File: 20July10 On the Future of Numerical Linear Algebra Version dated July 10, 2010 7:44 amProf. W. Kahan, U.C. Berkeley for the Panel @ Pete StewartÕs 70th É Page 1/2 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 floating-point was deemed refractory to error-analysis, thus undebuggable?File: 20July10 On the Future of Numerical Linear Algebra Version dated July 10, 2010 7:44 amProf. W. Kahan, U.C. Berkeley for the Panel @ Pete StewartÕs 70th É Page 2/2 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,
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