Abstract Can An Evolutionary Process Create English Text? (2009)
Critics of the conventional theory of biological evolution have asserted that while natural processes might result in some limited diversity, nothing fundamentally new can arise from “random”...
High-Precision Computation and Mathematical Physics (2009)
David H. Bailey, Jonathan M. Borwein
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most sci-entific applications. However, for a rapidly growing body of important scientific computing...
Peri Auto-tuning, David H Bailey, Jacqueline Chame, Chun Chen, Jack Dongarra, Mary Hall, ...
Abstract. The enormous and growing complexity of today’s high-end systems has increased the already significant challenges of obtaining high performance on equally complex scientific applications....
A Hot Spot Proof of Normality for the Alpha Constants, available at (2009)
In [1] Richard Crandall and I establish p-normality (i.e., normality base p) for the class of constants αp,q = k=1 1 q k p qk where p and q are co-prime. The proof given in [1] is somewhat difficult...
Advances in the theory of box integrals (2009)
Bailey, David H., Borwein, Jonathan M., Crandall, Richard E.
Box integrals, being expectations such as $\langle |\vec r|^s \rangle$ or $\langle |\vec r - \vec q|^s \rangle$ with $\vec r, \vec q$ chosen randomly over the unit $n$-cube, have over the years been...
Experimental computation with oscillatory integrals (2009)
Bailey, David H., Borwein, Jonathan M.
A previous study by one of the present authors, together with D. Borwein and I. Leonard [7], studied the asymptotic behavior of the p-norm of the sinc function: sinc(x) = (sin x)/x and along the way...
A Strong Hot Spot Theorem (2008)
Abstract. A real number α is said to be b-normal if every mlong string of digits appears in the base-b expansion of α with limiting frequency b −m. We prove that α is b-normal if and only if it...
Introduction Welcome to the 21st Century: The Uncharted Future Ahead (2008)
The second half of the twentieth century was quite unlike any other 50-year period in human
Effective Bounds in Euler-Maclaurin-Based Quadrature (Summary for HPCS06) (2008)
We analyze the behavior of Euler-Maclaurin-based integration schemes with the intention of deriving accurate and economic estimations of the error. These schemes typically provide very high-precision...
Elliptic integral evaluations of Bessel moments (2008)
David H. Bailey, Jonathan M. Borwein, David Broadhurst, M. L. Glasser
We record what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. More generally, we...
Integer Relation Detection and Lattice Reduction (2008)
Let x =(x1,x2, ···,xn) be a vector of real or complex numbers. x is said to possess an integer relation if there exist integers ai, not all zero, such that a1x1 + a2x2 + ···+ anxn = 0 By an...
Advanced variational approach for high-precision bound-state calculations in (2008)
David H. Bailey, Alexei M. Frolov
three-body systems.
Elliptic integral evaluations of Bessel moments (2008)
Bailey, David H., Borwein, Jonathan M., Broadhurst, David, Glasser, M.L.
We record what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. More generally, we...
Performance Engineering: Understanding and Improving the Performance of Large-Scale Codes (2008)
Bailey, David H., Lucas, Robert, Hovland, Paul, Norris, Boyana, Yelick, Kathy, Gunter, Dan, ...
Durgin, Natalie J., Garcia, Sofia M., Flournoy, Tamara, Bailey, David H.
This work extends the analytical and computational investigation of the Quinn-Rand-Strogatz (QRS) constants from non-linear physics. The QRS constants (c1, c2, ..., cN) are found in a Winfree...
Effective Error Bounds in Euler-Maclaurin-Based Quadrature Schemes (2008)
Bailey, David H., Borwein, Jonathan M.
We analyze the behavior of Euler-Maclaurin-based integrationschemes with the intention of deriving accurate and economicestimations of the error term.
Hypergeometric Forms for Ising-Class Integrals (2008)
Bailey, David H., Borwein, David, Borwein, Jonathan M., Crandall, Richard E.
We apply experimental-mathematical principles to analyze certain integrals relevant to the Ising theory of solid-state physics. We find representations of the these integrals in terms of Meijer...
Performance modeling: Understanding the past and predicting the future (2008)
Abstract. We present an overview of current research in performance modeling, focusing on efforts underway in the Performance Evaluation Research Center (PERC). Using some new techniques, we are able...
Ten Problems in Experimental Mathematics (2008)
David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor, Eric W. Weisstein
Challenge ” of Nick Trefethen, beautifully described in [12] (seealso[13]). Indeed, these ten numeric challenge problems are also listed in [15, pp. 22–26], where they are followed by the ten...
Peter B. Borwein, David H. Bailey, Mathematics Experiment, ...
[Bai00] David H. Bailey, A compendium of BPP-type formulas for mathematical constants, manuscript, November 2000,
Government and no official endorsement should be inferred. (2008)
Xiaoyes. Li, James W. Demmel, David H. Bailey, Greg Henry, Yozo Hida, Jimmy Iskandar, ...
This article describes the design rationale, a C implementation, and conformance testing of a subset of the new Standard for the BLAS (Basic Linear Algebra Subroutines): Extended and Mixed Precision...
Elliptic integral evaluations of Bessel moments and applications (2008)
David H. Bailey, Jonathan M. Borwein, David Broadhurst, M. L. Glasser
We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical...
