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Numerical Computing with IEEE Floating Point Arithmetic by Michael L. Overton

By Michael L. Overton

Are you acquainted with the IEEE floating element mathematics average? do you want to appreciate it greater? This ebook provides a huge assessment of numerical computing, in a ancient context, with a distinct specialise in the IEEE general for binary floating aspect mathematics. Key rules are built step-by-step, taking the reader from floating aspect illustration, accurately rounded mathematics, and the IEEE philosophy on exceptions, to an figuring out of the an important suggestions of conditioning and balance, defined in an easy but rigorous context. It supplies technical info that aren't on hand somewhere else and contains not easy workouts that transcend the themes coated within the textual content.

Numerical Computing with IEEE Floating element mathematics presents an simply obtainable but specific dialogue of IEEE Std 754-1985, arguably crucial usual within the computing device undefined. the results of an remarkable cooperation among educational computing device scientists and the innovative of undefined, it truly is supported through nearly each sleek desktop. different themes comprise the floating aspect structure of the Intel microprocessors and a dialogue of programming language aid for a standard.

The booklet might be available to scholars at any point, in addition to to any reader with an curiosity in pcs and arithmetic. It offers sufficient number of content material that each one however the such a lot specialist readers will locate anything of curiosity.

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Extra resources for Numerical Computing with IEEE Floating Point Arithmetic

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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. He was well aware that the range limitations of fixed point would be too severe to be practical, but he believed that the necessary scaling by a power of 2 should be done by the programmer, not the machine; he argued that bits were too precious to be wasted on storing an exponent when they could be used to extend the precision of the significand.

It also justifies referring to the left end of the representation as the "most significant" end. 13, which considered the toy number system with one additional bit in the significand. 13. 3: Range of IEEE Floating Point Formats The Double Format The single format is not adequate for many applications, either because higher precision is desired or (less often) because a greater exponent range is needed. The IEEE standard specifies a second basic format, double, which uses a 64-bit double word. 2.

6 What are the values of the expressions 0/(—0), oo/(—oo), and -oo/(-0)? 1) if R1 = 1 and R2 = -0? More about NaNs The square root operation provides a good example of the use of NaNs. Before the IEEE standard, an attempt to take the square root of a negative number might result only in the printing of an error message and a positive result being returned. The user might not notice that anything had gone wrong. Under the rules of the IEEE standard, the square root operation is invalid if its argument is negative, and the standard response is to return a NaN.

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