IA-64 and Elementary Functions

IA-64 and Elementary Functions : Speed and Precision

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After years of development and anticipation, the new Intel IA-64 processor architecture is set to begin shipping in mid-2000. In this book, leading HP computer architect Dr. Peter Markstein presents the first comprehensive look at IA-64's breakthrough elementary math functions. This information will be crucial to every developer and computer scientist who wants to build IA-64 server applications and operating systems with optimum speed and power. In the first half of the book, Markstein introduces the IA-64 architecture, the objectives that motivated its design, and the unique architectural features that can be exploited by developers of high-performance elementary function libraries. Markstein reviews software pipelining, instruction grouping, pre-fetching, predication, speculative execution, explicit parallelism, and other key features of the IA-64 architecture. Next, he discusses each major elementary function, demonstrating how it can be implemented to provide optimal IA-64 performance and accuracy. The book introduces several techniques that lend themselves to software pipelining, which is exceptionally well-supported by the IA-64 architecture, and can lead to dramatic performance gains.
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Product details

  • Paperback | 298 pages
  • 183.4 x 241.6 x 26.7mm | 816.48g
  • Prentice Hall
  • Upper Saddle River, United States
  • English
  • 0130183482
  • 9780130183484

Table of contents

I. IA-64 Architecture 1. NEW ARCHITECTURE OBJECTIVES. VLIW. Memory Enhancements. Software Pipelining. Floating Point Enhancements. Summary.2. IA-64 INSTRUCTIONS AND REGISTERS. Instructions. Register Sets. Accessing Memory. Assembly Language. Problems.3. INCREASING INSTRUCTION LEVEL PARALLELISM. Branching. Speculation. Problems.4. FLOATING POINT ARCHITECTURE. Floating Point Status Register. Precision. Fused Multiply-Add. Division and Square Root Assists. Floating Comparisons. Communication between Floating Point and General Purpose Registers. Fixed Point Multiplication. SIMD Arithmetic. Problems.5. PROGRAMMING FOR IA-. Compiler Options. Pragmas. Floating Point Data Types. In-Line Assembly. The fenv.h Header. Extended Examples. Quad Precision. Problems.II. Computation of Elementary Functions. 6. MATHEMATICAL PRELIMINARIES. Floating Point. Approximation and Error Analysis. The Exclusion Theorem. Ulps. Problems.7. APPROXIMATION OF FUNCTIONS. Taylor Series. Lagrangian Interpolation. Chebychev Approximation. Remez Approximation. Practical Considerations. Function Evaluation. Table Construction. Problems.8. DIVISION. Approximations for the Reciprocal. Computing the Quotient. Division Using Only Final Precision Results. Fast Variants of Division. Remainder. Integer Division. An Implementation of Division. Problems.9. SQUARE ROOT. Approximations. Rounding the Square Root. Computing the Square Root. Calculating the Reciprocal Square Root. An Implementation of Square Root. Problems.10. EXPONENTIAL FUNCTIONS. Definitions and Formulas. Argument Reduction. Error Containment. Computing the Exponential. The Function expm. Problems.11. LOGARITHMIC FUNCTIONS. General Relations. Argument Reductions. Error Analysis. The Function log1p. Computing the Logarithm. Problems.12. THE POWER FUNCTION. Definition. Single Precision. Double Precision. Double-Extended Precision. Quad Precision. Computing the Power Function. Problems.13. TRIGONOMETRIC FUNCTIONS. Formulas and Identities. Argument Reduction. Error Analysis. Computing the Trigonometric Functions. Problems.14. INVERSE SINE AND COSINE. Definitions and Formulas. Argument Reduction. Error Analysis. Computing the arcsin. Problems.15. INVERSE TANGENT FUNCTIONS. Definitions and Formulas. Argument Reduction. Error Analysis. Computing the arctan. Problems.16. HYPERBOLIC FUNCTIONS. Definitions and Formulas. Argument Reduction. Error Analysis. Computing the Hyperbolic Functions. Problems.17. INVERSE HYPERBOLIC FUNCTIONS. Definitions and Formulas. arcsinh. arccosh. arctanh. Problems.18. ODDS AND ENDS. Correctly Rounded Functions. Monotonicity. Alternative Algorithms. Testing. New Architectural Directions. Problems.A. IN-LINE ASSEMBLY. B. SOLUTIONS TO PROBLEMS. BIBLIOGRAPHY. SUBJECT INDEX.
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About Peter Markstein

PETER MARKSTEIN, Ph.D., is a Senior Technical Contributor at Hewlett-Packard. He holds over 15 patents in computer architecture, compilation techniques, numerical computation, and computer security. Markstein has a Ph.D. from New York University.
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