OR682Math685CSI700

1
OR682/Math685/CSI700

• Lecture 13
• Fall 2000

2
Todays Topics

• Memory
• Chapter 3
• Floating-Point Numbers not in lecture
• Chapter 4
• Much of this material discussed earlier
• Compilers
• Chapter 5

3
Memory

• Memory access can slow computations
• slower memory units
• limited connections to memory
• hierarchies of memory
• Understanding memory can help you write better
  software (and help you diagnose performance
  problems)

4
Memory Technology

• DRAM (needs dynamic refreshing)
• lower cost
• less space on chip
• less power and heat
• slower
• SRAM (static no refreshing)
• higher speed, cost, heat, power, and space

5
Access Time

• Time to read/write a memory location
• Cycle time time for a repeat reference
• may be longer (memory needs to recover)
• may be shorter (pipelining, multiple memory
  banks, etc.)
• Different levels of memory have different speeds
• registers, cache, main memory, virtual memory

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Registers

• Registers part of main processor (and as fast)
• Very limited storage (perhaps a few dozen
  locations)
• Compilers must decide how to use registers
  effectively
• re-use of numbers without storing to memory

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Cache

• Small amounts of (fast) SRAM
• Layers of cache (on-chip and off-chip)
• Want processor and compiler to guess correctly
  which memory locations to put in cache
• hit rate percentage of memory references that
  are satisfied by cache
• Cache memory must be kept consistent
• Cache divided into lines to reduce effort of
  tracking locations in memory

Fortran files ex37.f, ex37a.f
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Timing Output

• time f1
• 0.14u 0.14s 000 43 047k 76io 0pf0w
• u user time (seconds)
• s system time
• elapsed time
• CPU time as of elapsed time
• k text plus data space
• io of blocks (read/write)
• pf page faults, w of process swaps

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Cache Misses

• Organization of
• SUM SUM A(I,J)
• Traversing a linked list
• Indirect addressing
• SUM SUM A(IND(J))
• Thrashing a lot of cache misses (and slow
  performance)

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Cache Organization

• Direct-mapped cache
• Each cache location maps onto a fixed set of
  memory locations (only one of which is stored in
  the cache)
• problems if the program needs to access two such
  locations simultaneously
• Fully associative cache
• any memory location can map into any cache line
• remove least recently used line as necessary

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Virtual Memory

• Separate physical space (actual memory) from
  address space (memory that can be referenced)
• Extra memory on auxiliary devices (e.g., disks)
• Memory is often divided into units called pages
  (about 1Mbyte, say)

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Virtual Memory (cont.)

• Page table translate from address space to
  physical space (and yet another cache to watch
  for repeated usage)
• Page fault the desired page is on an auxiliary
  device
• computer/compiler must manage memory
• depends on number of users
• can seriously degrade performance

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What Can You Do?

• Localized use of memory
• Program with BLAS (see Lecture 3)

Fortran files ex38.f, ex38a.f,
http//www.netlib.org/lapack/index.html
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What a Compiler Does

• Focus optimization of machine instructions
• Convert high-level language into fastest possible
  machine language (in an accurate way)
• Essential for getting good performance from
  complicated processors and memory
• May require human guidance

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Choice of Language

• C, C
• pointers (unpredictable before run time)
• harder to optimize
• Fortran
• older, standardized Fortran (Fortran 77)
• Fortran 90, etc.
• better data structures, but

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Compilation Process

• Preprocessing (including files, text
  substitutions, etc.)
• Lexical analysis (identify variables, constants,
  comments, )
• Parsing (analyze syntax) into intermediate
  language suitable for optimization
• Optimization (one or more passes)
• Translation to assembly language

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Levels of Optimization

• Often an option at compile time
• basic optimizations described below
• interprocedural (across subroutines)
• runtime profile
• floating-point optimizations (e.g., algebraic
  transformations)
• data flow analysis (identify parallelism)
• advanced (vectorization, parallelization, data
  decomposition)

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Basic Optimization

• Copy propagation
• Change
• X Y
• Z 1.0 X
• to
• X Y
• Z 1.0 Y
• so statements can execute simultaneously

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Constant Folding

• Look for disguised constants
• INTEGER I,K
• PARAMETER (I100)
• K 200
• J I K

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Strength Reduction

• Change
• Y X2
• J K2
• to
• Y XX
• J KK
• for faster execution

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Loop Invariants

• Change
• DO I1,N
• A(I)B(I)CD
• EG(K)
• ENDDO
• to
• TEMPCD
• DO I1,N
• A(I)B(I)TEMP
• ENDDO
• EG(K)

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Other Techniques

• Dead code removal
• between procedures?
• Variable renaming (when variables are re-used)
• to allow more flexibility in register, memory use
• Common sub-expressions
• D C (A B)
• E (A B)/2

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Object Code Generation

• Specific to the target computer processor
• Compiler may have to
• manage use of registers
• schedule instructions
• distribute resources
• balance the instruction mix
• exploit fast operations (e.g., for loop
  indices)
• exploit parallelism

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For Next Class

• Homework see web site
• Reading
• Dowd chapters 6, 7, and 8