/* Assumes len1 != 0 != len2 */
int
_fmpz_poly_gcd_heuristic(fmpz * res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2)
{
ulong bits1, bits2, max_bits, pack_bits, bound_bits, bits_G, bits_Q;
ulong limbs1, limbs2, limbsg, pack_limbs, qlimbs;
ulong log_glen, log_length;
long sign1, sign2, glen, qlen;
fmpz_t ac, bc, d, gc;
fmpz * A, * B, * G, * Q, * t;
mp_ptr array1, array2, arrayg, q, temp;
int divides;
fmpz_init(ac);
fmpz_init(bc);
fmpz_init(d);
/* compute gcd of content of poly1 and poly2 */
_fmpz_poly_content(ac, poly1, len1);
_fmpz_poly_content(bc, poly2, len2);
fmpz_gcd(d, ac, bc);
/* special case, one of the polys is a constant */
if (len2 == 1) /* if len1 == 1 then so does len2 */
{
fmpz_set(res, d);
fmpz_clear(ac);
fmpz_clear(bc);
fmpz_clear(d);
return 1;
}
/* divide poly1 and poly2 by their content */
A = _fmpz_vec_init(len1);
B = _fmpz_vec_init(len2);
_fmpz_vec_scalar_divexact_fmpz(A, poly1, len1, ac);
_fmpz_vec_scalar_divexact_fmpz(B, poly2, len2, bc);
fmpz_clear(ac);
fmpz_clear(bc);
/* special case, one of the polys is length 2 */
if (len2 == 2) /* if len1 == 2 then so does len2 */
{
Q = _fmpz_vec_init(len1 - len2 + 1);
if (_fmpz_poly_divides(Q, A, len1, B, 2))
{
_fmpz_vec_scalar_mul_fmpz(res, B, 2, d);
if (fmpz_sgn(res + 1) < 0)
_fmpz_vec_neg(res, res, 2);
}
else
{
fmpz_set(res, d);
fmpz_zero(res + 1);
}
fmpz_clear(d);
_fmpz_vec_clear(A, len1);
_fmpz_vec_clear(B, len2);
_fmpz_vec_clear(Q, len1 - len2 + 1);
return 1;
}
/*
Determine how many bits (pack_bits) to pack into. The bound
bound_bits ensures that if G | A and G | B with G primitive
then G is the gcd of A and B. The bound is taken from
http://arxiv.org/abs/cs/0206032v1
*/
bits1 = FLINT_ABS(_fmpz_vec_max_bits(A, len1));
bits2 = FLINT_ABS(_fmpz_vec_max_bits(B, len2));
max_bits = FLINT_MAX(bits1, bits2);
bound_bits = FLINT_MIN(bits1, bits2) + 6;
pack_bits = FLINT_MAX(bound_bits, max_bits); /* need to pack original polys */
pack_limbs = (pack_bits - 1)/FLINT_BITS + 1;
if (pack_bits >= 32) /* pack into multiples of limbs if >= 32 bits */
pack_bits = FLINT_BITS*pack_limbs;
/* allocate space to pack into */
limbs1 = (pack_bits*len1 - 1)/FLINT_BITS + 1;
limbs2 = (pack_bits*len2 - 1)/FLINT_BITS + 1;
array1 = flint_calloc(limbs1, sizeof(mp_limb_t));
array2 = flint_calloc(limbs2, sizeof(mp_limb_t));
arrayg = flint_calloc(limbs2, sizeof(mp_limb_t));
/* pack first poly and normalise */
sign1 = (long) fmpz_sgn(A + len1 - 1);
_fmpz_poly_bit_pack(array1, A, len1, pack_bits, sign1);
while (array1[limbs1 - 1] == 0) limbs1--;
/* pack second poly and normalise */
sign2 = (long) fmpz_sgn(B + len2 - 1);
_fmpz_poly_bit_pack(array2, B, len2, pack_bits, sign2);
while (array2[limbs2 - 1] == 0) limbs2--;
/* compute integer GCD */
limbsg = mpn_gcd_full(arrayg, array1, limbs1, array2, limbs2);
/*
Make space for unpacked gcd. May have one extra coeff due to
1 0 -x being packed as 0 -1 -x.
