LIP6 2003/003

• Reports «Arithmétique réelle en précision arbitraire: conception et algorithmes»
• V. Ménissier-Morain
• 67 pages - 05/23/2003 - document en - http://www.lip6.fr/lip6/reports/2003/lip6.2003.003.pdf 632 Ko
• Contact Valerie.Menissier-Morain (at) nulllip6.fr
• Ancien Thème : CALFOR
We describe here a representation of computable real numbers and a set of algorithms for the elementary functions associated to this representation. A real number is represented as a sequence of finite $B$-adic numbers and for each classical function (rational, algebraic or transcendental), we describe how to produce a sequence representing the result of the application of this function to its arguments, according to the sequences representing these arguments. For each algorithm we prove that the resulting sequence is a valid representation of the exact real result. This arithmetic is the first abritrary precision real arithmetic with mathematically proved algorithms.