Floating-Point Residual Encoding with Exponent-Aligned Mantissas
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Solution Overview
Problem
Existing methods for lossless compression of floating-point data fail to maintain a high compression rate when the exponent value of the encoding target data differs from that of the predicted value, leading to meaningless residuals and reduced compression efficiency.
Innovation Solution
An encoding apparatus that adjusts the mantissa value of the predicted value based on the exponent value difference between the encoding target and predicted values, generating a specific exponent and mantissa for the encoding target value to ensure alignment and maintain data structure integrity during compression.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a residual is obtained by simple floating-point calculations, then calculation simplicity is maintained, but information loss occurs and lossless compression cannot be performed
Solution Approach 1:
The patent segments floating-point data into three distinct parts: sign part, exponent part, and mantissa part. By treating each part separately as integer data for residual calculation, the method avoids information loss while maintaining calculation feasibility. This segmentation allows the system to process each component independently using integer arithmetic, thereby achieving lossless compression.
Solution Approach 2:
The patent introduces an intermediary approach by converting floating-point components into integer representations for residual calculation. This intermediary transformation enables the use of simple integer arithmetic operations while preserving the original floating-point information, thus bridging the gap between calculation simplicity and information preservation.
2Loss of information
If a residual is obtained by regarding floating-point data as integer data, then information loss is avoided, but the data structure of floating-point data is ignored and an appropriate residual may not be obtained
Solution Approach 1:
The patent divides floating-point data into sign part, exponent part, and mantissa part, and processes each segment separately. This segmentation ensures that the unique characteristics of floating-point representation are preserved while enabling integer-based residual calculation for each component, thereby maintaining both information integrity and calculation precision.
Solution Approach 2:
The patent applies different processing approaches to different parts of the floating-point data structure. Each component (sign, exponent, mantissa) is handled with appropriate integer conversion rules that respect its specific role in floating-point representation, ensuring locally optimized precision for each segment while maintaining overall data integrity.
3Adaptability or versatility
If the exponent part values of encoding target data and predicted value are different, then variable representation flexibility is maintained, but the mantissa parts have different numbers of digits and meaningful residual cannot be obtained
Solution Approach 1:
The patent separates the exponent part and mantissa part processing. By treating the exponent part as an independent integer component, the method preserves the flexibility of variable exponent representation. The mantissa part is then processed separately with appropriate digit alignment, ensuring meaningful residual calculation despite exponent differences.
Solution Approach 2:
The patent changes the parameter representation by converting mantissa values to integer form with explicit digit position tracking. This parameter transformation allows the system to handle different exponent values while maintaining meaningful mantissa comparison through proper integer conversion and digit alignment.
4Ease of manufacture
If mantissa parts with different numbers of digits are compared directly, then processing simplicity is maintained, but no meaningful residual value is obtained and compression rate is reduced
Solution Approach 1:
The patent changes the parameter representation of mantissa values by converting them to integer form with explicit digit position information. This parameter change enables meaningful comparison and residual calculation even when original mantissas have different digit counts, thereby improving compression rate while maintaining processing efficiency through systematic integer arithmetic.
Data Source
AI summary
A data predicted value generating unit generates a predicted value (data predicted value) for original data intended to be encoded, based on a history of original data which is floating-point data. A data predicted value modifying unit adjusts a mantissa value of the data predicted value by aligning an exponent value of the data predicted value with an exponent value of the original data. A first residual generating unit generates a residual (first residual) between new original data and the data predicted value after being adjusted. A first residual predicted value generating unit generates a predicted value for the first residual (first residual predicted value), based on a history of first residuals. A second residual generating unit generates a residual (second residual) between the first residual and the first residual predicted value. A residual encoding unit generates encoded data by encoding the second residual.