Boost.Histogram contains useful and well-designed features, like excess (over/underflow) bins, and axis transforms to name a few. As this is a review, I am going to spent most time below on critical scrutiny. I. DESIGN --------- Iterators are const. This prevents us from bootstrapping the histogram with a prior distribution using STL algorithms like std::fill(), std::generate(), or std::sample(). The adaptive_storage does not work well with STL algorithms, because weight_counter is not an arithmetic type. See the Implementation section below for more detail. I therefore propose that the default storage policy is changed to something without weight_counter. The adaptive_storage has two responsibilities: data compaction and weights. Would it be possible to split this into two separate storage policies? I have no real use for arrival variance. I am not too fond of using operator() for insertion. The code looks like a function call with side-effect. I prefer an explicitly named member function. The axis::ouflow_type is oddly named. I suggest that this is renamed to something like axis::excess_type. II. IMPLEMENTATION ------------------ The implementation is generally of high quality. However, I did encounter the three problem areas listed below. (A) Integration with STL algorithms can be improved. Here are some examples: First, std::distance() does not work on a histogram with array_storage. This means that other STL algorithms, like std::any_of(), fails to compile. I solved this problem by copying the distance_to() function from the axis iterator to the histogram iterator. Second, std::max_element (and brethren) cannot be used on a histogram. Consider the following example: auto element = std::max_element(h.begin(), h.end()); Compilation fails for adaptive_storage because weight_counter has no less-than operator. Furthermore, compilation fails for array_storage because iterator_over<H>::operator= fails. It attempts to re-assign a reference, but accidentally triggers a copy-constructor instead. Letting the iterator store a pointer instead of a reference solves the problem. Apropos, iterator_over<H>::operator= does not return *this. Consider adding the -Werror=return-type compiler flag and a unit-test to that calls this operator. Third, std::inner_product fails to compile for adaptive_storage because weight_counter does not have a binary operator*. The inner product of two histograms is useful for calculating the cosine similarity, which can be used to compare two distributions. std::inner_product works for array_storage though. (B) Indexing and size use different types (int versus std::size_t.) I assume that this is because of the underflow bin, which is indexed by -1. I am not certain whether or not this is a real problem, but it does cause some oddities when stressed to the limit. For example, if we need a histogram that counts each unsigned int, then we get an "lower < upper" exception during construction: using range_type = unsigned int; auto h = make_static_histogram_with( array_storage<int>(), axis::integer<>(0, std::numeric_limits::max())); It works if we reduce the end by 2, but then we are not collecting all values (unless we shift the range left by 1 and misuse the excess bins for the two missing values.) A possible solution could be to replace the -1 and N excess indices with an "enum struct excess { lower, upper }" and let operator[] et al use overloading on this enum. (C) Sometimes the compilation errors are nonsensical. For example: // Forgot to use make_static_histogram_with() auto h = make_static_histogram(array_storage<int>, axis::regular<>(10, 0, 1)); triggers an incomprehensible static_assert plus an error about a missing .shape() function. III. DOCUMENTATION ------------------ User guide is clear and pedagogical. I would like to see more examples that uses STL algorithms, such as calculating the CDF using std::partial_sum(), or calculating the cosine similarity of two histograms using std::inner_product(). Most examples use std::cout plus a comment to document the results of operations. Consider using assert() instead. Consider using a tabular layout similar to that of the C++ standard (or cppreference.com for that matter) on the Concepts page. Reference documentation is rather meager and shows implementation details. The documentation contains both a "Reference" and a "References" chapter which are completely different. Consider renaming the latter to something like "External references" , "Literature references", or "Bibliography". IV. MISC -------- I have spent around 15 hours on the review, mainly writing small examples that uses STL algorithms on Boost.Histogram. I am well-versed in the topic. I work with statistical distributions for real-time analysis of data, although I mainly dabble around in one dimension. I have written a library for online/streaming statistical algorithms. V. VERDICT ---------- While Boost.Histogram is a small niche library, it has a wide range of practical applications to warrant the inclusion into Boost. Boost.Histogram should be ACCEPTED into Boost, provided: 1. Reference documentation is finalized. I furthermore strongly recommend that the default storage policy is changed to something without weight_counter because of the various problems with STL algorithms. This recommendation is not a prerequisite for acceptance.