[MPFR] Re: digits of Pi

[Paul Zimmermann]

       Dear Richard,

> Using CLN's code (which is binary splitting Chudnovskys' formula) on a 
> Core 2 Duo @ 3.0GHz one computes the same number of digits (301029996 
> decimal digits, to be precise) in 27m31s (user), 0m34s (sys).

quite impressive!

> What's interesting is that I see no measureable difference using GMP 
> 4.3.2 and GMP 5.0.0. This is with CLN-1.3.1 where the bulk of 
> multiplication is in mpn_mul, so I do wonder about the reasons for that.

I guess this is because mpn_mul did not improve in GMP 5.0.0 over 4.3.2
for huge operands (using FFT). It did improve in the range where Toom-6
and Toom-8 are used. The MPFR code did improve because it uses div/sqrt,
which are now O(M(n)) in GMP 5.

Paul