Exponential Function Calculation Processor for Sensor Applications
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Solution Overview
Problem
Conventional microprocessors are inefficient in calculating exponential functions required in sensor applications, often requiring large memory and/or area, and their speed is insufficient for continuous processing of sensor signals.
Innovation Solution
An improved calculation concept that iteratively refines an error factor to determine the output value of an exponential function, using a first calculation block to initialize values, a second block to perform iterations until an exit criterion is met, and a final block to set the output value, allowing for high accuracy without the need for extensive memory or microprocessor involvement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional microprocessors with standard calculation algorithms are used, then the calculation can be performed with standard components, but the calculation speed is insufficient for continuous processing
Solution Approach 1:
The exponential calculation is segmented into multiple iterative steps, where each step refines the result by a factor of 2 in accuracy. The calculation is divided into initialization, iterative refinement with error correction, and final output stages, enabling parallel processing potential and higher speed while maintaining accuracy through systematic error reduction.
Solution Approach 2:
The invention uses a dynamic iterative approach where the number of iterations can be adjusted based on required precision. The error factor is dynamically reduced by half in each iteration, allowing the system to adapt between speed and accuracy requirements by choosing the appropriate number of iteration cycles.
2Productivity
If a look-up table with precalculated values is used, then calculation speed is improved, but a large amount of memory and/or area is required
Solution Approach 1:
The invention extracts only the essential calculation logic for exponential functions with specific exponent values (0.3, 0.45, 0.5, 0.6, 0.8) into a dedicated hardware circuit, removing the need for large look-up tables. The error factor method extracts the core mathematical relationship without requiring storage of all possible input-output pairs.
Solution Approach 2:
The invention replaces the mechanical look-up table approach with a mathematical iterative calculation method implemented in hardware. Instead of storing precalculated values in memory, the system uses repeated multiplication and error correction to compute results, substituting memory access with arithmetic operations that can be performed faster in dedicated circuitry.
3Measurement precision
If more iterations are performed to increase accuracy, then the output value precision is improved, but the calculation time increases
Solution Approach 1:
The invention uses periodic iterative action where each iteration cycle performs a fixed set of operations (error calculation, comparison, correction) that systematically reduces the error by a predictable factor. This periodic structure allows timing to be precisely controlled and optimized, with each period contributing a known amount to the final accuracy.
Solution Approach 2:
The iterative calculation structure can be copied multiple times in parallel to process multiple input values simultaneously. Each iteration block can be replicated to handle different exponent types or to process multiple pixels in image processing applications, achieving both high accuracy and throughput through parallel copying of the calculation logic.
Data Source
AI summary
A calculation processor for determining a digital output value from a digital input value based on an exponent value a, the processor comprising a first calculation block, a second calculation block and a final calculation block. The first calculation block initializes an intermediate value and an error value depending on a position of a Most Significant Bit of a significant part of the input value. The second calculation block is configured to perform repeatedly, until an exit criterion is fulfilled, the incrementation of a counter value, the determination of a power error value based on the error value and, if the power error value is larger than or equal to an error threshold, adjustment of the intermediate value y by multiplying the intermediate value with an adaptation value and setting the error value to the power error value divided by the base value. If the power error value is smaller than the error threshold, the error value is set to the power error value. The final calculation block is configured to set the output value to the intermediate value.