Floating Point Normalization via Mantissa Segmentation
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Solution Overview
Problem
Existing floating point units (FPUs) face challenges in efficiently normalizing or denormalizing full-precision intermediate results without stalling or incurring high hardware costs, as current methods either require extensive resources for brute-force approaches or stall pipeline stages in iterative methods.
Innovation Solution
The FPU partitions the full-precision intermediate mantissa into separate regions, computes the required left shift count for each region, and uses leading zero anticipators to determine the position of the leading bit, allowing for normalization or denormalization in a single pass without stalling, while optimizing the normalizer width based on the widest region.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the brute-force method is used with full-width LZA and normalizer, then the design can be fully-pipelined without stalling, but the area requirements and delay increase significantly
Solution Approach 1:
The full-width intermediate mantissa is divided into multiple narrower regions, each processed by a corresponding narrower LZA and normalizer. This segmentation reduces the area and delay of individual components while maintaining full pipelining capability through coordinated processing of all regions.
Solution Approach 2:
Multiple narrower LZA units and normalizer units are merged/combined to process different regions simultaneously. The results from all regions are then combined to produce the final normalized or denormalized result, achieving both area reduction and full pipelining.
2Area of stationary object
If the iterative method is used with reduced-width normalizer and LZA, then the area requirements and delay are reduced, but pipeline stalls are required
Solution Approach 1:
The intermediate mantissa is segmented into multiple regions that can be processed in parallel by narrower LZA and normalizer units. This segmentation enables simultaneous processing of all regions within a single pipeline cycle, eliminating the need for iterative stalls while using reduced-width hardware.
Solution Approach 2:
The problem is transformed from a single-dimensional iterative approach to a multi-dimensional parallel approach by processing multiple regions simultaneously. Different regions are handled in parallel across multiple hardware units, converting time-based iteration into space-based parallelism.
3Adaptability or versatility
If separate denormalization units are added to achieve denormalized results, then denormalization capability is provided, but hardware complexity and performance are detrimentally impacted
Solution Approach 1:
The normalizer is designed to perform both normalization and denormalization operations using the same hardware unit. By making the normalizer multi-functional, the need for separate denormalization units is eliminated, reducing hardware complexity while maintaining full capability for both operations.
Solution Approach 2:
The normalizer's behavior is made dynamic and adjustable based on the input conditions. The same normalizer hardware can adapt its operation mode (normalization or denormalization) depending on the exponent value and control signals, providing versatility without additional dedicated hardware.
Data Source
AI summary
A data processor includes a first bit field of a first plurality of bits representing a mantissa of a floating point number and a second bit field of a second plurality of bits representing an exponent of the floating point number. The first plurality of bits is partitioned into a plurality of regions, each of the plurality of regions comprises more than one bit of the first plurality of bits. A leading zero anticipator or other type of leading bit indication circuit is coupled to each region and determines a position of a leading bit of the first plurality of bits. A normalizer is coupled to receive a region of the plurality of regions that contains the leading bit, the normalizer may normalize or denormalize the region to produce a normalized or denormalized floating point number.