Faster exp calculation #399
Draft
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Use
exp(x) = exp(x.round(k)) * exp(x - x.round(k))
.exp(x.round(k))
is fast because calculation ofx**n
is fast.exp(x-x.round(k)
is fast becausex**n/n!
converges fast.Why this optimization?
Currently,
exp(x)
usesexp(x/10**cnt)**(10**cnt)
to make|x|<1
.We can make
|x|
even smaller, but the computation cost ofy**10
is large currentlyO(prec**2)
.exp(x) = exp(x.round(k)) * exp(x - x.round(k))
might not be optimal for the long run, but considering the simplicity of the change, improvement is significant and worth enough.