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Volumn 4, Issue 1, 1978, Pages 57-70

A Fortran Multiple-Precision Arithmetic Package

Author keywords

arithmetic; Bernoulli numbers; Bessel functions; elementary function evaluation; Euler's constant; exponential integral; extended precision; floating point; Fortran; gamma function; logarithmic integral; machine independent software; multiple precision; polyalgorithm; portable; software package; special function evaluation; zeta function

Indexed keywords

COMPUTER PROGRAMMING LANGUAGES - FORTRAN;

EID: 0017950568     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/355769.355775     Document Type: Article
Times cited : (143)

References (54)
  • 1
    • 0016101918 scopus 로고
    • precise numerical analysis program
    • Sept.
    • Aberth, O. A precise numerical analysis program. Comm. ACM 179 (Sept. 1974), 509-513.
    • (1974) Comm. ACM , vol.179 , pp. 509-513
    • Aberth, O.1
  • 3
    • 84976791744 scopus 로고
    • American National Standard Fortran ANSI X3
    • New York
    • American National Standard Fortran (ANSI X3.9-1966), Amer. Nat. Standards Inst., New York, 1966.
    • (1966) Amer. Nat. Standards Inst.
  • 4
    • 0014508064 scopus 로고
    • Comm. ACM 18, 5 (May 1969), 289-294.
    • (1969) Comm. ACM , vol.18 , Issue.5 , pp. 289-294
  • 5
    • 0015142475 scopus 로고
    • Oct.
    • Comm. ACM 14, 10 (Oct. 1971), 628-642.
    • (1971) Comm. ACM , vol.14 , Issue.10 , pp. 628-642
  • 6
    • 84945709667 scopus 로고
    • Multiple-precision arithmetic and the exact calculation of the 3-j, 6-j, and 9-j symbols
    • Nov.
    • Baek, R M., and Redlich, M.G. Multiple-precision arithmetic and the exact calculation of the 3-j, 6-j, and 9-j symbols. Comm. ACM 7, 11 (Nov. 1964), 657-659.
    • (1964) Comm. ACM , vol.7 , Issue.11 , pp. 657-659
    • Baek, R.M.1    Redlich, M.G.2
  • 7
    • 84976666975 scopus 로고    scopus 로고
    • Decimals and partial quotients of Euler's constant and In(2)
    • Submitted to
    • Beyer, W.A., AND Waterman, M.S. Decimals and partial quotients of Euler's constant and In(2). Submitted to Math. Comput.
    • Math. Comput.
    • Beyer, W.A.1    Waterman, M.S.2
  • 8
    • 84966222878 scopus 로고
    • Error analysis of a computation of Euler's constant
    • April
    • Beyer, W.A., AND Waterman, M S. Error analysis of a computation of Euler's constant. Math. Comput. 28 (April 1974), 599-604.
    • (1974) Math. Comput. , vol.28 , pp. 599-604
    • Beyer, W.A.1    Waterman, M.S.2
  • 9
    • 27144520033 scopus 로고
    • An extended arithmetic package
    • May
    • Blum, B.I. An extended arithmetic package. Comm. ACM 8, (May 1965), 318-320.
    • (1965) Comm. ACM , vol.8 , pp. 318-320
    • Blum, B.I.1
  • 10
    • 0011019140 scopus 로고
    • MACSYMA Reference Manual
    • Mathlab. Group, Project MAC, M.I.T., Cambridge, Mass.
    • Bogen, R. MACSYMA Reference Manual, Ver 8. Mathlab. Group, Project MAC, M.I.T., Cambridge, Mass., 1975.
    • (1975)
    • Bogen, R.1
  • 11
    • 84976818612 scopus 로고    scopus 로고
    • Algorithm 524. MP, A Fortran multiple-precision arithmetic package
    • Brent, R.P. Algorithm 524. MP, A Fortran multiple-precision arithmetic package. ACM Trans. Math. Software 4, 1 (March 1978), 71-81.
    • ACM Trans. Math. Software , vol.4 , Issue.1 , pp. 71-81
    • Brent, R.P.1
  • 12
    • 84966236204 scopus 로고
    • Computation of the continued fraction for Euler's constant
    • July
    • Brent, R P. Computation of the continued fraction for Euler's constant. Math. Comput. 31 (July 1977), 771-777.
    • (1977) Math. Comput. , vol.31 , pp. 771-777
    • Brent, R.P.1
  • 13
    • 0016939583 scopus 로고
    • Fast multiple-precision evaluation of elementary functions
    • April
    • Brent, R.P. Fast multiple-precision evaluation of elementary functions. J. ACM 83, 2 (April 1976), 242-251.
    • (1976) J. ACM , vol.83 , Issue.2 , pp. 242-251
    • Brent, R.P.1
  • 14
    • 84976856407 scopus 로고
