BeDoPBeyondDoublePrecision-Loria.PDFVIP

BeDoP: Beyond Double Precision Paul Zimmermann ANR FastRelax, Lyon, 27 May 2015 The BeDoP project Research project written in 2014, after interaction with many colleagues (including those involved in FastRelax) Timeframe over 2016-2020 with one junior researcher, 3 PhD students, 2 post-doctoral students, one development engineer. Submitted to the European Research Council (ERC) Advanced Grant proposal Did not pass Step 1 of the evaluation (score B, ranking range 62-74%) Full project available on http://www.loria.fr/~zimmerma Motivation Fact 1: petaflop milestone (1015 flops) reached in 2008 (IBM’s Roadrunner), expect exaflop milestone (1018 flops) reached around 2020 Fact 2: hardware floating-point (double precision, about 16 decimal digits) will not change soon Fact 3: in most applications, rounding errors can increase linearly with the number of operations Thus more and more applications will require beyond double precision in software it is our responsibility to make those computations fast and correct How: using formal proof techniques The European Exascale Software Initiative (EESI): the ability to perform floating-point arithmetic with different precisions (e.g., 32-, 64-, and 128-bit) will likely be necessary in Exascale systems. ... The fundamental challenge of library software design is to develop and provide robust and reliable algorithms and implementations that deliver accurate results or at least compute results with accuracy estimates. Reference: Working group report on numerical libraries, solvers and algorithms, http://www.eesi-project.eu/, 2011. Bailey, Barrio, Borwein: High-precision computation: Mathematical physics and dynamics, Applied Mathematics and Computation, 2012 several applications already need more than double: evolution of