I think whitepaper is just a summary, so it's not very detail. While the source code is everything that make Bitcoin run, probably there's other thing that didn't mentioned in whitepaper besides halving.
It is best to have the bitcoin github[1] as reference since all the updates and upgrades are mentioned on that repository.
To be more accurate, on lines 1752-1763.
CAmount GetBlockSubsidy(int nHeight, const Consensus::Params& consensusParams)
{
int halvings = nHeight / consensusParams.nSubsidyHalvingInterval;
// Force block reward to zero when right shift is undefined.
if (halvings >= 64)
return 0;
CAmount nSubsidy = 50 * COIN;
// Subsidy is cut in half every 210,000 blocks which will occur approximately every 4 years.
nSubsidy >>= halvings;
return nSubsidy;