Computer Approximations [Hardcover]

John Fraser Hart (Author)

Book Description

ISBN-10: 0882756427 | ISBN-13: 978-0882756424 | Publication Date: July 1, 1978

This handbook is intended to acquaint users with methods for designing function subroutines and, in the case of the most commonly needed functions, to provide them with the necessary tables to do so efficiently.

Product Details

• Hardcover: 352 pages
• Publisher: Krieger Pub Co (July 1, 1978)
• Language: English
• ISBN-10: 0882756427
• ISBN-13: 978-0882756424
• Product Dimensions: 9 x 6.2 x 1 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 3.8 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #1,137,066 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

5.0 out of 5 stars A must for algorithm developers, February 14, 2009

By 

M. Rapkin (New Jersey, USA) - See all my reviews
(REAL NAME)   

This review is from: Computer Approximations (Hardcover)

When computers were slow and memory expensive, 2 score and 4 years ago, John Hart published "Computer Approximations" as a means of implementing complex numerical calculations for greater efficiency. Trigonometric functions expressed as a finite series can take up valuable resources in a real-time processing application. Hart shows you haw to implement some of the most widely used numerical functions in minimal memory and minimal time and still obtain high precision and accuracy in the results. The treatment of trigonometric and logarithmic functions alone is worth the price of the book.

1 of 1 people found the following review helpful:

3.0 out of 5 stars Aging, but still useful, May 20, 2008

By 

wiredweird "wiredweird" (Earth, or somewhere nearby) - See all my reviews
(HALL OF FAME REVIEWER)    (TOP 500 REVIEWER)   

This review is from: Computer Approximations (Hardcover)

As long as computers have finite precision and the world around them doesn't, there's going to be a need for approximations to exact functions. This book helps even modern practitioners work out the most effective and economical choices for common and not-so-common mathematical functions.

The book's most noteworthy feature appears at the end, where nearly half the book presents tables of coefficients for rational polynomial approximations, giving the reader a wide range of choices in both the functions being approximated and in the degree of the polynomials. I'd approach these carefully, though - the notation tends toward the opaque, and there's no clear statement of the range over which the approximation works best or the error in each approximation. Although they represent a useful starting point, serious practitioners will use the techniques elsewhere in this book with modern extended precision algebra-handling tools to work out values on their own.

Even though the bulk of this book dates back to 1968 - over 20 Moore's Law generations ago - most of the discussion remains salient. In fact, things like error analysis are fast becoming lost arts, so parts of the discussion remain especially valuable. The basics are timeless, though, and that includes things like piecewise approximations, basis functions, range reduction, and subtleties of different ways to evaluate polynomials - Horner's rule is hardly the last word, or even the best. Only discussions really show their age, all of them having to do with the details of number representation. This pre-IEEE-754 text doesn't give as much as modern texts do regarding the last bit of precision.

If you think things like sines, cosines, and logs have been done - well, given your computing needs, you're probably right. New computing fabrics continue to emerge, though, with new quirks and performance characteristics. The standard (and non-standard) functions need to be done again for each new platform. Despite its age, this book still offers some help to those of us with needs not met by the Fortran, C, or Java libraries.

-- wiredweird

1 of 1 people found the following review helpful:

5.0 out of 5 stars an excellent reference, November 11, 2006

By 

W "W" (South of the border, West of the sun) - See all my reviews

This review is from: Computer Approximations (SIAM Series In Applied Mathematics) (Hardcover)

It is a pity that this book had gone out of print for many years. The material in the book is still useful in today's work. If you enjoy implementing numerical solutions on computing hardware, hunt down a copy in the used book market.

This book is an excellent reference in the way it furnishes a comphrehensive list of algorithms for each function you want to approximate, trading numerical precisions for computational complexities. Taking the list and experiment with the implementations, perhaps extending it, and then verifying and seeing the trade-offs for yourself, is very useful as well as fun.