Resolving Numerical Anomalies in Scientific Computation (2008)
The increasing numbers of large scientific computer systems in use, together with the rapidly increasing scale of computations being attempted on such systems, means that numerical anomalies pose a...
Elliptic integral evaluations of Bessel moments and applications (2008)
David H. Bailey, Jonathan M. Borwein, David Broadhurst, M. L. Glasser
We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical...
Elliptic integral evaluations of Bessel moments and applications (2008)
David H Bailey, Jonathan M Borwein, David Broadhurst, M L Glasser
We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical...
Integer Relation Detection and Lattice Reduction (2007)
Let x =(x 1�x 2 � �xn) beavector of real or complex numbers. x is said to possess an integer relation if there exist integers ai, not all zero, such that a 1x 1 + a 2x 2 + + anxn = 0 By an...
Integer Relation Detection and Lattice Reduction (2007)
Introduction Let x = (x 1 ; x 2 ; \Delta \Delta \Delta ; x n ) be a vector of real or complex numbers. x is said to possess an integer relation if there exist integers a i , not all zero, such that a...
Array Transposition in SSD David H. Bailey October 3, 1989 (2007)
One obstacle to running very large two- and three-dimensional codes on the Cray X-MP and Y-MP systems is to efficiently perform array transpositions using SSD storage. This article discusses how such...
High Performance Computing Meets Experimental Mathematics (2007)
David H. Bailey, David Broadhurst, Yozo Hida, Xiaoye S. Li, Lawrence Berkeley, National Labratory, ...
In this paper we describe some novel applications of high performance computing in a discipline now known as “experimental mathematics. ” The paper reviews some recent published work, and then...
This note discuses Little's law and relates the form cited in queuing theory with a form often cited in the eld of high performance computing. A rigorous mathematical proof of Little's law...
the fractional Fourier transform is based on fractional roots of unity e (2007)
David H. Bailey, Paul N. Swarztrauber
available from the same web directory as this paper This paper describes the "fractional Fourier transform", which admits computation by an algorithm that has complexity...
Numerical Results on Relations Between Fundamental Constants Using a New Algorithm (2007)
Let x = (x 1; x 2; \Delta \Delta \Delta; x n) be a vector of real numbers. x is said to possess an integer relation if there exist integers a i not all zero such that a 1 x 1 + a 2 x 2 + \Delta...
Yozo Hida, Xiaoye S. Li, David H. Bailey
A quad-double number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of signicand. Algorithms for various arithmetic operations (including the...
Performance Engineering: Understanding and Improving the Performance of Large-Scale Codes (2007)
Achieving good performance on high-end computing systems is growing ever more challenging due to enormous scale, increasing architectural complexity, and increasing application complexity. To address...
Natalie J. Durgin, Sofia M. Garcia, David H. Bailey, Tamara Flournoy
This work extends the analytical and computational investigation of the Quinn-Rand-Strogatz (QRS) constants from non-linear physics. The QRS constants (c1, c2,... cN) are found in a Winfree...
Performance Engineering: Understanding and Improving the Performance of Large-Scale Codes (2007)
Achieving good performance on high-end computing systems is growing ever more challenging due to enormous scale, increasing architectural complexity, and increasing application complexity. To address...
Integrals of the Ising Class (2006)
Bailey, David H., Borwein, Jonathan M., Crandall, Richard E.
From an experimental-mathematical perspective we analyze "Ising-class" integrals. Our experimental results involved extreme-precision, multidimensional quadrature on intricate integrands; thus,...
Bailey, David H., Borwein, Jonathan M., Crandall, Richard E.
By a "box integral" we mean here an expectation $\langle |\vec r - \vec q|^s \rangle$ where $\vec r$runs over the unit $n$-cube, with $\vec q$ and $s$ fixed, explicitly:\begin eqnarray* &&\int_01...
Performance Modeling and Optimization of a High Energy Colliding Beam Simulation Code (2006)
Shan, Hongzhang, Strohmaier, Erich, Qiang, Ji, Bailey, David H., Yelick, Kathy
The BBP Algorithm for Pi (2006)
The “Bailey-Borwein-Plouffe ” (BBP) algorithm for π is based on the BBP formula for π, which was discovered in 1995 and published in 1996 [3]: π =
Ten Problems in Experimental Mathematics (2006)
David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor, Eric W. Weisstein
Challenge ” of Nick Trefethen, beautifully described in [12] (see also [13]). Indeed, these ten numeric challenge problems are also listed in [15, pp. 22–26], where they are followed by the ten...
Experimental Determination of Apéry-Like Identities for ζ(2n + 2) (2006)
David H. Bailey, Jonathan M. Borwein, David M. Bradley
We document the discovery of two generating functions for ζ(2n + 2), analogous to earlier work for ζ(2n + 1) and ζ(4n + 3), initiated by Koecher and pursued further by Borwein, Bradley and others....
Ten Problems in Experimental Mathematics (2006)
David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor, Eric W. Weisstein
Challenge ” of Nick Trefethen, beautifully described in [12] (see also [13]). Indeed, these ten numeric challenge problems are also listed in [15, pp. 22–26], where they are followed by the ten...
Background: Computing binary digits of log 2 What is now known as the “Bailey-Borwein-Plouffe ” (BBP) algorithm for π was discovered in 1995 and published in 1996 [3]. It all began when Peter...
