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A Fortran Multiple-Precision Arithmetic Package

Editor: John R. Rice Author:

Richard P. BrentAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 4, Issue 1

Pages 57 - 70

https://doi.org/10.1145/355769.355775

Published: 01 March 1978 Publication History

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References

[1]

ABERTH, O. /ix precise numerical analysis program. Comm. ACM 17, 9 (Sept. 1974), 509-513.

Crossref

Google Scholar

[2]

ABRAMOWlTZ, M, AND STEGUN, I.A. Handbook of Mathematwal Function,s. Nat. Bur. of Standards, Washington, D.C., 1964.

Google Scholar

[3]

American National Standard Fortran (ANSI X3.9-1966), Amer. Nat. Standards Inst., New York, 1966. See also Comm. ACM 12, 5 (May 1969), 289-294 and Comm. ACM 1~, 10 (Oct. 1971), 628-642.

Google Scholar

[4]

BAE~, R M., AND REDLICH, M.G. Multiple-precision arithmetic and the exact calculation of the 3-j, 6-j, and 9-3 symbols. Comm. ACM 7, 11 (Nov. 1964), 657-659.

Crossref

Google Scholar

[5]

BEYER, W.A., AND WATERMAN, M.S. Decimals and partial quotients of Euler's constant and ln(2). Submitted to Math. Comput.

Google Scholar

[6]

BEYER, W.A., AND WATERMAN, M S. Error analysls of a computation of Euler's constant. Math. Comput. 28 (April 1974), 599-604.

Google Scholar

[7]

BLUM, B.I. An extended arithmetic package. Comm. ACM 8, (May 1965), 318-320.

Crossref

Google Scholar

[8]

BOGEN, R. MACSYMA Reference Manual, Vet 8. Mathlab. Group, Project MAC, M.I.T., Cambridge, Mass., 1975.

Google Scholar

[9]

BRENT, R.P. Algorithm 524. MP, A Fortran multzple-precision arithmetic package. ACM Trans. Math. Software ~, 1 (March 1978), 71-81.

Crossref

Google Scholar

[10]

BRENT, R P. Computation of the continued fraction for Euler's constant. Math. Compul. 81 (JuIy 1977), 771-777.

Google Scholar

[11]

BRI!~NT, R.P. Fast multiple-precision evaluation of elementary functions, d. ACM 23, 2 (April 1976), 242-251.

Crossref

Google Scholar

[12]

BRENT, R.P. Knuth's constants to 1000 decimal and 1100 octal places. Tech. Rep. 47, Comptr. Ctr., Australian National U., Canberra, Sept. 1975.

Google Scholar

[13]

BRENT, R.P. MP users guide Tech Rep. 54, Comptr. Ctr., Australian National U., Canberra, Sept. 1976.

Google Scholar

[14]

BRENT, R.P. Multiple-precision zero-finding methods and the complexity of elementary function evaluation. In Analytic Computational Complexity, J.F. Traub, Ed., Academic Press, New York, 1976, pp. 151-176.

Google Scholar

[15]

BR~NT, R.P. On the precision attainable with various floating-point number systems. IEEE Trans. Comptrs. C-22 (June 1973), 601-607.

Google Scholar

[16]

BRENT, R.P. Some high-order zero-finding methods using almost orthogonal polynomials. J. Auslral Math. Soc. Series B, 19 (1975), 1-29.

Google Scholar

[17]

BRENT, R.P. The complexity of multiple-precision arithmetic. In Complexity of Compuational Problem Solving, R S. Anderssen and R.P. Brent, Eds., U. of Queensland Press, Brisbane, 1976, pp. 126-165.

Google Scholar

[18]

COLLINS, G E. PM, A system for polynomial manipulation. Comm. ACM 9, 8 (Aug. 1966), 578-589.

Crossref

Google Scholar

[19]

DECKER, T.J. A floating-point technique for extending the available precision. Numer. Math. 18 (1971), 224-242.

Google Scholar

[20]

EHRMAN, J.R. A multiple-precision floating-point arithmetic package for System/360. Rep. CGTM 18, Stanford Linear Accelerator Ctr., Stanford, Calif., 1967.

Google Scholar

[21]

GA~ANT, D. C., AND BYRD, P.F. High accuracy gamma function values for some rational arguments. Math Comput. 22 (1968), 885-887

Google Scholar

[22]

GAUTSCHI, W Algorithm 236. Bessel functions of the first kind. Comm. ACM 7, 8 (Aug. 1964), 479-480.

Crossref

Google Scholar

[23]

GOSPER, R.W Acceleration of series. Memo 304, AI Lab, M.I.T., Cambridge, Mass., March 1974.

Crossref

Google Scholar

[24]

HART, J.F., ET AL. Computer Approx~matwns. Wiley, New York, 1968.

Google Scholar

[25]

I-IEttMITE, C. Oeuvres de Charles Hermzte, Vol. 2. Gauthier-ViUars, Paris, 1908, pp. 38-82.

Google Scholar

[26]

HILL, I D. Algorithm 34, Procedures for the basic arithmetical operations in multiplelength working. Computer J II (Aug. 1968), 232-235.

Google Scholar

[27]

HULL, T.E., AND HOFBAUER, J J. Language facilities for multiple-precision floating-point computation. Dept. Comptr. Sci, U. of Toronto, Toronto, Ont., 1974.

