void bn_rsh(bn_t c, bn_t a, int bits) {
int digits = 0;
if (bits <= 0) {
bn_copy(c, a);
return;
}
SPLIT(bits, digits, bits, BN_DIG_LOG);
if (digits > 0) {
bn_rshd_low(c->dp, a->dp, a->used, digits);
}
c->used = a->used - digits;
c->sign = a->sign;
if (c->used > 0 && bits > 0) {
if (digits == 0 && c != a) {
bn_rshb_low(c->dp, a->dp + digits, a->used - digits, bits);
} else {
bn_rshb_low(c->dp, c->dp, c->used, bits);
}
}
bn_trim(c);
}
void fp_rdcs_low(dig_t *c, dig_t *a, dig_t *m) {
align dig_t q[2 * FP_DIGS], _q[2 * FP_DIGS];
align dig_t _r[2 * FP_DIGS], r[2 * FP_DIGS], t[2 * FP_DIGS];
int *sform, len;
int first, i, j, b0, d0, b1, d1;
dig_t carry;
sform = fp_prime_get_sps(&len);
SPLIT(b0, d0, FP_BITS, FP_DIG_LOG);
first = (d0) + (b0 == 0 ? 0 : 1);
/* q = floor(a/b^k) */
dv_zero(q, 2 * FP_DIGS);
bn_rshd_low(q, a, 2 * FP_DIGS, d0);
if (b0 > 0) {
bn_rshb_low(q, q, 2 * FP_DIGS, b0);
}
/* r = a - qb^k. */
dv_copy(r, a, first);
if (b0 > 0) {
r[first - 1] &= MASK(b0);
}
carry = 0;
while (!fp_is_zero(q)) {
dv_zero(_q, 2 * FP_DIGS);
for (i = len - 1; i > 0; i--) {
j = (sform[i] < 0 ? -sform[i] : sform[i]);
SPLIT(b1, d1, j, FP_DIG_LOG);
dv_zero(t, 2 * FP_DIGS);
bn_lshd_low(t, q, FP_DIGS, d1);
if (b1 > 0) {
bn_lshb_low(t, t, 2 * FP_DIGS, b1);
}
if (sform[i] > 0) {
bn_subn_low(_q, _q, t, 2 * FP_DIGS);
} else {
bn_addn_low(_q, _q, t, 2 * FP_DIGS);
}
}
if (sform[0] > 0) {
bn_subn_low(_q, _q, q, 2 * FP_DIGS);
} else {
bn_addn_low(_q, _q, q, 2 * FP_DIGS);
}
bn_rshd_low(q, _q, 2 * FP_DIGS, d0);
if (b0 > 0) {
bn_rshb_low(q, q, 2 * FP_DIGS, b0);
}
dv_copy(_r, _q, first);
if (b0 > 0) {
_r[first - 1] &= MASK(b0);
}
fp_add(r, r, _r);
}
while (fp_cmpn_low(r, m) != CMP_LT) {
fp_subn_low(r, r, m);
}
fp_copy(c, r);
}
void bn_divn_low(dig_t *c, dig_t *d, dig_t *a, int sa, dig_t *b, int sb) {
int norm, i, n, t, sd;
dig_t carry, t1[3], t2[3];
/* Normalize x and y so that the leading digit of y is bigger than
* 2^(BN_DIGIT-1). */
norm = util_bits_dig(b[sb - 1]) % BN_DIGIT;
if (norm < (int)(BN_DIGIT - 1)) {
norm = (BN_DIGIT - 1) - norm;
carry = bn_lshb_low(a, a, sa, norm);
if (carry) {
a[sa++] = carry;
}
carry = bn_lshb_low(b, b, sb, norm);
if (carry) {
b[sb++] = carry;
}
} else {
norm = 0;
}
n = sa - 1;
t = sb - 1;
/* Shift y so that the most significant digit of y is aligned with the
* most significant digit of x. */
bn_lshd_low(b, b, sb, (n - t));
/* Find the most significant digit of the quotient. */
while (bn_cmpn_low(a, b, sa) != CMP_LT) {
c[n - t]++;
bn_subn_low(a, a, b, sa);
}
/* Shift y back. */
bn_rshd_low(b, b, sb + (n - t), (n - t));
/* Find the remaining digits. */
for (i = n; i >= (t + 1); i--) {
if (i > sa) {
continue;
}
if (a[i] == b[t]) {
c[i - t - 1] = ((((dbl_t)1) << BN_DIGIT) - 1);
} else {
dbl_t tmp;
tmp = ((dbl_t)a[i]) << ((dbl_t)BN_DIGIT);
tmp |= (dbl_t)(a[i - 1]);
tmp /= (dbl_t)(b[t]);
c[i - t - 1] = (dig_t)tmp;
}
c[i - t - 1]++;
do {
c[i - t - 1]--;
t1[0] = (t - 1 < 0) ? 0 : b[t - 1];
t1[1] = b[t];
carry = bn_mul1_low(t1, t1, c[i - t - 1], 2);
t1[2] = carry;
t2[0] = (i - 2 < 0) ? 0 : a[i - 2];
t2[1] = (i - 1 < 0) ? 0 : a[i - 1];
t2[2] = a[i];
} while (bn_cmpn_low(t1, t2, 3) == CMP_GT);
carry = bn_mul1_low(d, b, c[i - t - 1], sb);
sd = sb;
if (carry) {
d[sd++] = carry;
}
carry = bn_subn_low(a + (i - t - 1), a + (i - t - 1), d, sd);
sd += (i - t - 1);
if (sa - sd > 0) {
carry = bn_sub1_low(a + sd, a + sd, carry, sa - sd);
}
if (carry) {
sd = sb + (i - t - 1);
carry = bn_addn_low(a + (i - t - 1), a + (i - t - 1), b, sb);
carry = bn_add1_low(a + sd, a + sd, carry, sa - sd);
c[i - t - 1]--;
}
}
/* Remainder should be not be longer than the divisor. */
bn_rshb_low(d, a, sb, norm);
}