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I get an error saying that the fitter requires 13555 LABs to implement but device only contains 13520 LABs.
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If the report suggests that there are enough LEs but too few LABs then it's probably a routing problem rather than a logic problem.
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I think I've never known of this kind of no-fit error being related to routing other than at the LAB control signal level. The device handbook documents how many clocks, clock enables, asynchronous clears, etc. are available in each LAB. For example, a device might support only two clock enables in a LAB. If the Fitter has placed two registers in the LAB using two different clock enables, then the Fitter can't place any registers in that LAB using any other clock enable. When the "Control Signals" table in the Fitter report lists a huge number of one of these categories of signals (typically it will be clock enables), this device restriction can make it difficult or impossible for the Fitter to group registers into few enough LABs to fit. This can happen even when the logic utilization is well below 100%.