GMP precision with mpf_set_d

[Jørgen Fulsebakke]

Hello! Someone at a forum advised me to ask my question here, so I hope I'm
following the rules etc. Anyway:

When using the gmp library for high precision calculations, is it right that
if I use mpf_set_d(...) to assign a double value to an mp float, the
precision of other mp floats used together with this one is truncated to
double precision, potentially losing information?

As a test I use this program:

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	mpf_t x, y, z;
	mpf_init2(x, 1000000);
	mpf_init2(y, 1000000);
	mpf_init2(z, 1000000);
	mpf_set_str(x, "1e0", 10);
	mpf_set_d(y, 3.3124365842565);
	mpf_set_d(z, 3.3124365842566);
	mpf_mul(y, x, y);
	mpf_mul(z, x, z);
	mpf_sub(x, y, z);
	cout << setprecision(100) << x << endl;



(Notice the difference in the last digits of y and z), and get the output
-9.9920...e-14. If I add even more digits to y and z I get output 0. Thus it
seems that although I initialized the variables to 1000000 bits the
precision is still around 15 digits.

(Also: according to the tutorial at http://gmplib.org/manual/ it should not
be necessary to use init2 like this but only init, however to get high
enough precision in other small test programs I have to use init2)

Thanks!