Best way to find many minimums

[Robert_Crovella]

ps:
Ie each of the 3000 odd outputs is processed by a
block of threads which do a reduction in shared memory, save the intermediate
answer in a register and then move onto the next 64/128 inputs again do a reduction
in shared memory and then minimise with the value from the previous 64/128 and
save the new min back into the register.

It should be possible to read and minimize without doing any sort of parallel reduction sweep, until all the reading of input data is done by the block. Take a look at the code I indicated earlier. It appears that you are doing a full shared memory sweep each time you load a set of 64/128 inputs. This should not be necessary.