Geodesic
Time- and space-efficient evaluation of a complex exponential function on machine Schonhage
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2011), pp. 105-118
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Quasi-linear time and linear space algorithms for evaluation of a complex exponential function on machine Schonhage are presented. These algorithms are based on a modified method of fast evaluation of an exponential function and on a modified method of binary splitting for hypergeometris series.
Keywords: exponential function, constructive real functions, quasi-linear time complexity, linear space complexity. 
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     title = {Time- and space-efficient evaluation of a complex exponential function on machine {Schonhage}},
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S. V. Yakhontov. Time- and space-efficient evaluation of a complex exponential function on machine Schonhage. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2011), pp. 105-118. http://geodesic.mathdoc.fr/item/VSPUI_2011_4_a10/

[1] Schonhage A., Grotefeld A. F. W., Vetter E., Fast algorithms. A multitape Turing machine implementation, Brockhaus AG, Leipzig, 1994, 298 pp.

[2] Ko K., Complexity theory of real functions, Birkhauser, Boston, 1991, 310 pp. | MR

[3] Yakhontov S. V., $FLINSPACE$ konstruktivnye veschestvennye chisla i funktsii, LAMBERT Academic Publ., Saarbrucken, 2010, 167 pp.

[4] Karatsuba E. A., “Bystrye vychisleniya transtsendentnykh funktsii”, Problemy peredachi informatsii, 27:4 (1991), 76–99 | MR

[5] Haible B., Papanikolaou T., “Fast multiple-presicion evaluation of series of rational numbers”, Proc. of the Third Intern. Symposium on Algorithmic Number Theory (June 21–25), 1998, 338–350 | DOI | MR | Zbl

[6] Aho A., Hopcroft J., Ullman J., The design and analysis of computer algorithms | MR

[7] Kosovskaya T. M., Kosovskii N. K., “Prinadlezhnost klassu $FP$ dvazhdy polinomialnykh paskalevidnykh funktsii nad podprogrammami iz $FP$”, Kompyuternye instrumenty v obrazovanii, 2010, no. 3, 3–7