Using the mpz_powm functions from the GMP/MPIR libraries with negative exponents
- by Mihai Todor
Please consider the following code:
mpz_t x, n, out;
mpz_init_set_ui(x, 2UL);
mpz_init_set_ui(n, 7UL);
mpz_init(out);
mpz_invert(out, x, n);
gmp_printf ("%Zd\n", out);//prints 4. 2 * 4 (mod 7) = 1. OK
mpz_powm_ui(out, x, -1UL, n);//prints 1. 2 * 1 (mod 7) = 2. How come?
gmp_printf ("%Zd\n", out);
mpz_clear(x);
mpz_clear(n);
mpz_clear(out);
I am unable to understand how the mpz_powm functions handle negative exponents, although, according to the documentation, it is supposed to support them. I would expect that raising a number to -1 modulo n is equivalent to inverting it modulo n. What am I missing here?
