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Mapping Floating-Point Computations to Ordered Binary Trees - derFunkenstein
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pieterr
It seems that one could also map floating point computations to Cartesian trees
(aka binary search trees). In which case, the number you need to look up in
the tree is the exponent you want to apply to the computed number and the
result is then in the first node of the tree.
I.e., if you look up a number that has the exponent e, you'll start on the
first node of the tree and then recurse on the subtree. If you can optimize
the recursion, you'll end up traversing the tree by just doing n-log(n), and
returning the first node you hit.
While this would not be as efficient as a vectorized map for floating-point
computations, it would be better than a linked list (assuming it can be
vectorized), and much more logical and human-readable than an algorithm
represented in an ordered binary tree.
It would also be a much better way to represent floating-point computations in
a programming language, while at the same time allowing more complex
applications to be written.
For example, if we tried to generalize Cartesian trees to allow more than two
children, the representation would be much more compact and understandable
(more binary trees than linked lists).
~~~
jordigh
I was trying to do something like that for emulating fp computations. Turns
out I can do it much more efficiently than cartesian trees:
[
to-emulate-floating-point-computation-using-divide-and-conquer/)
~~~
pieterr
You can basically just do the cartesian trees if you don't need to search in
parallel. In the end you'll still get O(n-log 01e38acffe
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