+#include <tommath.h>
+#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* 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)
+/* Greatest Common Divisor using the binary method */
+int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
- mp_int u, v, t;
- int k, res, neg;
+ mp_int u, v;
+ int k, u_lsb, v_lsb, res;
/* either zero than gcd is the largest */
if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
- return mp_copy (b, c);
+ return mp_abs (b, c);
}
if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
- return mp_copy (a, c);
+ return mp_abs (a, c);
}
- if (mp_iszero (a) == 1 && mp_iszero (b) == 1) {
- mp_set (c, 1);
+
+ /* optimized. At this point if a == 0 then
+ * b must equal zero too
+ */
+ if (mp_iszero (a) == 1) {
+ mp_zero(c);
return MP_OKAY;
}
- /* if both are negative they share (-1) as a common divisor */
- neg = (a->sign == b->sign) ? a->sign : MP_ZPOS;
-
+ /* get copies of a and b we can modify */
if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
return res;
}
if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
- goto __U;
+ goto LBL_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 the common power of two for u and v */
+ u_lsb = mp_cnt_lsb(&u);
+ v_lsb = mp_cnt_lsb(&v);
+ k = MIN(u_lsb, v_lsb);
- /* B1. Find power of two */
- k = 0;
- while (mp_iseven(&u) == 1 && mp_iseven(&v) == 1) {
- ++k;
- if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
- goto __T;
- }
- if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
- goto __T;
- }
- }
+ if (k > 0) {
+ /* divide the power of two out */
+ if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
- /* B2. Initialize */
- if (mp_isodd(&u) == 1) {
- /* t = -v */
- if ((res = mp_copy (&v, &t)) != MP_OKAY) {
- goto __T;
- }
- t.sign = MP_NEG;
- } else {
- /* t = u */
- if ((res = mp_copy (&u, &t)) != MP_OKAY) {
- goto __T;
- }
+ if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
}
- do {
- /* B3 (and B4). Halve t, if even */
- while (t.used != 0 && mp_iseven(&t) == 1) {
- if ((res = mp_div_2 (&t, &t)) != MP_OKAY) {
- goto __T;
- }
- }
+ /* divide any remaining factors of two out */
+ if (u_lsb != k) {
+ if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
- /* 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;
- }
+ if (v_lsb != k) {
+ if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
- /* B6. t = u - v, if t != 0 loop otherwise terminate */
- if ((res = mp_sub (&u, &v, &t)) != MP_OKAY) {
- goto __T;
- }
- } while (mp_iszero(&t) == 0);
+ while (mp_iszero(&v) == 0) {
+ /* make sure v is the largest */
+ if (mp_cmp_mag(&u, &v) == MP_GT) {
+ /* swap u and v to make sure v is >= u */
+ mp_exch(&u, &v);
+ }
+
+ /* subtract smallest from largest */
+ if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ /* Divide out all factors of two */
+ if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
- /* multiply by 2^k which we divided out at the beginning */
- if ((res = mp_mul_2d (&u, k, &u)) != MP_OKAY) {
- goto __T;
+ /* multiply by 2**k which we divided out at the beginning */
+ if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
+ goto LBL_V;
}
-
- mp_exch (&u, c);
- c->sign = neg;
+ c->sign = MP_ZPOS;
res = MP_OKAY;
-__T:mp_clear (&t);
-__V:mp_clear (&u);
-__U:mp_clear (&v);
+LBL_V:mp_clear (&u);
+LBL_U:mp_clear (&v);
return res;
}
+#endif