What's the difference between std::partial_sum and std::inclusive_scan?

Question

While reading about std::inclusive_scan, there does not appear to be any examples.
It strikes me as very similar to std::partial_sum.

partial_sum:

template< class InputIt, class OutputIt >
OutputIt partial_sum( InputIt first,
                      InputIt last, OutputIt d_first );

inclusive_scan:

template< class InputIt, class OutputIt >
OutputIt inclusive_scan( InputIt first,
                         InputIt last, OutputIt d_first );

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Can someone elaborate on their differences? When would I choose one over the other?

Answer 1

Documentation of std::inclusive_scan states:

In other words, the summation operations may be performed in arbitrary order. The behavior is nondeterministic if binary_op is not associative.

Documentation of std::partial_sum states without any reservation that:

*(d_first+k) = *first + *(first+1) + ... + *(first+k);

Thus, std::inclusive_scan is equivalent to std::partial_sum only if binary_op is associative, i.e. when (aopb)opc = aop(bopc).

In case of non-associative binary_op, std::partial_sum will produce a deterministic result, whereas you don't know what to expect from std::inclusive_scan.