Z-Order Data Parsing for Non-Power-of-2 Valid Regions
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Solution Overview
Problem
The use of Z-ordering functions to map multidimensional scene data into one-dimensional sequences can result in inefficiencies when the valid region of the grid is not an exact power-of-2, leading to the generation of invalid coordinates and wasted cycles due to the inability to trivially determine the next valid grid value.
Innovation Solution
A method is provided to identify work packets by determining an overflow value that, when added to a first value, causes a least significant bit to flip from 1 to 0, allowing efficient skipping over invalid positions and determining the next valid position in the sequence, thereby reducing unnecessary processing of invalid coordinates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of energy
If Z-ordering function is used to map multidimensional scene data into one-dimensional sequence, then spatial locality of reference is improved and cache efficiency is increased, but when the valid region is not an exact power-of-2, invalid coordinates are generated and processing efficiency deteriorates
Solution Approach 1:
The patent pre-calculates and stores the maximum valid index for each dimension in a lookup table before processing. This preliminary action allows the system to quickly determine whether a Z-order mapped index is valid without complex runtime calculations, thus maintaining processing efficiency while using Z-ordering for cache optimization.
Solution Approach 2:
The patent introduces an intermediary validation mechanism that checks whether a Z-order mapped index falls within the valid region boundaries. This intermediary layer separates the Z-order mapping function from the actual data access, allowing the system to benefit from Z-ordering's cache efficiency while filtering out invalid coordinates through the validation checkpoint.
2Stability of the object's composition
If Z-ordering function is used with non power-of-2 grid dimensions, then spatial locality is improved, but the complexity of determining valid coordinates increases and wasted cycles occur
Solution Approach 1:
The patent pre-calculates the maximum valid index for each dimension and stores these values in a lookup table. This preliminary computation transforms the complex runtime validation problem into a simple comparison operation, reducing the complexity of determining valid coordinates while maintaining spatial locality benefits.
Solution Approach 2:
The patent changes the validation approach from complex geometric calculations to simple parameter comparisons against pre-computed maximum indices. By transforming the validation criterion into a straightforward parameter check, the system maintains spatial locality while significantly reducing the complexity of coordinate validation.
3Ease of operation
If strided order scanning is used, then implementation simplicity is maintained, but cache efficiency deteriorates and cache misses increase
Solution Approach 1:
The patent segments the scene data into tiles and applies Z-ordering specifically within each tile rather than across the entire grid. This segmentation allows the system to maintain implementation simplicity by processing smaller, manageable units while achieving cache efficiency through spatially localized Z-ordering within each tile.
Solution Approach 2:
The patent applies Z-ordering locally within each tile rather than globally across the entire scene. This local application of Z-ordering maintains cache efficiency for frequently accessed rectangular regions while keeping the overall implementation simpler by limiting the complexity to localized areas rather than the entire grid.
Data Source
AI summary
Multidimensional data mapped into one-dimensional data using a Z-ordering function is parsed to identify work packets to be processed. Dimensions of the multidimensional data and information identifying a valid region of the multidimensional data are obtained, where the valid region identifies work packets. At least part of a sequence within the one-dimensional data is determined, corresponding to positions within the multidimensional data lying in the valid region, by determining whether a position defined by a first value lies within the valid region. If the position does not lie within the valid region, an overflow value is calculated which causes a least significant bit that is a 1 in a binary representation of the first value to flip to a 0. The first value and the overflow value are summed to obtain a trial value which if lying within the valid region forms part of the sequence, wherein the sequence identifies work packets to be processed.