MATLAB: Does num2str of a single output up to 17 digits

MATLABnum2strsinglesingle precision

I've noticed the calling num2str using a single but asking for up to 20 digits produces a lot more digits than should be stored with a single. These digits are not visible in the workspace but they are persistent; they are passed between functions and can be consistently recreated if you call the double function on the single. They do not represent the lost digits from the initial conversion to single, but running this script multiple times produces the same digits, even on different machines and versions.
What is really going on here? Is matlab really keeping track and moving these digits around, or are they somehow a function of the single precision number that is stored?
format long g
y=1.234567890123456789 %only stores 1.23456789012346
x=single(y) %only stores 1.234568 
num2str(x,20) %displays 1.2345678806304932

z=double(x); %stores 1.2345678806304932
num2str(z,20) %displays 1.2345678806304932

Best Answer

Point #1:
The behavior of num2str is platform specific. On Windows machines (at least the ones I have used), num2str will truncate the display to the underlying accuracy of the number and pad 0's on the end if you request "too many" digits. On other platforms (I believe linux is one) you will get an exact conversion of the binary floating point bit pattern into decimal for as many digits as you request.
Point #2:
On those platforms that do print many more digits than 7 or 8, num2str is simply doing the exact binary floating point bit pattern conversion into decimal with no implied precision for those remaining digits in the sense you are talking about. Nothing "extra" is being passed around or retained in memory between function calls etc. It is always only a 32-bit floating point number. E.g., compare num2str(1) and num2str(1+eps). Those numbers are right next to each other in the IEEE double representation of floating point numbers. There is nothing inbetween them in this system. To see that try num2str(1+eps/2) and see what you get. A similar situation exists for the single precision numbers.
If you are on a computer that does not do the full conversion (e.g. Windows) you can use my num2strexact utility function from the FEX:
http://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str
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