IEEE 754. Standard for binary floating-point arithmetic 0
Год: 1985
Количество страниц: 20
Язык: Английский
Формат: PDF / RAR
Формат файла: RAR
This standard is a product of the Floating-Point Working Group of the Microprocessor Standards Subcommittee of the Standards Committee of the IEEE Computer Society. This work was sponsored by the Technical Committee on Microprocessors and Minicomputers. Draft 8.0 of this standard was published to solicit public comments. Implementation techniques can be found in An Implementation Guide to a Proposed Standard for Floating-Point Arithmetic by Jerome T. Coonen, which was based on a still earlier draft of the proposal.
This standard defines a family of commercially feasible ways for new systems to perform binary floating-point arithmetic. The issues of retrofitting were not considered. Among the desiderata that guided the formulation of this standard were
1) Facilitate movement of existing programs from diverse computers to those that adhere to this standard.
2) Enhance the capabilities and safety available to programmers who, though not expert in numerical methods, may well be attempting to produce numerically sophisticated programs. However, we recognize that utility and safety are sometimes antagonists.
3) Encourage experts to develop and distribute robust and efficient numerical programs that are portable, by way of minor editing and recompilation, onto any computer that conforms to this standard and possesses adequate capacity. When restricted to a declared subset of the standard, these programs should produce identical results on all conforming systems.
4) Provide direct support for
a) Execution-time diagnosis of anomalies
b) Smoother handling of exceptions
c) Interval arithmetic at a reasonable cost
5) Provide for development of
a) Standard elementary functions such as exp and cos
b) Very high precision (multiword) arithmetic
c) Coupling of numerical and symbolic algebraic computation
6) Enable rather than preclude further refinements and extensions.
- Geometric algorithms and combinatorial optimization Grotschel M., Lovasz L., Schnjver A.
Historically, there is a close connection between geometry and optimization This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc - IEEE floating point representation 0
- Division by invariant integers using multiplication Granlund T.
Integer division remains expensive on today's processors as the cost of integer multiplication declines We present code sequences for division by arbitrary nonzero integer constants and run-time invariants using integer multiplication The algorithms assume a two's complement architecture - Arithmetic tutorials Jones D.W.
These tutorials are characterized by an interest in doing arithmetic on machines with just binary add, subtract, logical and shift operators, making no use of special hardware support for such complex operations as BCD arithmetic or multiplication and division