Exact arithmetic on the Stern–Brocot tree

B.P. Bates, Self-matching and interleaving in some integer sequences and the Gauss map, PhD thesis, University of Wollongong, 2001 Bertot, 2003, Simple canonical representation of rational numbers, vol. 85.7 Brocot, 1861, Calcul des rouages par approximation, nouvelle méthode, Revue chronométrique. Journal des horlogers, scientifique et pratique, 3, 186 Conway, 1976 The Coq Development Team Edalat, 1997, A new representation for exact real numbers, vol. 6 Gosper Gosper Graham, 1994 Hayes, 2000, On the teeth of wheels, American Scientist, 88, 296, 10.1511/2000.29.3334 Hughes M. Konečný, Many-valued real functions computable by finite transducers using IFS-representations, PhD thesis, School of Computer Science, The University of Birmingham, October 2000 Kornerup, 1988, An on-line arithmetic unit for bit-pipelined rational arithmetic, J. Parallel Distrib. Comput., 5, 310, 10.1016/0743-7315(88)90023-8 Kornerup, 1995, LCF: A lexicographic binary representation of the rationals, J. Universal Comput. Sci., 1, 484 Kornerup, 1990, An algorithm for redundant binary bit-pipelined rational arithmetic, IEEE Trans. Comput., C-39, 1106, 10.1109/12.57048 Lester, 2001, Effective continued fractions, 163 Liardet, 1998, Algebraic computations with continued fractions, J. Number Theory, 73, 92, 10.1006/jnth.1998.2274 Mamane V. Ménissier-Morain, Arithmétique exacte, conception, algorithmique et performances d'une implémentation informatique en précision arbitraire, Thèse, Université Paris 7, December 1994 M. Niqui, Formalising exact arithmetic: representations, algorithms and proofs, PhD thesis, Radboud Universiteit Nijmegen, September 2004 Niqui Niqui, 2004, QArith: Coq formalisation of lazy rational arithmetic, vol. 3085, 309 P.J. Potts, Exact real arithmetic using Möbius transformations, PhD thesis, University of London, Imperial College, July 1998 P.J. Potts, A. Edalat, Exact real computer arithmetic, Technical Report DOC 97/9, Department of Computing, Imperial College, March 1997 Raney, 1973, On continued fractions and finite automata, Math. Ann., 206, 265, 10.1007/BF01355980 Stern, 1858, Ueber eine zahlentheoretische Funktion, Journal für die Reine und Angewandte Mathematik, 55, 193, 10.1515/crll.1858.55.193 Vuillemin, 1990, Exact real computer arithmetic with continued fractions, IEEE Trans. Comput., 39, 1087, 10.1109/12.57047