Binomial: Faster sampling for n * p >= 10

[vks]

Before:

test misc_binomial_1      ... bench:          13 ns/iter (+/- 0)
test misc_binomial_10     ... bench:          69 ns/iter (+/- 2)
test misc_binomial_100    ... bench:          70 ns/iter (+/- 2)
test misc_binomial_1000   ... bench:         599 ns/iter (+/- 9)
test misc_binomial_1e12   ... bench:         660 ns/iter (+/- 15)

After:

test misc_binomial_1      ... bench:          13 ns/iter (+/- 1)
test misc_binomial_10     ... bench:          70 ns/iter (+/- 10)
test misc_binomial_100    ... bench:          74 ns/iter (+/- 5)
test misc_binomial_1000   ... bench:         136 ns/iter (+/- 3)
test misc_binomial_1e12   ... bench:          57 ns/iter (+/- 3)

This requires #735.

[vks]

cc @geq1t

[dhardy]

Great. I will hold off merging this until after #735.

[geq1t]

I don't really have a say in this, but from what I've seen BTPE is a very fast algorithm for binomial sampling, so implementing it would almost certainly be a win. I'll see if I can get a copy of the paper to compare against.

[dhardy]

Rebase please

[vks]

I rebased on master.

[vks]

Rebased again. This includes the fix for MIPS.

[dhardy]

Ah, sorry, I'll try to get to reviewing this this week.

[dhardy]

The implementation appears to correspond to the algorithm in the K&S paper except where mentioned (apparently an error in the paper).

Why do you think some parts of the algorithm should be carried out with integers? It seems to me better to stick with floats until the result is ready.