Imprecise Basic operations

Hi everyone,

I am using Matlab 2009a. When I try to calculate

0.9 - 0.8 - 0.1

then the result is

-2.775557561562891 e-017

Close to zero, but not zero. Is it not possible to get a precise solution for a floating point operation? This minor imprecision has large implications for my programs.

Is there a way to get precise calculations? Why does matlab get this (quite easy task) wrong?

Thanks for your help!

[James Tursa]

You might find this FEX submission useful:

http://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str

Answer 1

[Nathan Greco]

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

Welcome to the world of floating point computing.

A computer can't exactly represent most floating point numbers.

Example: Try calculating 3*(1/3) by hand, with writing out 1/3 to as many decimal places as you please. You will get .9999..., which is CLOSE to 1, but is not equal to 1 (which the true answer should be).

[Jan]

+1: Exactly. The behaviour is neither "wrong" nor "inprecise". It simply demonstrates the limited precision.

[Walter Roberson]

Though if you go an infinite number of decimal places, 0.99999999999999.... (with infinite 9's) *is* equal to 1.

If you had an infinite number of bits, you could get an exact binary representation for 0.1 -- but of course no physically realizable computer can be infinite.

Answer 2

[Philipp]

Thanks for your quick responses. I was aware of the numerical issues when calculation 1/3 * 3, or using non-rational numbers. But I was not aware of the fact that the binary representation of 0.1 has a infinite number of digits. Thanks.