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November 05, 2009

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If one wants to know everything about floating point but is afraid to ask there is the bible of computer programming in particular the Semi-numerical Algorithms section. Fundamentally the issue is that the floating point number line is not dense, i.e. there are points on the line that have no representation in the floating point space, because recall that between any two numbers on that line there is another number. Unless one had an infinitely long floating point number, the above condition can not be satisfied.

Opps forgot to add that the book cited is by Donald Knuth.

The Ariane5 did not crash due to a floating point error but due to an integer overflow. Rather different beast...

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