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

  • 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.

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You could check out the standard, itself: ieeexplore.ieee.org/servlet/opac?punumber=4610933 –  dls Jan 24 '12 at 5:30

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up vote 4 down vote accepted

You could try the

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.

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There is plenty literature about accurate dot products. See for instance Ogita et al., Accurate sum and dot product. SIAM J. Sci. Comput. 26 (2005), no. 6, 1955–1988 and other papers by S. Rump and collaborators. –  lhf Jan 24 '12 at 10:25
    
Took a look at the table of contents for "Handbook of Floating Point Arithmetic" and it looks close to what I want. –  user782220 Jan 24 '12 at 10:27

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