K. Mehlhorn, S. Naher, M. Seel, and Ch. Uhrig. The LEDA User Manual (Version R 4.1), 2000. Max-Planck-Institut fur Informatik, Saarbrucken, Germany. See also http://www.mpi-sb.mpg. de/LEDA/leda.html.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... X XXXXX XXXXXX XXXXXX XXXXXX XXXXXX input86 XXXXXX XXXX XXXXXXXX XXXXX X XXXXX X Figure 7: A hierarchical graph drawn with di erent modules for the third phase 4 Design Details AGD [AGD00] is an object oriented C class library, which is based on the two libraries LEDA [MN99, MNSU00] and ABACUS [JT98, JT00] LEDA provides basic data types and algorithms, e.g. the data type for the representation of graphs. ABACUS is a framework for the implementation of branch and cut algorithms. The ABACUS library is only used by branch and cut algorithms, whereas the whole basic ....

K. Mehlhorn, S. Naher, M. Seel, and Ch. Uhrig. The LEDA User Manual (Version R 4.1), 2000. Max-Planck-Institut fur Informatik, Saarbrucken, Germany. See also http://www.mpi-sb.mpg. de/LEDA/leda.html.

....formal power series, polynomials, and integers. Indeed, 3 http: algo.inria.fr libraries software.html 52 Relax But Don t Be Too Lazy one of the by products of Joris van der Hoeven s report is a division algorithm with remainder in K(n) operations, whereas the best known algorithm was in 2K(n) [7, 2, 5]. Related work. For truncated division and square root, new algorithms based on Karatsuba s multiplication are detailed in the report [4] Acknowledgement. People who don t read French may thank Gina Pierrel ee Grisvard who helped to translate this summary. ....

Burnikel (Christoph) and Ziegler (Joachim). { Fast recursive division. { Research Report n MPI-I-98-1-022, Max-Planck-Institut fur Informatik, Saarbrucken, Germany, October 1998.

....and over or under ow, basic laws of arithmetic are violated. There are also various software packages [11, 2] and libraries [16, 14] 7 that provide further models of number types, e.g. arbitrary precision integral types. A very useful model for geometric computations is the number type leda real [4, 16]. This type models a subset of algebraic numbers. leda reals subsume (arbitrary precision) integers and are closed under addition, subtraction, multiplication, division, and k root operations. Invisible to the user, this number type uses adaptive computation to speed up exact comparison ....

C. Burnikel, K. Mehlhorn, and S. Schirra. The LEDA class real number. Technical Report MPI-I-96-1-001, Max-Planck-Institut fur Informatik, 1996.

.... e.g. trees can be drawn nicely in AGD using the algorithm by Reingold and Tilford [46] and Walker [52] Moreover, st planar graphs can be drawn by the algorithm suggested in [10] 4 Design Details AGD [1] is an object oriented C class library, which is based on the two libraries LEDA [41, 42] and ABACUS [33, 34] LEDA provides some basic data types and algorithms, i.e. the data type for the representation of graphs. ABACUS is a framework for the implementation of branch and cut 9 X X XXXXXXXX XXXXXXXX XXXXXXXX XXXXXXXX XXXXXXXX XXXX XXXX XXXXX XXXXX XXXX XXXX XXXXX XXXXX ....

K. Mehlhorn, S. Naher, M. Seel, and Ch. Uhrig. The LEDA User Manual (Version R 4.1), 2000. Max-Planck-Institut fur Informatik, Saarbrucken, Germany. See also http://www. mpi-sb.mpg.de/LEDA/leda.html.

....calculation dominates the runtime. It is remarkable how badly LEDA reals perform in degenerate cases. 5.1.2. Incircle test In this experiment we use a predicate occurring in the construction of the Voronoi diagram of line segments and measure the di erent implementations. The code is taken from [4], page 59. Let v = v x ; v y ; v z ) v z 0 be a Voronoi vertex de ned by three sites p; l 1 ; l 2 , where p = 0; 0; 0) is the origin and l 1 ; l 2 are lines. Given a line l 3 , does l 3 touch, intersect or miss the clearance circle of v Assuming that the input variables are all of ....

....3 level (double integer real, as suggested in 4.1) EXPCOMP 2 level (double real) We will measure both, incircle tests with randomly chosen as well as degenerate input. For the degenerate cases we construct three lines that touch a common circle passing through p = 0; 0) as described in [4] page 59. The test results are listed in tables 4 and 5. As for the tests with signs of determinants, it turns out that LEDA reals perform badly in degenerate cases. In the non degenerate cases, the overhead of LEDA real compared to double is by far not as large as for the determinants tests. ....

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C. Burnikel: Exact Computation of Voronoi Diagrams and Line Segment Intersections, (PhD thesis, Max-Planck-Institut fur Informatik, 1996)

....way of writing the number zero. When the same chunk is evaluated with doubles instead of leda reals, E evaluates to 4:44 10 16 and consequently the output statement prints 1. We next discuss the key features of the implementation of leda reals. The detailed implementation can be found in [8]. A leda real is represented as a directed acyclic graph (dag) that records its construction. The nodes of the dag for an expression E correspond to the subexpressions of E. The leaves of the dag are integers, and each internal node of the dag is labeled with a unary or binary operation and points ....

....length L guarantees an error B for e E. We use the number type leda bigfloat for it; it supports oating point arithmetic with arbitrary mantissa length. Next, we explain precision driven computation in more detail for the case of a multiplication, for the other operations we refer the reader to [8] . Consider a multiplication x y. Assume that x and y are approximations of x and y, respectively, and that is the relative error of the oating point realization of the multiplication. Let q x = j x x j and q y = j y y j be the errors in the approximations of x and y, respectively. ....

C. Burnikel, K. Mehlhorn, and S. Schirra. The LEDA class real number. Research Report MPI-I-96-1001, Max-Planck-Institut fur Informatik, 1996. A more recent documentation of the implementation is available at http://www.mpi-sb.mpg.de/~burnikel/ reports/real.ps.gz.

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