Natural Exponential Circuit Using Dual Lookup Tables
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Solution Overview
Problem
Current hardware and methods for performing natural exponential function computations are inefficient, requiring long computing times and high circuit design costs.
Innovation Solution
A computing device and method utilizing a first and second lookup table, storing reduced sets of natural exponent values based on floating point number formats, coupled with an operation circuit to perform natural exponential function computations efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional hardware methods are used for natural exponential function computations, then computing accuracy is maintained, but computing time becomes excessively long and circuit design cost increases
Solution Approach 1:
The patent segments the natural exponential function computation into two parts: a lookup table approach for the integer exponent part and a series expansion approach for the fractional mantissa part. This segmentation allows the majority of the computation to be performed through simple table lookup rather than complex real-time calculation, dramatically reducing computing time while maintaining accuracy.
Solution Approach 2:
The patent pre-computes and stores natural exponential values for common exponent combinations in lookup tables during system initialization or offline processing. This preliminary action eliminates the need for time-consuming real-time computation of exponential functions, as the required values are already available for immediate retrieval during actual computation.
2Productivity
If conventional hardware methods are used for natural exponential function computations, then computing accuracy is maintained, but circuit design cost becomes excessively high
Solution Approach 1:
The patent extracts the complex exponential computation functionality and replaces it with simpler components: lookup tables for integer exponent handling and basic arithmetic operations for fractional parts. This extraction removes the need for complex hardware circuits that would be required to implement full exponential function computation in real-time, significantly reducing circuit design cost while maintaining computational accuracy.
3Device complexity
If lookup tables with reduced storage are used, then circuit design cost is reduced, but computation accuracy may be compromised
Solution Approach 1:
The patent applies local quality by using different approximation strategies for different parts of the computation. High-precision lookup tables are used for the integer exponent part where exact values are critical, while series expansion with variable precision is applied for the fractional mantissa part. This localized approach ensures accuracy where needed while reducing overall storage requirements and circuit complexity.
Solution Approach 2:
The patent uses partial action by computing only the necessary precision levels required for the mantissa part through series expansion, rather than pre-computing all possible values in lookup tables. This partial computation approach reduces storage requirements while maintaining sufficient accuracy for practical applications, avoiding the excessive storage cost of complete lookup tables.
Data Source
AI summary
A nature exponential function computing device and a computing method for the nature exponential function computing device are provided. The nature exponential function computing device includes a first lookup table, a second lookup table, and an operation circuit. The first lookup table selects a first natural exponent value from first natural exponent values according to an input exponent part of an input value conforming to a floating point number format. The second lookup table selects at least one selected second natural exponent value from second natural exponent values according to the input exponent part and an input mantissa part of the input value. The operation circuit operates on the selected first natural exponent value and the at least one selected second natural exponent value to generate an output exponent part and an output mantissa part conforming to the floating point number format.