Kneusel Review Numbers and Computers 2nd Edition Review
Numbers, wonderful mathematical idealizations that they are, have fascinated humans for every bit long equally in that location have been humans. Computers, much more recent creations, are fascinating in their own mode. For many, both are useful but intractable and hard to understand beyond the surface. Students and programmers learn that within computers numbers are just estimate, and for many this degree of acquaintance is sufficient to acquit them through their careers without excessive trouble. Scientists and engineers demand a deeper level of understanding to have confidence in the results they obtain from their computers. Computer scientists and computer designers must, of course, fully sympathize the relation between numbers, calculator circuits, and the software to manipulate them. In Numbers and computers, Kneusel offers a book for all these audiences, and for anyone who would like to delve deeper into this co-operative of engineering science.
The aim is to provide a thorough introduction to the representation and operation of numbers inside computers. This is done through detailed descriptions of the means different numbers (integers, reals, and decimals) are represented internally; how they are manipulated is shown both through detailed descriptions of the processes involved and through lawmaking given in C and in Python.
The first part of the book, capacity ane through 4, deals with integers and floating-betoken numbers. The second role, chapters 5 through 10, deals with other number representations. Chapter titles provide an fantabulous summary of the contents: (1) "Number Systems," (ii) "Integers," (3) "Floating Point," (4) "Pitfalls of Floating-Point Numbers (and How to Avert Them)," (five) "Big Integers and Rational Arithmetic," (half dozen) "Stock-still-Betoken Numbers," (7) "Decimal Floating Signal," (viii) "Interval Arithmetic," (nine) "Arbitrary Precision Floating Point," and (x) "Other Number Systems."
The material includes information about current standards such equally the IEEE 754 standard for binary floating-point arithmetics, emerging standards such as the IEEE 754-2008 standard for floating-signal numbers using base 10 rather than base ii, capricious precision floating-point representations, and other piffling-used number representations such equally unlimited-precision integers--very large integers limited only by hardware capacity.
Kneusel's presentation of the material is detailed, concise, and clear. The accompanying lawmaking provides additional insights, can be useful in its own correct, and provides a springboard for further work or for translation into other languages. Each chapter concludes with exercises and references; the exercises are first-class, and the references all-encompassing.
Kneusel provides knowledgeable commentary and advice from time to time. He mentions some widely available libraries, provides extensive details on them, and suggests how to install them and when to use them.
The second edition contains three new capacity non nowadays in the showtime edition, and some other additional material. (My review of the book's offset edition [1] takes a more detailed look at that edition.) The near significant new material is chapter nine on arbitrary precision floating-indicate arithmetic. This chapter introduces the ideas and benefits underlying this numerical representation and develops a Python library using one of the ii options available for implementation, namely, fixed bespeak for the exponent and, taking advantage of Python's support for unlimited digits, a very large number of digits in the fractional part. As well included are implementations of trigonometry and transcendental functions--sine, cosine, and the exponential function, square root, and natural logarithms. Usage of arbitrary floating-bespeak precision in libraries mpmath for Python and GNU MPFR for C and other languages is illustrated in detail.
Chapter x, likewise new to the second edition, looks from a software perspective at some number systems usually implemented in hardware: logarithmic number systems, double-base number system, balance number organization, and redundant signed-digit number system. The intent is to understand how these systems operate and when they become advantageous to use.
Chapter iv is an expanded version of Department 3.10 of the starting time edition. Two failures due to erroneous numerical results--the recount of a German election, and recalculation, by manus, of the index of a stock commutation--are added to the more spectacular failures previously listed: the explosion of an Ariane rocket and the failure of a Patriot missile (which resulted in loss of war machine lives).
Finally, Section 6.4, "An Emerging Utilize Instance," likewise new to the second edition, illustrates the utilise of stock-still-signal numbers in neural networks, which is maybe the most fruitful technique underlying recent rapid advances in artificial intelligence.
This book should exist an excellent resources in the classroom. It can serve as a skilful reference for future employ and tin can likewise be used very profitably for self-study.
Source: https://www.computingreviews.com/review/review_review.cfm?review_id=146045
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