• Publications
  • Influence
On the rapid computation of various polylogarithmic constants
TLDR
These algorithms can be easily implemented, require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired make it feasible to compute the billionth binary digit of log(2) or π on a modest work station in a few hours run time.
Algorithms for quad-double precision floating point arithmetic
TLDR
The algorithms for various arithmetic operations (including the four basic operations and various algebraic and transcendental operations) on quad-double numbers are presented.
Design, implementation and testing of extended and mixed precision BLAS
TLDR
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 BLAS are described, which achieves excellent performance.
On the binary expansions of algebraic numbers
TLDR
By using number-theoretical analysis and extended computations, the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet the authors can also handle numbers with a substantially denser occurrence of 1's.
Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance
Recent computational advances allow investment managers to methodically search through thousands or even millions of potential options for a pro�table investment strategy. In many instances, the
Experimental Evaluation of Euler Sums
TLDR
Numerical computations using an algorithm that can determine, with high confidence, whether or not a particular numerical value can be expressed as a rational linear combination of several given constants are presented.
Mathematics by experiment - plausible reasoning in the 21st century
TLDR
Pi and its friends, and “Normality: A stubborn question,” from Mathematics by Experiment: Plausible Reasoning in the 21st Century, A. K. Peters, Natick, MA, 2nd edition, 2008.
On the Random Character of Fundamental Constant Expansions
TLDR
A theory to explain random behavior for the digits in the expansions of fundamental mathematical constants and proofs of base-2 normality for a collection of celebrated constants, including π, log 2, ζ(3), and others are proposed.
A Comparison of Three High-Precision Quadrature Schemes
TLDR
The objective here is a quadrature facility that can efficiently evaluate to very high precision a large class of integrals typical of those encountered in experimental mathematics, relying on a minimum of a priori information regarding the function to be integrated.
High-precision floating-point arithmetic in scientific computation
  • D. Bailey
  • Computer Science
    Computing in Science & Engineering
  • 31 December 2004
TLDR
Software packages have yielded interesting scientific results that suggest numeric precision in scientific computations could be as important to program design as algorithms and data structures.
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