    • Knuth's constants to 1000 decimal and 1100 octal places
    • Comptr. Ctr., Australian National U., Canberra, Sept.
    • Brent, R.P. Knuth's constants to 1000 decimal and 1100 octal places. Tech. Rep. 47, Comptr. Ctr., Australian National U., Canberra, Sept. 1975.
    • (1975) Tech. Rep. , pp. 47
    • Brent, R.P.1
  • 15
    • 84976757343 scopus 로고
    • Comptr. Ctr., Australian National U., Canberra, Sept.
    • Brent, R.P. MP users guide Tech Rep. 54, Comptr. Ctr., Australian National U., Canberra, Sept. 1976.
    • (1976) MP users guide Tech Rep. , pp. 54
    • Brent, R.P.1
  • 16
    • 0141591962 scopus 로고
    • Multiple-precision zero-finding methods and the complexity of elementary function evaluation
    • J.F. Traub, Ed., Academic Press, New York
    • 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.
    • (1976) Analytic Computational Complexity , pp. 151-176
    • Brent, R.P.1
  • 17
    • 0015631003 scopus 로고
    • On the precision attainable with various floating-point number systems
    • June
    • Brent, R.P. On the precision attainable with various floating-point number systems. IEEE Trans. Comptrs. 22 (June 1973), 601-607.
    • (1973) IEEE Trans. Comptrs. , vol.22 , pp. 601-607
    • Brent, R.P.1
  • 18
    • 84976779937 scopus 로고
    • Some high-order zero-finding methods using almost orthogonal polynomials
    • Brent, R.P. Some high-order zero-finding methods using almost orthogonal polynomials. J. Austral Math. Soc. Series B, 19 (1975), 1-29.
    • (1975) J. Austral Math. Soc. Series B , vol.19 , pp. 1-29
    • Brent, R.P.1
  • 19
    • 1842605930 scopus 로고
    • The complexity of multiple-precision arithmetic
    • R S. Anderssen and R.P. Brent, Eds., U. of Queensland Press, Brisbane
    • Brent, R.P. The complexity of multiple-precision arithmetic. In Complexity of Computational Problem Solving, R S. Anderssen and R.P. Brent, Eds., U. of Queensland Press, Brisbane, 1976, pp. 126-165.
    • (1976) Complexity of Computational Problem Solving , pp. 126-165
    • Brent, R.P.1
  • 20
    • 84915523417 scopus 로고
    • system for polynomial manipulation
    • Aug.
    • Collins, G.E.P.M., A system for polynomial manipulation. Comm. ACM 9, 8 (Aug. 1966), 578-589.
    • (1966) Comm. ACM , vol.9 , Issue.8 , pp. 578-589
    • Collins, G.E.P.M.1
  • 21
    • 0000810983 scopus 로고
    • floating-point technique for extending the available precision
    • Dekker, T.J. A floating-point technique for extending the available precision. Numer. Math. 18 (1971), 224-242.
    • (1971) Numer. Math. , vol.18 , pp. 224-242
    • Dekker, T.1
  • 22
    • 84976802799 scopus 로고
    • multiple-precision floating-point arithmetic package for System/360
    • Rep. CGTM18, Stanford Linear Accelerator Ctr., Stanford, Calif.
    • Ehrman, J.R. A multiple-precision floating-point arithmetic package for System/360. Rep. CGTM18, Stanford Linear Accelerator Ctr., Stanford, Calif., 1967.
    • (1967)
    • Ehrman, J.R.1
  • 23
    • 84968498682 scopus 로고
    • High accuracy gamma function values for some rational arguments
    • Galant, D. C., AND Byrd, P.F. High accuracy gamma function values for some rational arguments. Math Comput. 88 (1968), 885-887
    • (1968) Math Comput. , vol.88 , pp. 885-887
    • Galant, D.C.1    Byrd, P.F.2
  • 24
    • 0343680089 scopus 로고
    • Algorithm 236. Bessel functions of the first kind
    • Aug.
    • Gautschi, W. Algorithm 236. Bessel functions of the first kind. Comm. ACM 7, 8 (Aug. 1964), 479-480.
    • (1964) Comm. ACM , vol.7 , Issue.8 , pp. 479-480
    • Gautschi, W.1
  • 25
    • 0343587912 scopus 로고
    • Acceleration of series
    • Memo AI Lab M.I.T., Cambridge, Mass., March
    • Gosper, R.W. Acceleration of series. Memo 304, AI Lab M.I.T., Cambridge, Mass., March 1974.
    • (1974) , pp. 304
    • Gosper, R.W.1
  • 27
  • 28
    • 84918382294 scopus 로고    scopus 로고
    • Algorithm 34, Procedures for the basic arithmetical operations in multiple-length working
