Extending Logarithmic and Exponential Circuits for Nonlinear Computations
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Solution Overview
Problem
Configuring processors to compute various functions such as multiplication, division, nonlinear functions, square roots, reciprocals, and reciprocal square roots is a complex task, as existing methods are inefficient and not well-suited for handling negative inputs or unknown input signs.
Innovation Solution
The solution involves extending the functionality of existing logarithmic and exponential circuits to perform computations in the logarithmic domain, using absolute value and XOR operations to handle sign changes, and enabling/disabling reciprocal and root circuits based on the specific function to be computed, allowing for efficient calculation of nonlinear functions like reciprocals, square roots, and reciprocal square roots.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing methods are used to compute multiplication, division, and nonlinear functions, then the processor can perform these operations, but the configuration is complex and efficiency is poor
Solution Approach 1:
The patent extends the functionality of existing logarithmic and exponential circuits to perform multiple functions including multiplication, division, square roots, reciprocals, and reciprocal square roots by translating these operations into logarithmic domain computations. This multi-functional approach eliminates the need for dedicated circuits for each operation, reducing overall device complexity while improving computation efficiency through unified circuit utilization
2Adaptability or versatility
If existing methods are used to handle nonlinear functions, then the functions can be computed, but the methods are not well-suited for handling negative inputs or unknown input signs
Solution Approach 1:
The patent introduces an intermediary logarithmic domain as a intermediate representation between the input linear domain and the output linear domain. This logarithmic intermediary allows for unified handling of multiplication, division, and nonlinear functions through addition, subtraction, and scaling operations, while separate sign management handles the sign information. This intermediary representation improves both adaptability to different input types and computational reliability
Data Source
AI summary
Embodiments of the present disclosure are based on a recognition that some processors are configured with instructions to compute logarithms and exponents (i.e. some processors include log and exp circuits). Embodiments of the present disclosure are further based on an insight that the use of the existing log and exp circuits could be extended to compute certain other functions by using the existing log and exp circuits to transform from a Cartesian to a logarithmic domain and vice versa and performing the actual computations of the functions in the logarithmic domain, which may be computationally easier than performing the computations in the Cartesian domain.