abs(0.01) > 0.01 is false? The answer is weired!

K>> abs(currentTradePrice - lastPrice)

ans =

    0.0100

K>> 0.0100 >= 0.01

ans =

     1

K>> abs(currentTradePrice - lastPrice) >= 0.01

ans =

     0

Answer 1

[Wayne King]

You actually are using >= in your code even though your post says >, I think you should consider the following wiki:

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

This is a often encountered problem when you have to compare floating-point numbers in any computing environment.

Answer 2

[John D'Errico]

You have just won the award for being the millionth person to ask this question! Sorry, but first prize in this contest is only a bobble head doll modeled after me. Second prize is TWO bobble head dolls of me. :)

Try this:

X = 0.01 - eps
X =
         0.01

See that X is displayed as 0.01, even though it is just a tiny bit less. Now, if we compare it to 0.01, we see that MATLAB sees a difference, even though the number was displayed as 0.01.

X < 0.01
ans =
     1

In fact, if we display X in a long format, we will see that it is not truly 0.01, even though the short format rounded it off for display purposes.

format long g
X
X =
       0.00999999999999978

Of course, a deeper investigation will reveal that 0.01 is not even truly 0.01. If I convert the number that you put into MATLAB as 0.01 from the IEEE double precision form into a true decimal form...

hpf(0.01)
ans =
0.01000000000000000020816681711721685132943093776702880859375

This is true because MATLAB stores the number as a binary number. But most decimal numbers are not exactly representable in binary. Avoid testing for equality in floating point arithmetic. And always be careful with tests done on non-integers.

The moral of the story is to understand floating point numbers. And never totally trust what you see.