    • Hill, I D. Algorithm 34, Procedures for the basic arithmetical operations in multiple-length working. Computer J 11 (Aug. 1968), 232-235.
    • Computer J , vol.11 , pp. 232-235
    • Hill, I.D.1
  • 29
    • 84976673843 scopus 로고
    • Language facilities for multiple-precision floating-point computation
    • U. of Toronto, Toronto, Ont.
    • Hull, T.E., AND Hofbauer, J J. Language facilities for multiple-precision floating-point computation. Dept. Comptr. Sci U. of Toronto, Toronto, Ont., 1974.
    • (1974) Dept. Comptr. Sci
    • Hull, T.E.1    Hofbauer, J.J.2
  • 30
    • 84976671831 scopus 로고
    • Algorithm 72. Multiple integer arithmetic procedures in Algol
    • Jones, H.S.P. Algorithm 72. Multiple integer arithmetic procedures in Algol. Computer J. 15 (1972), 281-282.
    • (1972) Computer J. , vol.15 , pp. 281-282
    • Jones, H.S.P.1
  • 31
    • 0005395785 scopus 로고
    • Multiplication of multidigit numbers on automata
    • (in Russian).
    • Karatsuba, A., AND Ofman, Y. Multiplication of multidigit numbers on automata. Dokl. Akad. Nauk SSSR 146 (1962), 293-394 (in Russian).
    • (1962) Dokl. Akad. Nauk SSSR , vol.146 , pp. 293-394
    • Karatsuba, A.1    Ofman, Y.2
  • 33
    • 84968466607 scopus 로고
    • Euler's constant to 1271 places
    • Knuth, D.E. Euler's constant to 1271 places. Math. Comput. 16 (1962), 275-281.
    • (1962) Math. Comput. , vol.16 , pp. 275-281
    • Knuth, D.E.1
  • 34
    • 0003657590 scopus 로고
    • Seminumerical Algorithms, Addison Wesley, Reading, Mass
    • Knuth, D.E. The Art of Computer Programming, Vol 2. Seminumerical Algorithms, Addison Wesley, Reading, Mass 1969
    • (1969) The Art of Computer Programming , vol.2
    • Knuth, D.E.1
  • 35
    • 0015616992 scopus 로고
    • A statistical study of the accuracy of floating-point number systems
    • April
    • 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.
    • (1973) Comm. ACM , vol.16 , Issue.4 , pp. 223-230
    • Kuki, H.1    Cody, W.J.2
  • 36
    • 84945711118 scopus 로고
    • Basic Q-precision arithmetic subroutines including input and output
    • Tech Memo Jet Propulsion Lab., Pasadena, Calif Oct.
    • Lawson, C L Basic Q-precision arithmetic subroutines including input and output. Tech Memo 170, Jet Propulsion Lab., Pasadena, Calif Oct. 1967.
    • (1967) , pp. 170
    • Lawson, C.L.1
  • 37
    • 84976760196 scopus 로고
    • Q-precision subroutines for the elementary functions and aids for testing single-precision and double-precision function subroutines
    • Jet Propulsion Lab Pasadena, Calif., April
    • Lawson, C.L. Q-precision subroutines for the elementary functions and aids for testing single-precision and double-precision function subroutines. Tech. Memo 188, Jet Propulsion Lab Pasadena, Calif., April 1968.
    • (1968) Tech. Memo , pp. 188
    • Lawson, C.L.1
  • 38
    • 84976761563 scopus 로고
    • Summary of Q-precision subroutines as revised in October
    • Jet Propulsion Lab Pasadena, Calif., Jan
    • Lawson, C L Summary of Q-precision subroutines as revised in October 1968. Tech Memo 211, Jet Propulsion Lab Pasadena, Calif., Jan 1969.
    • (1968) , pp. 211
    • Lawson, C.L.1
  • 39
    • 0012087413 scopus 로고
    • Tables to many places of decimals
    • (now Math Comput.).
    • Lehmer, D.H. Tables to many places of decimals. Math. Tables Aids Comput. 1 (1943), 30-31 (now Math Comput.).
    • (1943) Math. Tables Aids Comput. , vol.1 , pp. 30-31
    • Lehmer, D.H.1
  • 40
    • 84945711122 scopus 로고
    • Fortran programs for arbitrary precision arithmetic
    • Rep. 10563, Nat. Bur. of Standards, Washington, D.C., April
    • Maximon, L.C. Fortran programs for arbitrary precision arithmetic. Rep. 10563, Nat. Bur. of Standards, Washington, D.C., April 1971.
    • (1971)
    • Maximon, L.C.1
  • 42
    • 84976827684 scopus 로고
    • multiple precision arithmetic package for the IBM 360/370 systems
    • SHARE Program Library, March
