An algorithm for computing logarithms and arctangents

Carlson, B. C.

doi:10.1090/S0025-5718-1972-0307438-2

An algorithm for computing logarithms and arctangents
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by B. C. Carlson PDF

Math. Comp. 26 (1972), 543-549 Request permission

Abstract:

An iterative algorithm with fast convergence can be used to compute logarithms, inverse circular functions, or inverse hyperbolic functions according to the choice of initial conditions. Only rational operations and square roots are required. The method consists in adding an auxiliary recurrence relation to Borchardt’s algorithm to speed the convergence.

References

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B. C. Carlson, Algorithms involving arithmetic and geometric means, Amer. Math. Monthly 78 (1971), 496–505. MR 283246, DOI 10.2307/2317754
B. C. Carlson, The logarithmic mean, Amer. Math. Monthly 79 (1972), 615–618. MR 302842, DOI 10.2307/2317088

Computer Approximations

Eduard L. Stiefel, An introduction to numerical mathematics, Academic Press, New York-London, 1963. Translated by Werner C. Rheinboldt and Cornelie J. Rheinboldt. MR 0181077
Henry C. Thacher Jr., Iterated square root expansions for the inverse cosine and inverse hyperbolic cosine, Math. Comp. 15 (1961), 399–403. MR 135228, DOI 10.1090/S0025-5718-1961-0135228-5