/*
* Compute a = a % m.
* Input in first alen words of a and first mlen words of m.
* Output in first alen words of a
* (of which first alen-mlen words will be zero).
* The MSW of m MUST have its high bit set.
* Quotient is accumulated in the `quotient' array, which is a Bignum
* rather than the internal bigendian format. Quotient parts are shifted
* left by `qshift' before adding into quot.
*/
static void internal_mod(BignumInt *a, int alen,
BignumInt *m, int mlen,
BignumInt *quot, int qshift)
{
BignumInt m0, m1;
unsigned int h;
int i, k;
m0 = m[0];
if (mlen > 1)
m1 = m[1];
else
m1 = 0;
for (i = 0; i <= alen - mlen; i++) {
BignumDblInt t;
unsigned int q, r, c, ai1;
if (i == 0) {
h = 0;
} else {
h = a[i - 1];
a[i - 1] = 0;
}
if (i == alen - 1)
ai1 = 0;
else
ai1 = a[i + 1];
/* Find q = h:a[i] / m0 */
if (h >= m0) {
/*
* Special case.
*
* To illustrate it, suppose a BignumInt is 8 bits, and
* we are dividing (say) A1:23:45:67 by A1:B2:C3. Then
* our initial division will be 0xA123 / 0xA1, which
* will give a quotient of 0x100 and a divide overflow.
* However, the invariants in this division algorithm
* are not violated, since the full number A1:23:... is
* _less_ than the quotient prefix A1:B2:... and so the
* following correction loop would have sorted it out.
*
* In this situation we set q to be the largest
* quotient we _can_ stomach (0xFF, of course).
*/
q = BIGNUM_INT_MASK;
} else {
DIVMOD_WORD(q, r, h, a[i], m0);
/* Refine our estimate of q by looking at
h:a[i]:a[i+1] / m0:m1 */
t = MUL_WORD(m1, q);
if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {
q--;
t -= m1;
r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */
if (r >= (BignumDblInt) m0 &&
t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--;
}
}
/* Subtract q * m from a[i...] */
c = 0;
for (k = mlen - 1; k >= 0; k--) {
t = MUL_WORD(q, m[k]);
t += c;
c = t >> BIGNUM_INT_BITS;
if ((BignumInt) t > a[i + k])
c++;
a[i + k] -= (BignumInt) t;
}
/* Add back m in case of borrow */
if (c != h) {
t = 0;
for (k = mlen - 1; k >= 0; k--) {
t += m[k];
t += a[i + k];
a[i + k] = (BignumInt) t;
t = t >> BIGNUM_INT_BITS;
}
q--;
}
if (quot)
internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));
}
/*
* Compute a = a % m.
* Input in first alen words of a and first mlen words of m.
* Output in first alen words of a
* (of which first alen-mlen words will be zero).
* The MSW of m MUST have its high bit set.
* Quotient is accumulated in the `quotient' array, which is a Bignum
* rather than the internal bigendian format. Quotient parts are shifted
* left by `qshift' before adding into quot.
*/
static void internal_mod(BignumInt *a, int alen,
BignumInt *m, int mlen,
BignumInt *quot, int qshift)
{
BignumInt m0, m1;
unsigned int h;
int i, k;
m0 = m[0];
if (mlen > 1)
m1 = m[1];
else
m1 = 0;
for (i = 0; i <= alen - mlen; i++) {
BignumDblInt t;
unsigned int q, r, c, ai1;
if (i == 0) {
h = 0;
} else {
h = a[i - 1];
a[i - 1] = 0;
}
if (i == alen - 1)
ai1 = 0;
else
ai1 = a[i + 1];
/* Find q = h:a[i] / m0 */
DIVMOD_WORD(q, r, h, a[i], m0);
/* Refine our estimate of q by looking at
h:a[i]:a[i+1] / m0:m1 */
t = MUL_WORD(m1, q);
if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {
q--;
t -= m1;
r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */
if (r >= (BignumDblInt) m0 &&
t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--;
}
/* Subtract q * m from a[i...] */
c = 0;
for (k = mlen - 1; k >= 0; k--) {
t = MUL_WORD(q, m[k]);
t += c;
c = t >> BIGNUM_INT_BITS;
if ((BignumInt) t > a[i + k])
c++;
a[i + k] -= (BignumInt) t;
}
/* Add back m in case of borrow */
if (c != h) {
t = 0;
for (k = mlen - 1; k >= 0; k--) {
t += m[k];
t += a[i + k];
a[i + k] = (BignumInt) t;
t = t >> BIGNUM_INT_BITS;
}
q--;
}
if (quot)
internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));
}