Fixed Point Algorithm Range Determination via Constraint Optimization
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Solution Overview
Problem
Microprocessors in precision guided munitions using fixed point arithmetic face challenges in determining valid ranges to prevent arithmetic overflow errors, which is crucial for maintaining precision and expressiveness, especially in high-g environments like those encountered by inertial measurement units (IMUs).
Innovation Solution
A method using constraint equation solving and optimization with a global hybrid optimization constraint equation solver (GHOCES) tool to express overflow, precision, and expressiveness requirements as inequalities, finding optimal ranges for algorithmic variables to ensure overflow-free arithmetic and optimal precision, particularly in sensor compensation algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fixed point arithmetic is used in microprocessors for precision guided munitions, then computational efficiency and reliability in harsh environments are improved, but determining valid ranges becomes complex and critical to prevent arithmetic overflow errors
Solution Approach 1:
The patent applies preliminary action by using static analysis tools to determine valid ranges for algorithmic variables before the actual computation occurs. The tool analyzes the algorithm structure and data types in advance to calculate safe range boundaries, preventing overflow errors before they can occur during execution. This proactive approach ensures reliability without requiring complex runtime checks.
Solution Approach 2:
The patent introduces an intermediary tool that acts as a mediator between the algorithm designer and the fixed point arithmetic system. This static analysis tool translates high-level algorithm specifications into concrete range constraints, serving as a bridge that automatically handles the complexity of range determination while keeping the main computation simple and reliable.
2Measurement precision
If the range of algorithmic variables is widened to preserve arithmetic expressiveness, then precision is improved, but the risk of arithmetic overflow errors increases
Solution Approach 1:
The patent applies parameter changes by dynamically adjusting the range parameters of algorithmic variables based on the specific algorithm structure and data types. The static analysis tool calculates optimal range boundaries that maximize precision while maintaining safety margins to prevent overflow. This involves changing the numerical parameters (min/max ranges) according to the computational context rather than using fixed conservative values.
Solution Approach 2:
The patent implements feedback mechanisms where the static analysis tool continuously validates algorithm specifications against established safety criteria. The tool provides feedback about potential overflow conditions and suggests range adjustments, creating a iterative process that refines variable ranges to achieve optimal precision while maintaining overflow-free operation.
3Reliability
If conservative range limits are imposed to prevent overflow, then arithmetic overflow errors are prevented, but arithmetic expressiveness and precision are reduced
Solution Approach 1:
The patent applies dynamics by moving from static conservative range limits to dynamic, algorithm-specific range determination. The static analysis tool examines the actual computational patterns and data characteristics to establish optimal ranges that adapt to the specific algorithm being implemented. This dynamic approach allows the system to achieve both reliability and expressiveness by tailoring ranges to actual usage patterns rather than applying uniform conservative limits.
Data Source
AI summary
A method of determining ranges for algorithmic variables for a processor that uses fixed point arithmetic is provided. The method comprises expressing overflow requirements of processor instructions as inequalities. The method also expresses precision requirements and expressiveness requirements as inequalities and merit functions. A global constraint and optimizer tool is used to find ranges for algorithmic variables based on the inequalities and the merit functions. The use of constraint equation solving and optimization finds optimal algorithmic ranges that provide overflow-free arithmetic as well as optimal expressiveness and precision.