Modal Interval Processor Design for Reliable Arithmetic
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Solution Overview
Problem
Existing interval processor designs are inadequate for performing reliable computations on modal intervals due to their reliance on set-theoretical interval arithmetic, which is flawed and lacks completeness and correctness, and they fail to handle modal quantifiers, leading to poor performance and inefficiencies in interval computations.
Innovation Solution
A modal interval processor that converts data formats to a file format with a greater dynamic range, includes a register file and processing unit for modal interval operations, handles exceptional conditions, and supports signed zeros, signed infinity, and empty intervals, enabling mixed-mode computations and efficient rounding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If set-theoretical interval arithmetic is used in existing interval processors, then the processors can perform basic interval operations, but the computations are fundamentally flawed and lack completeness and correctness for modal intervals
Solution Approach 1:
The patent extends the traditional one-dimensional set-theoretical interval representation by adding a modal quantifier dimension. Each interval is now represented as a modal interval containing both the set-theoretical interval bounds and a modal quantifier that indicates whether the interval contains the exact value, transforms the inadequate set-theoretical framework into a capable modal interval framework that can correctly represent and compute with uncertain values while maintaining computational reliability
Solution Approach 2:
The patent changes the fundamental parameters of interval representation by introducing the modal quantifier parameter alongside the traditional lower and upper bounds. This parameter change enables the processor to distinguish between intervals that contain exact values and those that represent pure uncertainties, thereby achieving both computational correctness and adaptability to modal interval requirements
2Productivity
If set-theoretical interval processors are designed, then the device structure can be simplified, but they fail to handle modal quantifiers leading to poor performance
Solution Approach 1:
The patent segments the interval processing functionality into distinct components: set-theoretical interval operations and modal quantifier operations. The processor is divided into units that independently handle bound calculations and quantifier propagation, allowing each segment to be optimized for its specific function while working together to achieve high-performance modal interval computations without excessive overall complexity
Solution Approach 2:
The patent designs a universal modal interval processor that can handle both set-theoretical interval operations and modal quantifier operations within a single integrated architecture. The processor structure is designed to perform multiple functions including arithmetic operations, logical operations, and quantifier propagation, eliminating the need for separate specialized processors and improving productivity through unified multi-functional design
3Reliability
If existing interval processors are used, then hardware implementation is achieved, but they lack completeness and correctness for modal interval computations
Solution Approach 1:
The patent implements a nested architecture where the set-theoretical interval processing unit is nested within the broader modal interval processing framework. The modal quantifier processing unit encapsulates the traditional interval arithmetic unit, allowing the hardware to be manufactured with layered functionality where simpler set-theoretical operations are embedded within the more comprehensive modal interval processing structure, achieving both reliability and manufacturability
Data Source
AI summary
A logic circuit computes various modal interval arithmetic values using a plurality of arithmetic function units. A multiplexer gates the desired arithmetic values to a storage register.