Conversion to single is out of range

I have an algorithm prototyped in MATLAB that needs to match with the prodcution single precision C-code. I understand the limitations of single vs double and that MATLAB uses double precision internally. What I am struggling with is that the single() type in MATLAB apparently produces values that are out of range for IEEE 754, 32-bit single precision. This causes problems when comparing the output of MATLAB against the output of the C-code.

Check range of single in MATLAB

>> realmax('single')

ans =

single

3.4028e+38

>> realmin('single')

ans =

single

1.1755e-38

>> single(2.0e+39)

ans =

single

Inf

>> single(2.0e-39)

ans =

single

2.0000e-39

As you can see, single() of a small number outside of the valid range returns an invalid value.

Answer 1

[Stephen23]

The keyword here is normalized.

Note that the realmin documentation clearly states "Smallest normalized floating-point number" (I added the bold), so what realmin returns is not the smallest possible single value... it is the smallest possible normalized single value... and clearly there are a few subnormal (or denormal) values that are smaller than that!

There are plently of resources on the web that will explain subnormal floating point numbers much better than I can, you might as well start here: https://en.wikipedia.org/wiki/Denormal_number

https://blogs.mathworks.com/cleve/2014/07/21/floating-point-denormals-insignificant-but-controversial-2/

"single() of a small number outside of the valid range returns an invalid value."

No, that value is a perfectly valid subnormal single floating point number.

"MATLAB apparently produces values that are out of range for IEEE 754, 32-bit single precision"

In fact MATLAB correctly interpreted IEEE 754-2008, which allows for subnormal values. Apparently by default many C compilers do NOT handle denormal floating point numbers according to IEEE 754.

[Ronald Smith]

Yes, thank you. It really is an issue with how subnormal (or denormalized) numbers are handled. I realized this after I posted, but thanks for responding.

[Steven Lord]

To reinforce what Stephen posted, let's look at four numbers.

% The smallest positive single precision value
% is the distance between 0 and the next number after 0
>> eps(single(0))
ans =
  single
  1.4013e-45

% Similar for double precision
>> eps(0)
ans =
  4.9407e-324

% For comparison, the smallest normalized positive single precision value
>> realmin('single')
ans =
  single
  1.1755e-38

% And double
>> realmin
ans =
  2.2251e-308

But getting back to the original question, whose first sentence was:

I have an algorithm prototyped in MATLAB that needs to match with the prodcution single precision C-code.

You may be interested in generating your single precision C code directly from your MATLAB code. Depending on the functions and functionality you're using, the product MATLAB Coder may be able to do that for you automatically.