On Fri, 27 Jun 2003 14:23:22 GMT, Jack Crenshaw
wrote:

I've run across a peculiarity concerning the format used inside the
Intel math coprocessor. I have always
thought that the format used was in accordance with the IEEE 794

Unless IEEE 794 is something new, I think you mean IEEE 754.

standard, and every reference I've seen
on the web seems to imply that. But, as nearly as I can tell, it's not
the same.

The IEEE standard for 32-bit floats says the format should be

sign -- 1 bit
exponent -- 8 bits, power of 2, split on 127

With the proviso that the values of 0 and 255 for the exponent are
special cases reserved for 0, Inf, denormals, and NaN.

mantissa -- 23 bits + phantom bit in bit 24.

The Intel processor seems to use the following:

sign -- 1 bit
exponent -- _SEVEN_ bits, power of _FOUR_
mantissa -- sometimes 23 bits, sometimes 24. Sometimes phantom bit,
sometimes not.
When it's there, it's in bit _TWENTY_THREE_ !

I don't think so. Are you mistaking the lsb of the exponent for the
"visible" phantom bit?

[...]

You'll see that 1 -- 3f800000 (high bit is visible)

seee eeee emmm mmmm mmmm mmmm mmmm mmmm
0011 1111 1000 0000 0000 0000 0000 0000

s = 0, e = 127, m = 0

(-1)^s * 2^(e-127) * (1+m/(2^23)) = 1*1*1 = 1.0

but 2 -- 40000000 (high bit is not)

seee eeee emmm mmmm mmmm mmmm mmmm mmmm
0100 0000 0000 0000 0000 0000 0000 0000

s = 0, e = 128, m = 0

(-1)^s * 2^(e-127) * (1+m/(2^23)) = 1*2*1 = 2.0



Try a few others and see what you get. Some will surprise you.

I'm not finding any surprises.

1.5 - 3fc00000
seee eeee emmm mmmm mmmm mmmm mmmm mmmm
0011 1111 1100 0000 0000 0000 0000 0000
s = 0, e = 127, m = 0x400000
(-1)^s * 2^(e-127) * (1+m/(2^23)) = 1*1*1.5 = 1.5


2.5 - 40200000
seee eeee emmm mmmm mmmm mmmm mmmm mmmm
0100 0000 0020 0000 0000 0000 0000 0000
s = 0, e = 128, m = 0x400000
(-1)^s * 2^(e-127) * (1+m/(2^23)) = 1*2*1.25 = 2.5

Perhaps I'm misunderstanding your point?

Regards,

-=Dave
--
Change is inevitable, progress is not.