OR682Math685CSI700

1
OR682/Math685/CSI700

• Lecture 14
• Fall 2000

2
Todays Topics

• Timing Profiling
• Chapter 6
• Eliminating Clutter
• Chapter 7
• Loop Optimizations
• Chapter 8

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Timing

• The Unix time command (last week)
• User time time spent executing the instructions
  in your program
• System time Input/Output, page faults,
  floating-point exceptions
• CPU time sum of above
• Elapsed time wall-clock time
• Useful for timing entire programs

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Timing a Section of a Program

• Use software that is part of the language
• Fortran etime
• real4 tarray(2), etime
• start etime(tarray)
• finish etime(tarray)
• print , finish-start
• Matlab tic, toc
• Work on an empty machine
• Average several runs

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Profiling

• ltexample using Matlabgt
• Gives detailed information on execution times of
  individual functions and statements
• In many cases, dominated by a single function or
  statement

Matlab files Heath10_3.m, etc.
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Using .mex Files

• Replace a Matlab function with a function
  programmed in C or Fortran
• ltsee examplegt
• Rest of lecture
• other ways to improve performance
• eliminating clutter
• loop optimizations

Matlab files run_mex_setup.m, run_mex.m, yp.m,
yprime.c
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Eliminating Clutter

• Contributions to overhead
• subroutine calls, indirect memory references,
  tests within loops, type conversions
• Restrictions to compiler flexibility
• subroutine calls, indirect memory references,
  tests within loops, ambiguous pointers

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Subroutine Calls

• Overhead to process subroutine call
• Compiler often cannot optimize code across
  subroutines (especially if in different files)
• ltsee example pages 129-130gt
• BUT dont make your program unreadable

fortran files eg_sub1.f, eg_sub2.f, eg_sub_run
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Alternatives to Subroutines

• Macros simple procedures
• substituted at pre-processor stage
• Procedure inlining
• handled by compiler directives
• useful for not so simple procedures
• see man f77 search for inlin

fortran files eg_macro.F, eg_macro_run
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Branches Within Loops

• Can lead to severe inefficiencies
• see examples on pages 134-139
• go over
• loop invariant conditionals
• loop index dependent conditionals
• conditionals that transfer control

fortran files eg_except1.f, eg_except2.f,
eg_except_run, man f77 search for except
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Data Type Conversions

• Conversions integer, single, double
• Adds overhead to loops
• Can be subtle
• 1, 0.3, 3.0e-1, 3.0d-1, .3000000000000000

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Loop Optimizations

• Loop unrolling
• Loop interchange
• Blocking
• plus others in text

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Loop Unrolling

• Sometimes done automatically by compiler
• Reduce loop overhead by explicitly expanding
  several iterations
• DO I 1,N,4
• A(I) A(I) B(I) C
• A(I1) A(I1) B(I1) C
• A(I2) A(I2) B(I2) C
• A(I3) A(I3) B(I3) C
• END DO
• Needs tidy up calculations at end

http//www.netlib.org/slatec/lin/scopy.f
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Loop Interchange

• For nested loops, consider changing the order of
  the inner and outer loops
• example pages 156-161
• May not be possible for the compiler to figure out

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Example Matrix Multiplication

• Traditional formula for C AB
• In original form, not ideal for computation
• Can be improved by re-arrangement

fortran files eg_matmul1.f, eg_matmul2.f,
eg_matmul_run
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Example Blocking

• Organize a matrix calculation to work with
  submatrices of a specified size k
• Allows program to exploit
• cache
• parallelism
• computation proportional to k2 or k3
• communication proportional to k

fortran file eg_block.f
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To Finish Up

• What weve accomplished
• What comes next