i have used a fild instruction to load a set of variables:



my debug returned me this:


i dont get it. can someone explain me this representation?
i read that highest bit is sign [ok], next 15 bits are exponent [not ok] and the rest is mantisa.
lets take -3 - its C000C000000000000000.

1 100000000000000 110000000000...
sign ok, exponent is 1, mantisa 3. -3*2^0

-4 is C0018000000000000000.
1 100000000000001 100000...
sign ok, mantisa 1, exponent how much? shuld be 2. but its not 2, its something else... it is 1 since 100.. is 0?


4 is 40018000000000000000.
0 100000000000001 1000...

same here. i dont get it, how its done.


lets take a rnadom number, C03C83D17DC7833EDC28

sign:1
exponent: 100000000111100 (16444)
mantisa: 10000011110100010111110111000111100001101111101101110000101000 (0.2374627846254418984)
0.2374627846254418984 * 2^16444 = ???


C02A8000000000000000
1 100000000101010 10000000
sign 1, exponent
exponent 16426, mantisa 1. 1*2^16426 = propably ok.



i dont understand it...

I think the FPU assumes that 3FFF has been added to the exponent (it's called a "biased" exponent). So to get the real exponent value, you subtract 3FFF from the exponent value your debugger is showing you. Your calculations should all work out then. (The bias is different for qwords and dwords). I got this from:

http://www.website.masmforum.com/tutorials/fptute/fpuchap2.htm#real10

thank you, but i managed to understand it myself.

when you have a float representation
SEEEEEMMMMMMMMMM

its real value is equivalent to:

sign tells if its + or -, nothing more, just sign.
E is exponent. MSB = 0, rest = 1 (0111111...) is 0. in order to convert to real number, you have to add it (depends on ammount of exponent bits).
For example is you have 7 exponent bits, 0 is 0111111, 1 is 1000000, 2 is 1000001, and so on. -1 is 0111110, etc.

M is mantisa.
lets say exponent is 1000101 (1000101 - 0111111 = 110 (6)).
mantisa is 011010 (22).
real number is
0 * 2^6 = 0
1 * 2^5 = 32
1 * 2^4 = 16
0 * 2^3 = 0
1 * 2^2 = 4
0 * 2^1 = 0

32+16+4 = 52. sign is 0, so +52.

lets check in bochs:
+52
4004D000000000000000

0 100000000000100 1101000000000...

exponent = 100000000000100 - 011111111111111 = 101 (5)
mantisa = 11


1 * 2^5 = 32
1 * 2^4 = 16
0 * 2^3 = 0
1 * 2^2 = 4
0 * 2^1 = 0
0 * 2^0 = 0
0 * 2^-1 = 0
0 * 2^-2 = 0
0 * 2^-3 = 0
0 * 2^-4 = 0
...
0 * 2^-58 = 0



32 + 16 + 4 = 52