Reciprocal Approximation Circuit Using Operand MSBs
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Solution Overview
Problem
Conventional reciprocal approximation circuits for determining reciprocal values in image processing are bulky and consume a large area on integrated circuits due to the need for multiple multipliers and initial value selection circuits, which is undesirable for efficient image processing applications.
Innovation Solution
A reciprocal approximation circuit that includes a first bit-shifting circuit, a selection circuit, an adder, and a subtractor, which generates approximate reciprocal values by shifting and selecting operand multiples based on select bits, eliminating the need for additional multipliers and initial value selection circuits, thereby reducing chip area.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional reciprocal approximation circuits use multiple multipliers and initial value selection circuits, then the accuracy of reciprocal values is improved, but the chip area consumed increases significantly
Solution Approach 1:
The patent extracts and eliminates the initial value selection circuit from the conventional reciprocal approximation circuit. By directly using the most significant bits of the operand as the initial value for Newton-Raphson iteration, the circuit removes the need for separate initial value selection logic, thereby reducing chip area while maintaining accuracy through the iterative refinement process
Solution Approach 2:
The patent makes the operand itself serve multiple functions: it is both the input to be processed and the source of the initial value for iteration. The most significant bits of the operand directly provide the initial reciprocal estimate, eliminating the need for dedicated initial value selection circuits and reducing overall circuit complexity
2Speed
If conventional reciprocal approximation circuits include initial value selection circuits with memory and multiplexers, then the convergence speed is improved, but the device complexity increases
Solution Approach 1:
The patent removes the initial value selection circuit including memory and multiplexer components. Instead of storing multiple preset initial values and using multiplexers to select among them, the circuit directly uses the most significant bits of the operand as the initial value, significantly reducing device complexity while maintaining convergence performance
Solution Approach 2:
The operand itself provides the initial value information needed for the iteration process. The most significant bits of the operand serve as the initial reciprocal estimate, eliminating the need for external initial value selection circuits and making the system self-sufficient
3Measurement precision
If the Newton-Raphson method uses more iterations, then the accuracy of reciprocal values is improved, but the loss of time increases
Solution Approach 1:
The patent performs preliminary action by using the most significant bits of the operand as the initial value for Newton-Raphson iteration. This preliminary estimate is sufficiently accurate to require only 2-3 iterations to achieve the desired precision, reducing the total time compared to using less accurate initial values that would require more iterations
Data Source
AI summary
A reciprocal approximation circuit has a first iteration circuit for generating an approximate reciprocal value of an operand. The operation of the first iteration circuit is controlled by two bits of the operand, which indicate a range in which the operand lies. The first iteration circuit uses hardware friendly initial values based on the two bits for generating the approximate reciprocal value. The reciprocal approximation circuit does not require any additional circuit for selecting an initial value for the first iteration circuit.