Tanh-Sinh High-Precision Quadrature (2006)
In the past few years, computation of definite integrals to high precision has emerged as a very useful tool in experimental mathematics. In particular, it is often possible to recognize an otherwise...
Performance modeling and optimization of a high energy colliding beam simulation code (2006)
Hongzhang Shan, Erich Strohmaier, Ji Qiang, David H. Bailey, Kathy Yelick
An accurate modeling of the beam-beam interaction is essential to maximizing the luminosity in existing and future colliders. BeamBeam3D was the first parallel code that can be used to study this...
A Strong Hot Spot Theorem (2005)
Bailey, David H., Misiurewicz, Michal
A real number alpha is said to be b-normal if every m-long string of digits appears in the base-b expansion of alpha with limiting frequency b-m. We prove that alpha is b-normal if and only if it...
Performance Modeling: Understanding the Present and Predicting the Future (2005)
Bailey, David H., Snavely, Allan
We present an overview of current research in performance modeling, focusing on efforts underway in the Performance Evaluation Research Center (PERC). Using some new techniques, we are able to...
Future Prospects for Computer-Assisted Mathematics (2005)
Bailey, David H., Borwein, Jonathan M.
The recent rise of "computer-assisted" and "experimental" mathematics raises intriguing questions as to the future role of computation in mathematics. These results also draw into question the...
Positron Annihilation in the Bipositronium Ps2 (2005)
Bailey, David H., Frolov, Alexei M.
The electron-positron-pair annihlation in the bipositronium PS2 is considered. In particular, the two-, three-, one- and zero-photon annihlation rates are determined to high accuracy. The...
Experimental Determination of Apery-Like Identities for Zeta(2n+2) (2005)
Bailey, David H., Borwein, Jonathan M., Bradley, David M.
We document the discovery of two generating functions for zeta(2n+2), analogous to earlier work for zeta(2n+1) and zeta(4n+3), initiated by Koecher and pursued further by Borwein, Bradley and others.
Highly Parallel, High-Precision Numerical Integration (2005)
Bailey, David H., Borwein, Jonathan M.
This paper describes a scheme for rapidly computing numerical values of definite integrals to very high accuracy, ranging from ordinary machine precision to hundreds or thousands of digits, even for...
Experimental Mathemataics: Examples, Methods and Implications (2005)
Bailey, David H., Borwein, Jonathan M.
Recent years have seen the flowering of 'experimental' mathematics,namely the utilization of modern computer technology as an active toolin mathematical research. This development is not limited to a...
Performance Modeling: Understanding the present and predicting the future (2005)
David H. Bailey, Allan Snavely
We present an overview of current research in performance modeling, focusing on efforts underway in the Performance Evaluation Research Center (PERC). Using some new techniques, we are able to...
Future Prospects for Computer-Assisted Mathematics (2005)
David H. Bailey, Jonathan M. Borwein
The recent rise of “computer-assisted ” and “experimental ” mathematics raises intriguing questions as to the future role of computation in mathematics. These results also draw into question...
David H. Bailey, Jonathan M. Borwein
We analyze the behavior of Euler-Maclaurin-based integration schemes with the intention of deriving accurate and economic estimations of the error term. 1
David H. Bailey, Jonathan M. Borwein
We analyze the behavior of Euler-Maclaurin-based integration schemes with the intention of deriving accurate and economic estimations of the error term. 1
High-precision floating-point arithmetic in scientific computation (2005)
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing...
Performance Modeling: Understanding the present and predicting the future (2005)
David H. Bailey, Allan Snavely
Abstract. We present an overview of current research in performance modeling, focusing on efforts underway in the Performance Evaluation Research Center (PERC). Using some new techniques, we are able...
Experimental Mathematics: Examples, Methods and Implications (2005)
Jonathan M. Borwein, David H. Bailey, David H. Bailey, Lawrence Berkeley National
The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it. —Jacques Hadamard 1 If mathematics describes an objective...
High-Precision Floating-Point Arithmetic in Scientific Computation (2004)
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing...
A Pseudo-Random Number Generator Based on Normal Numbers (2004)
In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer b...
Ten Problems in Experimental Mathematics (2004)
Bailey, David H., Borwein, Jonathan M., Kapoor, Vishaal, Weisstein, Eric
This article was stimulated by the recent SIAM "100 Digit Challenge" of Nick Trefethen, beautifully described in a recent book. Indeed, these ten numeric challenge problems are also listed in a...
A Pseudo-Random Number Generator Based on Normal Numbers (2004)
In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is bnormal, for an integer b...
A comparison of three high-precision quadrature schemes (2004)
David H. Bailey, Karthik Jeyabalan, Xiaoye S. Li
The authors have implemented three numerical quadrature schemes, using the Arbitrary Precision (ARPREC) software package. The objective here is a quadrature facility that can efficiently evaluate to...
Ten Problems in Experimental Mathematics: (2004)
David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor, Eric Weisstein
This article was stimulated by the recent SIAM “100 Digit Challenge ” of Nick Trefethen,
Random generators and normal numbers (2004)
David H. Bailey, Richard E. Cr, For Example
Pursuant to the authors ' previous chaotic-dynamical model for random digits of fundamental constants [3], we investigate a complementary, statistical picture in which pseudorandom number...
