Logarithmic Number System Processor with Lookup Table Addition
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Solution Overview
Problem
Implementing addition and subtraction operations in logarithmic number systems is computationally complex, reducing the efficiency of these systems in applications like signal processing and data transmission.
Innovation Solution
A processor with an execution unit that performs logarithmic addition and subtraction using a look-up table to efficiently map differences between numbers, allowing for efficient implementation of addition and subtraction operations by retrieving and adding or subtracting bias values based on predetermined thresholds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If logarithmic number system is used to represent numbers, then dynamic range and even spacing are improved, but addition and subtraction operations become computationally complex
Solution Approach 1:
The patent changes the operational parameters of logarithmic number system by introducing a lookup table that stores pre-computed logarithmic addition results. This transforms the complex continuous mathematical operation into discrete table lookups and simple additions, resolving the contradiction between maintaining dynamic range benefits and simplifying operational complexity
Solution Approach 2:
The patent introduces a lookup table as an intermediary structure that mediates between the two logarithmic numbers to be added. Instead of directly performing complex logarithmic addition, the system uses the lookup table to find pre-computed results, then performs simple addition with the first operand, greatly simplifying the operation while preserving accuracy
2Measurement precision
If traditional logarithmic addition method is used, then accuracy is maintained, but computational efficiency deteriorates
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing logarithmic addition results in a lookup table before actual operations are needed. This preparation work is done once and reused repeatedly, transforming complex real-time computations into simple table lookups and additions, thereby maintaining accuracy while dramatically improving computational efficiency
Data Source
AI summary
A processor comprising a register file comprising a bias register for holding a bias and a plurality of operand registers each for holding a respective number which together with the bias represents a respective value in a logarithmic number system; and an execution unit configured to, in response to receiving a logarithmic addition opcode: retrieve first and second numbers from first and second sources respectively; subtract the first number from the second number to determine a difference; and if the determined difference is less than or equal to a predetermined number, retrieve, from a look-up table, a third number mapped to the determined difference, and add the third number to the first number to determine a result; if the determined difference is greater than the predetermined number, determine the result to be the greatest of the first and second numbers; and store the result.