Algorithm 719

Algorithm 719: Multiprecesion translation and execution of FORTRAN programs. This paper describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose. The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls. This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 41 articles , 1 standard article )

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  1. Gentle, James E.: Matrix algebra. Theory, computations and applications in statistics (2017)
  2. Cheng, Alexander H.-D.: Multiquadric and its shape parameter -- a numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation (2012)
  3. Blackhurst, Jonathan: Polynomials of the bifurcation points of the logistic map (2011)
  4. Kormanyos, Christopher: Algorithm 910: A portable C++ multiple-precision system for special-function calculations (2011)
  5. Smith, David M.: Algorithm 911: Multiple-precision exponential integral and related functions (2011)
  6. Sokolovski, D.; Akhmatskaya, E.; Sen, S. K.: Extracting (S)-matrix poles for resonances from numerical scattering data: type-II Padé reconstruction (2011)
  7. Grau-Sánchez, Miquel; Noguera, Miquel; Gutiérrez, José Manuel: On some computational orders of convergence (2010)
  8. Takahashi, Daisuke: Parallel implementation of multiple-precision arithmetic and 2,576,980,370,000 decimal digits of (\pi) calculation (2010)
  9. Gumerov, Nail A.; Duraiswami, Ramani: Fast multipole methods on graphics processors (2008)
  10. Heinzmann, Dominik: A filtered polynomial approach to density estimation (2008)
  11. Takahashi, Daisuke: A parallel algorithm for multiple-precision division by a single-precision integer (2008)
  12. Demmel, James; Dumitriu, Ioana; Holtz, Olga: Toward accurate polynomial evaluation in rounded arithmetic (2006)
  13. Grau, Miquel; Díaz-Barrero, José Luis: An improvement to Ostrowski root-finding method (2006)
  14. Bailey, David H.; Jeyabalan, Karthik; Li, Xiaoye S.: A comparison of three high-precision quadrature schemes (2005)
  15. Barrio, R.; Blesa, F.; Lara, M.: VSVO formulation of the Taylor method for the numerical solution of ODEs (2005)
  16. Barrio, R.; Serrano, S.: Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces. II: numerical stability (2005)
  17. Takahashi, Daisuke: An algorithm for multiple-precision floating-point multiplication (2005)
  18. Altman, Micah; Gill, Jeff; McDonald, Michael P.: Numerical issues in statistical computing for the social scientist. (2004)
  19. Grau, Miquel: An improvement to the computing of nonlinear equation solutions (2003)
  20. Karassiov, V. P.; Gusev, A. A.; Vinitsky, S. I.: Polynomial Lie algebra methods in solving the second-harmonic generation model: some exact and approximate calculations (2002)

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