logical less than thinks values are the same?

I have wracked my brain over this one. It must be a dumb mistake.

                    if scalarMin < 1.0
                        fprintf('*scalarMin %f.\n',scalarMin);
                    end

scalarMin is exactly 1.000000, but it insists on printing anyway. Just want an output when it's actually <1.

What could it be?

[Walter Roberson]

What is the output of

num2hex(scalarMin)

?

[dpb]

Well, as you're going to find out when answer Walter's question, it's not < that's the problem; scalarMin actually is going to be somewhat less than 1 in memory; with default format in command window if it were actually integer one the printed value would show as an integer --

>> format short
>> scalarMin=1    % make it exactly 1; shows up as "1"
scalarMin =
   1
>> scalarMin=scalarMin-2*eps(1)  % make it just a tad less...
scalarMin =
  1.0000
>>

Note the difference.

Don't trust comparisons to floating point as being exact; even < can lead to unexpected results if not wary.

[John D'Errico]

format long g
x = 1 - eps
x =
                       1

It sure looks like 1. But is it?

sprintf('%0.55f',x)
ans =
  '0.9999999999999997779553950749686919152736663818359375000'

No, it is not 1. And MATLAB confirms that fact.

x < 1
ans =
  logical
   1

[David Pesetsky]

num2hex gives

3fefffffffffffff

What's that?

Answer 1

[John D'Errico]

You don't seem to believe what we are telling you. Here is 1.

num2hex(1)
ans =
    '3ff0000000000000'

That is 1. Creating something slightly smaller than 1? Try this:

num2hex(1-eps)
ans =
    '3feffffffffffffe'

Just because a number displays at the command line as looking like 1, it need not be exactly 1.

[Walter Roberson]

>> fprintf('%.99g\n', 1 - hex2num('3fefffffffffffff'))
1.1102230246251565404236316680908203125e-16

[David Pesetsky]

I'll compare to 0.99999999 instead.

That works fine.

[John D'Errico]

Just a teeny tiny, itsy bitsy amount less than 1. But not 1.

sprintf('%0.55f',hex2num('3fefffffffffffff'))
ans =
  '0.9999999999999998889776975374843459576368331909179687500'

As much as it looks like 1,

format long g
hex2num('3fefffffffffffff')
ans =
                         1

What is the saying? Close is only good in horseshoes and hand grenades.

[Walter Roberson]

Consider using ismembertol()