Google Scholar

[28]

JONES, H.S.P. Algorithm 72. Multiple integer arithmetic procedures in Algol. Computer J. 15 (1972), 281-282.

Google Scholar

[29]

~ARATSUBA, h., AND OFMAN, Y. Multiplication of multidigit numbers on automata. Dokl. Akad. Nauk SSSR 146 (1962), 293-394 (m Russian).

Google Scholar

[30]

KERNIGHAN, B.W, AND PLAUGER, P.J. The Elements of Programnting Style. McGraw-Hill, New York, 1974.

Crossref

Google Scholar

[31]

KNUTH, D.E. Euler's constant to 1271 places. Math. Comput. I6 (1962), 275-281.

Google Scholar

[32]

KNVTH, D.E. The Art of Computer Programming, Vol 2" Seminumerical Algorithms Addison Wesley, Reading, Mass, 1969

Crossref

Google Scholar

[33]

KUKI, H, AND CODY, W.J. A statistical study of the accuracy of floating-point number systems Comm. ACM 16, 4 (April 1973), 223-230.

Crossref

Google Scholar

[34]

LAWSON, C L Basic Q-precision arithmetic subroutines including input and output. Tech Memo 170, Jet Propulsion Lab., Pasadena, Cahf, Oct. 1967.

Google Scholar

[35]

LAWSON, C.L. Q-precision subroutines for the elementary functmns and aids for testing single-precision and double-precision function subroutines. Tech. Memo 188, Jet Propulsion Lab, Pasadena, Calif., April 1968.

Google Scholar

[36]

L.~WSON, C L Summary of Q-precision subroutines as revised in October 1968. Tech Memo 211, Jet Propulsion Lab, Pasadena, Calif., Jan 1969.

Google Scholar

[37]

LEHMER, D.H. Tables to many places of decimals. Math. Tables Aids Comput. 1 (1943), 30-31 (now Math Comput.).

Google Scholar

[38]

MAXIMON, L.C Fortran programs for arbitrary precision arithmetic. Rep. 10563, Nat. Bur. of Standards, Washington, D.C., April 1971.

Google Scholar

[39]

RAMANUJAN, S Collected Papers of Srinwasa Ramar~u3an Cambridge U. Press, Cambridge, 1927, pp 23-39.

Google Scholar

[40]

REID, C E, AND KNOBLE, H D. A multiple precision arithmetic package for the IBM 360/370 systems. SHARE Program Library, March 1974.

Google Scholar

[41]

RYDER, B.G The PFORT verffier Software--Practice and Experience ~ (1974), 359-377

Google Scholar

[42]

SALAMIS, E. Computation of ~r using arithmetic-geometrm mean. Math. Comput. SO (July 1976), 565-570.

Google Scholar

[43]

SCHONFELDER, J.L. The production of special function routines for a multi-machine library. Soft~xare--Pract~ce and E~pemence 6 (lC~7~), 71-82.

Google Scholar

[44]

SCHONFELDER, J L The testing of mathematical function software in a multi-machine enwronment. Tech. Rep. 107, Basser Dept Comptr. Scl., U. of Sydney, Sydney, Australm, Nov. 1975.

Google Scholar

[45]

SCHONFELDER, J.L., AND THOMASON, J.T. Applications support by direct language extension-an arbitrary precision arithmetic facility m Algol 68 Computer Ctr., U. of B~rmmgham, Birmingham, 1975.

Google Scholar

[46]

SC~ONHXGE, A, AND STRASSEN, V Schnelle Multiplikation grosser Zahlen. Computing 7 (1971), 281-292.

Google Scholar

[47]

SPIRA, R. Fortran multiple precision, Pt. 1, 2. Dept. of Math., Michigan State U., East Lansing, M1ch, 1973.

Google Scholar

[48]

SWEENEY, D.W. On the computation of Euler's constant. Math. Comput. 17 (1963), 170-178.

Google Scholar

[49]

TIENARt, M., AND SUOKONAUTIO, V A set of procedures making real arithmetic of unlimited accuracy possible within Algol 60. BIT 6 (1966), 322-338.

Google Scholar

[50]

WYATT, W.W., LOZIER, D.W., AND ORSER, D.J. A portable extended precision arithmetic package and l~brary with Fortran precompiler. Nat Bur. of Standards, Washington, D C, 1975; Trans. Math Software 2, 3 (Sept. 1976), 209-231.

Crossref

Google Scholar

[51]

CRARY, F.D. Multiple precision arithmetic design with an implementation on the Univac 1108. Tech. Summary Rep. 1123, Mathematics Research Center, U. of Wisconsin, Madison, Wis., 1971.

Google Scholar

[52]

CRARY, F.D. The Augment precompiler, Pt. I--User information. Tech. Summary Rep. 1469, Mathematics Research Center, U of Wisconsin, Madison, Wis. 1974 (revised April 1976)

Google Scholar

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Index Terms

A Fortran Multiple-Precision Arithmetic Package
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Arbitrary-precision arithmetic
      2. Interval arithmetic
  2. Mathematical software
2. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 4, Issue 1

March 1978

96 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/355769

Editor:
John R. Rice

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 1978

Published in TOMS Volume 4, Issue 1

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