std::partial_sum( first, last, result, binary_op ) (§26.4.2) is defined as

  binary_op(binary_op(..., binary_op(*first, *(first + 1)),...),
  *(first + (i - result)))

Ambiguity notwithstanding (what is the first value??), the result of each application is clearly supposed to be forwarded to the next.

However, the current implementation does this:

      typedef typename iterator_traits<_InputIterator>::value_type _ValueType;
…
	  __value = __binary_op(__value, *__first);

This would be safer:

      typedef typename _BinaryOperation::result_type _ValueType;

Copying *first to *result would require an implicit cast from iterator_traits<_InputIterator>::value_type to _BinaryOperation::result_type, which is not required. Since an additional __binary_op() is not allowed,

      _ValueType __value( *__first );

might be the best compromise. Anyway, implicit casting the result_type to the input iterator type, as the current implementation does, seems much riskier.

The motivating case is pretty simple: I was specifically trying to avoid overflow by summing a std::vector<char> into a std::vector<int>. Furthermore, std::accumulate does correctly avoid overflow.