Research Opportunities in Hardware Design for Number System

Number System

Number system is the way of representing and manipulating numerical values in hardware. Different number systems have different trade-offs in terms of accuracy, range, performance, and energy efficiency. In this post, I will discuss some of the most common number systems used in hardware, such as IEEE 754 SP FP 32, half precision, bfloat, fixed point, integer based, FP8, INT4, and posit number system. I will also highlight their importance and application, challenges and open problems, recent advances and solutions, and future directions and opportunities.

Its importance and application

Number system is important for hardware design because it affects the quality and efficiency of computation. Depending on the application domain and the workload characteristics, different number systems may be more suitable than others. Some of the common number systems used in hardware are:

1. IEEE 754 Single Precision Floating Point (SP FP 32): This is the standard format for representing 32-bit floating point numbers, which can store values from about 1.18e-38 to 3.4e38 with 6-9 decimal digits of precision. It is widely used in scientific and engineering applications that require high dynamic range and accuracy.
2. Half Precision (HP): This is a 16-bit format that can store values from about 5.96e-8 to 6.55e4 with 3-4 decimal digits of precision. It is mainly used for graphics and machine learning applications that can tolerate lower accuracy and higher speed.
3. Bfloat (BF): This is a 16-bit format that has the same exponent range as SP FP 32 but only 7 bits for the significand. It is designed for deep learning applications that need high dynamic range but not high precision.
4. Fixed Point (FX): This is a format that uses a fixed number of bits for the integer and fractional parts of a number, such as Q15 (15 bits for the fractional part) or Q31 (31 bits for the fractional part). It is used for applications that require low latency and deterministic behavior, such as audio and video processing.
5. Integer Based (IB): This is a format that uses only integer values to represent numbers, such as INT8 (8-bit integers) or INT32 (32-bit integers). It is used for applications that do not need fractional values, such as indexing and hashing.
6. FP8, INT4: These are formats that use only 8 bits or 4 bits to represent numbers, respectively. They are mainly used for low-power and edge devices that have limited resources and bandwidth.
7. Posit Number System (PN): This is a novel format that uses a variable number of bits for the exponent and the significand, depending on the value of the number. It can achieve higher accuracy and dynamic range than SP FP 32 with fewer bits. It is still an emerging research topic that has potential applications in various domains. Refer Stanford Seminar: Beyond Floating Point: Next Generation Computer Arithmetic : https://www.youtube.com/watch?v=aP0Y1uAA-2Y

Challenges and open problems

One of the main challenges in hardware for number system is to find the optimal trade-off between accuracy, range, performance, and energy efficiency for different applications and workloads. There is no one-size-fits-all solution, and different number systems may have different advantages and disadvantages in different scenarios. Some of the open problems include:

1. How to design hardware architectures and circuits that can support multiple number systems and switch between them dynamically according to the application needs and the data characteristics?
2. How to design hardware algorithms and data structures that can exploit the features and benefits of different number systems, such as variable precision, tapered precision, and quire accumulation?
3. How to design hardware compilers and tools that can automatically generate and optimize code for different number systems and hardware platforms?
4. How to design hardware testing and verification methods that can ensure the correctness and robustness of different number systems and hardware implementations?
5. How to design hardware benchmarks and evaluation metrics that can measure and compare the performance and energy efficiency of different number systems and hardware platforms?

Recent advances and solutions

In recent years, there have been many advances and solutions in hardware for number system, both in academia and industry. Some of the examples are:

1. The New Hardware Development Trend and the Challenges in Data Management and Analysis(1), a paper that introduces the development trend of the new hardware in computation, storage, and network dimensions, and reviews the related research techniques that affect the upper data management system design.
2. Explainer: Number Representations in Computer Hardware(2), an article that explains the history and evolution of number representations in hardware, from the early inception of binary numbers to the modern world of floating point.
3. A systematic literature review on hardware implementation of artificial intelligence algorithms(3), a paper that covers hardware implementation research over the period between 2009 and 2019, and addresses the subject from three angles, namely application perspective, AI algorithms and tools perspective, and hardware platform perspective.
4. FlexFloat(https://github.com/oprecomp/flexfloat), an open-source library that enables the emulation of reduced-precision floating-point formats in software, and provides a flexible interface for tuning the precision and range of floating-point operations.
5. SoftPosit(https://gitlab.com/cerlane/SoftPosit), an open-source library that implements the posit number system in software, and supports various posit configurations and operations.
6. Posit-HDL(https://github.com/Posit-HDL), an open-source project that provides hardware implementations of the posit number system in Verilog, and supports various posit configurations and operations.

Future directions and opportunities

The field of hardware for number system is still evolving and expanding, and there are many opportunities for further research and innovation. Some of the possible future directions are:

1. Exploring new number systems and formats that can offer better trade-offs between accuracy, range, performance, and energy efficiency, such as logarithmic number system, unum number system, and stochastic number system.
2. Developing new hardware architectures and circuits that can support multiple number systems and formats, and enable dynamic and adaptive precision scaling and switching, such as reconfigurable computing, approximate computing, and neuromorphic computing.
3. Developing new hardware algorithms and data structures that can leverage the features and benefits of different number systems and formats, such as variable precision, tapered precision, and quire accumulation, and apply them to various domains and applications, such as machine learning, deep learning, scientific computing, and artificial intelligence.
4. Developing new hardware compilers and tools that can automatically generate and optimize code for different number systems and formats, and provide user-friendly interfaces and abstractions for programming and debugging.
5. Developing new hardware testing and verification methods that can ensure the correctness and robustness of different number systems and formats, and detect and handle errors and exceptions, such as overflow, underflow, rounding, and NaN.
6. Developing new hardware benchmarks and evaluation metrics that can measure and compare the performance and energy efficiency of different number systems and formats, and provide meaningful and realistic results and insights.

Hardware design for number systems is a fascinating and important research area that has many applications and implications for various fields and industries. I hope this post has given you some insights and inspirations about this topic.

(1) The New Hardware Development Trend and the Challenges in Data .... https://link.springer.com/article/10.1007/s41019-018-0072-6.

(2) Explainer: Number Representations in Computer Hardware. https://www.techspot.com/article/2630-number-representation-in-hardware/.

(3) A systematic literature review on hardware implementation of ... - Springer. https://link.springer.com/article/10.1007/s11227-020-03325-8.