Iterative Stage Dividend Prescaler for Fixed-Radix Division
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Solution Overview
Problem
Existing high fixed-radix division methods in integrated circuit devices require significant resources and delay due to prescaling both the dividend and divisor operands, particularly with larger dividends leading to lengthy carry chain propagation delays.
Innovation Solution
An iterative stage is introduced as a dividend operand prescaler, where the divisor is prescaled using a reciprocal estimate, and the dividend is apportioned into portions to be processed in a redundant number representation, reducing the need for extensive prescaling of the dividend and optimizing the prescaling process within the iteration engine.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If both dividend and divisor are prescaled using multipliers, then division accuracy is improved, but circuit complexity and delay increase significantly
Solution Approach 1:
The patent extracts the prescaling operation from a separate multiplier circuit and integrates it into the iterative division stage. The iterative stage performs both division and prescaling functions, eliminating the need for a dedicated prescaler circuit. This is achieved by using the iterative multiplication unit to compute prescaled values during the division process itself, thereby reducing overall circuit complexity while maintaining division accuracy.
Solution Approach 2:
The iterative division stage is designed to perform multiple functions: it conducts the division operation and simultaneously performs prescaling of the dividend. The same iterative multiplication unit used for division iterations is also employed for prescaling computations, making the circuit multi-functional and reducing the total number of required components.
2Measurement precision
If both dividend and divisor are prescaled using multipliers, then division accuracy is improved, but processing delay increases
Solution Approach 1:
The patent performs prescaling of the dividend during the first iteration of the division process rather than as a separate preliminary step. The iterative stage computes prescaled values on-the-fly during initialization, eliminating the need for a separate prescaling phase and reducing total processing delay while still achieving accurate division results.
Solution Approach 2:
The patent merges the prescaling operation with the division operation by using the same iterative multiplication unit for both purposes. The prescaling computations are integrated into the division algorithm's iteration process, allowing both functions to be performed simultaneously and reducing the overall processing time compared to sequential execution.
3Measurement precision
If a dedicated prescaler multiplier is used for dividend prescaling, then prescaling accuracy is improved, but resource consumption increases
Solution Approach 1:
The iterative multiplication unit serves dual purposes: it performs the main division iterations and also executes prescaling computations. By using the same hardware resources for both functions, the patent eliminates the need for a dedicated prescaler multiplier, thereby reducing circuit resource consumption while maintaining prescaling accuracy through proper algorithmic control.
Solution Approach 2:
The patent extracts the prescaling function from a separate dedicated circuit and integrates it into the existing iterative division infrastructure. This eliminates redundant hardware components while preserving the mathematical accuracy of prescaling operations through software-controlled iteration sequences.
Data Source
AI summary
Radix-based division is described. A dividend operand and a divisor operand are obtained. An estimate that is a reciprocal of the divisor operand is obtained. For a prescaling mode, a prescaling iteration is performed which includes: multiplying the divisor operand with the estimate to provide a prescaled divisor; apportioning the dividend operand into portions from most significant to least significant; providing the estimate to iteration blocks ordered from highest to lowest; providing the most significant to the least significant of the portions of the dividend operand respectively to the highest to the lowest of the iteration blocks; respectively multiplying the portions of the dividend operand with the estimate to provide first partial products; and parsing most significant residue portions and least significant residue portions as associated with order of the iteration blocks from the first partial products.