Dynamic Multiplication Selection for Faster Decimal Remainders
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Solution Overview
Problem
Existing COBOL-based systems face inefficiencies in processing millions of arithmetic operations per second due to the varying computing cycles required by different multiplication algorithms for decimal number operations, particularly in calculating remainders, which can be optimized through dynamic selection based on input data.
Innovation Solution
A method for dynamically selecting a multiplication algorithm by determining the difference between operands, scaling them if necessary, estimating the number of quotient digits, and choosing between digit-wise and multi-digit multiplication algorithms based on this estimation to optimize computing cycles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a single multiplication algorithm is used for all operations, then the system is simple to implement, but the processing efficiency decreases due to varying computing cycles for different input sizes
Solution Approach 1:
The system dynamically selects between different multiplication algorithms (digit-wise vs. multi-digit) based on the characteristics of the input operands, specifically the number of digits in the divisor and dividend. This dynamic adaptation allows the system to optimize processing efficiency for each operation while maintaining a relatively simple overall structure through a decision-based selection mechanism.
Solution Approach 2:
The invention changes the algorithm selection based on parameters of the input data, specifically comparing the number of digits in the divisor and dividend against a threshold. When the difference exceeds the threshold, one algorithm is selected; otherwise, another algorithm is used. This parameter-based selection resolves the contradiction by adapting to input characteristics without requiring complex overhead.
2Use of energy by moving object
If the number of computing cycles is reduced through algorithm selection, then energy consumption decreases, but the system requires additional logic to determine which algorithm to use
Solution Approach 1:
The system performs a preliminary assessment of the input operands by comparing the number of digits in the divisor and dividend before executing the multiplication. This preliminary action determines which algorithm will be most efficient, allowing the system to avoid unnecessary computing cycles and reduce energy consumption from the outset, while the selection logic remains relatively simple.
Solution Approach 2:
The invention uses a simple parameter comparison (number of digits difference against a threshold) to drive algorithm selection. This parameter-based approach minimizes the complexity of the selection logic while effectively reducing the number of computing cycles required, thereby lowering energy consumption without requiring complex decision-making structures.
3Productivity
If digit-wise multiplication is used for all operations, then the algorithm is simple to implement, but it requires more computing cycles for larger numbers compared to multi-digit multiplication
Solution Approach 1:
The system dynamically adapts its multiplication approach based on the size of the input numbers. For smaller numbers where digit-wise multiplication is sufficient, it uses the simpler algorithm. For larger numbers where the difference in digit count exceeds a threshold, it switches to the more efficient multi-digit multiplication algorithm, thereby optimizing computing cycles while managing implementation complexity.
Solution Approach 2:
The invention changes the multiplication algorithm based on the parameter of input size, specifically the difference in the number of digits between divisor and dividend. This parameter-driven approach allows the system to use the simpler digit-wise algorithm when appropriate and the more efficient multi-digit algorithm when needed, resolving the contradiction between simplicity and efficiency.
Data Source
AI summary
Dynamic selection of a multiplication algorithm by receiving operands A and B, determining a difference between A and B, selecting a first multiplication algorithm if the difference falls below a threshold, selecting a second multiplication algorithm if the difference equals or exceeds the threshold, pre-scaling the operands, calculating a quotient for the scaled operands, back multiplying the quotient using the selected algorithm, yielding a product, subtracting the product from operand A, yielding a remainder, and providing the remainder as an output.