skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


This content will become publicly available on May 6, 2026

Title: Mixing Condition Numbers and Oracles for Accurate Floating-point Debugging
Recent advances have made numeric debugging tools much faster by using double-double oracles, and numeric analysis tools much more accurate by using condition numbers. But these techniques have downsides: double-double oracles have correlated error so miss floating-point errors while condition numbers cannot cleanly handle over- and underflow. We combine both techniques to avoid these downsides. Our combination, EXPLANIFLOAT, computes condition numbers using double- double arithmetic, which avoids correlated errors. To handle over- and underflow, it introduces a separate logarithmic oracle. As a result, EXPLANIFLOAT achieves a precision of 80.0% and a recall of 96.1% on a collection of 546 difficult numeric benchmarks: more accurate than double-double oracles yet dramatically faster than arbitrary-precision condition number computations.  more » « less
Award ID(s):
2346394
PAR ID:
10582085
Author(s) / Creator(s):
;
Editor(s):
Melquiond, Guillaume; Tang, Ping_Tak_Peter
Publisher / Repository:
IEEE ARITH
Date Published:
Subject(s) / Keyword(s):
floating-point debugging number systems
Format(s):
Medium: X
Location:
El Paso, Texas, USA
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Advances in neural information processing systems)
    Ranzato, M.; Beygelzimer, A.; Dauphin Y.; Liang, P.S.; Wortman Vaughan, J. (Ed.)
    Hyperbolic space is particularly useful for embedding data with hierarchical structure; however, representing hyperbolic space with ordinary floating-point numbers greatly affects the performance due to its \emph{ineluctable} numerical errors. Simply increasing the precision of floats fails to solve the problem and incurs a high computation cost for simulating greater-than-double-precision floats on hardware such as GPUs, which does not support them. In this paper, we propose a simple, feasible-on-GPUs, and easy-to-understand solution for numerically accurate learning on hyperbolic space. We do this with a new approach to represent hyperbolic space using multi-component floating-point (MCF) in the Poincar{\'e} upper-half space model. Theoretically and experimentally we show our model has small numerical error, and on embedding tasks across various datasets, models represented by multi-component floating-points gain more capacity and run significantly faster on GPUs than prior work. 
    more » « less
  2. ; ; (, 2020 ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI-2020))
    Posit is a recently proposed alternative to the floating point representation (FP). It provides tapered accuracy. Given a fixed number of bits, the posit representation can provide better precision for some numbers compared to FP, which has generated significant interest in numerous domains. Being a representation with tapered accuracy, it can introduce high rounding errors for numbers outside the above golden zone. Programmers currently lack tools to detect and debug errors while programming with posits. This paper presents PositDebug, a compile-time instrumentation that performs shadow execution with high pre- cision values to detect various errors in computation using posits. To assist the programmer in debugging the reported error, PositDebug also provides directed acyclic graphs of instructions, which are likely responsible for the error. A contribution of this paper is the design of the metadata per memory location for shadow execution that enables productive debugging of errors with long-running programs. We have used PositDebug to detect and debug errors in various numerical applications written using posits. To demonstrate that these ideas are applicable even for FP programs, we have built a shadow execution framework for FP programs that is an order of magnitude faster than Herbgrind. 
    more » « less
  3. ; ; ; ; ; ; ; ; ; ; et al (, Computing and Software for Big Science)
    Abstract The ATLAS experiment at the Large Hadron Collider has a broad physics programme ranging from precision measurements to direct searches for new particles and new interactions, requiring ever larger and ever more accurate datasets of simulated Monte Carlo events. Detector simulation with Geant4 is accurate but requires significant CPU resources. Over the past decade, ATLAS has developed and utilized tools that replace the most CPU-intensive component of the simulation—the calorimeter shower simulation—with faster simulation methods. Here, AtlFast3, the next generation of high-accuracy fast simulation in ATLAS, is introduced. AtlFast3 combines parameterized approaches with machine-learning techniques and is deployed to meet current and future computing challenges, and simulation needs of the ATLAS experiment. With highly accurate performance and significantly improved modelling of substructure within jets, AtlFast3 can simulate large numbers of events for a wide range of physics processes. 
    more » « less
  4. ; ; (, Quantum)
    Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity p o l y ( 1 / ϵ ) , where ϵ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be p o l y ( d , log ⁡ ( 1 / ϵ ) ) , where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations. 
    more » « less
  5. ; ; ; ; ; ; (, ACM)
    With the increasing importance of deep learning workloads, many hardware accelerators have been proposed in both academia and industry. However, software tooling for the vast majority of them does not exist compared to the software ecosystem and innovations proposed for established platforms such as CPUs and GPUs. We observed that the lack of well-de!ned hardware-software interfaces and correctness testing tools like fast and scalable test oracles (also known as functional simulators) act as significant barriers to adopting these emerging accelerators in the software community. These interfaces and tools are essential in building software such as retargetable compilers and optimized kernels. To bridge these gaps, we first present TAIDL, an instruction specification language that provides novel constructs to describe the instruction set architectures (ISAs) of tensor accelerators. Next, given ISA definitions in TAIDL, we introduce techniques to automatically generate fast and scalable test oracles for diverse sets of accelerators, which are needed for testing software correctness of code that targets pre-silicon hardware designs. Automated generation of such tools reduces the burden on hardware architects and the repeated development efforts required across different accelerator platforms. Further, our techniques allow us to execute these simulators on GPUs, leading to highly scalable simulations. To demonstrate the expressivity of TAIDL, we instantiated several tensor accelerator ISAs with different compute capabilities and memory hierarchies. Further, we show that test oracles generated using TAIDL definitions are orders of magnitude faster and more scalable than existing instruction-level functional simulators, making them suitable for integration into software development cycles. TAIDL is available at https://github.com/act-compiler/taidl. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email