Numerical analysis textbooks and floating point numbers What are some recommended numerical analysis books on floating point numbers? I'd like the book to have the following


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*In depth coverage on the representation of floating point numbers on modern hardware (the IEEE standard).

*How to do arbitrary precision floating point calculations with a reasonably fast modern algorithm.

*How to compute the closest 32-bit floating point representation of a dot product and cross product. And do this fast, so no relying on generic arbitrary precision calculations to get the bits of the 32-bit floating point number right.
From what I can infer from doing some searches most books tend to focus on stuff like the runge kutta and not put much emphasis on how to make floating point calculations that are ultra precise.

You could try the book written by J.M. Muller, N. Brisebarre:

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*Handbook of Floating Point Arithmetic (amazon.com)

The literature of numerical mathematics concentrates on algorithms for mathematical problems, not on implementation issues of arithmetic operations.

How to compute the closest 32-bit floating point representation of a dot product and cross product. 

Since these are concatenations of addition and multiplication, I expect that you won't find much about dot and cross products themselves.