On the binary expansions of algebraic numbers (2003)
Bailey, David H., Borwein, Jonathan M., Crandall, Richard E., Pomerance, Carl
Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic...
I will first give some historical background, condensed from [1]. Several of the commonly used algorithms for calculating π have their roots in classical arctangent-based formulas, such as tan −1...
High Performance Computing Meets Experimental Mathematics (2003)
David H. Bailey, David Broadhurst, Yozo Hida, Xiaoye S. Li, Lawrence Berkeley, National Labratory, ...
In this paper we describe some novel applications of high performance computing in a discipline now known as “experimental mathematics. ” The paper reviews some recent published work, and then...
Random Generators and Normal Numbers (2003)
David H. Bailey, Richard E. Crandall
Pursuant to the authors' previous chaotic-dynamical model for random digits of fundamental constants [5], we investigate a complementary, statistical picture in which pseudorandom number...
ARPREC: An arbitrary precision computation package (2002)
Bailey, David H., Yozo, Hida, Li, Xiaoye S., Thompson, Brandon
This paper describes a new software package for performing arithmetic with an arbitrarily high level of numeric precision. It is based on the earlier MPFUN package \cite mpf90, enhanced with special...
ARPREC: An arbitrary precision computation package (2002)
David H. Bailey, Yozo Hida, Xiaoye S. Li, On Thompson
This paper describes a new software package for performing arithmetic with an arbitrarily high level of numeric precision. It is based on the earlier MPFUN package [2], enhanced with special IEEE...
David H. Bailey, Daniel J. Rudolph
Lemma 1. (Birkoff ergodic theorem) Let f(t) be an integrable function on a measure space with probability measure µ, andletT be an ergodic transformation (i.e. T −1 A = A implies µ(A) =0or1)....
On the random character of fundamental constant expansions (2001)
David H. Bailey, Richard E. Cr
We propose a theory to explain random behavior for the digits in the expansions of fundamental mathematical constants. At the core of our approach is a general hypothesis concerning the distribution...
Algorithms for Quad-Double Precision Floating Point Arithmetic (2001)
Yozo Hida, Xiaoye S. Li, David H. Bailey
A quad-double number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of significand. We present the algorithms for various arithmetic operations...
ESP: A system utilization benchmark (2000)
Wong, Adrian T., Oliker, Leonid, Kramer, William T.C., Kaltz, Teresa L., Bailey, David H.
Algorithms for quad-double precision floating point arithmetic (2000)
Hida, Yozo, Li, Xiaoye S., Bailey, David H.
A quad-double number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of significand. We present the algorithms for various arithmetic operations...
ESP: A system utilization benchmark (2000)
Adrian T. Wong, Leonid Oliker, Teresa L. Kaltz, David H. Bailey
This article describes a new benchmark, called the Effective System Performance (ESP) test, which is designed to measure system-level performance, including such factors as job scheduling efficiency,...
Parallel Integer Relation Detection: Techniques and Applications (2000)
David H. Bailey, David J. Broadhurst
Let {x1,x2, ···,xn} be a vector of real numbers. An integer relation algorithm is a computational scheme to find the n integers ak, if they exist, such that a1x1 +a2x2 +···+ anxn = 0. In the...
A compendium of BBP-type formulas for mathematical constants (2000)
A 1996 paper by the author, Peter Borwein and Simon Plouffe showed that any mathematical constant given by an infinite series of a certain type has the property that its n-th digit in a particular...
Experimental Mathematics: Recent Developments and Future Outlook,” pp (2000)
David H. Bailey, Jonathan M. Borwein, Centre For Experimental
While extensive usage of high-performance computing has been a staple of other scientific and engineering disciplines for some time, research mathematics is one discipline that has heretofore not yet...
Quad-double arithmetic: Algorithms, implementation, and application (2000)
Yozo Hida, Xiaoye S. Li, David H. Bailey
A quad-double number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of significand. Algorithms for various arithmetic operations (including the...
ESP: A system utilization benchmark (2000)
Adrian T. Wong, Leonid Oliker, Teresa L. Kaltz, David H. Bailey
This article describes a new benchmark, called the Effective System Performance (ESP) test, which is designed to measure system-level performance, including such factors as job scheduling efficiency,...
ESP: A system utilization benchmark (2000)
Adrian T. Wong, Leonid Oliker, Teresa L. Kaltz, David H. Bailey
This article describes a new benchmark, called the Effective System Performance (ESP) test, which is designed to measure system-level performance, including such factors as job scheduling efficiency,...
Parallel Integer Relation Detection: Techniques and Applications (2000)
David H. Bailey, David J. Broadhurst
Let fx 1�x 2 � �xng be a vector of real numbers. An integer relation algorithm is a computational scheme to nd the n integers ak, if they exist, such that a 1x 1 +a 2x 2 + + anxn = 0. In the...
Quad-Double Arithmetic: Algorithms, Implementation, and Application (2000)
Yozo Hida, Xiaoye S. Li, David H. Bailey
A quad-double number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of signi cand. Algorithms for various arithmetic operations (including the...
Experimental Mathematics: Recent Developments and Future Outlook (2000)
David H. Bailey, Jonathan M. Borwein
This article briey discusses the nature of mathematical experiment. It then presents a few instances primarily of our own recent computeraided mathematical discoveries, and sketches the outlook for...
