Robert Kern wrote:
Ryan Krauss wrote:
Sorry to bring this back up again (this thread has been dormant since 12/21/05), but I think this is the key road block between me and really understanding this problem (and I think it went over my head when it was originally posted). If double precision numbers use 52 bits for the mantissa, what does it mean to say that 2**-52 is the approximate fractional precision of double precision floats?
I don't have time right now to go into a lecture on condition numbers and other such stuff, but let give you an example to chew on and a good reference:
If I can jump in and show something even simpler: In [1]: x,sum=0.1,0 In [2]: for m in range(10): ...: sum = sum + x ...: In [3]: sum Out[3]: 0.99999999999999989 In [4]: sum-1 Out[4]: -1.1102230246251565e-16 As for books, I've always liked Kahaner, Moler and Nash. Steve