IA-64 and Elementary Functions
Speed and Precision
Published on 12. May 2000
Book
Paperback/Softback
298 pages
978-0-13-018348-4 (ISBN)
Description
*Covers every major elementary function, including square root and division *IA-64 architecture and Explicit Parallel Instruction Computing (EPIC), in depth *By an active participant in HP's IA-64 development team *For every professional building high-performance IA-64 server applications and operating systems Optimizing code for the new IA-64 architecture. "...a timely and valuable book. It will appeal to those interested separately or jointly in IA-64 and the elementary math functions." -William S. Worley, Jr., Distinguished Contributor, Hewlett-Packard Laboratories In IA-64 and Elementary Functions: Speed and Precision, leading HP computer architect Dr. Peter Markstein introduces the IA-64 architecture and its breakthrough elementary math functions. This information-essential to the development of optimized IA-64 server applications and operating systems-was formerly available only in specialized journals, or not available at all.Markstein first 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, including software pipelining, instruction grouping, prefetching, predication, speculative execution, and explicit parallelism.
He then 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. The book covers all major elementary functions, demonstrating how they can be implemented to deliver optimal IA-64 performance and accuracy. Among the functions covered: square root and division, which must be performed in software on the IA-64. For professional computer scientists, system software developers, mathematicians, and anyone building high-performance IA-64 software, IA-64 and Elementary Functions: Speed and Precision will be absolutely indispensable.
He then 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. The book covers all major elementary functions, demonstrating how they can be implemented to deliver optimal IA-64 performance and accuracy. Among the functions covered: square root and division, which must be performed in software on the IA-64. For professional computer scientists, system software developers, mathematicians, and anyone building high-performance IA-64 software, IA-64 and Elementary Functions: Speed and Precision will be absolutely indispensable.
More details
Language
English
Place of publication
Upper Saddle River
United States
Publishing group
Pearson Education (US)
Target group
College/higher education
Dimensions
Height: 242 mm
Width: 182 mm
Thickness: 25 mm
Weight
816 gr
ISBN-13
978-0-13-018348-4 (9780130183484)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
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.
Content
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.
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.