speed of mpq_cmp vs mpq_sub

[Marc Glisse]

Hello,

in http://stackoverflow.com/q/37366527/1918193 , someone noticed that 
calling mpq_cmp can, in some cases like comparing 2 equal numbers, be much 
slower (10 times or more) than calling mpq_sub and checking the sign of 
the result. With the program below, no macro defined, it takes 1.4s. With 
-DSLOW (use cmp instead of sub) it jumps to 23.8s. On the other hand, if I 
define DIFF so that the denominators are different, the version with cmp 
keeps roughly the same performance, while the version with sub takes 
35.6s. I am not sure we should change anything, but I was surprised at how 
much the cost of the cmp operation could dwarf the rest of the 
computations in that stackoverflow post (you can replace mpq_rational 
with mpq_class from gmpxx.h if you want to test that code).

#include <gmp.h>
int main(){
   mpq_t x;
   mpq_t y;
   mpq_t z;
   mpq_init(x);
   mpq_init(y);
   mpq_init(z);
   mpq_set_d(x,1.037);
   volatile int b;
   for(int i=0;i<20;++i) mpq_mul(x,x,x);
   mpq_set(y,x);
#ifdef DIFF
   mpz_add_ui(mpq_denref(y),mpq_denref(y),1);
#endif
   for(int i=0;i<10;++i){
#ifdef SLOW
     b=mpq_cmp(x,y);
#else
     mpq_sub(z,x,y);
     b=mpq_sgn(z);
#endif
   }
   mpq_clear(z);
   mpq_clear(y);
   mpq_clear(x);
   return 0;
}

-- 
Marc Glisse