A B737-800 DEPARTING DFW ON THE CEOLA 3 DEP DEVIATED FROM THE CHARTED TRACK WHEN THEY EXPERIENCED A MAP SHIFT.

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CLRED CEOLA3.CEOLA RWY 18L; RTE/LEGS CHKED AT GATE. FIXES CHKED DURING TAXI BUT PRIOR TO XING TO W SIDE. 5 NM RANGE SELECTED FOR PRECISION. AFTER ROTATION NOTED UNUSUAL TURN TO R FOLLOWED BY NO SPD RESTR ON RMS. HAD FO VERIFY DEP PROC AT WHICH TIME BOTH OF US REALIZED THAT LARRN HAD DROPPED FROM RTE AND WE WERE DIRECT GIGEM. IMMEDIATELY NOTIFIED ATC WHO GAVE US A 270 DEG HDG. SUBSEQUENT DIRECT CLRNC TO CNX SHOWED DISAGREEMENT BTWN MAPS OF APPROX 3 NM. NO FURTHER FMC ANOMALIES NOTED. AS PLTS WE TEND TO WANT TO GET TASKS DONE EARLY WHICH IS NOT ALWAYS GOOD. IN THE FUTURE I WILL CHK RNAV INITIAL FIX JUST PRIOR TO TAKING RWY AND LEAVE THE RANGE IN 10 NM OR GREATER FOR RTE. SUPPLEMENTAL INFO FROM ACN 708731: CAPT AND MYSELF DID PROPER LEG AND WAYPOINT CHKS AT GATE WHICH INCLUDED CEOLA DEP ALT; SPD XINGS. AFTER TKOF WE COMPLIED FOLLOWING MAGENTA LINE AND NOTICED THAT IT HAD US STARTING A TURN ABOUT 400 FT WHICH SEEMED UNUSUAL. XREFED THE DEP AND NOTICED THAT WE HAD LOST OUR FIRST WAYPOINT. I IMMEDIATELY TYPED IT BACK IN AND ADVISED ATC. ATC ADVISED US TO TURN TO A HDG AND CONTINUE OUR CLB. IT HAPPENED TO BE A VERY SLOW WORKLOAD MEANING NOT A LOT OF DEPS. ATC THEN GAVE US DIRECT A FIX; SELECTED ABEAM POINTS AND ASKED HOW DID IT LOOK IN PLAN MODE; LOOKS GOOD; AND EXECUTED. OUR TRACK WAS TO THE R OF OUR ACFT SYMBOL AND WE HAD TO TRY IT AGAIN IN WHICH IT WORKED. THIS ACFT IN MY 3000+ HRS IS NOT KNOWN FOR HAVING THESE KIND OF ANOMALIES; BUT NEVER SAY NEVER.