Mathematical Function Precision Allocation for Efficient Global Accuracy

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Solution Overview

Problem

Existing methods fail to systematically and universally determine the required internal accuracies of mathematical functions in computer programs to ensure a target global accuracy while optimizing computational efficiency and resource consumption.

Innovation Solution

A method that automatically identifies the required internal accuracies of mathematical functions by simulating precision lowering combinations, evaluating errors, and using combinatorial search algorithms to find optimal combinations that meet a target global accuracy and resource-consuming criteria.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If high precision reference implementations of mathematical functions are used, then the target global accuracy is ensured, but the execution time and resource consumption increase significantly

Engineering Contradiction:

Improveglobal accuracyVSAvoidexecution efficiency

Core Design Contradiction:

Measurement precisionVSProductivity

Solution Approach 1:

The patent applies local quality by determining different precision requirements for different mathematical functions within the program. Instead of uniformly using high precision for all functions, the system analyzes each function's contribution to the global error and assigns appropriate precision levels locally, thereby reducing overall computational cost while maintaining the required global accuracy target.

Inventive Principle:

Principle #3Local quality

Solution Approach 2:

The patent changes the precision parameter of mathematical function implementations dynamically. By lowering the precision parameter from reference implementation levels to custom implementation levels where acceptable, the system reduces execution time and resource consumption while ensuring the global accuracy target is still met through systematic error analysis.

Inventive Principle:

Principle #35Parameter changes

2Productivity

If low precision custom implementations of mathematical functions are used, then the execution efficiency improves, but the total error may exceed the target global accuracy

Engineering Contradiction:

Improveexecution efficiencyVSAvoidglobal accuracy

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The patent performs preliminary error analysis and precision determination before actual program execution. By pre-calculating the maximum acceptable error for each mathematical function based on the global accuracy target and the function's influence on the final result, the system can select appropriate precision levels in advance, avoiding both over-precision and under-precision during execution.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The system uses feedback from error propagation analysis to adjust precision requirements. By tracking how errors from individual functions propagate through the program and contribute to the global error, the system can provide feedback to determine the optimal precision level for each function, ensuring the total error remains within the target bound.

Inventive Principle:

Principle #23Feedback

3Use of energy by moving object

If the precision of mathematical function implementations is lowered, then the resource consumption decreases, but the reliability of achieving the target global accuracy is compromised

Engineering Contradiction:

Improveresource consumptionVSAvoidaccuracy guarantee

Core Design Contradiction:

Use of energy by moving objectVSReliability

Solution Approach 1:

The patent segments the global accuracy requirement into individual function-level precision requirements. By dividing the overall error budget and allocating it to each mathematical function based on its impact on the final result, the system can reliably determine the minimum acceptable precision for each function, ensuring the cumulative error does not exceed the global target while optimizing resource consumption.

Inventive Principle:

Principle #1Segmentation

Data Source

PatentEP4538907B1Automatic identification of required internal accuracies of arbitrary functions calls depending on a program global target accuracy on an arbitrary program

Publication Date: 2025.09.03 MITSUBISHI ELECTRIC R&D CENTRE EUROPE BV

AI summary

The invention relates to a computer implemented method (10) for determining required internal accuracies of at least one function, in a computer program, to reach a target global accuracy (TGA), comprising at least one iteration of the following steps: - lowering (S01) the precision of reference implementations of functions to obtain custom implementations, - obtaining (S02) errors induced by the precision lowering (S01) between custom implementations and reference implementations, - obtaining (S03), as a function of said errors, a plurality of acceptable combinations of custom implementations meeting the target global accuracy (TGA), - evaluating (S04) an execution efficiency of acceptable combinations as a function of at least one resource consuming criterion and delivering the required internal accuracies of functions when said at least one resource consuming criterion is met.