**Algorithm 722: Functions to support the IEEE standard for binary floating-point arithmetic**

W. J. Cody, Jerome T. Coonen

Pages: 443-451

DOI: 10.1145/168173.168185

This paper describes C programs for the support functions copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x), and isnan(x) recommended in the Appendix to the IEEE Standard for Binary...

**Algorithm 723: Fresnel integrals**

W. van Snyder

Pages: 452-456

DOI: 10.1145/168173.168193

An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.

**Toward parallel mathematical software for elliptic partial differential equations**

Calvin J. Ribbens, Layne T. Watson, Colin Desa

Pages: 457-473

DOI: 10.1145/168173.168383

Three approaches to parallelizing important components of the mathematical software package ELLPACK are considered: an explicit approach using compiler directives available only on the target machine, an automatic approach using an optimizing...

**Applying series expansion to the inverse beta distribution to find percentiles of the F-distribution**

Roger W. Abernathy, Robert P. Smith

Pages: 474-480

DOI: 10.1145/168173.168387

Let 0 ≤ 1 and F be the cumulative distribution function (cdf) of the F-Distribution. We wish to find xp such that...

**Algorithm 724; Program to calculate F-Percentiles**

Roger W. Abernathy, Robert P. Smith

Pages: 481-483

DOI: 10.1145/168173.168405

Let 0← p ←1 be given and let F be the cumulative distribution function of the F-Distribution with (M, N,) degrees of freedom. This FORTRAN 77 routine is a complement to [1] where a...

**A remark on algorithm 643: FEXACT**: an algorithm for performing Fisher's exact test in r x c contingency tables

Douglas B. Clarkson, Yuan-an Fan, Harry Joe

Pages: 484-488

DOI: 10.1145/168173.168412

**A portable random number generator well suited for the rejection method**

W. Hörmann, G. Derflinger

Pages: 489-495

DOI: 10.1145/168173.168414

Up to now, all known efficient portable implementations of linear congruential random number generators with modulus 231 – 1 have worked only with multipliers that are small compared with the modulus. We show that for...

**Rounding errors in certain algorithms involving Markov chains**

Winfried K. Grassmann

Pages: 496-508

DOI: 10.1145/168173.168416

A number of algorithms involving Markov chains contain no subtractions. This property makes the analysis of rounding errors particularly simple. To show this, some principles for analyzing the propagation and generation of rounding errors in...

**A test problem generator for the Steiner problem in graphs**

B. N. Khoury, P. M. Pardalos, D.-Z. Du

Pages: 509-522

DOI: 10.1145/168173.168420

In this paper we present a new binary-programming formulation for the Steiner problem in graphs (SPG), which is well known to be NP-hard. We use this formulation to generate test problems with known optimal solutions. The technique uses the KKT...

**Implementation of a lattice method for numerical multiple integration**

Stephen Joe, Ian H. Sloan

Pages: 523-545

DOI: 10.1145/168173.168425

An implementation of a method for numerical multiple integration based on a sequence of imbedded lattice rules is given. Besides yielding an approximation to the integral, this implementation also provides an error estimate which does not...

**Corrigendum**: Algorithm 725: Computation of the multivariate normal integral

Zvi Drezner

Page: 546

DOI: 10.1145/168173.168428