Processor Reciprocal Execution Circuitry for Fractional Operations
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Solution Overview
Problem
Current computer processor architectures lack efficient methods for performing fractional reciprocal and reciprocal square root operations, which are essential for various digital signal processing tasks, leading to suboptimal performance in applications such as digital signal processing, image processing, and machine learning.
Innovation Solution
The implementation of specific instructions and execution circuitry within the processor architecture that enables fractional reciprocal and reciprocal square root operations through polynomial approximations and coefficient table lookups, allowing for accurate calculations of 1/x and 1/sqrt(x) for packed data elements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If polynomial approximations and coefficient table lookups are implemented, then calculation accuracy is improved, but device complexity increases
Solution Approach 1:
Coefficient tables are pre-computed and stored in the execution circuitry, allowing the processor to perform accurate reciprocal and reciprocal square root operations by simply looking up pre-calculated values and combining them with input data through simple arithmetic operations, rather than performing complex calculations in real-time
Solution Approach 2:
The polynomial approximation method divides the complex reciprocal calculation into multiple simpler terms (e.g., using a polynomial series expansion with multiple coefficients), where each term can be computed separately and then summed to achieve high accuracy without requiring a single complex operation
2Productivity
If fractional reciprocal operations are implemented, then productivity is improved, but device complexity increases
Solution Approach 1:
The patent replaces complex iterative mechanical computation methods with a streamlined execution circuitry that uses polynomial approximations and table lookups, significantly reducing the number of computational steps required while maintaining accuracy
Solution Approach 2:
The execution circuitry changes the computational approach by using fixed polynomial coefficients and pre-calculated table values instead of dynamic iterative methods, allowing for faster parallel computation of reciprocal operations across multiple data elements
Data Source
AI summary
An apparatus and method for performing a reciprocal. For example one embodiment of a processor comprises: a decoder to decode a reciprocal instruction to generate a decoded reciprocal instruction; a source register to store at least one packed input data element; a destination register to store a result data element; and reciprocal execution circuitry to execute the decoded reciprocal instruction, the reciprocal execution circuitry to use a first portion of the packed input data element as an index to a data structure containing a plurality of sets of coefficients to identify a first set of coefficients from the plurality of sets, the reciprocal execution circuitry to generate a reciprocal of the packed input data element using a combination of the coefficients and a second portion of the packed input data element.