andishgar opened a new issue, #46739:
URL: https://github.com/apache/arrow/issues/46739

   ### Describe the bug, including details regarding any error messages, 
version, and platform.
   
   In the code below, two `NaN` values are considered equal regardless of 
whether` EqualOptions::nan_equal `is set to `true` or `false`. The root of the 
problem lies 
[here](https://github.com/apache/arrow/blob/0e5249b0e8f060f8ee5136579bfeed8c92d0d1ab/cpp/src/arrow/compare.cc#L173),
 where `float16` values with the same memory representation are not correctly 
handled, and also 
[here](https://github.com/apache/arrow/blob/0e5249b0e8f060f8ee5136579bfeed8c92d0d1ab/cpp/src/arrow/compare.cc#L112-L114),
 where `HalfFloat` is implemented as a `uint16_t`, causing the comparison to 
return `true`.
   
   ```c++
   TEST(FloatComparasion, Float16NaN) {
     auto half_float_array = ArrayFromJSON(float16(), R"([16.0,NaN])");
     auto half_float_array_1 = ArrayFromJSON(float16(), R"([16.0,NaN])");
     ASSERT_TRUE(half_float_array->Equals(half_float_array_1, 
EqualOptions::Defaults().nans_equal(false)));
     ASSERT_TRUE(half_float_array->Equals(half_float_array, 
EqualOptions::Defaults().nans_equal(false)));
   }
   ``` 
   
   ### Component(s)
   
   C++


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