Rounding Circuitry Parallel Floor Ceiling Candidate Selection
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Solution Overview
Problem
Existing data processing apparatuses face inefficiencies in rounding operations due to the time-consuming process of determining the sign of a residual value in redundant representation, which can hinder the speed of rounding operations.
Innovation Solution
The apparatus employs floor and ceiling calculation circuitry to generate two candidates for each in non-redundant representation, with selection circuitry determining the output based on the sign of the residual value, allowing for parallel processing and reducing the critical path dependency on residual value determination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the residual value sign determination is performed sequentially before rounding, then the rounding accuracy is ensured, but the rounding speed is reduced
Solution Approach 1:
The patent pre-calculates and stores both possible floor and ceiling values in advance, along with their corresponding residual value sign requirements. This allows the rounding operation to simply select from pre-computed values based on the residual sign, eliminating the need for sequential calculation during the rounding process itself.
Solution Approach 2:
The patent divides the rounding operation into independent parallel paths: one path handles positive residual values (selecting from first floor/ceiling candidates) and another path handles negative residual values (selecting from second floor/ceiling candidates). This segmentation allows simultaneous preparation of all candidate values without dependency on residual sign determination.
2Reliability
If the critical path includes residual value sign determination, then correct rounding decision is made, but the overall processing time increases
Solution Approach 1:
The patent pre-calculates floor and ceiling values for both positive and negative residual sign scenarios, storing them as candidate pairs. This preliminary computation removes the residual sign determination from the critical path, as the selection logic only needs to compare pre-computed candidates rather than wait for sequential residual evaluation.
Solution Approach 2:
The patent transforms the sequential decision process into a parallel selection process by introducing candidate value pairs organized in a two-dimensional structure (floor/ceiling × positive/negative residual). This allows the system to evaluate multiple rounding outcomes simultaneously and select the correct one based on residual sign, rather than computing them sequentially.
3Device complexity
If sequential processing is used for rounding operations, then resource usage is minimized, but productivity is reduced
Solution Approach 1:
The patent segments the rounding circuit into independent parallel modules: floor calculation units, ceiling calculation units, and selection logic units that operate simultaneously. Each module handles specific candidate value computations independently, allowing the circuit to process multiple rounding operations in parallel without requiring complex sequential control logic.
Solution Approach 2:
The patent pre-computes and stores candidate floor and ceiling values along with their associated residual sign requirements. This preliminary action allows the rounding circuit to function as a simple selection device rather than a complex sequential calculator, significantly improving throughput while keeping the actual rounding logic relatively simple.
Data Source
AI summary
A data processing apparatus for performing rounding on an input value to produce a rounded form output value includes floor calculation circuitry that receives the input value in redundant-representation and generates two candidates of a floor of the input value in non-redundant representation. Ceiling calculation circuitry receives the input value in redundant-representation and generates two candidates of a ceiling of the input value in non-redundant representation. Selection circuitry outputs one of the two candidates of the floor of said input value and the two candidates of the ceiling of said input value as the rounded form output value, based on a sign of a residual value associated with the input value. Each of the two candidates of the floor of the input value correspond with different values of the sign of the residual value and each of the two candidates of the ceiling of said input value correspond with different values of the sign of said residual value.