Why does FPCMP not detect inequality?

Hi,

first of all I have to state that I'm aware of the fact that comparing floating point values
directly with ==, !=, <, > is a bad idea. But this is a special case ;)

I have the following few lines of code:

    if (sqrt(2) != SQRT2) //#define SQRT2 1.4142135
    {
        do something;
    }
    return error;

This results to the following lines in the C166 Simulator:

00012A32 E008      MOV      R8,#0x00
00012A34 E6F90040  MOV      R9,#0x4000
00012A38 CA006E12  CALLA    CC_UC,sqrt(0x1126E)
00012A3C E6F6F304  MOV      R6,#0x04F3
00012A40 E6F7B53F  MOV      R7,#0x3FB5
00012A44 CA00B411  CALLA    CC_UC,?C_FPCMP(0x111B4)
00012A48 2D01      JMPR     CC_Z,0x012A4C
   522:         do something;
00012A4A E0FD      MOV      R13,#0x0F
   523:     }
   524:     return error;
00012A4C F04D      MOV      R4,R13

Let us execute this code until "line" 00012A44.
At this point R5 (0x3fb5) and R4 (0x04f3) hold the result of the sqrt(2) computation.
Registers R7 and R6 have the same values.
Now if I change the value of R4 slightly to 0x03f2, FPCMP does not detect the inequality between both register sets. Why is that? Why is FPCMP so complicated? Why does
simply comparing both register pairs to each other not work?
An inequality is not detected until I change the value of R4 to 0x04EB (downwards) 0x04FB (upwards).

I'm quite sure that this is an intended behavior but I just don't understand why.
Would be great, if someone explains it to me.

Thanks in advance!

Cheers
Peter