How Optifine Gives You Reach and Speed

This one took lots of research to make, but hope you guys enjoy.
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Links and everything
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"OPTIFINE IS AN UNFAIR ADVANTAGE"
https://www.youtube.com/watch?v=uWjBtA5Opn8

Java array definition
https://www.w3schools.com/java/java_arrays.asp#:~:text=Java%20Arrays,holds%20an%20array%20of%20strings.

Extra precise reach display mod to test the extra reach
https://www.mediafire.com/file/6hfs0hjbc5fa31l/ReachDisplayMod_%28Extra_Precision%29.jar/file

Jump that is only possible with optifine https://www.youtube.com/watch?v=19CNqn5r95o
Notes/Corrections/Edits

#1 - When I say vector throughout the video it may not be the correct term, if it isn't just think of the vector as "value"

#2 - At 12:20 I say that position packets go out to 16 decimal places, this is incorrect. Position packets are doubles, meaning they have 53 significant bits which translates to 15.95 decimal digits. This then gets rounded down to 15. See: https://stackoverflow.com/questions/9999221/double-precision-decimal-places for a technical explanation

#3 - Throughout the video I say that fastmath gives up to 3.000253 blocks of reach, this might not be entirely true as it was done by subtracting the difference in the precise reach display mod. In reality this was just taken at one angle and at other slightly different angles the rounding might be even more wrong. I have some information that optifine can give up to 3.0023 blocks of reach which is actually much more significant.

Видео How Optifine Gives You Reach and Speed канала Tenebrous