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feat(code quality): Add comments for parallel welford variance calculation #423

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Nov 16, 2023
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feat(code quality): Add comments for parallel welford variance calculation #423

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13 changes: 13 additions & 0 deletions transformer_engine/common/utils.cuh
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Expand Up @@ -591,6 +591,19 @@ struct DynamicReducer : public Reducer<T, 1, WARPS_M, WARPS_N> {

////////////////////////////////////////////////////////////////////////////////////////////////////

/*
This is an implementation of the parallel Welford algorithm for incrementally computing variance
This algorithm is known as Chan's update formulae (Chat et al '79):
http://i.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf
An introduction is provided by Wikipedia here:
https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance?section=5#Parallel_algorithm
A detailed reference on the exact version implemented (with better numerical stability) is provided here:
https://dbs.ifi.uni-heidelberg.de/files/Team/eschubert/publications/SSDBM18-covariance-authorcopy.pdf
*/

template<typename T>
inline __device__ void warp_chan_upd_dynamic(T &m_a, T &m2_a, T &n_a, int num_active) { // NOLINT(*)
// Assume at least leftmost is valid and
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