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Subject: [boost] [histogram] Formal review
From: Bjorn Reese (breese_at_[hidden])
Date: 2018-09-23 14:26:45

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


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

The axis::ouflow_type is oddly named. I suggest that this is renamed to
something like axis::excess_type.


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

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

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(
     axis::integer<>(0, std::numeric_limits<range_type>::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.


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 for that matter) on the Concepts page.

Reference documentation is rather meager and shows implementation

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


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


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.

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