KIPA Game Engine Seminars

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KIPA Game Engine Seminars
Day 15

• Jonathan Blow
• Seoul, Korea
• December 12, 2002

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Bit Tricks

• Generating Bit Masks
• Is some number a power of two?
• Avoiding if statements (branch prediction)
• Floating-point absolute value
• Floating-point compare
• Floating-point log2

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Generating Bit Masks

• Suppose we want to mask the low n bits of a
  machine word
• We can generate that with a loop
• Show summation equation for the loop
• Identity that lets us do something faster

4
Is some number a power of two?

• The power-of-two will be a single bit somewhere
  in the middle of the word
• The power-of-two minus one will be a bit mask
  like the ones we just looked at
• ANDing them together will produce 0

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Counting the numberof set bits in a machine word

• Slow loop version
• Trick O(num set bits) version
• Discussion of tree version

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Pentium 4 fireball

• A 16-bit integer unit at the core of the chip
  that runs at very high clock speeds
• 32-bit integer operations are pipelined through
  the fireball as multi-stage 16-bit operations
• Pipeline is organized for bits to flow from
  bottom to top of the word (as with addition and
  subtraction)
• Right-shifts require a dependency that goes in
  the opposite direction (slower!)

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How many bits does it take to store this range
of values?

• Application network or file i/o
• Want ceil(log2(n_max)) assuming the values go
  from 0 to n_max
• Slow floating-point versions
• Fast bit-extraction versions

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Floating-Point log2

• Show slow version
• Fast version utilizing the IEEE-754 format

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Fast absolute value

• Utilizing IEEE-754 floating point format

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Fast floating-point compare

• Description of how x86 machines compare floating
  point numbers
• Get at least one of them on the stack
• Perform fcomp instruction
• Load the floating point control word
• Bit-mask it to see if the desired field is set

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Decision-making without branching

• (And without writing in assembly language, to use
  instructions like CMOV)
• Build a mask based on whether some intermediate
  result is negative or not
• Use that to mask values and add them, or whatever
  you want
• Examples

12
Collision Detection

• Speedbox and Schnitzel as alternatives to the
  prevent tunneling raycast

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Collision Detection

• Dont forget to optimize mainly for the expected
  case!
• To miss a lot, or to hit a lot?
• Example of Shock Force and the early hit test
• We expect to miss usually!
• So the early hit test was not so effective

14
Collision detection

• More Shock Force examples
• Hierarchy of tests bounding sphere, OBB, simple
  plane divide, BSP hard case

15
Profiling

• Motivation
• You cant optimize unless you profile. For some
  reason some people think they can theyre wrong.
• Demo of sample app
• Goals
• Know where the overall CPU is being spent
• May depend on which kind of behavior is
  happening!
• Know which routines are stable and which ones are
  not

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Profiling

• Example of getting the current time on Windows
• At different accuracy levels
• Description of how this is slow, and why
• Too slow to call very often in code!

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Profiling (2)

• Using the rdtsc instruction
• Converting this to realtime units by calling
  QueryPerformanceCounter once per frame

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Profiling (3)

• Define macros that put rdtsc calls into preambles
  and postambles for functions
• Measure and categorize CPU time this way
• Measure self time and hierarchical time
• Code review of macros / constructors

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Problem with rdtsc

• Theres this SpeedStep thing on Intel laptops
• Change the CPUs clock speed based on performance
  / temperature demands
• Does not adjust rdtsc to compensate
• May spread beyond laptops in the future
• Power consumption of CPUs is becoming an
  important concern for businesses

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We can detect if rdtsc is screwing up profiling
data

• But we cant fix the profiling data
• Solution just draw a big warning on the screen

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Division of Profiler

• Low-Level Profiler
• High-Level Profiler

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Walkthrough of first demo app

• How it uses the macros
• How it collects and draws the profiling data

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Measuring varianceof profiling data

• To figure out how stable each function is
• Draw which functions are hot in the realtime
  display

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Behaviors

• We would like some better analysis of what the
  different behaviors are for our program
• Just eyeing the results is not very scientific
• Examples of different behaviors
• Fill rate limited, AI limited, etc

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Batch Profiling vs Interactive Profiling

• Batch profiling averages a bunch of data together
  over a session
• Maybe it provides a way to peek at individual
  samples but the processing is never very
  convenient
• Interactive profiling is about seeing results as
  soon as they happen
• But interactive profilers are usually hacked
  together
• What if we made a good one?

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Want to detect and analyzespecific behaviors

• But without preconceived ideas of what they might
  be
• Treat incoming frames of profiling data as
  vectors, and cluster them
• Description of k-means clustering

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Clustering algorithms tend tobe pretty slow

• And they require batch data to process
• k-means needs random access to the input!
• Online k-means
• Faster, non-batch. But quality?

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Self-Organizing Map

• Kohonen Self-Organizing Map
• Description of the algorithm
• Much like online k-means
• But with coherence in a separate space

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Demo of SOM-enabledProfiling Tool

• Visualizations are still early
• Hopefully they will mature into something truly
  useful (people in other visualization fields like
  SOMs, so hopes are high)

30
Discussions of changes made to SOM to support
online clustering