Processor Coefficient Calculation for Exponential Functions
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Solution Overview
Problem
Conventional processors require numerous instructions and data transfers to perform arithmetic operations for exponential functions using Taylor series, leading to decreased performance due to inefficient calculation processing of coefficients.
Innovation Solution
A processor configuration with an exponent generating unit, storage unit, and selecting unit that allows for direct calculation of coefficients using a single instruction, reducing the need for multiple instructions and data transfers by utilizing a constant table for mantissa parts of coefficients.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If coefficient calculation is performed using conventional instructions with multiple data transfers between floating-point register and integer register, then calculation precision is maintained, but instruction throughput deteriorates due to the large number of instructions required
Solution Approach 1:
The patent combines the exponent generation unit, storage unit for mantissa parts, and selecting unit into an integrated coefficient calculation system. This merging eliminates the need for multiple separate instructions and data transfers between registers, reducing the instruction count from many conventional instructions to a streamlined sequence that maintains precision while improving throughput.
Solution Approach 2:
The storage unit pre-stores mantissa parts of coefficients in a constant table during processor initialization or setup. This preliminary action eliminates the need for real-time calculation of mantissa values, allowing the selecting unit to directly retrieve pre-computed values during exponential function execution, thereby improving instruction throughput without sacrificing precision.
2Measurement precision
If multiple data transfers are performed between floating-point register and integer register for coefficient calculation, then accurate coefficient values are obtained, but processing time increases due to numerous instructions
Solution Approach 1:
The patent extracts the mantissa parts of coefficients from the calculation process and stores them separately in a dedicated storage unit (constant table). This extraction allows the selecting unit to directly retrieve pre-computed mantissa values without performing time-consuming data transfers and calculations during runtime, reducing processing time while maintaining coefficient accuracy.
Solution Approach 2:
The mantissa parts of coefficients are pre-calculated and stored in the storage unit before actual exponential function execution. This preliminary computation eliminates the need for time-consuming real-time calculations and multiple data transfers, significantly reducing processing time while ensuring accurate coefficient values are available when needed.
3Measurement precision
If integer arithmetic operations and bit operations are used for coefficient calculation, then precise control over coefficient values is achieved, but the number of instructions increases leading to performance deterioration
Solution Approach 1:
The patent merges the exponent generating unit, storage unit, and selecting unit into an integrated coefficient calculation system that operates within the floating-point arithmetic pipeline. This consolidation eliminates the need for separate integer arithmetic operations and bit manipulation instructions, reducing the instruction count while maintaining precise control over coefficient values through the coordinated operation of the integrated units.
Data Source
AI summary
A processor includes: an exponent generating unit that generates an exponent part of a coefficient represented by a floating point number format based on a first part of received input data, the coefficient being obtained when an exponential function is decomposed into a series operation and the coefficient for the series operation; a storage unit that stores a mantissa part of the coefficient; a constant generating unit that reads constant data corresponding to a second part of the input data from the storage unit; and a selecting unit that selects and outputs the constant data from the constant generating unit when an instruction to be executed is a coefficient calculation instruction for calculation of the coefficient of the exponential function.