    • Reid, C E AND Knoble, H D. A multiple precision arithmetic package for the IBM 360/370 systems. SHARE Program Library, March 1974.
    • (1974)
    • Reid, C.E.1    Knoble, H.D.2
  • 44
    • 84966204708 scopus 로고
    • Computation of Π using arithmetic-geometric mean
    • July
    • Salamin, E. Computation of Π using arithmetic-geometric mean. Math. Comput. 30 (July 1976), 565-570.
    • (1976) Math. Comput. , vol.30 , pp. 565-570
    • Salamin, E.1
  • 45
    • 0016893003 scopus 로고
    • The production of special function routines for a multi-machine library
    • Schonfelder, J.L. The production of special function routines for a multi-machine library. Software—Practice and Experience 6 (1976), 71-82.
    • (1976) Software—Practice and Experience , vol.6 , pp. 71-82
    • Schonfelder, J.L.1
  • 46
    • 84976840164 scopus 로고
    • The testing of mathematical function software in a multi-machine environment
    • Basser Dept Comptr. Sci., U. of Sydney, Sydney, Australia, Nov.
    • Schonfelder, J L The testing of mathematical function software in a multi-machine environment. Tech. Rep. 107, Basser Dept Comptr. Sci., U. of Sydney, Sydney, Australia, Nov. 1975.
    • (1975) Tech. Rep. , pp. 107
    • Schonfelder, J.L.1
  • 47
    • 84976751015 scopus 로고
    • Applications support by direct language extension—an arbitrary precision arithmetic facility in Algol 68 Computer Ctr
    • U. of Birmingham, Birmingham
    • Schonfelder, J.L., AND Thomason, J.T. Applications support by direct language extension—an arbitrary precision arithmetic facility in Algol 68 Computer Ctr., U. of Birmingham, Birmingham, 1975.
    • (1975)
    • Schonfelder, J.L.1    Thomason, J.T.2
  • 48
    • 34250459760 scopus 로고
    • Schnelle Multiplikation grosser Zahlen
    • Schonhage, A AND Strassen, V Schnelle Multiplikation grosser Zahlen. Computing 7 (1971), 281-292.
    • (1971) Computing , vol.7 , pp. 281-292
    • Schonhage, A.1    Strassen, V.2
  • 49
    • 84976670789 scopus 로고
    • Fortran multiple precision
    • Michigan State U., East Lansing, Mich
    • Spira, R. Fortran multiple precision, Pt. 1, 2. Dept, of Math., Michigan State U., East Lansing, Mich 1973.
    • (1973) Dept, of Math.
    • Spira, R.1
  • 50
    • 84968466258 scopus 로고
    • On the computation of Euler's constant
    • Sweeney, D.W. On the computation of Euler's constant. Math. Comput. 17 (1963), 170-178.
    • (1963) Math. Comput. , vol.17 , pp. 170-178
    • Sweeney, D.W.1
  • 51
    • 34250526712 scopus 로고
    • A set of procedures making real arithmetic of unlimited accuracy possible within Algol 60
    • Tienari, M., AND Suokonautio, V A set of procedures making real arithmetic of unlimited accuracy possible within Algol 60. BIT 6 (1966), 322-338.
    • (1966) BIT , vol.6 , pp. 322-338
    • Tienari, M.1    Suokonautio, V.2
  • 52
    • 0017001962 scopus 로고
    • portable extended precision arithmetic package and library with Fortran precompiler
    • Nat Bur. of Standards, Washington, D C Sept.
    • Wyatt, W.T., Lozier, D.W., AND Orser, D.J. A portable extended precision arithmetic package and library with Fortran precompiler. Nat Bur. of Standards, Washington, D C 1975 Trans. Math Software 2, 3 (Sept. 1976), 209-231.
    • (1975) Trans. Math Software , vol.2 , Issue.3 , pp. 209-231
    • Wyatt, W.T.1    Lozier, D.W.2    Orser, D.J.3
  • 53
    • 84966200407 scopus 로고
    • Multiple precision arithmetic design with an implementation on the Univac 1108
    • Tech. Summary Rep. Mathematics Research Center, U. of Wisconsin, Madison, Wis.
    • 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.
    • (1971) , pp. 1123
    • Crary, F.D.1
  • 54
    • 84976858331 scopus 로고
    • The Augment precompiler
    • information. Mathematics Research Center, U of Wisconsin, Madison, Wis.
    • 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).
    • (1974) Tech. Summary Rep. , pp. 1469
    • Crary, F.D.1


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