Processor Execution Unit Taylor Series Logarithm Computation
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Solution Overview
Problem
Existing execution units face challenges in quickly and accurately generating logarithm values, particularly in neural network processing, where resource optimization is crucial for efficient computation.
Innovation Solution
An execution unit is designed with a lookup table and preparatory circuit to determine an index value for locating a natural logarithm entry, and control circuitry to evaluate Taylor series expansions using multiplier and addition circuits, optimizing the generation of logarithm values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If traditional computation methods are used for generating logarithm values, then accuracy can be maintained, but processing speed is slow and resource utilization is inefficient
Solution Approach 1:
The execution unit is divided into specialized functional blocks: a lookup table unit for quick reference values, a preparatory circuit for input processing, control circuitry for coordinate transformations, and multiplier/addition circuits for Taylor series evaluation. This segmentation allows each component to perform its specific function efficiently, improving overall processing speed while managing complexity through modular design.
Solution Approach 2:
The lookup table pre-stores natural logarithm values for common inputs, allowing the execution unit to quickly retrieve reference values without performing complete calculations. The preparatory circuit also performs initial processing of input operands before they reach the main computation circuits, reducing the burden on subsequent stages and improving overall processing efficiency.
2Productivity
If resource optimization is prioritized in neural network processing, then efficiency improves, but the ability to perform accurate mathematical functions like logarithms deteriorates
Solution Approach 1:
The execution unit transforms the input operand from standard floating-point format into a different coordinate system or representation that is more suitable for efficient logarithm computation. The control circuitry adjusts parameters such as exponent and mantissa relationships, enabling the use of simplified calculation methods while maintaining the required precision through controlled parameter transformations.
Solution Approach 2:
The lookup table serves as an intermediary between the input operand and the final logarithm result, providing pre-computed reference values that bridge the gap between simple hardware operations and accurate mathematical functions. The Taylor series expansion acts as another intermediary, breaking down the complex logarithm calculation into a sequence of simpler multiplication and addition operations that are more efficient to compute.
3Loss of time
If specialized circuits are added to improve logarithm computation, then processing speed increases, but device complexity increases
Solution Approach 1:
The execution unit is designed with multi-functional circuits that can perform various operations: the multiplier circuits and addition circuits are used both for Taylor series expansion evaluation and for other floating-point arithmetic operations. The lookup table serves multiple purposes including direct logarithm retrieval and providing reference values for different computation methods. This universality allows the increased device complexity to be justified by the ability to perform multiple functions efficiently, including but not limited to logarithm computation.
Data Source
AI summary
An execution unit for a processor, the execution unit comprising: a look up table; a preparatory circuit configured to determine an index value in dependence upon the operand and search the look up table using the index value to locate an entry comprising a natural logarithm associated with the index value; control circuitry configured to provide a first value determined in dependence upon the operand and a second value determined in dependence upon the operand as inputs to at least one multiplier circuit of the execution unit so as to evaluate terms of a Taylor series expansion of a natural logarithm, wherein the control circuitry is configured to provide the natural logarithm associated with the index value and the terms of the Taylor series expansion as inputs to at least one addition circuit so as to generate a mantissa of a natural logarithm of the operand.