Floating Point Accumulator Splitter Compensation Mantissa Distortion
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Solution Overview
Problem
Existing digital processors face challenges in precisely performing floating-point operations due to exponent differences, leading to mantissa distortion and increased hardware requirements for high precision in multiply-adder operations.
Innovation Solution
An accumulating operator that splits a floating-point number into a third floating-point number with equal or greater exponent and a compensation number, allowing precise operations through an accumulator and compensator, avoiding mantissa distortion without increasing hardware complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a multiply-adder of improved precision is used to solve mantissa distortion, then manufacturing precision is improved, but device complexity increases due to increased number of operating units and enlarged memory size
Solution Approach 1:
The first floating point number is segmented into a third floating point number and a compensation number, where the third floating point number has an exponent equal to the exponent of the second floating point number. This segmentation allows the accumulator to operate with matched exponents, preventing mantissa distortion without requiring additional precision hardware.
Solution Approach 2:
A compensation number is introduced as an intermediary element to bridge the exponent difference between floating point numbers. The compensation number adjusts the first floating point number so that after splitting, the resulting third floating point number has an exponent matching the second floating point number, enabling precise addition without hardware expansion.
2Ease of operation
If exponent unification is performed by transforming small-value numbers, then addition operation is enabled, but manufacturing precision deteriorates due to mantissa distortion from shifting out of range
Solution Approach 1:
The splitting operation is performed in advance to restructure the first floating point number into components with compatible exponents. By pre-adjusting the exponent of the third floating point number to match the second floating point number before the addition operation, the need for problematic exponent transformation during addition is eliminated.
Solution Approach 2:
Instead of transforming the small-value number to match the large exponent (which causes mantissa distortion), the invention inverts the approach by splitting the large floating point number into components that naturally match the small exponent, thereby preserving mantissa precision while enabling addition.
Data Source
AI summary
An accumulating operator is applicable to a digital data processor to realize an output floating point number in response to a first floating point number and a second floating point number. The accumulating operator comprises a splitter dividing the first floating point number into a third floating point number and a compensation number, wherein an exponent of the third floating point number is equal to or greater than the exponent of the second floating point number; an accumulator electrically connected to the splitter for operating the second and third floating point numbers to realize a fourth floating point number; and a compensator electrically connected to the splitter and the accumulator for operating the fourth floating point number and the compensation number to realize the output floating point number. Via compensation, the precision of the floating point operation can be improved.