1e301-10^301 ~= 0 ?

Why does 1e301-10^301 not equal zero in matlab, but 1e300-10^300 does?

1e301-10^301 is 1.18961352678223e+285.

Answer 1

[Walter Roberson]

1e301 is computed entirely at parse time, as a double precision number.

10^301 involves computing 10 and 301 at parse time, each as double precision numbers, and then computing the one to the power of the other at run time, resulting in a double precision number. As this is a floating point calculation, it is subject to standard floating point roundoff .

1e301 comes out as the first representable double precision number greater than 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and 10^301 is one bit different, coming out as the last representable double precision number less than 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 . 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 itself is not exactly representable in double precision.

Answer 2

[Azzi Abdelmalek]

Read this http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F