Numeric Calculation Apparatus Using Lookup Table Reciprocal Multiplication
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Solution Overview
Problem
Current methods for performing division operations in computing devices, especially in multimedia processing, are inefficient as they require complex hardware and slow processing speeds, especially when dealing with floating-point operations and variable divisors.
Innovation Solution
A method and apparatus that use a lookup table to determine shift and index bits for a divisor scaled by an offset, allowing a multiplication operation followed by a right shift to emulate the division operation, thereby reducing hardware complexity and increasing processing speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a division operation is implemented with hardware, then the division function is achieved, but the hardware area occupied is majority of the total hardware area
Solution Approach 1:
The patent transforms the division operation into equivalent mathematical operations with different parameters - specifically converting division into multiplication by reciprocal values combined with bit shifting operations. This parameter transformation allows the same computational function to be achieved with significantly reduced hardware resources, replacing complex division circuits with simpler multiplication and shifting units.
Solution Approach 2:
The patent substitutes the mechanical division operation with an equivalent computational sequence involving multiplication and bit shifting. By replacing the direct division mechanism with this alternative computational path, the hardware complexity is dramatically reduced while maintaining the same functional outcome, thereby reducing the hardware area occupied.
2Productivity
If floating point operation is transformed into integer operation, then processing speed is increased and hardware resources are saved, but calculation precision may be reduced
Solution Approach 1:
The patent applies parameter transformation by introducing offset values and scaling factors that allow floating-point division to be emulated using integer operations. By adjusting the numerical parameters (adding offsets, scaling by powers of 2), the system achieves both speed improvement from integer operations and maintains precision through careful parameter selection and compensation techniques.
Solution Approach 2:
The patent introduces intermediate values and offset parameters as mediators between the floating-point division operation and integer arithmetic. These intermediary elements allow the transformation to preserve precision while enabling the use of faster integer operations, acting as a bridge that maintains accuracy during the speed-optimizing transformation.
3Device complexity
If division operation is replaced with multiplication and shift operations, then hardware complexity is reduced and processing speed is increased, but the implementation becomes more complex
Solution Approach 1:
The patent segments the division operation into distinct computational stages: determining the reciprocal, performing multiplication, applying offset corrections, and executing bit shifts. By dividing the operation into these manageable segments, the overall hardware complexity is reduced and each segment can be independently optimized and implemented, making the system easier to manufacture despite the multi-step process.
Solution Approach 2:
The patent performs preliminary actions by pre-calculating and storing reciprocal values in lookup tables before the actual division operation is needed. This preliminary preparation eliminates the need for complex real-time division circuits, reducing hardware complexity while the stored values are readily available for fast multiplication-based computation.
Data Source
AI summary
A method and apparatus for processing numeric calculation are provided. The method includes determining a shift bit and an index bit that falls within an index range of a lookup table from among bits representing a divisor scaled up by an offset, obtaining a replacement value corresponding to an index value of the determined index bit by using the lookup table, multiplying a dividend scaled up by the offset by the obtained replacement value, and outputting a value corresponding to a division operation by correcting a scale of a result of the multiplication using a right shift operation.