Section::entropy returns -0.0 for a one-byte section

[PaulDance]

Describe the bug
Whenever one parses a Mach-O file containing a section which contents only have one byte, the computed entropy for it is -0.0 instead of exactly 0.0, which is a bit surprising at first. It still has the property that >= 0.0 because -0.0 == 0.0, but not that str(-0.0) == str(0.0) because the - is kept in the string representation of the float. Having it consistent with the intuition of >= 0.0 would be nice, especially if one uses the string representation in CI for example.

To Reproduce

>>> import lief
>>> lief.MachO.Section("weird_section", [1, 2, 3]).entropy
1.584962500721156
>>> lief.MachO.Section("weird_section", [1, 2]).entropy
1.0
>>> lief.MachO.Section("weird_section", [1]).entropy
-0.0
>>> lief.MachO.Section("weird_section", []).entropy
0.0

Expected behavior

>>> lief.MachO.Section("weird_section", [1]).entropy
0.0

Environment:

• System and Version: Debian testing (Linux debian 6.5.0-1-amd64 #1 SMP PREEMPT_DYNAMIC Debian 6.5.3-1 (2023-09-13) x86_64 GNU/Linux).
• Target format: found for Mach-O, but the same could be applicable to other formats (see below).
• Python version: 3.10.13.
• LIEF commit version: 0.12.3-39115d10.

Additional context
I think the problem comes from the following subtlety: in src/Abstract/Section.cpp's Section::entropy implementation, one can see that entropy += freq * std::log2l(freq); in the loop is used to progressively sum the final entropy up and at the end that return (-entropy); is used to return the sum value, but turned positive first.

Listing cases:

• In the case of an empty section (last one in the example):
  • the loop is not ran because of the if (content.empty()) check above it ,
  • so the default 0. is returned.
• When the section has more than one byte (first two cases in the example):
  • probabilities will be strictly less than 1.0,
  • so their std::log2l will be strictly negative
  • and the finally-returned value will therefore be strictly positive.
• However, when content.size() == 1 (second to last case in the example):
  • the byte count for it will be exactly 1,
  • and the associated frequency will also be exactly 1.0 (because 1.0 / 1.0),
  • and so its std::log2l will be exactly 0.0,
  • therefore, at the end of the loop that ran only once, entropy is exactly 0.0,
  • hence the function returning exactly -0.0 because it negates it.

A potential fix should therefore be:

• Use entropy -= freq * std::log2l(freq); instead.
• Use return entropy; instead.

[romainthomas]

Hi @PaulDance ,

Thank you very much for the well detailed issue (highly appreciated!). I agree with your remark and
I would go for:

[...]
if (content.empty() || content.size() == 1) {
  return 0.;
}
[...]

[PaulDance]

Thank you very much @romainthomas for the quick response!