File 20July10 On the Future of Numerical Linear Algebra Version dated July 10 2010 7 44 am Undebuggability of Big Floating Point Programs for Scientific and Engineering Computations Inordinate effort and time are being expended on attempts often unsuccessful to debug floating point programs most of them presumed already debugged whose application to some ostensibly innocuous data not necessarily test data has produced results that arouse suspicion perhaps undeserved Wasted Time Instances have occurred when a bug was never found before the underlying system was upgraded and the bug went elsewhere or away How are floating point programs worse than others Though heir to the same ills as others these suffer three more 1 Roundoff What you see is not what you get and what you get is not what you asked for 2 Floating Point Exceptions Over Underflow Invalid Operations no flags to expose them 3 Overly Aggressive Compiler Optimizations O K for integers but not Flt Pt because of 1 2 Would you like to go back to the years of my youth when floatingpoint was deemed refractory to error analysis thus undebuggable Prof W Kahan U C Berkeley for the Panel Pete Stewart s 70th Page 1 2 File 20July10 On the Future of Numerical Linear Algebra Version dated July 10 2010 7 44 am Undebuggability of Big Floating Point Programs 1 Roundoff 2 Exceptions 3 Over Optimization Exploitation of parallelism worsens our situation To minimize communications costs cf J W Demmel al we use novel algorithms that have not yet been and may never be proved numerically stable for all innocuous data Hence more obscure bugs Two Palliatives No complete cure exists I To greatly attenuate damage from roundoff and exceptions carry by default extravagantly excessive precision and range during computation cf pre 1980 Kernighan Ritchie C II To diminish time spent debugging we need aids Compiler support for modes e g directed roundings and flags as scoped variables perhaps like APL s System Variables CT Linker planted Milestones for flags NaNs Retrospective Diagnostics Compiler Debugger collaboration to inject breaks etc in object modules too Current efforts towards that end at U C Berkeley eecs berkeley edu grevy publications files pdf BaDeKaSe10 pdf supported by Sun Microsystems and The MathWorks See too my web page eecs berkeley edu wkahan for History 7094II pdf BASCD08K pdf Counter Proposals 7Oct09 pdf Mindless pdf The Challenge Can we collect the necessary Coalition of Competencies Hardware Compilers Link and Loaders Debuggers Environments Prof W Kahan U C Berkeley for the Panel Pete Stewart s 70th Page 2 2
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