File: algo-refs.chapt.txt

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			References

[Abramowitz <i>et al.</i> 1964]
M. Abramowitz and I. A. Stegun,
<i>Handbook of Mathematical Functions</i>, National Bureau of Standards, Washington, D.C., 1964.

[Ahlgren <i>et al.</i> 2001]
S. Ahlgren and K. Ono,
<i>Addition and counting: the arithmetic of partitions</i>,
Notices of the AMS 48 (2001), p. 978.

[Bailey <i>et al.</i> 1997]
D. H. Bailey, P. B. Borwein, and S. Plouffe,
<i>On The Rapid Computation of Various Polylogarithmic Constants</i>,
Math. Comp. 66 (1997), p. 903.

[Bateman <i>et al.</i> 1953]
Bateman and Erdelyi,
<i>Higher Transcendental Functions</i>, McGraw-Hill, 1953.

[Beeler <i>et al.</i> 1972]
M. Beeler, R. W. Gosper, and R. Schroeppel,
Memo No. 239, MIT AI Lab (1972), now available online (the so-called "Hacker's Memo" or "HAKMEM").

[Borwein 1995]
P. Borwein,
<i>An efficient algorithm for Riemann Zeta function</i> (1995),
published online and in Canadian Math. Soc. Conf. Proc., 27 (2000), pp. 29-34.

[Borwein <i>et al.</i> 1999]
J. M. Borwein, D. M. Bradley, R. E. Crandall,
<i>Computation strategies for the Riemann Zeta function</i>, online preprint
CECM-98-118 (1999).

[Brent 1975]
R. P. Brent,
<i>Multiple-precision zero-finding methods and the complexity of elementary function evaluation</i>, in
<i>Analytic Computational Complexity</i>, ed. by J. F. Traub, Academic Press, 1975, p. 151; also available online from Oxford Computing Laboratory, as the paper {rpb028}.

[Brent 1976]
R. P. Brent,
<i>The complexity of multiple-precision arithmetic</i>,
Complexity of Computation Problem Solving, 1976;
R. P. Brent, 
<i>Fast multiple-precision evaluation of elementary functions</i>,
Journal of the ACM 23 (1976), p. 242.

[Brent 1978]
R. P. Brent, 
<i>A Fortran Multiple-Precision Arithmetic Package</i>,
ACM TOMS 4, no. 1 (1978), p. 57.

[Brent <i>et al.</i> 1980]
R. P. Brent and E. M. McMillan,
<i>Some new algorithms for high precision computation of Euler's constant</i>, Math. Comp. 34 (1980), p. 305.

[Crenshaw 2000]
J. W. Crenshaw,
<i>MATH Toolkit for REAL-TIME Programming</i>, CMP Media Inc., 2000.

[Damgard <i>et al.</i> 1993]
I. B. Damgard, P. Landrock and C. Pomerance, 
<i>Average Case Error Estimates for the Strong Probable Prime Test</i>,
Math. Comp. 61, (1993) pp. 177-194.

[Davenport <i>et al.</i> 1989]
J. H. Davenport, Y. Siret, and E. Tournier,
<i>Computer Algebra, systems and algorithms for algebraic computation</i>,
Academic Press, 1989.

[Davenport 1992]
J. H. Davenport,
<i>Primality testing revisited</i>, Proc. ISSAC 1992, p. 123.

[Fee 1990]
G. Fee,
<i>Computation of Catalan's constant using Ramanujan's formula</i>,
Proc. ISSAC 1990, p. 157; ACM, 1990.

[Godfrey 2001]
P. Godfrey (2001) (unpublished text):
<*http://winnie.fit.edu/~gabdo/gamma.txt*>.

[Gourdon <i>et al.</i> 2001]
X. Gourdon and P. Sebah,
<i>The Euler constant</i>;
<i>The Bernoulli numbers</i>;
<i>The Gamma Function</i>;
<i>The binary splitting method</i>;
and other essays, available online at <*http://numbers.computation.free.fr/Constants/*> (2001).

[Haible <i>et al.</i> 1998]
B. Haible and T. Papanikolaou,
<i>Fast Multiprecision Evaluation of Series of Rational Numbers</i>,
LNCS 1423 (Springer, 1998), p. 338.

[Johnson 1987]
K. C. Johnson,
<i>Algorithm 650: Efficient square root implementation on the 68000</i>,
ACM TOMS 13 (1987), p. 138.

[Kanemitsu <i>et al.</i> 2001]
S. Kanemitsu, Y. Tanigawa, and M. Yoshimoto,
<i>On the values of the Riemann zeta-function at rational arguments</i>,
The Hardy-Ramanujan Journal 24 (2001), p. 11.

[Karp <i>et al.</i> 1997]
A. H. Karp and P. Markstein,
<i>High-precision division and square root</i>,
ACM TOMS, vol. 23 (1997), p. 561.

[Knuth 1973]
D. E. Knuth,
<i>The art of computer programming</i>, Addison-Wesley, 1973.

[Lanczos 1964]
C. J. Lanczos,
J. SIAM of Num. Anal. Ser. B, vol. 1, p. 86 (1964).

[Luke 1975]
Y. L. Luke,
<i>Mathematical functions and their approximations</i>, Academic Press, N. Y., 1975.

[Olver 1974]
F. W. J. Olver,
<i>Asymptotics and special functions</i>, Academic Press, 1974.

[Pollard 1978]
J. Pollard,
<i>Monte Carlo methods for index computation mod p</i>,
Mathematics of Computation, vol. 32 (1978), pp. 918-924.

[Pomerance <i>et al.</i> 1980]
Pomerance et al.,
Math. Comp. 35 (1980), p. 1003.

[Rabin 1980]
M. O. Rabin, 
<i>Probabilistic algorithm for testing primality</i>,
J. Number Theory 12 (1980), p. 128.

[Smith 1989]
D. M. Smith,
<i>Efficient multiple-precision evaluation of elementary functions</i>, Math. Comp. 52 (1989), p. 131.

[Smith 2001]
D. M. Smith, 
<i>Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, Gamma and related functions</i>,
ACM TOMS 27 (2001), p. 377.

[Spouge 1994]
J. L. Spouge,
J. SIAM of Num. Anal. 31 (1994), p. 931.

[Sweeney 1963]
D. W. Sweeney,
Math. Comp. 17 (1963), p. 170.

[Thacher 1963]
H. C. Thacher, Jr.,
<i>Algorithm 180, Error function for large real X</i>,
Comm. ACM 6, no. 6 (1963), p. 314.

[Tsimring 1988]
Sh. E. Tsimring,
<i>Handbook of special functions and definite integrals: algorithms and programs for calculators</i>, Radio and communications (publisher), Moscow (1988) (in Russian).

[von zur Gathen <i>et al.</i> 1999]
J. von zur Gathen and J. Gerhard,
<i>Modern Computer Algebra</i>,
Cambridge University Press, 1999.