Transcendental Function Unit Using Coordinate Rotation
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Solution Overview
Problem
General-purpose processors face high overheads and poor precision in performing transcendental function operations, while pure linear approximation methods are limited in precision and cannot meet the needs of advanced applications like scientific computing and image processing.
Innovation Solution
An apparatus comprising a pre-processing unit group, a core unit, and a post-processing unit group that performs trigonometric or hyperbolic transformations on input variables, using iteration to ensure fixed rotation angles and reduce power consumption by simplifying multiplication operations through shifting, thereby enhancing precision and efficiency in transcendental function calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If general-purpose processor is used to calculate transcendental functions, then versatility is improved, but power consumption increases and precision deteriorates
Solution Approach 1:
The patent divides the transcendental function calculation into three distinct segments: pre-processing unit group (for input transformation and mode determination), core unit (for trigonometric/hyperbolic transformation), and post-processing unit group (for final computation). This segmentation allows each unit to be optimized for its specific function, reducing overall power consumption while maintaining versatility across different transcendental functions.
Solution Approach 2:
The patent introduces an intermediary coordinate transformation system that converts various transcendental function inputs into a standardized format (x, y, z coordinates and angle) that can be processed by the core unit. This intermediary layer reduces the computational overhead and power consumption by avoiding direct complex calculations in the general-purpose processor.
2Adaptability or versatility
If general-purpose processor is used to calculate transcendental functions, then versatility is improved, but calculation precision deteriorates
Solution Approach 1:
By segmenting the calculation process into specialized units, the patent achieves higher precision in each stage. The pre-processing unit handles input transformation with high precision, the core unit performs accurate trigonometric/hyperbolic transformations, and the post-processing unit completes the calculation with maintained precision, overcoming the precision limitations of general-purpose processors.
Solution Approach 2:
The patent changes the representation parameters of transcendental functions from direct function calls to coordinate transformations involving x, y, z coordinates and angles. This parameter change enables more precise computation by utilizing optimized transformation algorithms that maintain numerical accuracy throughout the calculation process.
3Use of energy by moving object
If linear approximation method is used to calculate transcendental functions, then power consumption is reduced, but calculation precision deteriorates
Solution Approach 1:
The patent segments the calculation into pre-processing transformation, core unit transformation, and post-processing computation stages. This segmentation enables the system to achieve high precision through multiple transformation steps while maintaining reasonable power consumption by avoiding the need for extensive segmentation of the input domain required by pure linear approximation methods.
Solution Approach 2:
The patent changes from using linear approximation coefficients to using trigonometric/hyperbolic transformations with coordinate systems. This parameter change enables the system to achieve high precision without requiring the extensive domain segmentation that characterizes linear approximation methods, thereby reducing power consumption while maintaining accuracy.
4Adaptability or versatility
If general-purpose processor decodes transcendental function calculations, then versatility is improved, but processing time increases
Solution Approach 1:
The patent segments the processing architecture into dedicated units that handle specific transformation tasks. This segmentation eliminates the need for time-consuming instruction decoding and interpretation by general-purpose processors, as each unit performs its specific transformation in a single clock cycle, dramatically reducing processing time while maintaining versatility.
Solution Approach 2:
The patent replaces the mechanical instruction decoding and execution process of general-purpose processors with a direct hardware transformation system. The pre-processing unit group, core unit, and post-processing unit group perform transformations through dedicated hardware paths that operate without instruction decoding overhead, substituting the software-based mechanical process with a faster hardware-based system.
Data Source
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AI summary
The present invention discloses an apparatus and a method for performing a variety of transcendental function operations. The apparatus comprises a pre-processing unit group, a core unit and a post-processing unit group, wherein the pre-processing unit group is configured to transform an externally input independent variable a into x, y coordinates, an angle z, and other information k, and determine an operation mode to be used by the core unit; the core unit is configured to perform trigonometric or hyperbolic transformation on the x, y coordinates and the angle z, obtain transformed x', y' coordinates and angle z', and output them to the post-processing unit group; and the post-processing unit group is configured to transform the x', y' coordinates and the angle z' input by the core unit according to the other information k and a function f input by the pre-processing unit group to obtain an output result c. The present invention solves the problems of excessive overheads in the general-purpose processor manner and poor precision in the pure linear approximation manner, and efficiently strengthens the support for various transcendental function operations.