Parallel Integer Relation Detection: Techniques and Applications (2000)
David H. Bailey, J. Broadhurst
Abstract. Let {x1,x2, ·· ·,xn} be a vector of real numbers. An integer relation algorithm is a computational scheme to find the n integers ak, ifthey exist, such that a1x1 + a2x2 + ···+ anxn =...
Abstract Evaluating System Effectiveness in High Performance Computing Systems (1999)
Adrian T. Wong, Leonid Oliker, Teresa L. Kaltz, David H. Bailey
High performance scientific computer systems traditionally have been compared using individual job performance metrics. However, such metrics tend to ignore high-level system issues, such as how...
Analysis of PSLQ, An Integer Relation Finding Algorithm (1999)
Let K be either the real, complex, or quaternion number system and let O(K) be the corresponding integers. Let × = (Xl, • • • , ×n) be a vector in K n. The vector × has an integer relation...
Abstract Evaluating System Effectiveness in High Performance Computing Systems (1999)
Adrian T. Wong, Leonid Oliker, Teresa L. Kaltz, David H. Bailey
High performance scientific computer systems traditionally have been compared using individual job performance metrics. However, such metrics tend to ignore high-level system issues, such as how...
A Seventeenth-Order Polylogarithm Ladder (1999)
David H. Bailey, David J. Broadhurst
Cohen, Lewin and Zagier found four ladders that entail the polylogarithms Li n (ff \Gammak 1 ) := P r?0 ff \Gammakr 1 =r n at order n = 16, with indices k 360, and ff 1 being the smallest known Salem...
Parallel Integer Relation Detection: Techniques and Applications (1999)
David H. Bailey, David J. Broadhurst
Let fx 1 ; x 2 ; \Delta \Delta \Delta ; x n g be a vector of real numbers. An integer relation algorithm is a computational scheme to find the n integers a k , if they exist, such that a 1 x 1 +a 2 x...
Analysis of PSLQ, An Integer Relation Finding Algorithm (1999)
Abstract. Let K be either the real, complex, or quaternion number system and let O(K) be the corresponding integers. Let x =(x1,...,xn) be a vector in K n. The vector x has an integer relation if...
Analysis of PSLQ, An Integer Relation Finding Algorithm (1999)
Abstract. Let K be either the real, complex, or quaternion number system and let O(K) be the corresponding integers. Let x =(x1,...,xn) be a vector in K n. The vector x has an integer relation if...
Finding new mathematical identities via numerical computations (1998)
This note gives an overview some recent developments in computational mathematics, where high-precision numerical computations, together with advanced integer relation algorithms, have beenemployed...
Finding New Mathematical Identities via Numerical Computations (1998)
This note gives an overview some recent developments in computational mathematics, where high-precision numerical computations, together with advanced integer relation algorithms, have been employed...
On the rapid computation of various polylogarithmic constants (1997)
David H. Bailey, L Peter Borwein, Simon Plouffj
We give algorithms for the computation of the d-th digit of certain transcendental numbers in various bases. These algorithms can be easily implemented (multiple precision arithmetic is not needed),...
Onward to Petaflops Computing (1997)
Program (HPCCP), the attention of scientists and engineers worldwide has been focused on the potential of very high performance scientific computing, namely systems that are hundreds or thousands of...
On the Khintchine constant (1997)
David H. Bailey, Jonathan M. Borwein, Richard E. Cr
We present rapidly converging series for the Khintchine constant and for general “Khintchine means ” of continued fractions. We show that each of these constants can be cast in terms of an...
NAS Applications and Advanced Architectures (1997)
David H. Bailey, Rupak Biswas, Rob Van, Der Wijngaart
This paper examines the applications most commonly run on the supercomputers at the Numerical Aerospace Simulation (NAS) facility. It analyzes the extent towhichsuch applications are fundamentally...
Little’s law and high performance computing (1997)
This note discuses Little’s law and relates the form cited in queuing theory with a form often cited in the field of high performance computing. A rigorous mathematical proof of Little’s law is...
David H. Bailey, Jonathan M. Borwein, Peter B. Borwein, Simon Plouffe
Ref: Mathematical Intelligencer, vol. 19, no. 1 (Jan. 1997), pg. 50–57 This article gives a brief history of the analysis and computation of the mathematical constant π = 3.14159..., including a...
Ju Ne, David H. Bailey, Jonathan M. Borwein, Peter B. Borwein, Simon Plouffe
This article gives a brief history of the analysis and computation of the mathematical constant ß = 3:14159 : : :, including a number of the formulas that have been used to compute ß through the...
Analysis Of PSLQ, An Integer Relation Finding Algorithm (1997)
David H. Bailey, Steve Arno, Log Mx
. Let K be either the real, complex, or quaternion number system and let O(K) be the corresponding integers. Let x = (x 1 ; : : : ; xn ) be a vector in K n . The vector x has an integer relation if...
Recognizing Numerical Constants (1997)
David H. Bailey, Simon Plouffe
The advent of inexpensive, high-performance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist...
Intelligencer Vol, David H. Bailey, Jonathan M. Borwein, Peter B. Borwein, Simon Plouffe
This article gives a brief history of the analysis and computation of the mathematical constant ß = 3:14159 : : :, including a number of the formulas that have been used to compute ß through the...
