Sun (IEEE) Floating point format

[Scott Leadley]

In article <7914 at brazos.Rice.edu> pmeese at govt.shearson.com (Philip Meese 36743) writes:
>In response to the message from PRABAL at rcgl1.eng.ohio-state.edu (Prabal Acharyya)
>in V9-162:
>> Can anybody explain the binary format used by SUN OS 4.0.3 to represent
>> floating point numbers.  I am trying to convert floating point numbers
>> from a Gould 32/77 machine to my SUN 4/330.
...
>SunOs uses standard IEEE floating point format. There are two variants:
>one for 4 byte numbers (floats) and one for 8 byte numbers (doubles). The
>format for floats escapes me right now but I could dig up my file on this
>if you you could use it. The 8 byte double format is:
>
>     Starting   length
>     position   in bits contents
>     ---------  ------- --------
>        1       1       sign bit
>        2       11      exponent
>        13      52      mantissa
>
>The ieee exponent is a decimal number biased by 0x3FF. In other words, add

Wrong polarity.  The bias of 0x3FF should be subtracted from the exponent.

>0x3ff to the number stored there to get the real exponent. The exponent
>can be thought of as representing the number of nibbles to move the
>"binary point" to arrive at the final number.

A common Sun manual that may help is the _C Programmer's Guide_, Appendix
D, "Sun-2, -3, and -4 Data Representations" (PN 800-1771-10).

IEEE single precision (4 bytes)

	 3 3      2 2
	 1 0      3 2                     0
	+----------------------------------+
	| |        |                       |
	+----------------------------------+
	 ^ ^        ^
         | exponent mantissa
	 sign bit

	The exponent bias is 127 (0x7F).

IEEE double precision (8 bytes)

	 6 6         5 5
	 3 2         2 1                                                  0
	+------------------------------------------------------------------+
	| |           |                                                    |
	+------------------------------------------------------------------+
	 ^ ^           ^
         | exponent(*) mantissa
	 sign bit

	The exponent bias is 1023 (0x3FF).

	(*) Table D-5 in the _C Programmer's Guide_ incorrectly states that
	the exponent length is 8 bits (it is actually 11 bits).

A normalized floating point number represents the real number:

	    sign bit (exponent-bias)
	(-1)    *   2         *     1.mantissa

The "1." in front of the mantissa represents the "hidden bit" in
normalized numbers.  I.e. the mantissa is stored with its most significant
bit (which is a 1 bit) removed.

Exponents of all 0s and all 1s are used to flag special representations:

	sign bit	exponent	mantissa	represents
	--------	--------	--------	----------
	0		0		0		+0
	1		0		0		-0
	0		all ones	0		+Infinity
	1		all ones	0		-Infinity
	0 or 1		all ones	non-zero	NaN (Not-a-Number)
	0 or 1		0		f		denormalized number(*)

	(*) a denormalized number is represents the real number:

	    sign bit (exponent-bias+1)
	(-1)    *   2         *       0.mantissa

NB. I have never had to deal with denormalized numbers and this
explanation is taken straight from the Sun manual with no judgement added.

Scott Leadley - leadley at cc.rochester.edu