Faster exp calculation #399
Merged
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Use
exp(x) = exp(x.round(k)) * exp(x - x.round(k)).exp(x.round(k))is fast because calculation ofx**nis 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**10is largeO(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.