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J.E. Vuillemin, "Exact Real Computer Arithmetic with Continued Fractions," IEEE Transactions on Computers, vol. 39, no. 8, pp. 10871105, August, 1990.  
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@article{ 10.1109/12.57047, author = {J.E. Vuillemin}, title = {Exact Real Computer Arithmetic with Continued Fractions}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {8}, issn = {00189340}, year = {1990}, pages = {10871105}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.57047}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Exact Real Computer Arithmetic with Continued Fractions IS  8 SN  00189340 SP1087 EP1105 EPD  10871105 A1  J.E. Vuillemin, PY  1990 KW  exact real computer arithmetic; continued fractions; computable real numbers; undecidable comparison; integer division; infinite 1/0; undefined 0/0 numbers; arithmetic operations; algebraic algorithm; sums; products; positional; transcendental algorithm; Gauss; exponentials; logarithms; trigonometric functions; special functions; LeLisp; digital arithmetic; number theory. VL  39 JA  IEEE Transactions on Computers ER   
A representation of the computable real numbers by continued fractions is introduced. This representation deals with the subtle points of undecidable comparison and integer division, as well as representing the infinite 1/0 and undefined 0/0 numbers. Two general algorithms for performing arithmetic operations are introduced. The algebraic algorithm, which computes sums and products of continued fractions as a special case, basically operates in a positional manner, producing one term of output for each term of input. The transcendental algorithm uses a general formula of Gauss to compute the continued fractions of exponentials, logarithms, trigonometric functions, and a wide class of special functions. A prototype system has been implemented in LeLisp and the performance of these algorithms is promising.
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