1、,Supercomputing in Plain English Part IX: Grab Bag,Henry Neeman, Director OU Supercomputing Center for Education & Research University of Oklahoma Wednesday November 7 2007,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,2,This is an experiment!,Its the nature of these kinds of v
2、ideoconferences that failures are guaranteed to happen! NO PROMISES! So, please bear with us. Hopefully everything will work out well enough.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,3,Access Grid/VRVS,If youre connecting via the Access Grid or VRVS, the venue is: NCSA Ven
3、ue Mosaic Its available Wed Oct 17 2007 1:00-4:30pm Central Time, but the workshop starts at 3:00pm Central Time. Many thanks to John Chapman of U Arkansas for setting this up for us.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,4,iLinc,We only have about 40-45 simultaneous iL
4、inc connections available. Therefore, each institution has at most one iLinc person designated. If youre the iLinc person for your institution, youve already gotten e-mail about it, so please follow the instructions. If you arent your institutions iLinc person, then you cant become it, because were
5、completely out of iLinc connections. Many thanks to Katherine Kantardjieff of California State U Fullerton for setting this up for us.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,5,QuickTime Broadcast,If you dont have iLinc, you can connect via QuickTime: rtsp:/129.15.254.141
6、/neeman_02.sdp We strongly recommend using QuickTime player, since weve seen it work. When you run it, traverse the menus File - Open URL Then paste in the rstp URL the Movie URL space, and click OK. Many thanks to Kevin Blake of OU for setting this up.,Supercomputing in Plain English: Grab Bag Wedn
7、esday November 7 2007,6,Phone Bridge,If all else fails, you can call into our phone bridge: 1-866-285-7778, access code 6483137# Please mute yourself and use the phone to listen. Dont worry, Ill call out slide numbers as we go. To ask questions, please use Google Talk or Gmail. Many thanks to Amy Ap
8、on of U Arkansas for setting this up for us, and to U Arkansas for absorbing the costs.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,7,Google Talk,To ask questions, please use our Google Talk group chat session (text only). You need to have (or create) a account to use Google
9、 Talk. Once youve logged in to your account, go to: http:/ and then contact the user named: oscer.sipe Alternatively, you can send your questions by e-mail to .,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,8,This is an experiment!,REMINDER: Its the nature of these kinds of vi
10、deoconferences that failures are guaranteed to happen! NO PROMISES! So, please bear with us. Hopefully everything will work out well enough.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,9,Outline,Scientific Computing Pipeline Scientific Libraries I/O Libraries Scientific Visua
11、lization,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,10,Scientific Computing Pipeline,Real World,Physics,Mathematical Representation (continuous),Numerical Representation (discrete),Algorithm,Implementation (program),Port (to a specific platform),Result (run),Thanks to Julia
12、Mullen of MIT Lincoln Lab for this concept.,Analysis,Verification,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,11,Five Rules of Scientific Computing,Know the physics. Control the software. Understand the numerics. Achieve expected behavior. Question unexpected behavior. Thanks
13、 to Robert E. Peterkin for these.,Scientific Libraries,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,13,Preinvented Wheels,Many simulations perform fairly common tasks; for example, solving systems of equations:Ax = b where A is the matrix of coefficients, x is the vector of un
14、knowns and b is the vector of knowns.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,14,Scientific Libraries,Because some tasks are quite common across many science and engineering applications, groups of researchers have put a lot of effort into writing scientific libraries: co
15、llections of routines for performing these commonly-used tasks (e.g., linear algebra solvers). The people who write these libraries know a lot more about these things than we do. So, a good strategy is to use their libraries, rather than trying to write our own.,Supercomputing in Plain English: Grab
16、 Bag Wednesday November 7 2007,15,Solver Libraries,Probably the most common scientific computing task is solving a system of equationsAx = b where A is a matrix of coefficients, x is a vector of unknowns, and b is a vector of knowns. The goal is to solve for x.,Supercomputing in Plain English: Grab
17、Bag Wednesday November 7 2007,16,Solving Systems of Equations,Donts: Dont invert the matrix (x = A-1b). Thats much more costly than solving directly, and much more prone to numerical error. Dont write your own solver code. There are people who devote their whole careers to writing solvers. They know
