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Why and the way to make use of arbitrary precision, with Kaveh R. Ghazi, Vincent Lefèvre and Philippe Théveny, March 2010, Computing in Science and Engineering, volume 12, number 3, pages 62-65, 2010 (© IEEE). We present an algorithm to seek out two non-linear polynomials for the Number Field Sieve integer factorization method. Computing predecessor and successor in rounding to nearest, with Siegfried Rump, Sylvie Boldo and Guillaume Melquiond, BIT Numerical Mathematics, volume 49, number 2, pages 419-431, 2009. - We give simple and efficient methods to compute and/or estimate the predecessor and successor of a floating-level quantity utilizing solely floating-level operations in rounding to nearest. A revised model appeared in a special subject of Contemporary Mathematics, volume 461, pages 47-58, 2008. - We give a brand new algorithm for performing the distinct-degree factorization of a polynomial P(x) over GF(2), utilizing a multi-degree blocking technique. A GMP-primarily based implementation of Schönhage-Strassen's giant integer multiplication algorithm, with Pierrick Gaudry and Alexander Kruppa, Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2007), Waterloo, Ontario, Canada, pages 167-174, editor C.W.Brown, 2007. - Schönhage-Strassen's algorithm is the most effective recognized algorithms for multiplying large integers

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We present here an improved implementation, primarily based on the one distributed throughout the GMP library. This article presents a few purposes where dependable computations are obtained utilizing the GNU MPFR library. On computers without double-extended precision, the GNU libc 2.10.1 incorrectly rounds the sine of (the double-precision closest to) 0.2522464. This can be a bug in IBM's Accurate Mathematical Library, which claims appropriate rounding, as recommended by IEEE 754-2008. We analyze this bug and suggest a repair. This work may be prolonged to other elementary features within the decimal64 format and permits the design of reasonably quick routines that can evaluate these features with right rounding, no less than in some domains. This work permits one to implement quick appropriately rounded division routines in a number of-precision software tools. What you discovered is that it may well often take many gates to implement simple units. The problem is to implement Newton's iteration for the reciprocal square root on high's of GNU MP's mpn layer, whereas guaranteeing a rigorous 1/2 ulp sure on the roundoff error. Reliable Computing with GNU MPFR, proceedings of the third International Congress on Mathematical Software (ICMS 2010), June 2010, pages 42-45, LNCS 6327, Springer

The watermark goals to discourage Internet users from taking a photograph or a video from one Web site and utilizing it for their very own purposes without acknowledging the supply. Landau's operate for one million billions, with Marc Deléglise and Jean-Louis Nicolas, Journal de Théorie des Nombres de Bordeaux, volume 20, quantity 3, pages 625-671, 2008. A Maple program implementing the algorithm described on this paper is available from Jean-Louis Nicolas web page. 2008: Worst Cases for the Exponential Function within the IEEE 754r decimal64 Format, with Vincent Lefèvre and Damien Stehlé, LNCS volume 5045, pages 114-126, particular LNCS concern following the Dagstuhl seminar 06021: Reliable Implementation of Real Number Algorithms: Theory and Practice, August 2008, - We searched for the worst instances for correct rounding of the exponential perform within the IEEE 754r decimal64 format, and computed all the bad circumstances whose distance from a breakpoint (for all rounding modes) is less than 10-15 ulp, and we give the worst ones. Implementation of the reciprocal square root in MPFR, March 2008 (prolonged abstract), Dagstuhl Seminar Proceedings following Dagstuhl seminar 08021 (Numerical validation in present hardware architectures), January 06-11, 2008. - We describe the implementation of the reciprocal square root --- also called inverse sq. root --- as a local operate in the MPFR library

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