Tootfinder

A Mathematics-Guided Approach to Floating-Point Error Detection
Youshuai Tan, Zhanwei Zhang, Zishuo Ding, Lianyu Zheng, Jinfu Chen, Weiyi Shang
https://arxiv.org/abs/2510.10081 …

A Mathematics-Guided Approach to Floating-Point Error Detection
Floating-point program errors can lead to severe consequences, particularly in critical domains such as military applications. Only a small subset of inputs may induce substantial floating-point errors, prompting researchers to develop methods for identifying these error-inducing inputs. Although existing approaches have achieved some success, they still suffer from two major limitations: (1) High computational cost: The evaluation of error magnitude for candidate inputs relies on high-precisio…

Ever wondered about #arithmetics in #JavaScript?
"For the most part, Javascript #numbers are double-precision floating point, so need to be treated the same as you would floating point…

from my link log —
Zmij: faster floating point double-to-string conversion.
https://vitaut.net/posts/2025/faster-dtoa/
saved 2025-12-14 https://

What Every Computer Scientist Should Know About Floating-Point Arithmetic #floats

OFP-Repair: Repairing Floating-point Errors via Original-Precision Arithmetic
Youshuai Tan, Zishuo Ding, Jinfu Chen, Weiyi Shang
https://arxiv.org/abs/2510.09938 https://…

OFP-Repair: Repairing Floating-point Errors via Original-Precision Arithmetic
Errors in floating-point programs can lead to severe consequences, particularly in critical domains such as military, aerospace, and financial systems, making their repair a crucial research problem. In practice, some errors can be fixed using original-precision arithmetic, while others require high-precision computation. Developers often avoid addressing the latter due to excessive computational resources required. However, they sometimes struggle to distinguish between these two types of erro…

Structured Sparsity and Weight-adaptive Pruning for Memory and Compute efficient Whisper models
Prasenjit K Mudi, Anshi Sachan, Dahlia Devapriya, Sheetal Kalyani
https://arxiv.org/abs/2510.12666

Structured Sparsity and Weight-adaptive Pruning for Memory and Compute efficient Whisper models
Whisper models have achieved remarkable progress in speech recognition; yet their large size remains a bottleneck for deployment on resource-constrained edge devices. This paper proposes a framework to design fine-tuned variants of Whisper which address the above problem. Structured sparsity is enforced via the Sparse Group LASSO penalty as a loss regularizer, to reduce the number of FLOating Point operations (FLOPs). Further, a weight statistics aware pruning algorithm is proposed. We also des…

Oh good! Someone from the @… community can weigh in on the benefits.
Oh wait…
Anyway, sooner or later the time for computable reals will come. I'm still HODLing stock in continued fractions (and teaching them every year to my first-year students).

Added 'a few' math tests to picolibc today. These create reference values using nickle with its arbitrary precision floating point arithmetic. The result is a list of functions which need work to improve their accuracy. Most are "close", with known errors of 1 or 2 ulp, but tgamma is in rough shape with errors of 56 ulp for binary64 and 97ulp for binary128. The complex functions are almost all in very rough shape with errors of thousands of ulps.

Microscaling Floating Point Formats for Large Language Models
Marco Cococcioni, Dario Pagani, Federico Rossi
https://arxiv.org/abs/2510.01863 https://arxiv…

Microscaling Floating Point Formats for Large Language Models
The increasing computational and memory demands of large language models (LLMs) necessitate innovative approaches to optimize resource usage without compromising performance. This paper leverages microscaling floating-point formats, a novel technique designed to address these challenges by reducing the storage and computational overhead associated with numerical representations in LLMs. Unlike traditional floating-point representations that allocate a dedicated scale for each value, microscalin…

:ruby: #Ruby's #Float contains interesting constants.
Like EPSILON, which is the
> difference between 1 and the smallest double-precision floating point number greater than 1.
What is it useful for, you ask?
Well, Floats are kinda difficult for computers and if you want to compare …

from my link log —
Floating point visually explained.
https://fabiensanglard.net/floating_point_visually_explained/
saved 2025-09-12 htt…

Hmm... Which would do a better job at driving physicists crazy? Travel
faster than light, or a floating-point boolean value?
-- Michael Mol

Performance and Numerical Aspects of Decompositional Factorizations with FP64 Floating-Point Emulation in INT8
Piotr Luszczek, Vijay Gadepally, LaToya Anderson, William Arcand, David Bestor, William Bergeron, Alex Bonn, Daniel J. Burrill, Chansup Byun, Michael Houle, Matthew Hubbell, Hayden Jananthan, Michael Jones, Peter Michaleas, Guillermo Morales, Julia Mullen, Andrew Prout, Albert Reuther, Antonio Rosa, Charles Yee, Jeremy Kepner

