Exponent-Indexed Accumulators for Fast Floating-Point Summation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Modern signal processing systems, neural networks, and machine learning systems require efficient methods for adding large numbers in floating-point, logarithmic, and posit formats, as existing technologies struggle with the complexity and precision of such operations.
Innovation Solution
A system is developed that includes an accumulation subsystem with partial sum registers, an adder/subtractor, an exponent-indexed decoder, and a reconstruction subsystem with a shifter and accumulator-register to efficiently accumulate and reconstruct the results, using exponent-indexed partial sum registers and a pipelined architecture to reduce the number of registers required.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional methods are used to add large numbers of floating-point numbers, then the system can handle the accumulation operation, but the time and computational resources required become excessive
Solution Approach 1:
The patent divides the accumulation operation into two distinct phases: an accumulation phase that processes many numbers efficiently using exponent-indexed partial sum registers, and a reconstruction phase that generates the final result. This segmentation allows the system to handle large numbers of inputs without excessive time requirements by optimizing each phase separately.
Solution Approach 2:
The patent performs preliminary grouping of numbers by exponent value during the accumulation phase, storing partial sums in exponent-indexed registers. This preliminary organization enables the reconstruction phase to efficiently generate the final result by processing groups rather than individual numbers, significantly reducing total accumulation time.
2Adaptability or versatility
If sufficient partial sum registers are allocated to handle all possible exponents, then all accumulation cases can be handled, but the number of registers and device complexity increases
Solution Approach 1:
The patent changes the indexing parameter from direct exponent values to compressed exponent codes. By mapping multiple exponent values to the same index in the partial sum registers, the system reduces the number of registers needed while maintaining the ability to handle a wide range of exponent values through the compression algorithm.
Solution Approach 2:
The exponent-indexed partial sum registers serve multiple functions: they accumulate partial sums for groups of numbers, store intermediate results for reconstruction, and enable efficient handling of different exponent ranges through compression. This multi-functionality reduces the overall device complexity while maintaining versatility.
3Measurement precision
If exact precision is maintained throughout the accumulation process, then the result accuracy is high, but the computational complexity and resources increase
Solution Approach 1:
The patent applies partial precision during the accumulation phase by maintaining only the necessary significant digits in partial sum registers, then performs exact reconstruction in the second phase. This approach maintains final result accuracy while reducing the computational complexity and resource requirements during the accumulation phase.
Solution Approach 2:
The patent introduces partial sum registers as intermediary storage structures that hold grouped accumulation results. These intermediaries enable the system to maintain precision by organizing calculations in a way that minimizes rounding errors while reducing the overall computational complexity through efficient grouping and reconstruction.
Data Source
AI summary
Aspects of the invention include a system for accumulating a plurality of input numbers to output a result. The system includes an accumulation subsystem that accepts input numbers that each have a sign bit, an exponent, and a mantissa. The accumulation subsystem includes: a plurality of partial sum registers, each for a particular one of the exponents accumulating a sum of mantissas of numbers having the particular exponent; an adder/subtractor for accumulating the sums; an exponent-indexed decoder to enable a corresponding partial sum register; and an exponent output multiplexor to select the corresponding partial sum register for output. The system further includes a reconstruction subsystem into which are read the partial sums from the partial sum registers, the reconstruction subsystem comprising an adder, a shifter and an output accumulator-register to output said result.