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Fix definitions of == and isless #103

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Fix definitions of == and isless #103

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Given the definitions of == and isequal in ForwardDiff#master, the PR reverts 337539f (see #10) and defines both ==(x, y) and isequal(x, y) in terms of both value(x) and epsilon(x) etc. This makes

  • the definitions in ForwardDiff and DualNumbers consistent,
  • the definitions of == and isequal in DualNumbers consistent,
  • the definitions of == and isequal mathematically correct.

Additionally, the PR fixes isless: According to its docstring, isless(x, y) should

Test whether `x` is less than `y`, according to a fixed total order (defined together with `isequal`). `isless` is not defined for pairs `(x, y)` of all types. However, if it is defined, it is expected to satisfy the following:
- If `isless(x, y)` is defined, then so is `isless(y, x)` and `isequal(x, y)`, and exactly one of those three yields true.
- The relation defined by `isless` is transitive, i.e., `isless(x, y)` && `isless(y, z)` implies `isless(x, z)`.

On the master branch, however, the first requirement is not satisfied (e.g., choose x = dual(3, 0.5) and y = dual(3, 1.0): then neither isless(x, y), isless(y, x), nor isequal(x, y) is satisfied).

cc @andreasnoack who was involved in #10

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codecov bot commented Mar 13, 2024

Codecov Report

Attention: Patch coverage is 83.33333% with 1 lines in your changes are missing coverage. Please review.

Project coverage is 51.88%. Comparing base (d9251a7) to head (d52f6a3).

Files Patch % Lines
src/dual.jl 83.33% 1 Missing ⚠️
Additional details and impacted files
@@            Coverage Diff             @@
##           master     #103      +/-   ##
==========================================
+ Coverage   50.94%   51.88%   +0.94%     
==========================================
  Files           2        2              
  Lines         212      212              
==========================================
+ Hits          108      110       +2     
+ Misses        104      102       -2     

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