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Algorithm 237: Greatest common divisor

J. E. L. Peck

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Abstract

real procedure t(y); value y; real y; commentThis is an auxiliary procedure which evaluates the inverse function t = t(y) of y = tin t (t~l) to an accuracy of about 1%.For the interval 0 ~ y ~ 10 a fifth degree approximating polynomial was obtained by truncating a series expansion in Chebyshev polynomials.For y > 10 the approximation t(y) =" (y/ln(y/a))(l+(lna--lnln(y/c~))/(l+ln(y/a))) -1 where in a = .775tis used; begin real p, z; ify =< 10then begin p := .000057941X y --.00176148; p := y X p + .0208645;p :=yX p--.129013; p :=yX p+.85777; t :

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real procedure t(y); value y; real y; commentThis is an auxiliary procedure which evaluates the inverse function t = t(y) of y = tin t (t~l) to an accuracy of about 1%.For the interval 0 ~ y ~ 10 a fifth degree approximating polynomial was obtained by truncating a series expansion in Chebyshev polynomials.For y > 10 the approximation t(y) =" (y/ln(y/a))(l+(lna--lnln(y/c~))/(l+ln(y/a))) -1 where in a = .775tis used; begin real p, z; ify =< 10then begin p := .000057941X y --.00176148; p := y X p + .0208645;p :=yX p--.129013; p :=yX p+.85777; t :

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Available abstract

real procedure t(y); value y; real y; commentThis is an auxiliary procedure which evaluates the inverse function t = t(y) of y = tin t (t~l) to an accuracy of about 1%.For the interval 0 ~ y ~ 10 a fifth degree approximating polynomial was obtained by truncating a series expansion in Chebyshev polynomials.For y > 10 the approximation t(y) =" (y/ln(y/a))(l+(lna--lnln(y/c~))/(l+ln(y/a))) -1 where in a = .775tis used; begin real p, z; ify =< 10then begin p := .000057941X y --.00176148; p := y X p + .0208645;p :=yX p--.129013; p :=yX p+.85777; t :

Key concepts: Citation, Greatest common divisor, Computer science, Peck (Imperial), Algorithm, Operations research, Database, Library science

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