/*
* Knuth, TAOCP, Volume 2, 4.3.1:
* w := product of u (len m) and v (len n)
* w must be initialized to zero
*/
void
_mpd_basemul(mpd_uint_t *w, const mpd_uint_t *u, const mpd_uint_t *v,
mpd_size_t m, mpd_size_t n)
{
mpd_uint_t hi, lo;
mpd_uint_t carry;
mpd_size_t i, j;
assert(m > 0 && n > 0);
for (j=0; j < n; j++) {
carry = 0;
for (i=0; i < m; i++) {
_mpd_mul_words(&hi, &lo, u[i], v[j]);
lo = w[i+j] + lo;
if (lo < w[i+j]) hi++;
lo = carry + lo;
if (lo < carry) hi++;
_mpd_div_words_r(&carry, &w[i+j], hi, lo);
}
w[j+m] = carry;
}
}
/* w := product of u (len n) and v (single word) */
void
_mpd_shortmul(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
{
mpd_uint_t hi, lo;
mpd_uint_t carry = 0;
mpd_size_t i;
assert(n > 0);
for (i=0; i < n; i++) {
_mpd_mul_words(&hi, &lo, u[i], v);
lo = carry + lo;
if (lo < carry) hi++;
_mpd_div_words_r(&carry, &w[i], hi, lo);
}
w[i] = carry;
}
/*
* Knuth, TAOCP Volume 2, 4.3.1, exercise 16:
* w := quotient of u (len n) divided by a single word v
*/
mpd_uint_t
_mpd_shortdiv(mpd_uint_t *w, const mpd_uint_t *u, mpd_size_t n, mpd_uint_t v)
{
mpd_uint_t hi, lo;
mpd_uint_t rem = 0;
mpd_size_t i;
assert(n > 0);
for (i=n-1; i != MPD_SIZE_MAX; i--) {
_mpd_mul_words(&hi, &lo, rem, MPD_RADIX);
lo = u[i] + lo;
if (lo < u[i]) hi++;
_mpd_div_words(&w[i], &rem, hi, lo, v);
}
return rem;
}
/*
* Knuth, TAOCP Volume 2, 4.3.1:
* q, r := quotient and remainder of uconst (len nplusm)
* divided by vconst (len n)
* nplusm >= n
*
* If r is not NULL, r will contain the remainder. If r is NULL, the
* return value indicates if there is a remainder: 1 for true, 0 for
* false. A return value of -1 indicates an error.
*/
int
_mpd_basedivmod(mpd_uint_t *q, mpd_uint_t *r,
const mpd_uint_t *uconst, const mpd_uint_t *vconst,
mpd_size_t nplusm, mpd_size_t n)
{
mpd_uint_t ustatic[MPD_MINALLOC_MAX];
mpd_uint_t vstatic[MPD_MINALLOC_MAX];
mpd_uint_t *u = ustatic;
mpd_uint_t *v = vstatic;
mpd_uint_t d, qhat, rhat, w2[2];
mpd_uint_t hi, lo, x;
mpd_uint_t carry;
mpd_size_t i, j, m;
int retval = 0;
assert(n > 1 && nplusm >= n);
m = sub_size_t(nplusm, n);
/* D1: normalize */
d = MPD_RADIX / (vconst[n-1] + 1);
if (nplusm >= MPD_MINALLOC_MAX) {
if ((u = mpd_alloc(nplusm+1, sizeof *u)) == NULL) {
return -1;
}
}
if (n >= MPD_MINALLOC_MAX) {
if ((v = mpd_alloc(n+1, sizeof *v)) == NULL) {
mpd_free(u);
return -1;
}
}
_mpd_shortmul(u, uconst, nplusm, d);
_mpd_shortmul(v, vconst, n, d);
/* D2: loop */
for (j=m; j != MPD_SIZE_MAX; j--) {
/* D3: calculate qhat and rhat */
rhat = _mpd_shortdiv(w2, u+j+n-1, 2, v[n-1]);
qhat = w2[1] * MPD_RADIX + w2[0];
while (1) {
if (qhat < MPD_RADIX) {
_mpd_singlemul(w2, qhat, v[n-2]);
if (w2[1] <= rhat) {
if (w2[1] != rhat || w2[0] <= u[j+n-2]) {
break;
}
}
}
qhat -= 1;
rhat += v[n-1];
if (rhat < v[n-1] || rhat >= MPD_RADIX) {
break;
}
}
/* D4: multiply and subtract */
carry = 0;
for (i=0; i <= n; i++) {
_mpd_mul_words(&hi, &lo, qhat, v[i]);
lo = carry + lo;
if (lo < carry) hi++;
_mpd_div_words_r(&hi, &lo, hi, lo);
x = u[i+j] - lo;
carry = (u[i+j] < x);
u[i+j] = carry ? x+MPD_RADIX : x;
carry += hi;
}
q[j] = qhat;
/* D5: test remainder */
if (carry) {
q[j] -= 1;
/* D6: add back */
(void)_mpd_baseadd(u+j, u+j, v, n+1, n);
}
}
/* D8: unnormalize */
if (r != NULL) {
_mpd_shortdiv(r, u, n, d);
/* we are not interested in the return value here */
retval = 0;
}
else {
retval = !_mpd_isallzero(u, n);
}
if (u != ustatic) mpd_free(u);
if (v != vstatic) mpd_free(v);
return retval;
}
