# libtom/libtommath

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 /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is library that provides for multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library is designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * The library is free for all purposes without any express * guarantee it works. * * Tom St Denis, tomstdenis@iahu.ca, http://libtommath.iahu.ca */ #include /* Greatest Common Divisor using the binary method [Algorithm B, page 338, vol2 of TAOCP] */ int mp_gcd (mp_int * a, mp_int * b, mp_int * c) { mp_int u, v, t; int k, res, neg; /* either zero than gcd is the largest */ if (mp_iszero (a) == 1 && mp_iszero (b) == 0) { return mp_copy (b, c); } if (mp_iszero (a) == 0 && mp_iszero (b) == 1) { return mp_copy (a, c); } if (mp_iszero (a) == 1 && mp_iszero (b) == 1) { mp_set (c, 1); return MP_OKAY; } /* if both are negative they share (-1) as a common divisor */ neg = (a->sign == b->sign) ? a->sign : MP_ZPOS; if ((res = mp_init_copy (&u, a)) != MP_OKAY) { return res; } if ((res = mp_init_copy (&v, b)) != MP_OKAY) { goto __U; } /* must be positive for the remainder of the algorithm */ u.sign = v.sign = MP_ZPOS; if ((res = mp_init (&t)) != MP_OKAY) { goto __V; } /* B1. Find power of two */ k = 0; while ((u.dp[0] & 1) == 0 && (v.dp[0] & 1) == 0) { ++k; if ((res = mp_div_2d (&u, 1, &u, NULL)) != MP_OKAY) { goto __T; } if ((res = mp_div_2d (&v, 1, &v, NULL)) != MP_OKAY) { goto __T; } } /* B2. Initialize */ if ((u.dp[0] & 1) == 1) { if ((res = mp_copy (&v, &t)) != MP_OKAY) { goto __T; } t.sign = MP_NEG; } else { if ((res = mp_copy (&u, &t)) != MP_OKAY) { goto __T; } } do { /* B3 (and B4). Halve t, if even */ while (t.used != 0 && (t.dp[0] & 1) == 0) { if ((res = mp_div_2d (&t, 1, &t, NULL)) != MP_OKAY) { goto __T; } } /* B5. if t>0 then u=t otherwise v=-t */ if (t.used != 0 && t.sign != MP_NEG) { if ((res = mp_copy (&t, &u)) != MP_OKAY) { goto __T; } } else { if ((res = mp_copy (&t, &v)) != MP_OKAY) { goto __T; } v.sign = (v.sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; } /* B6. t = u - v, if t != 0 loop otherwise terminate */ if ((res = mp_sub (&u, &v, &t)) != MP_OKAY) { goto __T; } } while (t.used != 0); if ((res = mp_mul_2d (&u, k, &u)) != MP_OKAY) { goto __T; } mp_exch (&u, c); c->sign = neg; res = MP_OKAY; __T:mp_clear (&t); __V:mp_clear (&u); __U:mp_clear (&v); return res; }
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