CIS541

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CIS541 Lab1 Analysis

• Roger Crawfis

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Computers Do As Theyre Told

• Garbage in Garbage out
• Most of lifes problems emanate from an
  underlying communication problem.
• No different with computers
• You thought you told the computer to do one
  thing. It did another.
• You thought the input or intended use of your
  system was A. It was given B.

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Lab1 Results

• Results were identical to digits shown for Taylor
  series and sin(x). Results for different step
  sizes.

100K 1M 10M 100M
Reimann(sin) -1.0449 10-5 6.9785 10-5 3.7607710-4 -4.194310-3
Value of x at the end of the for loop 0.0998974 0.1007008 0.104126 -0.1
???
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Lab1 Results

• Why was the value of x equal to 0.1 at the end
  of the loop?
• 32-bit floating point accuracy
• x -0.1 0.00000001 ? -0.1
• The value of sin(-0.1) -0.09983342, why wasnt
  the result equal to this value as well?

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Forcing Floating-Point Arithmetic

• Do you believe the other numbers generated by
  your program?
• What is the difference between these two
  statements?
• Sum x // one term of the Taylor Series
• Sum x(1-xx( 1 / (321) ) )
• // two terms of the Taylor Series

Absolutely nothing!!!
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Lab1 Lessons Learned

• More work is not necessarily better.
• Do not trust the answers blindly. See if they
  make sense.
• Computer precision is limited.
• Round-off errors actually do happen.
• Sleep is for weenies ?!

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Lessons Learned

• Computers have limited capabilities!!!