Download Numerical computing with IEEE floating point arithmetic: by Michael L. Overton PDF

By Michael L. Overton

Are you conversant in the IEEE floating element mathematics commonplace? do you want to appreciate it greater? This ebook supplies a large evaluate of numerical computing, in a old context, with a unique specialize in the IEEE regular for binary floating aspect mathematics. Key rules are constructed step-by-step, taking the reader from floating element illustration, competently rounded mathematics, and the IEEE philosophy on exceptions, to an figuring out of the the most important options of conditioning and balance, defined in an easy but rigorous context. It provides technical info that aren't on hand in different places and comprises difficult workouts that transcend the themes coated within the textual content.

Numerical Computing with IEEE Floating aspect mathematics presents an simply available but particular dialogue of IEEE Std 754-1985, arguably an important normal within the machine undefined. the results of an exceptional cooperation among educational laptop scientists and the leading edge of undefined, it really is supported via almost each smooth laptop. different themes comprise the floating aspect structure of the Intel microprocessors and a dialogue of programming language help for a standard.

The e-book might be obtainable 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 each one however the so much professional readers will locate anything of curiosity.

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Additional info for Numerical computing with IEEE floating point arithmetic: including one theorem, one rule of thumb, and one hundred and one exercises

Sample text

This reduces by one the number of possible exponents E that are allowed for representing nonzero numbers. This is the approach taken by the IEEE standard, to be discussed in the next chapter. In either case, there is the question of what to do about the sign of zero. Traditionally, this was ignored, but we shall see a different approach in the next chapter. The Toy Number System It is quite instructive to suppose that the computer word size is much smaller than 32 bits and work out in detail what all the possible floating point numbers are in such a case.

000... 0)2 x 2~126 is certainly one way to write the number 0. 9 Let us postpone the discussion of subnormal numbers for the moment and go on to the other lines of the table. , all the floating point numbers that are not special in some way. Note 9 The word denormalized was used in IEEE 754. The word subnormal replaced it in IEEE 854. 20 NUMERICAL COMPUTING WITH IEEE ARITHMETIC especially the relationship between the exponent bitstring a1a2a3 • • • a8 and the actual exponent E. We see that the exponent representation does not use either the signand-modulus or the 2's complement integer representation discussed in the previous chapter, but something called biased representation; the bitstring that is stored is the binary representation of E + 127.

6). 5 to ±1. We shall show in the next chapter how these gaps can be filled in with the introduction of subnormal numbers. 13 Suppose we add another bit to the toy number system, allowing significands of the form 60-616263, with 60 stored explicitly as before and all nonzero numbers required to be normalized. The restrictions on the exponent are unchanged. 1. Fixed Point versus Floating Point Some of the early computers used fixed point representation and some used floating point. Von Neumann was initially skeptical of floating point and promoted the use of fixed point representation.

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