Arithmetic Processing Device Bypass Paths for Trig Function Efficiency
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Solution Overview
Problem
The existing arithmetic processing devices face a reduction in processing efficiency due to the need to execute multiply-add operations for Taylor series expansions of trigonometric functions only after completing auxiliary instructions, leading to inefficiencies in trigonometric function calculations.
Innovation Solution
The proposed arithmetic processing device includes a register file, coefficient memory, multiply-add arithmetic unit, multiplexers, OR circuits, and EOR circuits that allow for the calculation of trigonometric functions sin(x) and cos(x) by pre-processing expansion point identification data and using bypass paths to optimize the execution of auxiliary instructions and multiply-add operations, enabling efficient calculation of trigonometric functions without waiting for auxiliary instructions to complete.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If auxiliary instructions are executed before multiply-add operations for Taylor series expansion, then the trigonometric function calculation can be performed, but processing efficiency is reduced due to sequential execution
Solution Approach 1:
The patent pre-calculates and stores expansion point identification data (bxq) and coefficient data in bypass memory before the main calculation flow requires them. This preliminary action allows the multiply-add unit to immediately access pre-prepared data without waiting for auxiliary instructions to complete, thereby resolving the contradiction between calculation correctness and processing efficiency
Solution Approach 2:
The patent introduces bypass memory as an intermediary component that stores pre-calculated expansion point identification data and coefficients. This intermediary allows the main calculation path to proceed independently of the auxiliary instruction completion, enabling parallel execution and improving processing efficiency while maintaining calculation correctness
2Measurement precision
If auxiliary instructions are completed before executing multiply-add operations, then calculation accuracy is ensured, but processing time increases due to sequential execution
Solution Approach 1:
The expansion point identification data (bxq) and coefficient data are pre-calculated and stored in bypass memory before the multiply-add operations begin. This preliminary preparation ensures that accurate data is readily available when needed, maintaining calculation accuracy while eliminating the time loss associated with sequential execution
Solution Approach 2:
The patent enables continuous execution by allowing the multiply-add unit to operate continuously with pre-prepared data from bypass memory, rather than pausing to wait for auxiliary instructions. This continuity maintains calculation accuracy through proper data preparation while significantly reducing processing time
Data Source
AI summary
An arithmetic processing device includes a coefficient memory storing coefficients of a Taylor series expansion of a trigonometric function, a multiply-add arithmetic unit, a first bypass path supplying an output of the multiply-add arithmetic unit to a register file, an OR circuit calculating OR of a sign bit of the output of the multiply-add arithmetic unit and a least significant bit of a second input, a first selector selecting either a first input y or a value “1.0” an EOR circuit calculating an EOR of a first bit of the second input and a sign bit of an output of the first selector, and a second bypass path supplying the least significant bit of the second input to a coefficient selector. The multiply-add arithmetic unit executes an auxiliary instruction repeatedly while modifying a coefficient index from a maximum value to a minimum value to calculate sin (x).