Floating-Point Conversion for Associative Parallel Summation
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Solution Overview
Problem
Floating-point arithmetic is non-associative, leading to reproducibility issues and difficulties in parallelization, especially in high-performance computing, where programs need to add millions of numbers, resulting in different results depending on the order of operations and making debugging challenging.
Innovation Solution
The introduction of high-precision anchored (HPA) numbers, which are represented as a pair of a long two's complement integer and an anchor integer, allowing for associative addition and conversion between floating-point and HPA formats, enabling faster and correct accumulation of floating-point numbers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If floating-point arithmetic is used, then a wide range of values can be represented, but addition becomes non-associative leading to reproducibility issues
Solution Approach 1:
The patent segments floating-point numbers into integer components (significand bits) and uses separate exponent handling. By representing floating-point values as integers with an associated exponent value, the patent enables associative addition of the integer components while maintaining the ability to represent a wide range of values through exponent adjustment.
2Adaptability or versatility
If floating-point arithmetic is used, then real number calculations are supported, but parallelization becomes difficult due to non-associative addition
Solution Approach 1:
The patent segments floating-point operations into integer addition operations that are associative. By converting floating-point numbers to integer representations (storing significands as integers with separate exponent metadata), multiple threads can independently add integer components in any order, enabling efficient parallelization while maintaining floating-point calculation capability.
3Reliability
If high-precision anchored numbers are used, then associative addition is achieved, but conversion from floating-point format is required
Solution Approach 1:
The patent introduces an intermediary representation format that bridges floating-point and integer arithmetic. High-precision anchored numbers serve as this intermediary, allowing floating-point values to be converted into a format where the significand is stored as an integer with an associated anchor (exponent) value, enabling associative addition while maintaining compatibility with floating-point operations.
Data Source
AI summary
An apparatus comprises processing circuitry to perform a conversion operation to convert a vector comprising a plurality of data elements representing respective bit significance portions of a binary value to a scalar value comprising an alternative representation of said binary value.