Multipart Numeric Encoding for High-Precision SIMD Computing
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Solution Overview
Problem
There is a tradeoff between simplicity and precision in computing systems, where high precision often requires complex hardware and reduces computational throughput, and existing data types do not effectively mitigate this issue.
Innovation Solution
Implementing multipart encoded representations that split a source number into multiple parts, each with tailored precision, allowing for optimized encoding and decoding processes that simplify hardware complexity and improve computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high precision data types are used, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent divides a high-precision number representation into multiple lower-precision parts (e.g., splitting a 128-bit number into multiple 32-bit parts). Each part can be processed independently by simplified hardware units, achieving high overall precision without requiring complex single-unit hardware capable of handling the full precision in one operation.
2Measurement precision
If high precision data types are used, then measurement precision is improved, but productivity decreases
Solution Approach 1:
By segmenting high-precision computations into multiple parallelizable operations on lower-precision parts, the system can process multiple parts simultaneously or in efficient pipelines, maintaining high computational throughput while achieving high overall precision through combination of results.
Solution Approach 2:
The patent applies partial precision to intermediate calculations and only uses full precision when necessary for final results. This reduces the computational burden across most operations while maintaining required precision for critical outcomes, thereby improving overall productivity.
3Measurement precision
If high precision data types are used, then measurement precision is improved, but use of energy increases
Solution Approach 1:
The patent segments high-precision processing into multiple lower-precision steps, where each segment consumes less energy than a single high-precision operation would require. The cumulative energy consumption of multiple low-precision operations is less than that of equivalent high-precision operations, achieving energy efficiency while maintaining precision.
Data Source
AI summary
A multipart encoded representation or data type may be particularly useful for limited-capacity processors, such as those used in at-memory or single-instruction, multiple data (SIMD) devices. To encode a source number, the source number is quantized as a first binary representation defined by a first set of exponent bits and a first set of mantissa bits to obtain a first encoded part. A difference between the source number and a nearest dequantization of the first encoded part is computed. The difference is quantized as a second binary representation defined by a second set of exponent bits and a second set of mantissa bits to obtain a second encoded part. The first encoded part and the second encoded part are stored as an encoded representation of the source number. A computational operation may be performed using the encoded representation. The encoded representation may be decoded using an inverse process.