Performance and Numerical Aspects of Decompositional Factorizations with FP64 Floating-Point Emulation in INT8
Mixing precisions for performance has been an ongoing trend as the modern hardware accelerators started including new, and mostly lower-precision, data formats. The advantage of using them is a great potential of performance gain and energy savings. The disadvantage are the numerical issues not present in the standard-mandated floating-point formats. Split integer emulation of FP64 takes this to an extreme with the computation performed only by fixed-point tensor core units. We present the new …

parSAT: Parallel Solving of Floating-Point Satisfiability
Markus Krahl (University of Applied Sciences Munich HM), Matthias G\"udemann (University of Applied Sciences Munich HM), Stefan Wallentowitz (University of Applied Sciences Munich HM)
https://arxiv.org/abs/2509.16237

parSAT: Parallel Solving of Floating-Point Satisfiability
Satisfiability-based verification techniques, leveraging modern Boolean satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers, have demonstrated efficacy in addressing practical problem instances within program analysis. However, current SMT solver implementations often encounter limitations when addressing non-linear arithmetic problems, particularly those involving floating point (FP) operations. This poses a significant challenge for safety critical applications, where accur…

Hardware-Efficient CNNs: Interleaved Approximate FP32 Multipliers for Kernel Computation
Bindu G Gowda (International Institute of Information Technology Bangalore), Yogesh Goyal (International Institute of Information Technology Bangalore), Yash Gupta (International Institute of Information Technology Bangalore), Madhav Rao (International Institute of Information Technology Bangalore)

Hardware-Efficient CNNs: Interleaved Approximate FP32 Multipliers for Kernel Computation
Single-precision floating point (FP32) data format, defined by the IEEE 754 standard, is widely employed in scientific computing, signal processing, and deep learning training, where precision is critical. However, FP32 multiplication is computationally expensive and requires complex hardware, especially for precisely handling mantissa multiplication. In practical applications like neural network inference, perfect accuracy is not always necessary, minor multiplication errors often have little …

"What about the developers who start their careers during the 2020s? How will they deal with the ever-present issue of comparing floating-point values in a world that prefers TikTok to books? Well, they will probably ask an LLM how to do that, and not even bother about this issue anymore. Welcome to the future!"
ht…

The Smartest Concept In Computer Science
Every decade, programmers new to the industry must ingest a non-negligible amount of information in order to be proficient in their jobs. For the past five decades, however, this basic set of information has changed substantially, generating as a result a quite varied set of priorities in the minds of age-diverse programming teams.

Agora: Bridging the GPU Cloud Resource-Price Disconnect
Ian McDougall, Noah Scott, Joon Huh, Kirthevasan Kandasamy, Karthikeyan Sankaralingam
https://arxiv.org/abs/2510.05111 ht…

Agora: Bridging the GPU Cloud Resource-Price Disconnect
The historic trend of Moore's Law, which predicted exponential growth in computational performance per dollar, has diverged for modern Graphics Processing Units (GPUs). While Floating Point Operations per Second (FLOPs) capabilities have continued to scale economically, memory bandwidth has not, creating a significant price-performance disconnect. This paper argues that the prevailing time-based pricing models for cloud GPUs are economically inefficient for bandwidth-bound workloads. These mode…

from my link log —
Pezy SC: Japan is still investing in custom floating point accelerators.
https://www.nextplatform.com/2025/09/04/why-is-japan-still-investing-in-custom-floating-point-accelerators/
saved 202…

Why Is Japan Still Investing In Custom Floating Point Accelerators?
It has taken nearly two decades and an immense amount of work by millions of people for high performance computing to go mainstream with GenAI. And now,

Graphite: A GPU-Accelerated Mixed-Precision Graph Optimization Framework
Shishir Gopinath, Karthik Dantu, Steven Y. Ko
https://arxiv.org/abs/2509.26581 https://

Graphite: A GPU-Accelerated Mixed-Precision Graph Optimization Framework
We present Graphite, a GPU-accelerated nonlinear graph optimization framework. It provides a CUDA C++ interface to enable the sharing of code between a realtime application, such as a SLAM system, and its optimization tasks. The framework supports techniques to reduce memory usage, including in-place optimization, support for multiple floating point types and mixed-precision modes, and dynamically computed Jacobians. We evaluate Graphite on well-known bundle adjustment problems and find that it…

