machine precision

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1: 3.1 Arithmetics and Error Measures

… ► … ►The machine precision is $\frac{1}{2}{ϵ}_M=2^{-p}$. … ►The respective machine precisions are $\frac{1}{2}{ϵ}_M=0.596\times {10}^{-7}$, $\frac{1}{2}{ϵ}_M=0.111\times {10}^{-15}$ and $\frac{1}{2}{ϵ}_M=0.963\times {10}^{-34}$. … ►Symmetric rounding or rounding to nearest of $x$ gives $x_{-}$ or $x_{+}$, whichever is nearer to $x$, with maximum relative error equal to the machine precision $\frac{1}{2}{ϵ}_M=2^{-p}$. …

2: Bibliography B

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An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy. Comput. Phys. Comm. 21 (3), pp. 297–314.

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External Links:

Document

Referenced by:

§3.10(iii), §33.22(iv).

Encodings:

BibTeX

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

Encodings:

BibTeX

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A Fortran multiple-precision arithmetic package. ACM Trans. Math. Software 4 (1), pp. 57–70.

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External Links:

ISSN 0098-3500, Document

Referenced by:

1st item.

Encodings:

BibTeX

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Fast multiple-precision evaluation of elementary functions. J. Assoc. Comput. Mach. 23 (2), pp. 242–251.

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External Links:

Document, MathReview (Amnon Barak), ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

BibTeX

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Algorithm 524: MP, A Fortran multiple-precision arithmetic package [A1]. ACM Trans. Math. Software 4 (1), pp. 71–81.

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External Links:

ISSN 0098-3500, Document, Remark. GAMS (module 524; package TOMS)

Referenced by:

3rd item, 1st item, 1st item, 1st item, 3rd item, 1st item, 1st item.

Encodings:

BibTeX

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3: Bibliography C

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Determination of $\nu$-zeros of Hankel functions. Comput. Phys. Comm. 32 (3), pp. 333–339.

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Notes:

Double-precision Fortran, maximum accuracy 7S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

1st item.

Encodings:

BibTeX

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Algorithm AS 310. Computing the non-central beta distribution function. Appl. Statist. 46 (1), pp. 146–156.

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Notes:

Single-precision Fortran.

External Links:

FullText, Code, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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CRCWFN: Coupled real Coulomb wavefunctions. Comput. Phys. Comm. 79 (1), pp. 143–155.

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Notes:

Double-precision Fortran code.

External Links:

ISSN 0010-4655, Document, Code, ZentralBlatt

Referenced by:

5th item.

Encodings:

BibTeX

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Numerical evaluation of the Fermi-Dirac integrals. The Astrophysical Journal Supplement Series 71, pp. 677–699.

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Notes:

Double-precision Fortran, maximum precision 12D.

External Links:

ISSN 0067-0049, Document, Code

Referenced by:

§25.12(iii), §25.18(i), 3rd item, 3rd item.

Encodings:

BibTeX

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An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19 (90), pp. 297–301.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§3.11(v).

Encodings:

BibTeX

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