Anchored-Data Element Encoding for Associative Number Accumulation

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Solution Overview

Problem

Floating-point arithmetic is non-associative, leading to reproducibility issues in sums, making parallelization difficult and slow, especially in high-performance computing where millions of values need to be added, as the order of operations affects the result.

Innovation Solution

The introduction of high-precision anchored (HPA) numbers, which consist of a long two's complement integer and an anchor integer, allowing for associative and reproducible additions by maintaining the anchor value unchanged during operations, enabling parallel processing without the need for rounding or normalization.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If floating-point arithmetic is used, then a large range of numeric values can be represented, but calculations become non-associative leading to reproducibility issues

Engineering Contradiction:

Improverange of numeric valuesVSAvoidreproducibility of calculations

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The patent changes the parameter representation from floating-point (significand and exponent) to high-precision anchored format (long integer i and anchor integer a). This parameter transformation enables associative arithmetic operations while maintaining the ability to represent a large range of values, thus resolving the contradiction between versatility and reliability.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent introduces an intermediary conversion process that transforms floating-point values into HPA form before performing arithmetic operations. This intermediary representation acts as a mediator that preserves the large range capability of floating-point while enabling associative operations, thereby resolving the reproducibility issue.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If floating-point addition is performed sequentially to maintain reproducibility, then calculation accuracy is preserved, but processing speed decreases

Engineering Contradiction:

Improvereproducibility of sumsVSAvoidprocessing speed

Core Design Contradiction:

ReliabilityVSProductivity

Solution Approach 1:

By changing the arithmetic parameter representation to HPA format, the patent enables parallel and vectorized operations while maintaining reproducibility. The anchored representation allows multiple values to be processed simultaneously without sacrificing calculation reliability, thus resolving the speed-reproducibility tradeoff.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent segments the arithmetic operations into independent parallel tasks that can be executed simultaneously. The HPA format allows division of the computation into separate addition operations that don't depend on each other's intermediate results, enabling parallel processing while maintaining reproducibility through the associative property.

Inventive Principle:

Principle #1Segmentation

3Reliability

If high-precision anchored numbers are used, then associative and reproducible additions are enabled, but device complexity increases

Engineering Contradiction:

Improveassociativity of operationsVSAvoidhardware structure

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent uses copying by representing high-precision values in a format that can be replicated and processed using standard integer arithmetic units. The HPA format allows copying of the anchored representation across multiple processing elements, enabling parallel processing without requiring complex custom hardware for each operation.

Inventive Principle:

Principle #26Copying

Solution Approach 2:

The patent substitutes complex floating-point arithmetic mechanisms with simpler integer arithmetic operations. By representing floating-point values in HPA format, the system replaces complex FP addition logic with straightforward integer addition, reducing hardware complexity while maintaining reliability and associativity.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

4Productivity

If floating-point values are converted to HPA form, then parallel processing becomes possible, but conversion overhead is introduced

Engineering Contradiction:

Improveparallel processing capabilityVSAvoidconversion time

Core Design Contradiction:

ProductivityVSLoss of time

Solution Approach 1:

The patent applies preliminary action by performing the floating-point to HPA conversion once at the beginning of the computation pipeline. This upfront conversion enables all subsequent arithmetic operations to be performed in parallel using the efficient HPA format, amortizing the conversion cost across many parallel operations and achieving net productivity gain.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS10459688B1Encoding special value in anchored-data element

Publication Date: 2019.10.29 ARM LTD

AI summary

An apparatus comprises: processing circuitry to perform data processing; and an instruction decoder to control the processing circuitry to perform an anchored-data processing operation to generate an anchored-data element. The anchored-data element has an encoding including type information indicative of whether the anchored-data element represents: a portion of bits of a two's complement number, said portion of bits corresponding to a given range of significance representable using the anchored-data element; or a special value other than said portion of bits of a two's complement number.