Unary Function Evaluation Using Range-Specific Coefficient Sets
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Solution Overview
Problem
Existing processor systems face difficulties in efficiently implementing unary functions with floating-point numbers due to the non-uniform unit of least precision, making it challenging to determine the lookup table index and perform tabulated functions.
Innovation Solution
The implementation of unary functions using a set of power series approximations across possible input values, where coefficients are determined through a two-stage process involving range comparison and offset calculation within the processor's arithmetic engine, allowing for flexible and efficient calculation of unary functions with floating-point inputs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If a lookup table approach is used to perform unary functions, then function evaluation speed is improved, but the non-uniform unit of least precision for floating-point numbers makes it difficult to determine the lookup table index
Solution Approach 1:
The patent divides the floating-point number representation into distinct segments: the exponent field and the significand field. By segmenting the input processing, the system can apply different operations to different parts of the floating-point number. This segmentation allows the system to handle the non-uniform precision by treating the exponent and significand separately, ultimately enabling efficient lookup table indexing through the combined manipulation of these segments.
2Adaptability or versatility
If power series approximations are used for unary functions, then flexibility in handling different input ranges is improved, but computational complexity increases
Solution Approach 1:
The patent applies local quality by using different coefficient sets for different input ranges. Instead of using a single power series approximation for all inputs, the system selects specific coefficient sets based on the input value's range. This allows each local region of the input domain to be approximated with optimal coefficients, improving accuracy and flexibility while managing computational complexity through selective application.
Solution Approach 2:
The patent implements preliminary action by pre-calculating and storing coefficient sets for different input ranges before runtime. These coefficient sets are prepared in advance and stored in memory, allowing the system to quickly retrieve and apply the appropriate coefficients during function evaluation without performing complex calculations in real-time. This preliminary preparation reduces computational complexity during actual execution.
Data Source
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AI summary
A method comprising storing a plurality of entries, each entry of the plurality of entries associated with a portion of a range of input values, each entry of the plurality of entries comprising a set of coefficients defining a power series approximation; selecting first entry of the plurality of entries based on a determination that a floating point input value is within a portion of the range of input values that is associated with the first entry; and calculating an output value by evaluating the power series approximation defined by the set of coefficients of the first entry at the floating point input value.