Converting from Microsoft Binary Format floats to Python Float

[Bengt Richter]

On 26 Aug 2005 07:55:26 -0700, geskerrett at hotmail.com wrote:

>In the '80's, Microsoft had a proprietary binary structure to handle
>floating point numbers,  In a previous thread, Bengt Richter posted
>some example code in how to convert these to python floats;
>
>http://groups.google.com/group/comp.lang.python/browse_thread/thread/42150c=
>cc20a1d8d5/4aadc71be8aeddbe#4aadc71be8aeddbe
>
>I copied this code and modified it slightly, however, you will notice
>that for one of the examples, the conversion isn't exact.
>
I suspect a typo in the hex ;-)

>Can anyone advise me on how to modify this code to correct for this
>situation ?
>I think the problem may be related to the different lengths of the
>mantissa.   For double precision (8bytes) MBF format had 55 where as
>Python floats (IEEE) has only 52 ??
I believe that's 53 including the "hidden" msb. UIAM that means you
could lose precision if the LS byte had bits below 'F8' -- i.e.,
if bytes[0]&7 != 0 in the bytes passed to msd2float.

But the bits that make the difference between 1234567890.0 and 1234567895.5
are nowhere near there. Hence my suspicion of a typo.

>
>Sample Code Below ----------------------
># Conversion of Microsoft Binary Format numbers to Python Floats
>
>import binascii as bn
>import struct as st
>
>
>data =3D [(1234567890,'000000AF052C139F=AD'),
          [(1234567890,'000000A4052C139F=AD'),
Are you sure it's not a 4? ----^

>                (4069954144,'00000060929672A0'=AD),
>                (999999.99, '703D0AD7FF237494'),
>                ( 88888.88, '400ad7a3709c2d91'),
>                ( 22222.22, '400ad7a3709c2d8f'),
>                ( 33333.33, 'b047e17a54350290'),
>                (  1500.34, '7814ae47e18a3b8b'),
>                ( 42345.00, '0000000000692590'),
>                ]
>
>
>def msd2float(bytes):
>        #take out values that don't make sense possibly the NaN and
>Infinity ??
>        if sum(bytes) in [0,72,127]:
>            return 0.0
>        b =3D bytes[:]
>        sign =3D bytes[-2]&0x80
>        b[-2] |=3D 0x80        #hidden most sig bit in place of sign
>        exp =3D bytes[-1] - 0x80 - 56          #exponent offset
>        acc =3D 0L
>        for i,byte in enumerate(b[:-1]):
>            acc |=3D(long(byte)<<(i*8))
>        return (float(acc)*2.0**exp)*((1.,-1.=AD)[sign!=3D0])
>
>for line in data:
>        inval =3D line[0]
>        binval =3D bn.unhexlify(line[1])
>        le_bytes =3D list(st.unpack('BBBBBBBB',binv=ADal))
>        outval =3D msd2float(le_bytes)
>        print " In:",inval, "\nOut:",outval,"\n"
The above print will use str conversion for floats, so you are
not seeing a full representation of the two values. (BTW, even the repr
value is not necessarily an accurate representation of the exact
decimal represented by the IEEE double's bits, but it is guaranteed
to be converted back to those bits from the literal string representation.)
E.g. (using my exact decimal hack to show the full value),

 >>> from ut.exactdec import ED
 >>> print .1
 0.1

Which is the same as
 >>> print str(.1)
 0.1

but repr shows that's not exact

 >>> print repr(.1)
 0.10000000000000001

but the exact decimal representation for those bits is
 >>> print ED(.1, 'all')
 ED('0.1000000000000000055511151231257827021181583404541015625')

>
>Sample Output ------------------------
>C:/Python24/pythonw.exe -u  "C:/pytest/dms/Test MBF.pyw"
> In: 1234567890
>Out: 1234567895.5
>
try it with the typo fixed ;-)

Regards,
Bengt Richter