Date: Thu, 1 Feb 1996 09:38:45 -0800 (GMT)
From: Orlando Andico <oandico AT eee DOT upd DOT edu DOT ph>
To: Armin Herzer <herzer AT fbp DOT fh-weingarten DOT de>
cc: djgpp AT delorie DOT com
Subject: Re: binary representation of floats
Message-ID: <Pine.SOL.3.91.960201093116.5505A-100000@gollum>
MIME-Version: 1.0

On Wed, 31 Jan 1996, Armin Herzer wrote:

> What I want to do is to get the binary representation of a float
> or double (the way these numbers are stored in memory). How can I obtain
> them? How do I modify them? Is there a documentation from which I can see
> how the format of these binary represetations on PC's (and in DJGPP) is.

I'm sure you can find the description of IEEE floating-point numbers in 
any good computer architecture book, though I'm not sure how FP numbers 
are handled in DJGPP as the IEEE 754 standard specifies only 32-bit and 
64-bit floating point representations while the 80x87 math coprocessors 
(and DJGPP _always_ uses one, emulator or no) specify an 80-bit floating 
point format... maybe DJ will have something more to say about this.

Anyway, (as I remember) the basic 32-bit IEEE 754 FP number stores the 
sign bit in the leftmost bit, followed by 8 bits of normalized exponent. 
Since 8 bits can handle 0..255, exponents < 0 are normalized by adding 
127, so the range of _binary_ exponents allowed is -127..+128. The 
remaining 23 bits are the mantissa, with an implied 1 (i.e. the mantissa 
is always > 1).

The Intel architecture stores stuff in a little-endian fashion, so your 
IEEE number in 4321 format will probably come out as 1234... what you 
could do is convert some FP number to IEEE 754 format by hand, store it 
in memory, then dump the 4(8) bytes and analyze them to determine the way 
DJGPP stores the bytes. Then again, maybe it uses the 80x87 80-bit format 
partway through...

Anyways, once you got the binary representation, you could have a char * 
pointing to your float and use the ordinary bitwise manipulations to mess 
with it.

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|  Orlando A. Andico                 "I have no concept of time, other than  |
|  oandico AT eee DOT upd DOT edu DOT ph               it is flying." -- Alanis Morissette  |
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