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Computer Science Syllabus - Floating-Point Computation
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Floating-Point Computation

Lecturer: Professor A. Mycroft

No. of lectures: 4

This course is useful for the Part II courses Advanced Graphics and Digital Signal Processing.

Aims

This course has two aims: firstly to provide an introduction to (IEEE) floating-point data representation and arithmetic; and secondly to show, mainly by fun examples backed up by simple analysis, how naïve implementations of obvious mathematics can go badly wrong.

Lectures

  • IEEE Floating-point representation and arithmetic (32 and 64 bits). Overflow, underflow, progressive loss of significance. Rounding modes.

  • How floating-point computations diverge from real-number calculations. Absolute Error, Relative Error, Machine epsilon. Solving a quadratic.

  • Iteration and when to stop. Why summing a Taylor series is problematic (loss of all precision, range reduction, non-examinable hint at economisation).

  • Ill-conditioned or chaotic problems. Testing. Packages. Non-examinable: exact real arithmetic.

Objectives

At the end of the course students should

  • be able to convert simple decimal numbers to and from IEEE floating-point format, and to perform simple arithmetic

  • be able to identify problems with floating-point implementations of simple mathematical problems

  • know when a problem is likely to yield incorrect solutions no matter how it is processed numerically

  • know to use a professional package whenever possible

Recommended reading

None.



next up previous contents
Next: Group Project Up: Michaelmas Term 2006: Part Previous: ECAD   Contents
Christine Northeast
Tue Sep 12 09:56:33 BST 2006