On Mon, 25 Nov 2002, Spehro Pefhany wrote:

> At 03:08 PM 11/25/02 +0200, you wrote:
>
> >I have written a algorith on the pic to mathematically convert the 10-bit
> >number to a number between Ymin and Ymax but the algorithm takes far too
> >long. Is there a way (hopefully easy) that you more or less can convert
> >the 10-bit number to say between 100 and 200 almost directly (bit
> >manipulation) without long and cumbersome arithmetic.
>
> Nic,
>
> One idea amounts to multiplying by (about) 25 and then dividing by 256
> (throw away the LS byte).
>
> Assuming you want 100-200 *inclusive*, you could do something like this
> (I'll use pseudo-C code)
>
> Let's assume x (one byte) contains the MS byte of the left-aligned A/D
> value (0x00 to 0xFF as the A/D output
> goes 0x000 to 0x3FF)
>
> z = ((x + (x >> 1) >> 1) + (x >> 5) + (x >> 6);
>                    ^^^^^^
>          shift any carry from the addition in here
>
> z= (z >> 1) + 100;
>
>
> You'll recognize the shifts and adds as hard-coded multiplication.
>
> This will reduce down to just a handful of PIC assembly instructions,
> with no loops.


This is the right idea. In general, if you want to linearly scale one
range into another, then apply this formula (or a variation):

   X - Xmin     Y - Ymin
 ----------- = -----------
 Xmax - Xmin   Ymax - Ymin

Where X and Y are variables and the Xmin,etc are constants that describe
the ranges. In your case, if the X's are the ADC's,

   Y - 100 = (200-100) * (X - 0) / (1023 - 0)

   Y = 100 + 100 * X / 1023

At this point, I'd be tempted to use Nikolai G's automatic code generator.
But, this equation is especially simple to reduce:

   Y = 100 + 100 * ( 1023 - X) / 1023
     = 100 + 100 * ( 1024 - (X+1)) / (1024 - 1)

 recall

  1/(B+C) = 1/B * (1 - C/B + (C/B)^2 - (C/B)^3 +- ...)

 substitute

   Y = 100 + 100 * ( 1024 - (X+1)) *
          [ 1/1024 * ( 1 + 1/1024 + 1/1024^2 + ... ) ]

Keep just the first two terms:

   Y = 100 + 100 * ( 1024 * (1/1024 + 1/1024^2)  -
                     (X+1) * (1/1024 + 1/1024^2) )
     = 100 + 100 * ( 1 + 1/1024) -
                   ( (X+1)/1024 + (X+1)/1024^2)
     = 200 + 100/1024 - 100*(X+1)/1024 - 100*(X+1)/1024^2

The third term is what Spehro expands above (except that he didn't add 1
to the ADC value first). Now, depending on how much accuracy you want or
how fast the computation needs to be, you can make a judgement call on the
number of terms to keep.

Scott

--
http://www.piclist.com hint: The PICList is archived three different
ways.  See http://www.piclist.com/#archives for details.