algorithms are implemented on multi-core parallel computing system, then computational productivity increases, but it becomes difficult to implement several unique algorithms simultaneously
Solution Approach 1:
The patent creates a universal computing device architecture that can handle multiple unique algorithms through a common lookup table mechanism. By designing the device with multiple lookup table units that can be configured for different mathematical operations, the system achieves multi-functionality, allowing various algorithms to run in parallel on multi-core systems without requiring separate implementation paths.
Data Source
AI summary
A computing device for floating-point mathematic operation using look-up table is provided. The computing device includes: a bit arrangement unit used for receiving a floating-point input data and performing a bit arrangement or a format conversion on the floating-point input data to generate multiple index blocks; a first look-up table unit group used for receiving the index blocks and performing look-up operation using the index blocks as index to generate a plurality of look-up table results; and an operation unit used for performing operation on the look-up table results of the first look-up table unit group to generate an operation output.