why quaternions instead of 4x4 matrix

yo faggidz why should i use them

For one thing, quaternions are ¼ the size of a 4x4 matrix. What exactly do you need those extra 12 numbers for?

find a O(log n) matrix multiplication algorithm and then we'll tlak

>>3
Since any algorithm for multiplying two n×n-matrices has to process all 2×n²-entries, there is an asymptotic lower bound of Ω(n²) operations. Raz (2002) proves a lower bound of Ω(n² log n) for bounded coefficient arithmetic circuits over the real or complex numbers.

>>4
what does that even prove? i said O(log n) not O(n log n) fagshit dsfasdfasdfadsf i hate you cretin die in a fire stop mocking me

4x4 matrices will accumulate numerical error when you multiply them a lot, and some they start to become more distorsive linear transformations that rotations. And once they become like this, it isn't terribly intuitive how to make them a rotation again. Quanternions will also accumulate error when you multiply them, but you can always periodically renormalize them to get them back to a rotation.

>>5
It proves that you don't know what the fuck you're talking about.

Can't someone implement Decimal type on hardware already?

>>8
Yes, but it's not worth the added complexity to include such things in a modern CPU.

._._._._, .     .  .,,,.,,,.........
|| ._. |||`|: :|'|| ,__ ./|  ..,.,,/
|| | | ||| |: :| || | /./ |  \----~
|| | | ||| |: :| || |//   '\  \
|| |/ //'| |: :| || . \.   \\  \
|| / //' | |: :| || |\ |    \\  \
||  //'  | |: :| || | \ \    \\  \
|| //'   `| \_/ |'| |__\ \ ...!\  \
||//'      \   /  |_'___`')|_______')
`''         ```    `'`''`` ''`'"`'~"`

>>9
IBM managed to do it.

>>8
IBM on most of their enterprise architectures