Computer Arithmetic Algorithms, Second Edition,9781568811604

Computer Arithmetic Algorithms, Second Edition

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Edition: 2nd
ISBN13: 9781568811604
ISBN10: 1568811608
Format: Hardcover
Pub. Date: 2001-11-30
Publisher(s): A. K. Peters
List Price: $95.50

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Summary

This text explains the fundamental principles of algorithms available for performing arithmetic operations on digital computers. These include basic arithmetic operations like addition, subtraction, multiplication, and division in fixed-point and floating-point number systems as well as more complex operations such as square root extraction and evaluation of exponential, logarithmic, and trigonometric functions. The algorithms described are independent of the particular technology employed for their implementation.

Table of Contents

Forword to the Second Edition xi
Preface xiii
Conventional Number Systems
1(18)
The Binary Number System
1(1)
Machine Representations of Numbers
2(2)
Radix Conversions
4(2)
Representations of Negative Numbers
6(7)
Addition and Subtraction
13(2)
Arithmetic Shift Operations
15(1)
Exercises
16(1)
References
17(2)
Unconventional Fixed-Radix Number Systems
19(16)
Negative-Radix Number Systems
19(2)
A General Class of Fixed-Radix Number Systems
21(2)
Signed-Digit Number Systems
23(4)
Binary SD Numbers
27(5)
Exercises
32(1)
References
33(2)
Sequential Algorithms for Multiplication and Division
35(18)
Sequential Multiplication
35(4)
Sequential Division
39(3)
Nonrestoring Division
42(6)
Square Root Extraction
48(2)
Exercises
50(2)
References
52(1)
Binary Floating-Point Numbers
53(40)
Preliminaries
53(6)
Floating-Point Operations
59(6)
Choice of Floating-Point Representation
65(2)
The IEEE Floating-Point Standard
67(4)
Round-off Schemes
71(5)
Guard Digits
76(5)
Floating-Point Adders
81(3)
Exceptions
84(3)
Round-off Errors and Their Accumulation
87(2)
Exercises
89(2)
References
91(2)
Fast Addition
93(48)
Ripple-Carry Adders
93(2)
Carry-Look-Ahead Adders
95(4)
Conditional Sum Adders
99(3)
Optimality of Algorithms and Their Implementations
102(4)
Carry-Look-Ahead Addition Revisited
106(3)
Prefix Adders
109(1)
Ling Adders
110(3)
Carry-Select Adders
113(3)
Carry-Skip Adders
116(3)
Hybrid Adders
119(5)
Carry-Save Adders
124(8)
Pipelining of Arithmetic Operations
132(3)
Exercises
135(3)
References
138(3)
High-Speed Multiplication
141(40)
Reducing the Number of Partial Products
141(8)
Implementing Large Multipliers Using Smaller Ones
149
Accumulating the Partial Products
145(12)
Alternative Techniques for Partial Product Accumulation
157(8)
Fused Multiply-Add Unit
165(2)
Array Multipliers
167(7)
Optimality of Multiplier Implementations
174(2)
Exercises
176(3)
References
179(2)
Fast Division
181(32)
SRT Division
181(6)
High-Radix Division
187(11)
Speeding Up the Division Process
198(5)
Array Dividers
203(3)
Fast Square Root Extraction
206(3)
Exercises
209(1)
References
210(3)
Division Through Multiplication
213(12)
Division by Convergence
213(5)
Division by Reciprocation
218(4)
Exercises
222(1)
References
223(2)
Evaluation of Elementary Functions
225(22)
The Exponential Function
226(3)
The Logarithm Function
229(3)
The Trigonometric Functions
232(3)
The Inverse Trigonometric Functions
235(3)
The Hyperbolic Functions
238(1)
Bounds on the Approximation Error
239(2)
Speed-up Techniques
241(2)
Other Techniques for Evaluating Elementary Functions
243(1)
Exercises
244(1)
References
245(2)
Logarithmic Number Systems
247(12)
Sign-Logarithm Number Systems
247(2)
Arithmetic Operations
249(3)
Comparison to Binary Floating-Point Numbers
252(1)
Conversions to/from Conventional Representations
253(2)
Exercises
255(1)
References
256(3)
The Residue Number System
259(18)
Preliminaries
259(2)
Arithmetic Operations
261(3)
The Associated Mixed-Radix System
264(2)
Conversion of Numbers from/to the Residue System
266(1)
Selecting the Moduli
267(2)
Error Detection and Correction
269(5)
Exercises
274(1)
References
275(2)
Index 277

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