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As others have stated, we need to know the CYA (stabilizer) level in order to conclusively determine if the current chlorine (FC) level for the pool is adequate. Forget the conventional wisdom of maintaining an FC level between 1-3 ppm. The proper FC level is dependent on the pool's CYA level as shown here:
Chlorine/CYA Chart.
I'm assuming from your Salt level test results that you have a SWG pool (suggest adding pool info to signature). Even at the minimum 60 ppm CYA level that we recommend for SWG pools, an FC of 3 ppm is right at the
minimum recommended level. If FC were to consistently drop below 3 ppm, that would give algae a foothold to grow. OTOH, is the CYA level is higher than that, then the 3 ppm FC itself is inadequate.
Since you currently have algae, SLAMming the pool is in order to get rid of it. There again, you still need to know the CYA level in order to dose FC to the proper SLAM level. If the CYA level is greater than 80 ppm, I would do a partial drain & refill to get it in the range of 60-80 ppm. Then you can begin the SLAM. After the SLAM process is completed, I would aim to keep the FC level at the target range shown in the chart for the pool's CYA level.
Another thought...If this pool is regularly subjected to high bather loads, you would want to dose FC slightly above the target to account for the higher than average chlorine demand that comes with high bather loads.