18、 a lot more about writing solvers than we do.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,17,Solving Dos,Dos: Do use standard, portable solver libraries. Do use a version thats tuned for the platform youre running on, if available. Do use the information that you have about y
19、our system to pick the most efficient solver.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,18,All About Your Matrix,If you know things about your matrix, you maybe can use a more efficient solver. Symmetric: ai,j = aj,i Positive definite: xTAx 0 for all x 0 (e.g., if all eigen
20、values are positive) Banded:0 excepton thebands,Tridiagonal:,and ,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,19,Sparse Matrices,A sparse matrix is a matrix that has mostly zeros in it. “Mostly” is vaguely defined, but a good rule of thumb is that a matrix is sparse if more t
21、han, say, 90-95% of its entries are zero. (A non-sparse matrix is dense.),Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,20,Linear Algebra Libraries,BLAS 1,2 ATLAS3 LAPACK4 ScaLAPACK5 PETSc6,7,8,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,21,BLAS,The Basi
22、c Linear Algebra Subprograms (BLAS) are a set of low level linear algebra routines: Level 1: Vector-vector (e.g., dot product) Level 2: Matrix-vector (e.g., matrix-vector multiply) Level 3: Matrix-matrix (e.g., matrix-matrix multiply) Many linear algebra packages, including LAPACK, ScaLAPACK and PET
23、Sc, are built on top of BLAS. Most supercomputer vendors have versions of BLAS that are highly tuned for their platforms.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,22,ATLAS,The Automatically Tuned Linear Algebra Software package (ATLAS) is a self-tuned version of BLAS (it a
24、lso includes a few LAPACK routines). When its installed, it tests and times a variety of approaches to each routine, and selects the version that runs the fastest. ATLAS is substantially faster than the generic version of BLAS. And, its free!,Supercomputing in Plain English: Grab Bag Wednesday Novem
25、ber 7 2007,23,Goto BLAS,In the past few years, a new version of BLAS has been released, developed by Kazushige Goto (currently at UT Austin). This version is unusual, because instead of optimizing for cache, it optimizes for the Translation Lookaside Buffer (TLB), which is a special little cache tha
26、t often is ignored by software developers. Goto realized that optimizing for the TLB would be more efficient than optimizing for cache.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,24,ATLAS vs. BLAS Performance,ATLAS DGEMM: 2.76 GFLOP/s = 69% of peak,Generic DGEMM: 0.91 GFLOP/
27、s = 23% of peak,DGEMM: Double precision GEneral Matrix-Matrix multiply DGEMV: Double precision GEneral Matrix-Vector multiply,BETTER,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,25,LAPACK,LAPACK (Linear Algebra PACKage) solves dense or special-case sparse systems of equations
28、depending on matrix properties such as: Precision: single, double Data type: real, complex Shape: diagonal, bidiagonal, tridiagonal, banded, triangular, trapezoidal, Hesenberg, general dense Properties: orthogonal, positive definite, Hermetian (complex), symmetric, general LAPACK is built on top of
29、BLAS, which means it can benefit from ATLAS.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,26,LAPACK Example,REAL,DIMENSION(numrows,numcols) : A REAL,DIMENSION(numrows) : B REAL,DIMENSION(numcols) : X INTEGER,DIMENSION(numrows) : pivot INTEGER : row, col, info, numrhs = 1DO row
30、 = 1, numrowsB(row) = END DO DO col = 1, numcolsDO row = 1, numrowsA(row,col) = END DO END DO CALL sgesv(numrows, numrhs, A, numrows, pivot, & & B, numrows, info) DO col = 1, numcolsX(col) = B(col) END DO,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,27,LAPACK: A Library and an
31、 API,LAPACK is a library that you can download for free from the Web: lib.org But, its also an Application Programming Interface (API): a definition of a set of routines, their arguments, and their behaviors. So, anyone can write an implementation of LAPACK.,Supercomputing in Plain English: Grab Bag
32、 Wednesday November 7 2007,28,Its Good to Be Popular,LAPACK is a good choice for non-parallelized solving, because its popularity has convinced many supercomputer vendors to write their own, highly tuned versions. The API for the LAPACK routines is the same as the portable version from NetLib, but t
33、he performance can be much better, via either ATLAS or proprietary vendor-tuned versions. Also, some vendors have shared memory parallel versions of LAPACK.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,29,LAPACK Performance,Because LAPACK uses BLAS, its about as fast as BLAS.
