Numerical Computing with IEEE Floating Point Arithmetic - download pdf or read online

By Michael L. Overton

Are you accustomed to the IEEE floating element mathematics average? do you want to appreciate it larger? This e-book provides a large review of numerical computing, in a ancient context, with a unique concentrate on the IEEE general for binary floating element mathematics. Key principles are constructed step-by-step, taking the reader from floating element illustration, effectively rounded mathematics, and the IEEE philosophy on exceptions, to an knowing of the the most important ideas of conditioning and balance, defined in an easy but rigorous context. It provides technical info that aren't available in other places and comprises demanding workouts that transcend the themes lined within the textual content.

Numerical Computing with IEEE Floating aspect mathematics offers an simply obtainable but designated dialogue of IEEE Std 754-1985, arguably crucial normal within the computing device undefined. the results of an unheard of cooperation among educational desktop scientists and the leading edge of undefined, it's supported by way of almost each sleek desktop. different issues comprise the floating element structure of the Intel microprocessors and a dialogue of programming language help for a standard.

The e-book may be available to scholars at any point, in addition to to any reader with an curiosity in pcs and arithmetic. It presents adequate number of content material that every one however the so much specialist readers will locate whatever of curiosity.

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12 The pigeon-hole principle (J. Demmel, W. Kahan; see also fEde94]). 1, and (b) the IEEE single format numbers. 1. How many floating point numbers x satisfy 1 < x < 2? How many of these satisfy 1 < x < 3/2 and how many satisfy 3/2 < x < 2 ? 2. How many floating point numbers x satisfy 1/2 < x < I? Approximately how many of these satisfy 1/2 < x < 2/3 and approximately how many satisfy 2/3 < x

If we truncate this to fit the significand field size, we find that 1/10 is stored as We shall see other rounding options in the next chapter. Emax = 127. 1 shows that an exponent bitstring consisting of all 1s is a special pattern used to represent ±00 or NaN, depending on the fraction bitstring. We will discuss these in Chapter 7. Subnormals Finally, let us return to the first line of the table. The idea here is as follows: although 2~126 is the smallest normalized number that can be represented, we can use the combination of the special zero exponent bitstring and a nonzero fraction bitstring to represent smaller numbers called subnormal numbers.

A second IEEE floating point standard, for radix-independent floating point arithmetic, ANSI/IEEE Std 854-1987 [IEE87], was adopted in 1987. The second standard was motivated by the existence of decimal, rather than binary, floating point machines, particularly hand-held calculators, and set requirements for both binary and decimal floating point arithmetic in a common framework. The demands for binary arithmetic imposed by IEEE 854 are consistent with those previously established by IEEE 754. In this book, when we write "the IEEE standard," we refer to the binary standard, IEEE 754.

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