*/
glen = FLINT_MIN((limbsg*FLINT_BITS)/pack_bits + 1, len2);
G = _fmpz_vec_init(glen);
/* unpack gcd */
_fmpz_poly_bit_unpack(G, glen, arrayg, pack_bits, 0);
while (G[glen - 1] == 0) glen--;
/* divide by any content */
fmpz_init(gc);
_fmpz_poly_content(gc, G, glen);
if (!fmpz_is_one(gc))
limbsg = mpn_tdiv_q_fmpz_inplace(arrayg, limbsg, gc);
/* make space for quotient and remainder of first poly by gcd */
qlimbs = limbs1 - limbsg + 1;
qlen = FLINT_MIN(len1, (qlimbs*FLINT_BITS)/pack_bits + 1);
qlimbs = (qlen*pack_bits - 1)/FLINT_BITS + 1;
q = flint_calloc(qlimbs, sizeof(mp_limb_t));
temp = flint_malloc(limbsg*sizeof(mp_limb_t));
divides = 0;
if (mpn_divides(q, array1, limbs1, arrayg, limbsg, temp))
{
/* unpack quotient of first poly by gcd */
Q = _fmpz_vec_init(len1);
t = _fmpz_vec_init(len1 + glen);
_fmpz_poly_bit_unpack(Q, qlen, q, pack_bits, 0);
while (Q[qlen - 1] == 0) qlen--;
/* divide by content */
_fmpz_vec_scalar_divexact_fmpz(G, G, glen, gc);
/* check if we really need to multiply out to check for exact quotient */
bits_G = FLINT_ABS(_fmpz_vec_max_bits(G, glen));
bits_Q = FLINT_ABS(_fmpz_vec_max_bits(Q, qlen));
log_glen = FLINT_BIT_COUNT(glen);
log_length = FLINT_MIN(log_glen, FLINT_BIT_COUNT(qlen));
divides = (bits_G + bits_Q + log_length < pack_bits);
if (!divides) /* need to multiply out to check exact quotient */
divides = multiplies_out(A, len1, Q, qlen, G, glen, sign1, t);
if (divides) /* quotient really was exact */
{
mpn_zero(q, qlimbs);
if (mpn_divides(q, array2, limbs2, arrayg, limbsg, temp))
{
/* unpack quotient of second poly by gcd */
qlimbs = limbs2 - limbsg + 1;
qlen = FLINT_MIN(len2, (qlimbs*FLINT_BITS - 1)/pack_bits + 1);
_fmpz_poly_bit_unpack(Q, qlen, q, pack_bits, 0);
while (Q[qlen - 1] == 0) qlen--;
/* check if we really need to multiply out to check for exact quotient */
bits_Q = FLINT_ABS(_fmpz_vec_max_bits(Q, qlen));
log_length = FLINT_MIN(log_glen, FLINT_BIT_COUNT(qlen));
divides = (bits_G + bits_Q + log_length < pack_bits);
if (!divides) /* we need to multiply out */
divides = multiplies_out(B, len2, Q, qlen, G, glen, sign1, t);
}
}
_fmpz_vec_clear(t, len1 + glen);
_fmpz_vec_clear(Q, len1);
}
flint_free(q);
flint_free(temp);
flint_free(arrayg);
flint_free(array1);
flint_free(array2);
fmpz_clear(gc);
_fmpz_vec_clear(A, len1);
_fmpz_vec_clear(B, len2);
/* we found the gcd, so multiply by content */
if (divides)
{
_fmpz_vec_zero(res + glen, len2 - glen);
_fmpz_vec_scalar_mul_fmpz(res, G, glen, d);
}
fmpz_clear(d);
_fmpz_vec_clear(G, glen);
return divides;
}
void
_fmpz_poly_resultant(fmpz_t res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2)
{
if (len2 == 1)
{
fmpz_pow_ui(res, poly2, len1 - 1);
}
else
{
fmpz_t a, b, g, h, t;
fmpz *A, *B, *W;
const long alloc = len1 + len2;
long sgn = 1;
fmpz_init(a);
fmpz_init(b);
fmpz_init(g);
fmpz_init(h);
fmpz_init(t);
A = W = _fmpz_vec_init(alloc);
B = W + len1;
_fmpz_poly_content(a, poly1, len1);
_fmpz_poly_content(b, poly2, len2);
_fmpz_vec_scalar_divexact_fmpz(A, poly1, len1, a);
_fmpz_vec_scalar_divexact_fmpz(B, poly2, len2, b);
fmpz_set_ui(g, 1);
fmpz_set_ui(h, 1);
fmpz_pow_ui(a, a, len2 - 1);
fmpz_pow_ui(b, b, len1 - 1);
fmpz_mul(t, a, b);
do
{
const long d = len1 - len2;
if (!(len1 & 1L) & !(len2 & 1L))
sgn = -sgn;
_fmpz_poly_pseudo_rem_cohen(A, A, len1, B, len2);
for (len1--; len1 >= 0 && !A[len1]; len1--) ;
len1++;
if (len1 == 0)
{
fmpz_zero(res);
goto cleanup;
}
{
fmpz * T;
long len;
T = A, A = B, B = T;
len = len1, len1 = len2, len2 = len;
}
fmpz_pow_ui(a, h, d);
fmpz_mul(b, g, a);
_fmpz_vec_scalar_divexact_fmpz(B, B, len2, b);
fmpz_pow_ui(g, A + (len1 - 1), d);
fmpz_mul(b, h, g);
fmpz_divexact(h, b, a);
fmpz_set(g, A + (len1 - 1));
} while (len2 > 1);
fmpz_pow_ui(g, h, len1 - 1);
fmpz_pow_ui(b, B + (len2 - 1), len1 - 1);
fmpz_mul(a, h, b);
fmpz_divexact(h, a, g);
fmpz_mul(res, t, h);
if (sgn < 0)
fmpz_neg(res, res);
cleanup:
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(g);
fmpz_clear(h);
fmpz_clear(t);
_fmpz_vec_clear(W, alloc);
}
}
void _fmpq_poly_content(fmpq_t res, const fmpz * poly,
const fmpz_t den, long len)
{
_fmpz_poly_content(fmpq_numref(res), poly, len);
fmpz_set(fmpq_denref(res), den);
}
