You remind me that it is not difficult to implement digital
       frequency correction in a microcontroller.  With this
       technique, a 32kHz kHz xtal (or any crystal frequency) can be
       used to generate an accurate real time clock without adjusting
       the actual xtal frequency.  Consider that about 20 bits are
       required attain 1PPM accuracy (1 part in 2^20).

       Instead of adding 1 to a counter at each real time tic, you add
       1 plus a 20 bit signed fraction to the counter.   Only the
       least significant 8 bits of the fraction are adjusted.  The
       range of the fraction is (-128 to +127)/ 1048576, about +-121
       ppm.  So instead of 1, you are adding a number from  0.999879
       to 1.000121 to the counter.  This counter may be seconds,
       tenths of a second, 1/32 second or whatever you desire.  You
       can increase the number of bits for more precision.  The
       adjustment may be stored in one byte of eeprom.

       Here's an attempt at a PIC solution:

       correction     res  1    ;signed byte applied to accum1
       accum1         res  1    ;bits 0-7 of fraction
       accum2         res  1    ;bits 8-15 of fraction
       accum3         res  1    ;bits 16-20 of fraction, a '1' in bit
       4 is one tic

       update_real_time
            movfw     correction          ; get the fractional
       correction
            addwf     accum1,f       ; update the LSB of the fraction
            ; the remainder of this code sign extends the LSB fraction
       to the rest of the fraction
            movlw     0              ; assume positive correction
            btfsc     correction,7   ; skip if correction is positive
       sign
            movlw     -1             ; correction is negative
            btfsc     STATUS,C
            addlw     1              ;add in the carry
            addwf     accum2,f       ;update bits 8-15
            ;
            movlw     0              ; assume positive correction
            btfsc     correction,7   ; skip if correction is positive
       sign
            movlw     -1             ; correction is negative
            btfsc     STATUS,C
            addlw     1              ; add in the carry
            addwf     accum3,f       ; update bits 16-20
            ;
            ; Check the overflow bit for a "calibrated" real time tic.
            btfss     accum3,4       ; has a tic occured?
            goto dontupdate          ; don't update the real time
       counters...
            bcf  accum3,4       ; clear the tic keeping the fraction
       remainder
            goto update         ; update the real time clock
       counters...



       Barry King Wrote:
       <snip>
       Our data loggers use watch crystals and calibrate them by
       tweaking
       the load capacitance when needed to get to +/- 1ppm.  ST
       Microelectronics makes a real-time-clock chip with cool digital
       frequency correction.  (The chip will skip or double pulses to
       correct for crystal initial tolerance if you calibrate it.)
       If temperature is not varying wildly, they work very well.