add s_mp_log10

[minad]

@czurnieden Regarding our discussion in #371, this is somehow what I would like to have. But the test is failing right now, maybe some rounding issue?.

[czurnieden]

maybe some rounding issue?

Yes, but from an unexpected direction.
I was so concentrated on getting from log_2(x) to log_10(x) that I forgot to consider the rounding error in floor(log_2(x)) and now it's off by one and back where I started.

How preposterous of me to think that I'm better than the people at GMP! ;-)

There are some tricks available to get some more bits of information out of mp_count_bits but they all have quite some overhead:

e.g.: log(x^n)/n = log(x) (all numbers in decimal)
With one of the failures 1086654250330508058 and n = 2 we get floor(log_2(1086654250330508058)) = 119 round it up to 120 and divide by 2 to get 60 and feed that into the original machine to get the correctly rounded result. It is obvious that smaller numbers than that one need larger n and larger numbers get even larger when you square them.
Works quite well with floats but not with integers.

The other way is too take a couple of the most significant bits into consideration but I'm on my way already, needs to be put on hold until this evening.

[minad]

No hurry! But I guess it is good to have it put into mp_log after all otherwise we wouldn't have caught this bug ;)

[minad]

@czurnieden you can take over this PR if you want, it is your code after all.

[czurnieden]

@czurnieden you can take over this PR if you want, it is your code after all.

In that case let me take over to show some mercy and put it down.
*sigh*