Related papers: Sound Mixed-Precision Optimization with Rewriting
Precision tuning or customized precision number representations is emerging, in these recent years, as one of the most promising techniques that has a positive impact on the footprint of programs concerning energy consumption, bandwidth…
Traditional optimization methods rely on the use of single-precision floating point arithmetic, which can be costly in terms of memory size and computing power. However, mixed precision optimization techniques leverage the use of both…
Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…
The high computational complexity of the multiple signal classification (MUSIC) algorithm is mainly caused by the subspace decomposition and spectrum search, especially for frequent real-time applications or massive sensors. In this paper,…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are…
This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of…
Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is…
Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.…
In recent years, half precision floating-point arithmetic has gained wide support in hardware and software stack thanks to the advance of artificial intelligence and machine learning applications. Operating at half precision can…
Numerical software is usually shipped with built-in hyperparameters. By carefully tuning those hyperparameters, significant performance enhancements can be achieved for specific applications. We developed MindOpt Tuner, a new automatic…
Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…
A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…