The floating point standard is… complicated. These links might help.
It's likely not worth your time because someone else will handle it.
Only processor manufacturers really have the power to handle it.

[IEEE Standard 754 Floating Point
Numbers](https://geeksforgeeks.org/ieee-standard-754-floating-point-numbers)
[bfloat16 floating-point format -
Wikipedia](https://en.wikipedia.org/wiki/Bfloat16_floating-point_format)
[IEEE Standard 754 Floating Point Numbers -
GeeksforGeeks](https://www.geeksforgeeks.org/ieee-standard-754-floating-point-numbers/)
[ARITH 2020: Venue](http://arith2020.arithsymposium.org/programme.html)
[On the Systematic Creation of Faithfully Rounded Truncated Multipliers
and
](https://www.researchgate.net/publication/265339509_On_the_Systematic_Creation_of_Faithfully_Rounded_Truncated_Multipliers_and_Arrays)
[IEEE 754 - Wikipedia](https://en.wikipedia.org/wiki/IEEE_754) [2020
Conference for Computer
Arithmetic](http://arith2020.arithsymposium.org/programme.html)
<https://en.wikipedia.org/wiki/Bfloat16_floating-point_format> [On the
systematic creation of faithfully rounded truncated multipliers and
arrays](https://www.researchgate.net/publication/265339509_On_the_Systematic_Creation_of_Faithfully_Rounded_Truncated_Multipliers_and_Arrays)