Floating-Point Base Conversion With Bit-Vector Exception Rounding
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Solution Overview
Problem
Existing floating-point conversion methods require excessive intermediate precision and storage to ensure correct rounding across the entire exponent range, leading to increased computational costs and resource usage.
Innovation Solution
A system and method that identifies exceptional conversions for a given source precision to target precision, using a bit vector to store these exceptions for efficient rounding during conversion operations, reducing the need for high intermediate precision and storage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiple-precision arithmetic is used to achieve correct rounding, then rounding accuracy is improved, but computational cost and storage requirements increase significantly
Solution Approach 1:
The patent pre-computes and stores rounding threshold information in lookup tables during an offline phase. During online conversion, the system queries these pre-computed tables to determine correct rounding without performing expensive multiple-precision arithmetic, thus resolving the contradiction between rounding accuracy and computational cost
Solution Approach 2:
The patent introduces lookup tables as an intermediary structure that stores pre-computed rounding threshold values. This intermediary allows the system to achieve correct rounding by simple table queries rather than complex arithmetic operations, reducing computational cost while maintaining rounding accuracy
2Measurement precision
If multiple-precision arithmetic is used to achieve correct rounding, then rounding accuracy is improved, but storage requirements increase due to extended-precision intermediate results
Solution Approach 1:
The patent pre-computes rounding threshold information and stores it in compact lookup tables during an offline phase. During online conversion, only these compact tables need to be stored in memory, eliminating the need for large amounts of scratch storage that would be required to hold extended-precision intermediate results, thus resolving the contradiction between rounding accuracy and storage requirements
3Productivity
If simple conversion is used, then computational cost is reduced, but rounding accuracy deteriorates
Solution Approach 1:
The patent pre-computes rounding threshold information and stores it in lookup tables during an offline phase. During online conversion, the system performs simple conversions by querying these pre-computed tables, achieving both fast conversion speed and correct rounding accuracy simultaneously
Solution Approach 2:
The patent introduces lookup tables as an intermediary that enables simple conversions to achieve correct rounding. The tables store pre-computed threshold values that guide rounding decisions, allowing the system to maintain both high conversion speed and high rounding accuracy
Data Source
AI summary
A system and method for converting bases of floating point numbers with improved rounding over an entire exponent range includes identifying exceptional conversions for a given source precision to target precision. A representation of the exceptions is stored in a bit vector for use during conversion execution.