/* c = (a, b) */
void fp_gcd(fp_int *a, fp_int *b, fp_int *c)
{
fp_int u, v, r;
/* either zero than gcd is the largest */
if (fp_iszero (a) == 1 && fp_iszero (b) == 0) {
fp_abs (b, c);
return;
}
if (fp_iszero (a) == 0 && fp_iszero (b) == 1) {
fp_abs (a, c);
return;
}
/* optimized. At this point if a == 0 then
* b must equal zero too
*/
if (fp_iszero (a) == 1) {
fp_zero(c);
return;
}
/* sort inputs */
if (fp_cmp_mag(a, b) != FP_LT) {
fp_init_copy(&u, a);
fp_init_copy(&v, b);
} else {
fp_init_copy(&u, b);
fp_init_copy(&v, a);
}
fp_zero(&r);
while (fp_iszero(&v) == FP_NO) {
fp_mod(&u, &v, &r);
fp_copy(&v, &u);
fp_copy(&r, &v);
}
fp_copy(&u, c);
}
void fp_to_unsigned_bin(fp_int *a, unsigned char *b)
{
int x;
fp_int t;
fp_init_copy(&t, a);
x = 0;
while (fp_iszero (&t) == FP_NO) {
b[x++] = (unsigned char) (t.dp[0] & 255);
fp_div_2d (&t, 8, &t, NULL);
}
fp_reverse (b, x);
}
int fp_radix_size(fp_int *a, int radix, int *size)
{
int digs;
fp_int t;
fp_digit d;
*size = 0;
/* check range of the radix */
if (radix < 2 || radix > 64) {
return FP_VAL;
}
/* quick out if its zero */
if (fp_iszero(a) == 1) {
*size = 2;
return FP_OKAY;
}
fp_init_copy(&t, a);
/* if it is negative output a - */
if (t.sign == FP_NEG) {
(*size)++;
t.sign = FP_ZPOS;
}
digs = 0;
while (fp_iszero (&t) == FP_NO) {
fp_div_d (&t, (fp_digit) radix, &t, &d);
(*size)++;
}
/* append a NULL so the string is properly terminated */
(*size)++;
return FP_OKAY;
}
/* a/b => cb + d == a */
int fp_div(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
{
fp_int q, x, y, t1, t2;
int n, t, i, norm, neg;
/* is divisor zero ? */
if (fp_iszero (b) == 1) {
return FP_VAL;
}
/* if a < b then q=0, r = a */
if (fp_cmp_mag (a, b) == FP_LT) {
if (d != NULL) {
fp_copy (a, d);
}
if (c != NULL) {
fp_zero (c);
}
return FP_OKAY;
}
fp_init(&q);
q.used = a->used + 2;
fp_init(&t1);
fp_init(&t2);
fp_init_copy(&x, a);
fp_init_copy(&y, b);
/* fix the sign */
neg = (a->sign == b->sign) ? FP_ZPOS : FP_NEG;
x.sign = y.sign = FP_ZPOS;
/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
norm = fp_count_bits(&y) % DIGIT_BIT;
if (norm < (int)(DIGIT_BIT-1)) {
norm = (DIGIT_BIT-1) - norm;
fp_mul_2d (&x, norm, &x);
fp_mul_2d (&y, norm, &y);
} else {
norm = 0;
}
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
n = x.used - 1;
t = y.used - 1;
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
fp_lshd (&y, n - t); /* y = y*b**{n-t} */
while (fp_cmp (&x, &y) != FP_LT) {
++(q.dp[n - t]);
fp_sub (&x, &y, &x);
}
/* reset y by shifting it back down */
fp_rshd (&y, n - t);
/* step 3. for i from n down to (t + 1) */
for (i = n; i >= (t + 1); i--) {
if (i > x.used) {
continue;
}
/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
if (x.dp[i] == y.dp[t]) {
q.dp[i - t - 1] = ((((fp_word)1) << DIGIT_BIT) - 1);
} else {
fp_word tmp;
tmp = ((fp_word) x.dp[i]) << ((fp_word) DIGIT_BIT);
tmp |= ((fp_word) x.dp[i - 1]);
tmp /= ((fp_word) y.dp[t]);
q.dp[i - t - 1] = (fp_digit) (tmp);
}
/* while (q{i-t-1} * (yt * b + y{t-1})) >
xi * b**2 + xi-1 * b + xi-2
do q{i-t-1} -= 1;
*/
q.dp[i - t - 1] = (q.dp[i - t - 1] + 1);
do {
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1);
/* find left hand */
fp_zero (&t1);
t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
t1.dp[1] = y.dp[t];
t1.used = 2;
fp_mul_d (&t1, q.dp[i - t - 1], &t1);
/* find right hand */
t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
t2.dp[2] = x.dp[i];
t2.used = 3;
} while (fp_cmp_mag(&t1, &t2) == FP_GT);
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
fp_mul_d (&y, q.dp[i - t - 1], &t1);
fp_lshd (&t1, i - t - 1);
fp_sub (&x, &t1, &x);
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
if (x.sign == FP_NEG) {
fp_copy (&y, &t1);
fp_lshd (&t1, i - t - 1);
fp_add (&x, &t1, &x);
q.dp[i - t - 1] = q.dp[i - t - 1] - 1;
}
}
/* now q is the quotient and x is the remainder
* [which we have to normalize]
*/
/* get sign before writing to c */
x.sign = x.used == 0 ? FP_ZPOS : a->sign;
if (c != NULL) {
fp_clamp (&q);
fp_copy (&q, c);
c->sign = neg;
}
if (d != NULL) {
fp_div_2d (&x, norm, &x, NULL);
/* the following is a kludge, essentially we were seeing the right remainder but
with excess digits that should have been zero
*/
for (i = b->used; i < x.used; i++) {
x.dp[i] = 0;
}
fp_clamp(&x);
fp_copy (&x, d);
}
return FP_OKAY;
}