Greedy Thiele continued-fraction approximation on continuum domains in the complex plane
Tobin A. Driscoll, Yuxing Zhou
https://arxiv.org/abs/2510.07295 https://

Greedy Thiele continued-fraction approximation on continuum domains in the complex plane
We describe an adaptive greedy algorithm for Thiele continued-fraction approximation of a function defined on a continuum domain in the complex plane. The algorithm iteratively selects interpolation nodes from an adaptively refined set of sample points on the domain boundary. We also present new algorithms for evaluating Thiele continued fractions and their accessory weights using only a single floating-point division. Numerical experiments comparing the greedy TCF method with the AAA algorithm…

Algorithms and data structures for automatic precision estimation of neural networks
Igor V. Netay
https://arxiv.org/abs/2509.24607 https://arxiv.org/pdf/2…

Algorithms and data structures for automatic precision estimation of neural networks
We describe algorithms and data structures to extend a neural network library with automatic precision estimation for floating point computations. We also discuss conditions to make estimations exact and preserve high computation performance of neural networks training and inference. Numerical experiments show the consequences of significant precision loss for particular values such as inference, gradients and deviations from mathematically predicted behavior. It turns out that almost any neu…

A Novel Algorithm for Representing Positive Semi-Definite Polynomials as Sums of Squares with Rational Coefficients
Zhenbing Zeng, Yong Huang, Lu Yang, Yongsheng Rao
https://arxiv.org/abs/2510.01568

A Novel Algorithm for Representing Positive Semi-Definite Polynomials as Sums of Squares with Rational Coefficients
This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yield SOS decompositions with floating-point coefficients, our approach ensures that all coefficients in the decomposition remain rational. This is particularly useful in formal verification and symbolic computation, where exact arithmetic is required. We introduce a stepwise reduction technique that…

Stationary and stable varifolds with singularities
Camillo De Lellis, Jonas Hirsch, Luca Spolaor
https://arxiv.org/abs/2509.21508 https://arxiv.org/pdf/250…

Stationary and stable varifolds with singularities
We construct minimal $m$-dimensional immersions in $\mathbb{R}^{m+1}$, equipped with a $C^{m-1, α}$ metric, $α\in [0,1)$, with a sequence of catenoidal necks or floating disks converging to an isolated, multiplicity $2$, singular flat point.

from my link log —
Schubfach: The smallest state-of-the-art floating point double-to-string implementation.
https://vitaut.net/posts/2025/smallest-dtoa/
saved 2025-11-29

A Compact, Low Power Transprecision ALU for Smart Edge Devices
Ayushi Dube, Gian Singh, Sarma Vrudhula
https://arxiv.org/abs/2510.00333 https://arxiv.org/p…

A Compact, Low Power Transprecision ALU for Smart Edge Devices
Transprecision computing (TC) is a promising approach for energy-efficient machine learning (ML) computation on resource-constrained platforms. This work presents a novel ASIC design of a Transprecision Arithmetic and Logic Unit (TALU) that can support multiple number formats: Posit, Floating Point (FP), and Integer (INT) data with variable bitwidth of 8, 16, and 32 bits. Additionally, TALU can be reconfigured in runtime to support TC without overprovisioning the hardware. Posit is a new number…

"Truth is, on his smartphone, neither of these things were visible. Nor a push button, nor a shirt button, not a light switch, not a calculator button, not a door knob, not a push lever, nothing. What was visible was, instead, the blue word “Done” eerily floating in the top-right corner of the screen.
As my father said, there was no button."

The Button And The Spoon
As my father approaches his 80th birthday, his first contacts with the latest technologies become ever more interesting. As a pen-and-pencil architect and entrepreneur with 50 years of experience, technology is not a necessity; rather, just another useful tool. He setup his first fax machine at the end of the 90s, and got his first computer a decade after that. At some point in the 2010s he bought a smartphone, and one day asked me for help to finish some task on it. I remember his face when I …

Design and accuracy trade-offs in Computational Statistics
Tiancheng Xu, Alan L. Cox, Scott Rixner
https://arxiv.org/abs/2509.10934 https://arxiv.org/pdf/2…

Design and accuracy trade-offs in Computational Statistics
Statistical computations are becoming increasingly important. These computations often need to be performed in log-space because probabilities become extremely small due to repeated multiplications. While using logarithms effectively prevents numerical underflow, this paper shows that its cost is high in performance, resource utilization, and, notably, numerical accuracy. This paper then argues that using posit, a recently proposed floating-point format, is a better strategy for statistical com…