Transcendental Function Evaluation Circuit
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Solution Overview
Problem
Evaluating transcendental functions in digital systems is computationally intensive, consuming significant power and time due to the need for substantial digital computation, particularly in feedback control loops where functions like |x|α require high performance.
Innovation Solution
An apparatus that generates linear, quadratic, and constant terms of a transcendental function using dedicated circuits and tables, allowing for efficient evaluation by curve-fitting over equally or non-equally spaced segments, reducing the computational load and improving processing speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Taylor series expansion is used to evaluate transcendental functions in digital systems, then computation accuracy is improved, but computing power consumption and execution time increase substantially
Solution Approach 1:
The patent segments the transcendental function evaluation into multiple components: a lookup table for pre-computed values and a correction term calculation. The input is divided into integer and fractional parts, with the integer part used to index into a lookup table and the fractional part used to compute a correction term via a simplified polynomial. This segmentation reduces the computational burden while maintaining accuracy.
Solution Approach 2:
The patent employs preliminary action by pre-computing and storing function values in a lookup table during system initialization or offline processing. This allows the majority of function evaluations during real-time control to simply involve table lookup and minor corrections, significantly reducing online computational requirements and power consumption.
2Measurement precision
If Taylor series expansion is used to evaluate transcendental functions, then function evaluation accuracy is improved, but execution time increases substantially
Solution Approach 1:
The patent segments the function evaluation into a fast lookup table query and a quick polynomial correction, separating the heavy computational burden from the real-time execution path. This segmentation enables accurate evaluation without the substantial time penalty of full Taylor series computation.
Solution Approach 2:
By pre-computing function values and storing them in a lookup table, the patent eliminates the need for time-consuming iterative computations during real-time control. The preliminary computation is performed offline, allowing fast execution during online operations.
3Ease of manufacture
If CORDIC iterative process is used to evaluate transcendental functions, then hardware implementation is achieved, but convergence time and power consumption increase
Solution Approach 1:
The patent uses preliminary action by pre-computing and storing function values in a lookup table, eliminating the need for iterative convergence processes during real-time execution. This approach achieves fast, deterministic execution without the time variability and power consumption associated with iterative CORDIC methods.
4Measurement precision
If substantial digital computation is used to evaluate transcendental functions, then function evaluation accuracy is improved, but processing speed decreases
Solution Approach 1:
The patent segments the computation into a fast table lookup component and a minor correction component. This segmentation allows the system to maintain high processing speed by avoiding substantial digital computation during real-time operations, while still achieving accurate function evaluation through the combined result of the lookup and correction.
Data Source
AI summary
In described examples, an apparatus is arranged to generate a linear term, a quadratic term, and a constant term of a transcendental function with, respectively, a first circuit, a second circuit, and a third circuit in response to least significant bits of an input operand and in response to, respectively, a first, a second, and a third table value that is retrieved in response to, respectively, a first, a second, and a third index generated in response to most significant bits of the input operand. The third circuit is further arranged to generate a mantissa of an output operand in response to a sum of the linear term, the quadratic term, and the constant term.