Indeed, my apologies.  The long int size cannot be the explanation for the 21 million BTC limit.  

21 million BTC times 10^8 satoshis per BTC is 2'100'000'000'000'000 sat, much less than 2^64.  

It is just a little less than 2^51 = 2'251'799'813'685'248.  

A double-precision float in 64-bit IEEE format can represent exactly all unsigned integers up to 2^53.
Some languages (e.g. GNU Awk) use IEEE doubles as the default (or only) numeric format.  

It is good practice to leave a couple of extra bits in the representation of a quantity, to reduce the risk of overflow during computations,
e.g. in 'x = 3*amount/4'.

If the maximum number of satoshis had been set to exactly 2^51 (or 2^51 - 1), the initial block reward would have had to be a
fractional number of BTC, even if the halving period was set to a funny number like 225179 intead of the round 210000.

In other words, 50 BTC/block and halving every 210000 blocks are two round numbers that happen to result in a total number of satoshis just under 2^51.

EDIT: The exact number of satoshis that will ever be created is claimed to be 2'099'999'997'690'000, but I haven't checked that.