Mixed-Precision Floating-Point Operations in Programmable Integrated Circuits
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Solution Overview
Problem
In programmable integrated circuit devices, mixed-precision floating-point operations require excessive resources due to the need for promoting lower-precision operands to higher precision, leading to inefficient use of multipliers and increased resource consumption.
Innovation Solution
Configuring the device to perform multiplication and division operations by maintaining operands in their native precisions, breaking down operations into smaller segments, and using fewer multipliers, with exponents handled by higher-precision circuitry or general-purpose logic.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If lower-precision operands are promoted to higher precision before mixed-precision operations, then the higher precision of the higher-precision operand is maintained, but the number of multipliers required increases significantly
Solution Approach 1:
The patent segments the multiplication operation into separate handling of mantissa and exponent components. The mantissa multiplication is performed at the lower precision level, while the exponent addition is performed at the higher precision level, avoiding the need to promote the entire operand to higher precision
Solution Approach 2:
Different parts of the floating-point numbers are handled with different precision levels locally. The mantissa portion is processed at lower precision while the exponent portion is processed at higher precision, allowing each component to be handled at its native precision level
2Adaptability or versatility
If more multipliers are used to perform larger multiplications, then double-precision multiplication operations can be performed, but resource consumption increases
Solution Approach 1:
The patent divides the floating-point multiplication into separate operations: mantissa multiplication using available multipliers and exponent addition using specialized logic or general-purpose logic, allowing the system to perform double-precision operations without requiring proportional increases in multiplier quantity
Solution Approach 2:
The patent introduces an intermediary approach where the mantissa and exponent are processed separately through different computational paths, with the final result combining both components, thereby reducing the direct resource requirements for full double-precision multiplication
3Ease of operation
If the single-precision number is converted to double-precision for mixed-precision multiplication, then the operation can be performed as a double-precision operation, but up to 40% or more resource savings are lost
Solution Approach 1:
The patent segments the mixed-precision operation into mantissa handling at single precision and exponent handling at double precision, eliminating the need to convert the entire single-precision number to double-precision while maintaining operational correctness
Solution Approach 2:
The patent changes the precision parameter selectively for different components of the floating-point number, maintaining single precision for the mantissa and double precision for the exponent, thereby optimizing resource usage while preserving numerical accuracy
Data Source
AI summary
The resources needed—particularly in a programmable device—when carrying out a mixed-precision multiplication-based floating-point operation (i.e., multiplication or division) is reduced by maintaining the mantissas of the operands in their native precisions instead of promoting the lower-precision number to the higher precision. Exponents and other elements can be handled by the higher-precision logic as they do not consume significant resources.