Floating Point Chained Multiply Accumulate Rounding Circuit
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Solution Overview
Problem
Existing floating point data processing systems face inefficiencies in performing chained multiply accumulate operations due to the conventional practice of rounding intermediate results before accumulation, which can lead to errors and inaccuracies in the final result.
Innovation Solution
The apparatus and method for performing a floating point chained multiply accumulate operation involve a multiplier, an adder, and rounding circuitry that generate unrounded results and associated rounding data, allowing for accurate rounding of both multiplication and accumulation results in a single final phase, thereby improving precision and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If intermediate results are rounded before accumulation in conventional floating point multiply accumulate operations, then the device complexity is reduced and processing speed is improved, but the manufacturing precision and reliability of the final result deteriorate due to accumulated rounding errors
Solution Approach 1:
The patent segments the rounding operation into two distinct phases: (1) intermediate rounding of the multiplication result to produce a rounded multiply result, and (2) final rounding of the accumulation result. By separating these rounding operations and maintaining the unrounded multiply result in a register during the accumulation phase, the system achieves both intermediate processing efficiency and final result accuracy, resolving the contradiction between processing speed and manufacturing precision.
2Device complexity
If intermediate results are rounded before accumulation, then the device complexity is reduced, but the manufacturing precision deteriorates due to loss of information from premature rounding
Solution Approach 1:
The patent introduces an intermediary component - a register - that holds the unrounded multiply result during the accumulation phase. This intermediary allows the system to perform accumulation using the full precision unrounded value while still benefiting from the structured intermediate rounding process, thereby maintaining manufacturing precision without significantly increasing device complexity.
3Loss of time
If rounding is applied immediately after multiplication, then the processing time is reduced, but the reliability of the final accumulation result deteriorates due to propagation of rounding errors
Solution Approach 1:
The patent applies preliminary rounding to the multiplication result to produce a rounded multiply result that can be used immediately in the accumulation operation, reducing processing time. Simultaneously, the system preserves the unrounded multiply result in a register for the final accumulation step, ensuring that the most accurate data is used for the reliability-critical final result, thus resolving the contradiction between time efficiency and result reliability.
Data Source
AI summary
Floating point chained multiply accumulation is performed using a multiplier to multiply a first floating point operand by a second floating point operand to generate an unrounded multiplication result. An adder then adds a third floating point operand to the unrounded multiplication result to generate an unrounded accumulation result. Rounding circuitry then applies both the rounding associated with the unrounded multiplication result and rounding associated with the unrounded accumulation result to generate a rounded accumulation result.