NAS Applications and Advanced Architectures (1997)
David H. Bailey, Rupak Biswas, Rob Van
This paper examines the applications most commonly run on the supercomputers at the Numerical Aerospace Simulation (NAS) facility. It analyzes the extent to which such applications are fundamentally...
Recognizing Numerical Constants (1997)
David H. Bailey, Simon Plouffe
Abstract The advent of inexpensive, high-performance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques...
On the Khintchine Constant (1997)
David H. Bailey, Jonathan M. Borwein, Richard E. Crandall
We present rapidly converging series for the Khintchine constant and for general "Khintchine means" of continued fractions. We show that each of these constants can be cast in terms of an...
On the Khintchine constant (1997)
We present rapidly converging series for the Khintchine constant and for general \Khintchine means " of continued fractions. We showthateachof these constants can be cast in terms of an e...
On the Khintchine constant (1997)
David H. Bailey, Jonathan M. Borwein, E. Crandall
Abstract. We present rapidly converging series for the Khintchine constant and for general “Khintchine means ” of continued fractions. We show that each of these constants can be cast in terms of...
David H. Bailey, Ref Not Published
The “linear convolution ” of two n-long sequences x and y is commonly performed by extending the input sequences with zeroes to length 2p, wherep is the smallest power of two...
David H. Bailey, Ref Not Published
The "linear convolution " of two n-long sequences x and y is commonly performed by extending the input sequences with zeroes to length 2p, where p is the smallest power of two...
NAS Parallel Benchmark (Version 1.0) Results 11-96 (1996)
Subhash Saini, David H. Bailey, Sgi Origin
The NAS Parallel Benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputers. The eight benchmark problems are specified in a "pencil and...
David H. Bailey, Peter B. Borwein, Peter B. Borwein, Simon Plouffe
This article gives a brief history of the analysis and computation of the mathematical constant ß = 3:14159 : : :, including a number of the formulas that have been used to compute ß through the...
NAS parallel benchmark (version 1.0) results (1996)
Subhash Saini, David H. Bailey, Sgi Origin
The NAS Parallel Benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputers. The eight benchmark problems are specified in a ‘‘pencil and...
A fortran-90 based multiprecision system (1995)
The author has developed a new version of his Fortran multiprecision computation system that is based on the Fortran-90 language. With this new approach, a translator program is not required —...
Unfavorable strides in cache memory systems (1995)
Ref: Scienti c Programming, vol. 4 (1995), pg. 53{58 An important issue in obtaining high performance on a scienti c application running on a cache-based computer system is the behavior of the cache...
Recognizing numerical constants (1995)
David H. Bailey, Simon Plouffe
The advent of inexpensive, high-performance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist...
A fortran-90 based multiprecision system (1995)
The author has developed a new version of his Fortran multiprecision computation system that is based on the Fortran-90 language. With this new approach, a translator program is not required |...
NAS Parallel Benchmarks Results 3-95 (1995)
Subhash Saini, David H. Bailey
The NAS Parallel Benchmarks (NPB) were developed in 1991 at NASA Ames Research Center to study the performance of parallel supercomputers. The eight benchmark problems are specified in a "pencil...
A Fortran-90 Based Multiprecision System (1995)
The author has developed a new version of his Fortran multiprecision computation system that is based on the Fortran-90 language. With this new approach, a translator program is not required ---...
Unfavorable Strides in Cache Memory Systems David H. Bailey December 9, 1994 Ref: (1995)
Scientific Programming, David H. Bailey
An important issue in obtaining high performance on a scientific application running on a cache-based computer system is the behavior of the cache when data is accessed at a constant stride. Others...
NAS Parallel Benchmark Results 3-94 (1994)
David H. Bailey, Eric Barszcz, Leonardo Dagum, Horst D. Simon
The NAS Parallel Benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputers. The eight benchmark problems are specified in a "pencil and...
A fast method for the numerical evaluation of continuous Fourier and Laplace transforms (1994)
David H. Bailey, Paul N. Swarztrauber
The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems...
Experimental evaluation of Euler sums (1994)
David H. Bailey, Jonathan M. Borwein
In response to a letter from Goldbach, Euler considered sums of the form 1
Experimental Mathematics Vol, David H. Bailey, Jonathan M. Borwein
In response to a letter from Goldbach, Euler considered sums of the form 1 X k=1 ` 1 + 1 2 m + \Delta \Delta \Delta + 1 k m ' (k + 1) \Gamman for positive integers m and n. Euler was able to...
Nas Parallel Benchmark Results 3-94 (1994)
David H. Bailey, Eric Barszcz, Leonardo Dagum, Horst D. Simon
The NAS Parallel Benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputers. The eight benchmark problems are specified in a "pencil and...
NAS Parallel Benchmark Results 10-94 (1994)
David H. Bailey, Eric Barszcz, Leonardo Dagum, Horst D. Simon
The NAS Parallel Benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputers. The eight benchmark problems are specified in a "pencil and...
Experimental Evaluation of Euler Sums (1994)
David H. Bailey, Jonathan M. Borwein, Roland Girgensohn
this paper. It involves the compound application of the Euler--Maclaurin summation formula [Abramowitz and Stegun 1972, p. 806; Atkinson 1989, p. 289; Knuth 1973, p. 108], which 20 Experimental...
