To answer your question though, there is an example in the HDF5 User's Guide, section 6.5.2.1
To illustrate a user-defined floating point number, the example below shows how to create a 24-bit floating point number that starts 5 bits into a 4 byte word. The floating point number is defined to have a mantissa of 19 bits (bits 5-23), an exponent of 3 bits (25-27), and the sign bit is bit 28. (Note that this is an illustration of what can be done and is not necessarily a floating point format that a user would require.)
hid_t dt;
dt = H5Tcopy(H5T_IEEE_F32LE);
H5Tset_precision(dt, 24);
H5Tset_fields (dt, 28, 25, 3, 5, 19);
H5Tset_pad(dt, H5T_PAD_ZERO, H5T_PAD_ONE);
H5Tset_inpad(dt, H5T_PAD_ZERO);
Code Example 6-8. A user-defined 24-bit floating point datatype
[Dtypes_fig9.JPG]
Figure 6-9. A user-defined floating point datatype
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From: Hdf-forum [mailto:hdf-forum-bounces@lists.hdfgroup.org] On Behalf Of Nelson, Jarom
Sent: Thursday, March 16, 2017 1:38 PM
To: HDF Users Discussion List <hdf-forum@lists.hdfgroup.org>
Subject: Re: [Hdf-forum] High precision floats
The forum history is searchable on nabble:
http://hdf-forum.184993.n3.nabble.com/
From: Hdf-forum [mailto:hdf-forum-bounces@lists.hdfgroup.org] On Behalf Of Martin Shetty
Sent: Wednesday, March 15, 2017 4:55 PM
To: hdf-forum@lists.hdfgroup.org<mailto:hdf-forum@lists.hdfgroup.org>
Subject: [Hdf-forum] High precision floats
I see from documentation that you can define custom floating types. Are there any examples out there for how to do this with GMP or MPFR? Or perhaps even more conveniently with boost/multiprecision?
http://www.boost.org/doc/libs/1_63_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats.html
Would (should?) hdfview also be able to understand these types? It sees 'long double' as opaque, but this one is not truly multiplatform so it is not of as much interest anyway.
P.S. Is there any way to search the HDF mailing list's archive other than downloading the gzips and grepping them? 
I don't see any search capability on the website.
I don't see any search capability on the website.