[Bug libstdc++/47913] [C++0x] improve ratio_add to overflow less often

["marc.glisse at normalesup dot org" <gcc-bugzilla at gcc dot gnu dot org>]

http://gcc.gnu.org/bugzilla/show_bug.cgi?id=47913

--- Comment #17 from Marc Glisse <marc.glisse at normalesup dot org> 2011-03-02 20:50:42 UTC ---
Some more examples. Using the constants:
m=INTMAX_MAX;
n=INTMAX_MAX/2;
p=((intmax_t)1<<(4*sizeof(intmax_t)-1))-3

(m,2)-(m,3)==(m,6)  boost should manage this one

(m/7*5-1,5)-(m-2,7)  __big_mul would be enough (__big_div is the hard thing)

(n-5,15)+(n,35)  one could cheat by removing the integral part

(p^2,(2*p-3)*(p-2))-(p+2,(p-1)*(p-2))  one may be able to write gcd=(p-2), p^2
as (p+2)*gcd+4 and the computation of the numerator becomes
gcd*((p+2)*(p-1)-(2*p-3))+4*(p-1)-4*(2*p-3) and both computations
(p+2)*(p-1)-(2*p-3) and 4*(p-1)-4*(2*p-3) fit in a intmax_t. But with a larger
gcd, they may not (I'll try to add an example later).