A Fortran-90 Based Multiprecision System (1994)
The author has developed a new version of his Fortran multiprecision computation system that is based on the Fortran-90 language. With this new approach, a translator program is not required ---...
Experimental Evaluation of Euler Sums (1994)
David H. Bailey, Jonathan M. Borwein, Roland Girgensohn
In response to a letter from Goldbach, Euler considered sums of the form 1 X k=1 ` 1 + 1 2 m + \Delta \Delta \Delta + 1 k m ' (k + 1) \Gamman for positive integers m and n. Euler was able to...
Multiprecision translation and execution of Fortran programs (1993)
This paper describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions...
Multiple precision, multiple processor vortex sheet roll-up computation (1993)
David H. Bailey, Robert Krasny, Richard Pelz
This paper describes a vortex sheet roll-up computation implemented using multiple precision arithmetic on a highly parallel computer (an Intel iPSC/860).
AFast Method for the Numerical Evaluation of Continuous Fourier and Laplace Transforms (1993)
David H. Bailey, Paul N. Swarztrauber
The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems...
RISC microprocessors and scienti c computing (1993)
This paper discusses design features in currently available RISC microprocessors that result in less-than-optimal sustained performance on large-scale scienti c calculations. Recommendations for...
Multiple precision, multiple processor vortex sheet roll-up computation (1993)
David H. Bailey, Robert Krasny, Richard Pelz
This paper describes a vortex sheet roll-up computation implemented using multiple precision arithmetic on a highly parallel computer (an Intel iPSC/SSO).
A Portable High Performance Multiprecision Package (1993)
The author has written a package of Fortran routines that perform a variety of arithmetic operations and transcendental functions on oating point numbers of arbitrarily high precision, including...
RISC microprocessors and scientific computing (1993)
This paper discusses design features in currently available RISC microprocessors that result in less-than-optimal sustained performance on large-scale scientific calculations. Recommendations for...
Multiprecision Translation and Execution of Fortran Programs (1993)
This paper describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions...
Abstract RISC Microprocessors and Scientific Computing (1993)
This paper discusses design features in currently available RISC microprocessors that result in less-than-optimal sustained performance on large-scale scientific calculations. Rec-ommendations for...
Misleading Performance Reporting in the Supercomputing Field (1992)
In a previous humorous note, I outlined twelve ways in which performance gures for scienti c supercomputers can be distorted. In this paper, the problem of potentially misleading performance...
Automatic translation of fortran programs to multiprecision (1992)
Previously the author developed a package of Fortran subroutines to perform a variety of arithmetic operations and transcendental functions on oating point numbers of arbitrarily high precision. This...
Misleading Performance Reporting in the Supercomputing Field (1992)
In a previous humorous note, I outlined twelve ways in which performance figures for scientific supercomputers can be distorted. In this paper, the problem of potentially misleading performance...
Misleading Performance Reporting in the Supercomputing Field (1992)
In a previous humorous note, I outlined twelve ways in which performance figures for scientific supercomputers can be distorted. In this paper, the problem of potentially misleading performance...
Multiple Precision, Multiple Processor Vortex Sheet Roll-Up Computation (1992)
David H. Bailey, Robert Krasny, Richard Pelz
This paper describes a vortex sheet roll-up computation implemented using multiple precision arithmetic on a highly parallel computer (an Intel iPSC/860). Bailey: NAS Applied Research Branch, NASA...
Misleading Performance Reporting in the Supercomputing Field David H. Bailey December 1, 1992 (1992)
In a previous humorous note, I outlined twelve ways in which performance figures for scientific supercomputers can be distorted. In this paper, the problem of potentially misleading performance...
Performance Results for Two of the NAS Parallel Benchmarks (1991)
David H. Bailey, Paul O. Frederickson
Two problems from the recently published “NAS Parallel Benchmarks ” have been implemented on three advanced parallel computer systems. These two benchmarks are the following: (1) an...
A Polynomial Time, Numerically Stable Integer Relation Algorithm (1991)
Let x =(x1,x2, ···,xn) be a vector of real numbers. x is said to possess an integer relation if there exist integers ai not all zero such that a1x1 + a2x2 + ·· · + anxn =0. Beginning in 1977...
Experience with Parallel Computers at NASA Ames (1991)
Beginning in 1988, the Numerical Aerodynamic Simulation (NAS) organization at NASA Ames Research Center has studied the usability of highly parallel computers on computational fluid dynamics and...
Using Strassen's Algorithm to Accelerate the Solution of Linear Systems (1991)
David H. Bailey, King Lee, Horst D. Simon
Abstract. Strassen's algorithm for fast matrix-matrix multiplication has been implemented for matrices of arbitrary shapes on the CRAY-2 and CRAY Y-MP supercomputers. Several techniques have...
The fractional Fourier transform and applications (1991)
David H. Bailey, Paul N. Swarztrauber
available from the same web directory as this paper This paper describes the \fractional Fourier transform", which admits computation by an algorithm that has complexity proportional to the...
