Macro Placement Using Multi-Resolution Density Maps
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Solution Overview
Problem
Existing macro placement techniques face challenges in optimizing wirelength and congestion on semiconductor chips, often resulting in either excessive overlap or empty space due to inadequate grid discretization and refinement processes.
Innovation Solution
The method involves initializing a grid with density maps calculated using average-pooling filters of multiple resolutions and orientations, validating macro placements based on density thresholds to balance compactness and refinement, using multi-resolution and 1-D action masks to control macro placement and reserve space for further refinement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Area of moving object
If a placement tool places macros compactly on the grid, then the placement density is improved, but the amount of overlap among macros increases which degrades placement quality during refinement
Solution Approach 1:
The patent segments the grid into multiple resolution levels (coarse grid and fine grid) to handle placement at different scales. The coarse grid enables compact initial placement while the fine grid allows subsequent refinement without overlap, resolving the contradiction between placement density and placement quality
Solution Approach 2:
The patent introduces a multi-resolution dimensional structure by computing density maps at multiple resolutions. This additional dimensional aspect allows the system to evaluate placement validity across different scales, enabling compact placement at coarse level while maintaining quality at fine level
2Reliability
If a placement tool places macros less compactly on the grid, then the amount of overlap among macros is reduced, but the amount of empty space increases which reduces chip utilization
Solution Approach 1:
The patent segments the placement process into two stages: initial compact placement on coarse grid followed by refinement on fine grid. This segmentation allows the system to achieve high chip utilization through compact initial placement while ensuring placement quality through subsequent refinement that eliminates overlaps
Solution Approach 2:
The patent performs preliminary compact placement on the coarse grid before refinement. This preliminary action maximizes chip utilization by packing macros densely initially, and then the refinement process adjusts positions to eliminate overlaps, achieving both high utilization and quality
3Ease of operation
If grid discretization is used for macro placement, then the placement process is simplified, but the refinement process becomes difficult when macros overlap
Solution Approach 1:
The patent segments the grid into multiple resolution levels to simplify the placement process at coarse level while enabling refinement at fine level. The coarse grid provides simple discrete placement options, while the fine grid enables precise adjustment without complicating the overall process
Solution Approach 2:
The patent introduces density maps as an intermediary mechanism that bridges the coarse grid placement and fine grid refinement. The density maps provide a unified representation that works at multiple resolutions, simplifying the transition between placement stages and reducing refinement complexity
Data Source
AI summary
Macros are placed on a canvas based on density map calculations. First, a grid representing the canvas is initialized. The grid is formed by grid cells. To place a macro on the grid, a coordinate on the grid is chosen, and multiple density maps are calculated using average-pooling filters of multiple resolutions or orientations. The lowest-level density map is described by the grid with each grid cell having a corresponding density value. The density value in a higher-level density map is calculated by performing an average-pooling operation on density values in a lower- level density map. The placement of the macro at the coordinate is validated when no density value in the density maps exceeds a corresponding density threshold.