Автор курса - известный специалист по компьютерной арифметике Dr. Florent de Dinechin, университет Лиона, Франция. Dr. Florent de Dinechin – сотрудник института, в котором был разработан стандарт представления чисел с плавающий запятой IEEE-754, один из авторов книги по вещественной арифметике «Handbook of Floating-Point Arithmetic» http://www.amazon.com/gp/product/081764704X.
 
Цель курса: введение в проблематику решения задач вычислительного характера в условиях ограничений представления чисел на ЭВМ.
 
Предварительная программа курса:

Lecture 1: Introduction
  Number representation
  Introduction to floating-point

Lecture 2: The floating-point environment
    The dark ages of anarchy
  Floating-point as it should be (The IEEE754-1985 standard)
    Floating-point as it is in current processors
    Floating-point as it is in current languages
    Floating-point as it is in current operating systems

Lecture 3: Science around binary floating-point
  Representation tips and tricks
    Rounding to an integer
  Sterbenz Lemma
    Exact addition
    Exact multiplication
    Application: evaluating a polynomial to 60 bits of accuracy
    Compensated sums
    Compensated Horner evaluation

Lecture 4: The 2008 revision of the IEEE-754 standard
  The new binary formats
    The FMA
    The decimal fiasco
  Elementary functions
    Sums and sums of products

Lecture 5: Elementary functions and their evaluation
  Examples of argument reduction
  Polynomial approximation
  Evaluation of polynomials
  Overall error analysis
  Ziv's technique for correct rounding

Lecture 6: Variations on the exponential
  Baseline double-precision version
  Using double-extended
  Single-precision versions
  Vector versions
  Correctly rounded versions
  Correctly rounded vector versions
  GPU version
  FPGA version

Lecture 7: Automating error analysis
  Formal definitions of floating-point numbers
  Interval arithmetic
  Taylor and Chebychev models
  Computing infinite norms
  Managing rounding errors with high-level formal proof tools

Lecture 8: Automating code generation for function evaluation
  Machine-efficient polynomial approximation
  Constrained polynomial approximation
  Optimizing polynomial coefficient sizes
  Overlapping double-double and triple-double arithmetic

Lecture 9: Variations around the trigonometric functions
    Radian versus degrees
  Cody and Waite argument reduction
     Paine and Hainek argument reduction
    Inverse trigonometric functions

Lecture 10: Solving the table maker's dilemma
  Lefèvre algorithms
  Analysis of some surprising results
  SLZ algorithm
  Brute-force approaches

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