34、For example, DGESV (Double precision General SolVer) on a 2 GHz Pentium4 using ATLAS gets 65% of peak, compared to 69% of peak for Matrix-Matrix multiply. In fact, an older version of LAPACK, called LINPACK, is used to determine the top 500 supercomputers in the world.,Supercomputing in Plain Englis
35、h: Grab Bag Wednesday November 7 2007,30,ScaLAPACK,ScaLAPACK is the distributed parallel (MPI) version of LAPACK. It actually contains only a subset of the LAPACK routines, and has a somewhat awkward Application Programming Interface (API). Like LAPACK, ScaLAPACK is also available from lib.org.,Supe
36、rcomputing in Plain English: Grab Bag Wednesday November 7 2007,31,PETSc,PETSc (Portable, Extensible Toolkit for Scientific Computation) is a solver library for sparse matrices that uses distributed parallelism (MPI). PETSc is designed for general sparse matrices with no special properties, but it a
37、lso works well for sparse matrices with simple properties like banding and symmetry. It has a simpler, more intuitive Application Programming Interface than ScaLAPACK.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,32,Pick Your Solver Package,Dense Matrix Serial: LAPACK Shared M
38、emory Parallel: threaded LAPACK Distributed Parallel: ScaLAPACK Sparse Matrix: PETSc,I/O Libraries,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,34,I/O Challenges,I/O presents two important challenges to scientific computing: Performance Portability The performance issue arises
39、 because I/O is much more time-consuming than computation, as we saw in the “Storage Hierarchy” session. The portability issue arises because different kinds of computers can have different ways of representing real (“floating point” numbers).,Supercomputing in Plain English: Grab Bag Wednesday Nove
40、mber 7 2007,35,Storage Formats,When you use a PRINT statement in Fortran or a printf in C or output to cout in C+, you are asking the program to output data in human-readable form:x = 5PRINT *, x But what if the value that you want to output is a real number with lots of significant digits?1.3456789
41、E+23,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,36,Data Output as Text,1.3456789E+23 When you output data as text, each character takes 1 byte. So if you output a number with lots of digits, then youre outputting lots of bytes. For example, the above number takes 13 bytes to
42、 output as text. Jargon: Text is sometimes called ASCII (American Standard Code for Information Interchange).,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,37,Output Data in Binary,Inside the computer, a single precision real number (Fortran REAL, C/C+ float) typically requires
43、 4 bytes, and a double precision number (DOUBLE PRECISION or double) typically requires 8. Thats less than 13. Since I/O is very expensive, its better to output 4 or 8 bytes than 13 or more. Happily, Fortran, C and C+ allow you to output data as binary (internal representation) rather than as text.,
44、Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,38,Binary Output Problems,When you output data as binary rather than as text, you output substantially fewer bytes, so you save time (since I/O is very expensive) and you save disk space. But, you pay two prices: Readability: Humans
45、 cant read binary. Portability: Different kinds of computers have different ways of internally representing numbers.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,39,Binary Readability: No Problem,Readability of binary data isnt a problem in scientific computing, because: You c
46、an always write a little program to read in the binary data and display its text equivalent. If you have lots and lots of data (i.e., MBs or GBs), you wouldnt want to look at all of it anyway.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,40,Binary Portability: Big Problem,Bina
47、ry data portability is a very big problem in scientific computing, because data thats output on one kind of computer may not be readable on another, and so: You cant output the data on one kind of computer and then use them (e.g., visualize, analyze) on another kind. Some day the kind of computer th
48、at output the data will be obsolete, so there may be no computer in the world that can input it, and thus the data are lost.,Supercomputing in Plain English: Grab Bag Wednesday November 7 2007,41,Portable Binary Data,The HPC community noticed this problem some years ago, and so a number of portable
49、binary data formats were developed. The two most popular are: HDF (Hierarchical Data Format) from the National Center for Supercomputing Applications: http:/hdf.ncsa.uiuc.edu NetCDF (Network Common Data Form) from Unidata: http:/www.unidata.ucar.edu/packages/netcdf,Supercomputing in Plain English: G
50、rab Bag Wednesday November 7 2007,42,Advantages of Portable I/O,Portable binary I/O packages: give you portable binary I/O; have simple, clear APIs; are available for free; run on most platforms; allow you to annotate your data (e.g., put into the file the variable names, units, experiment name, grid description, etc). Also, HDF allows distributed parallel I/O.,
