Results 31 to 40 of about 95,300 (209)
Arbitrary-precision computation of the gamma function [PDF]
Maple Transactions, 2021 We discuss the best methods available for computing the gamma function Γ(z) in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small arguments; low or high ...
Fredrik Johansson
semanticscholar +1 more source
The Parallelism Tradeoff: Limitations of Log-Precision Transformers
Transactions of the Association for Computational Linguistics, 2023 Despite their omnipresence in modern NLP, characterizing the computational power of transformer neural nets remains an interesting open question. We prove that transformers whose arithmetic precision is logarithmic in the number of input tokens (and ...
William Merrill, Ashish Sabharwal
doaj +1 more source
Mathematics, 2021 In the present paper, a novel approach is introduced for the study, estimation and exact tracking of the finite precision error generated and accumulated during any number of multiplications.
Constantin Papaodysseus +4 more
doaj +1 more source
Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative
SIAM Journal on Matrix Analysis and Applications, 2022 . Existing algorithms for computing the matrix cosine are tightly coupled to a specific precision of floating-point arithmetic for optimal efficiency so they do not conveniently extend to an arbitrary precision environment.
Awad H. Al-Mohy, N. Higham, Xiaobo Liu
semanticscholar +1 more source
Computing hypergeometric functions rigorously [PDF]
, 2016 We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex parameters and ...
Johansson, Fredrik
core +5 more sources
PaCAL: A Python Package for Arithmetic Computations with Random Variables
Journal of Statistical Software, 2014 In this paper we present PaCAL, a Python package for arithmetical computations on random variables. The package is capable of performing the four arithmetic operations: addition, subtraction, multiplication and division, as well as computing many ...
Marcin Korze?, Szymon Jaroszewicz
doaj +1 more source
Correctly Rounded Arbitrary-Precision Floating-Point Summation [PDF]
, 2016 International audienceWe present a fast algorithm together with its low-level implementation of correctly rounded arbitrary-precision floating-point summation. The arithmetic is the one used by the GNU MPFR library: radix 2; no subnormals; each variable (
Lefèvre, Vincent
core +8 more sources
A Modified Staggered Correction Arithmetic with Enhanced Accuracy and Very Wide Exponent Range [PDF]
, 2008 A so called staggered precision arithmetic is a special kind of a multiple precision arithmetic based on the underlying floating point data format (typically IEEE double format) and fast floating point operations as well as exact dot product ...
Blomquist, Frithjof, Hofschuster, Werner
core +1 more source
Semantics, Specification Logic, and Hoare Logic of Exact Real Computation [PDF]
Logical Methods in Computer ScienceWe propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the algorithmic ...
Sewon Park +9 more
doaj +1 more source
Computing Puiseux series : a fast divide and conquer algorithm [PDF]
, 2017 Let $F\in \mathbb{K}[X, Y ]$ be a polynomial of total degree $D$ defined over a perfect field $\mathbb{K}$ of characteristic zero or greater than $D$. Assuming $F$ separable with respect to $Y$ , we provide an algorithm that computes the singular parts ...
Poteaux, Adrien, Weimann, Martin
core +5 more sources