How to convert half-precision number into hexadecimal representation?

Hi,

I am using matlab 2019B with support for complex half-precision operations. I want to store my results in a file but fwrite doesn't support class half. Some workaround is to convert to hex and then store as uint16. The problem is that num2hex also doesn't support half class. One way to obtain hexadecimal representation I have found is to use format hex, but parsing output string is not a solution for me.

My question is - Is there any native posibility to store half-precission numbers if file, or convert to hexadecimal representation for further processing?

Best Regards

Adam

Answer 1

[James Tursa]

I don't have R2019b installed so I don't know how half precision numbers are stored, but can you use typecast:

h = your half precision variable
u16 = typecast(h,'uint16');

Another option is a mex routine, but I would need to know how the half precision values are stored first.

EDIT

I just checked, and unfortunately the new half precision type is not a fundamental numeric type like double or uint16 ... it is an opaque type like OOP classdef objects. So even though isnumeric(half) returns true, half precision variables are not stored the same as the native numeric variables are. The data areas are hidden.

I have no idea why TMW would choose to implement a basic numeric type this way, but they must have their reasons. The half precision type is fundamentally different from all of the other numeric types. Not suprisingly, the typecast( ) function does not work since the storage scheme is fundamentally different. This also makes a mex option out of the question since the data area is hidden. What a pain ... why couldn't they have just made it compatible with all the other numeric types??? THERE WILL BE NO WAY TO EFFICIENTLY WORK WITH HALF VARIBLES IN A MEX ROUTINE BECAUSE OF THIS! (yes I am shouting)

SOLUTION

For your purpose, you only need the hex patterns or equivalent bit patterns to write out. So I can offer my C-mex code for this, which can be found here:

https://www.mathworks.com/matlabcentral/fileexchange/23173-ieee-754r-half-precision-floating-point-converter

You would convert your half precision variable to single, then call my C-mex routine to turn it into the uint16 half precision bit pattern. Then you can write that uint16 variable directly to a file in binary with fwrite( ). I just need to check to see if it still works in later versions of MATLAB. I will get back to you ...

UPDATE

I downloaded my halfprecision C-mex file and it seems to compile and run OK. Just don't use the -R2018a mex option because the code isn't updated yet for R2018a+. My halfprecision C code will also handle the inf, nan, and denorm patterns just fine. You would compile it as follows:

mex halfprecision.c

Sample run:

>> version
ans =
    '9.7.0.1190202 (R2019b)'
>> halfpi = half(pi) % The MATLAB half class
halfpi = 
  half
   3.1406250  % MATLAB is apparently using the single display code for this
>> hp = halfprecision(pi) % my C-mex routine ...
hp =
  uint16  % ... returns a uint16 variable that contains the half precision bit pattern
   16968
>> halfprecision(hp,'disp')  % my C-mex routine has a display option
    3.1406
>> halfprecision(hp,'single') % my C-mex routine can convert it back into other classes
ans =
  single
   3.1406250
>> sprintf('%04x',hp) % If you want the hex values as ASCII text, do this
ans =
    '4248'
>> 
>> halfinf = half(inf)
halfinf = 
  half
   Inf
>> hinf = halfprecision(inf)
hinf =
  uint16
   31744
>> halfprecision(hinf,'disp')
   Inf
>> halfprecision(hinf,'single')
ans =
  single
   Inf
>> sprintf('%04x',hinf)
ans =
    '7c00'
>> 
>> halfnan = half(nan)
halfnan = 
  half
   NaN
>> hnan = halfprecision(nan)
hnan =
  uint16
   65024
>> halfprecision(hnan,'disp')
   NaN
>> halfprecision(hnan,'single')
ans =
  single
   NaN
>> sprintf('%04x',hnan)
ans =
    'fe00'
>> format hex
>> halfpi
halfpi = 
  half
   4248
>> halfinf
halfinf = 
  half
   7c00
>> halfnan
halfnan = 
  half
   fe00

[Adam Przybyla]

Hi,

thanks a lot for your answer.

My workaround for this problem was to write simple mex based on http://half.sourceforge.net/ half-precision implementation. It works well but I just doubted it couldn't be done by Matlab itself.

I've already seen your solution when I tried to find an answer to my doubts. Many links lead to that site :)

I keep fingers crossed that in next releases it will be supported.

[James Tursa]

Update: My FEX half precision code has been updated for R2018a+, and my FEX num2strexact submission has been updated for half precision inputs as well.

Answer 2

[Krishna Bindumadhavan]

You can use half.typecast() and storedInteger functions as a workaround to convert to and from half precision and the underlying uint16 storage.

ex.

>>storedInteger(half(100))

ans =

uint16

22080

>>half.typecast(ans)

ans =

half

100

Appreciate your feedback regarding typecast,fwrite,num2hex, and mxArray limitations. We will consider better support for these in a future release.

Best Regards,

Krishna.

[James Tursa]

Thanks!

I would note that unlike the typecast( ) function for doubles and singles which produces shared data copies, the storedInteger( ) and half.typecast( ) functions listed above produce deep data copies. E.g.,

>> h = half(rand(1,100000000/2,'single'));
>> whos
  Name      Size                      Bytes  Class    Attributes

  h         1x50000000            100000000  half               

>> memory
Maximum possible array:       18314 MB (1.920e+10 bytes) *
Memory available for all arrays:       18314 MB (1.920e+10 bytes) *
Memory used by MATLAB:        1992 MB (2.088e+09 bytes)
Physical Memory (RAM):        8088 MB (8.481e+09 bytes)

*  Limited by System Memory (physical + swap file) available.
>> s = storedInteger(h);
>> memory
Maximum possible array:       18170 MB (1.905e+10 bytes) *
Memory available for all arrays:       18170 MB (1.905e+10 bytes) *
Memory used by MATLAB:        2097 MB (2.199e+09 bytes)
Physical Memory (RAM):        8088 MB (8.481e+09 bytes)

*  Limited by System Memory (physical + swap file) available.
>> H = half.typecast(s);
>> memory
Maximum possible array:       18128 MB (1.901e+10 bytes) *
Memory available for all arrays:       18128 MB (1.901e+10 bytes) *
Memory used by MATLAB:        2204 MB (2.311e+09 bytes)
Physical Memory (RAM):        8088 MB (8.481e+09 bytes)

*  Limited by System Memory (physical + swap file) available.

You can see in the above that the 100MB half variable h gets deep data copied for these steps (i.e., the Memory used by MATLAB increases by 100MB). This is an example of what I hope can be avoided in future versions of MATLAB. Shared data copy methods to get at the underlying data, and pointer access to the data inside mex routines. Making half a simple numeric class instead of an opaque class is one way to accomplish this.