Experiences with Parallel Computers at NASA/Ames NAS (1991)
Ref: Intl. J. of High Speed Computing, vol. 5, no. 1 (993), pg. 51{62. Beginning in 1988, the Numerical Aerodynamic Simulation (NAS) organization at NASA Ames Research Center has studied the...
FFTs in external or hierarchical memory (1990)
Conventional algorithms for computing large one-dimensional fast Fourier transforms (FFTs), even those algorithms recently developed for vector and parallel computers, are largely unsuitable for...
FFTs in external or hierarchical memory (1990)
Ref: Journal of Supercomputing, vol. 4, no. 1 (March 1990), p. 23--35 Conventional algorithms for computing large one-dimensional fast Fourier transforms (FFTs), even those algorithms recently...
Conventional algorithms for computing large one-dimensional fast Fourier transforms (FFTs), even those algorithms recently developed for vector and parallel computers, are largely unsuitable for...
Extra high speed matrix multiplication on the Cray-2 (1988)
The Cray-2 is capable of performing matrix multiplication at very high rates. Using library routines provided byCray Research, Inc., performance rates of 300 to 425 MFLOPS can be obtained on a single...
A High-Performance FFT Algorithm for Vector Supercomputers (1988)
Many traditional algorithms for computing the fast Fourier transform (FFT) on conventional computers are unacceptable for advanced vector and parallel computers because they involve nonunit,...
In a recent work [6], Borwein and Borwein derived a class of algorithms based on the theory of complete elliptic integrals that yield very rapidly convergent approximations to elementary constants....
Numerical Results on Relations Between Fundamental Constants Using a New Algorithm (1988)
Let x =(x 1�x 2 � �xn) beavector of real numbers. x is said to possess an integer relation if there exist integers ai not all zero such thata 1x 1 + a 2x 2 + + anxn =0. Beginning ten years ago,...
Numerical Results on the Transcendence of Constants Involving , e, and Euler's Constant (1988)
Let x =(x 1�x 2 � �xn) beavector of real numbers. x is said to possess an integer relation if there exist integers ai such that a 1x 1 + a 2x 2 + + anxn = 0. Recently Ferguson and Forcade...
Numerical Results on the Transcendence of Constants Involving , e, and Euler's Constant (1988)
Let x = (x 1; x 2; \Delta \Delta \Delta; x n) be a vector of real numbers. x is said to possess an integer relation if there exist integers a i such that a 1 x 1 +a 2 x 2 + \Delta \Delta \Delta +a n...
Extra high speed matrix multiplication on the Cray-2 (1988)
The Cray-2 is capable of performing matrix multiplication at very high rates. Using library routines provided by Cray Research, Inc., performance rates of 300 to 425 MFLOPS can be obtained on a...
In a recent work [6], Borwein and Borwein derived a class of algorithms based on the theory of complete elliptic integrals that yield very rapidly convergent approximations to elementary constants....
A High-Performance FFT Algorithm for Vector Supercomputers (1988)
Many traditional algorithms for computing the fast Fourier transform (FFT) on conventional computers are unacceptable for advanced vector and parallel computers because they involve nonunit,...
A High-Performance Fast Fourier Transform Algorithm for the Cray2 (1987)
Ref: Journal of Supercomputing, vol. 1, no. 1 (July 1987), pg. 43{60 Most implementations of a radix-2 fast Fourier transform on large scienti c computers use algorithms that involve memory accesses...
In a recent work [6], Borwein and Borwein derived a class of algorithms based on the theory of complete elliptic integrals that yield very rapidly convergent approximations to elementary constants....
A High-Performance Fast Fourier Transform Algorithm for the Cray2 (1987)
Ref: Journal of Supercomputing, vol. 1, no. 1 (July 1987), pg. 43--60 Most implementations of a radix-2 fast Fourier transform on large scientific computers use algorithms that involve memory...
Vector computer memory bank contention (1987)
A number of recent vector supercomputer designs have featured main memories with very large capacities, and presumably even larger memories are planned for future generations. While the memory chips...
Vector computer memory bank contention (1987)
Anumber of recent vector supercomputer designs have featured main memories with very large capacities, and presumably even larger memories are planned for future generations. While the memory chips...
NASA-lrM-112071 Abstract A High-Performance FFT Algorithm for Vector Supercomputers (1987)
Many traditional algorithms for computing the fast Fourier transform (FFT) on conventional computers are unacceptable for advanced vector and parallel computers because they involve nonunit,...
NASA-CR-203430 Abstract A High-Performance Fast Fourier Transform Algorithm for the Cray-2 (1986)
Most implementations of a radix-2 fast Fourier transform on large scientific computers use algorithms that involve memory accesses whose strides are powers of two. (The term str/de means the memory...
The David H. Bailey Papers (1958-2004) contain articles he wrote about the Church of Jesus Christ of Latter-day Saints (LDS Church), as well as articles by others on LDS Church subjects.; The David...
Onward to Petaflops Computing. (0000)
On December 16, 1996, a sustained rate of 1 teraflops was achieved by "ASCI Red," a system employing some 7,000 Intel Pentium Pro processors at Sandia National Laboratory in New Mexico. Much work...
Onward to Petaflops Computing.
On December 16, 1996, a sustained rate of 1 teraflops was achieved by "ASCI Red," a system employing some 7,000 Intel Pentium Pro processors at Sandia National Laboratory in New Mexico. Much work...