> -----Original Message-----
> From: piclist-bounces@mit.edu [mailto:piclist-bounces@mit.edu] On
Behalf
> Of Walter Banks
> Sent: 28 May 2008 19:53
> To: Microcontroller discussion list - Public.
> Subject: Re: [PIC] Custom floating point calculation
> 
> 
> 
> Michael Rigby-Jones wrote:
> 
> > > -----Original Message-----
> > > From: piclist-bounces@mit.edu [mailto:piclist-bounces@mit.edu] On
> > Behalf
> > > Of Timothy Weber
> > > Sent: 28 May 2008 18:06
> > > To: Microcontroller discussion list - Public.
> > > Subject: Re: [PIC] Custom floating point calculation
> > >
> > > Harold Hallikainen wrote:
> > > > If you swap the nybbles so the
> > > > exponent is in the high half, do you end up anywhere near a
steadily
> > > > increasing order?
> > >
> > > I think Harold is right (and Walter is almost right) - if you swap
> > > nibbles first, you can simply compare x and y directly.
> >
> > Sadly my spreadsheet says no (unless it has a fatal error of course,
> > quite possible).
> >
> > e.g. the following values are ordered by "swapped nibble"(SN) value:
> >
> > Hex    Float    SN
> > 0x10   0.0625   0x01
> > 0xE0   0.9375   0x0E
> > 0x01   0.0      0x10
> > 0xE1   0.09375  0x1E
> >
> > Note that the largest floating point value (0.9375) gives a SN
result
> > between the others, even though they have a lower floating point
value.
> >
> > I have attached the spreadsheet if anyone is interested.
> >
> > Regards
> >
> > Mike
> 
> Nybble swap xor with 0xF0 will put the numbers so they can be compared

Thanks Walter, that almost works. The only snag it gives incorrect
results on floating points that have differing exponents and mantissa
but the same value e.g.

0x1E =  1/16 * 10E-14 = 6.25*10E-16  XOR = 0x11
0xAF = 15/16 * 10E-15 = 6.25*10E-16  XOR = 0x0A

This is reasonably easily fixed by checking if the mantissa is == 1 and
the exponent < 15, if so multiply the mantissa by 10 and increment the
exponent.  In reality no multiply is needed, just replace 1 with 10.

A totally unoptimised function (just for clarity) that proves this
technique is below.  With a bit of optimisation this should compile down
to a small handful of assembler operations.

unsigned char ber_weight( unsigned char ber ) {
    
    unsigned char mantissa;
    unsigned char exponent;
    
    mantissa = ber >> 4;
    exponent = ber & 0x0F;
    
    /* If mantissa is zero result is always zero */
    if( mantissa == 0 ) {
        return 0;
    }
    
    /* Eliminate duplicate value cases */
    if( ( mantissa == 1 ) && ( exponent < 15 ) ) {
        mantissa *= 10;
        exponent += 1;
    }
    
    /* Invert the exponent and recombine nibbles in reverse order. */
    exponent ^= 0x0F;
    
    return ( exponent << 4 ) | mantissa;
} 

Thanks again, I knew the PIC list would yield results!

Regards

Mike

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