void _fmpz_poly_sqrlow_KS(fmpz * res, const fmpz * poly, long len, long n)
{
int neg;
long bits, limbs, loglen, sign = 0;
mp_limb_t *arr_in, *arr_out;
FMPZ_VEC_NORM(poly, len);
if (len == 0)
{
_fmpz_vec_zero(res, n);
return;
}
neg = (fmpz_sgn(poly + len - 1) > 0) ? 0 : -1;
if (n > 2 * len - 1)
{
_fmpz_vec_zero(res + 2 * len - 1, n - (2 * len - 1));
n = 2 * len - 1;
}
bits = _fmpz_vec_max_bits(poly, len);
if (bits < 0)
{
sign = 1;
bits = - bits;
}
loglen = FLINT_BIT_COUNT(len);
bits = 2 * bits + loglen + sign;
limbs = (bits * len - 1) / FLINT_BITS + 1;
arr_in = flint_calloc(limbs, sizeof(mp_limb_t));
arr_out = flint_malloc((2 * limbs) * sizeof(mp_limb_t));
_fmpz_poly_bit_pack(arr_in, poly, len, bits, neg);
mpn_sqr(arr_out, arr_in, limbs);
if (sign)
_fmpz_poly_bit_unpack(res, n, arr_out, bits, 0);
else
_fmpz_poly_bit_unpack_unsigned(res, n, arr_out, bits);
flint_free(arr_in);
flint_free(arr_out);
}
void
fmpz_poly_bit_unpack(fmpz_poly_t poly, const fmpz_t f, mp_bitcnt_t bit_size)
{
slong len;
mpz_t tmp;
int negate, borrow;
if (bit_size == 0 || fmpz_is_zero(f))
{
fmpz_poly_zero(poly);
return;
}
/* Round up */
len = (fmpz_bits(f) + bit_size - 1) / bit_size;
negate = (fmpz_sgn(f) < 0) ? -1 : 0;
mpz_init2(tmp, bit_size*len);
/* TODO: avoid all this wastefulness */
flint_mpn_zero(tmp->_mp_d, tmp->_mp_alloc);
fmpz_get_mpz(tmp, f);
fmpz_poly_fit_length(poly, len + 1);
borrow = _fmpz_poly_bit_unpack(poly->coeffs, len,
tmp->_mp_d, bit_size, negate);
if (borrow)
{
fmpz_set_si(poly->coeffs + len, negate ? WORD(-1) : WORD(1));
_fmpz_poly_set_length(poly, len + 1);
}
else
{
_fmpz_poly_set_length(poly, len);
_fmpz_poly_normalise(poly);
}
mpz_clear(tmp);
}
void
_fmpz_poly_mullow_KS(fmpz * res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2, long n)
{
int neg1, neg2;
long limbs1, limbs2, loglen;
long bits1, bits2, bits;
mp_limb_t *arr1, *arr2, *arr3;
long sign = 0;
FMPZ_VEC_NORM(poly1, len1);
FMPZ_VEC_NORM(poly2, len2);
if (!len1 | !len2)
{
_fmpz_vec_zero(res, n);
return;
}
neg1 = (fmpz_sgn(poly1 + len1 - 1) > 0) ? 0 : -1;
neg2 = (fmpz_sgn(poly2 + len2 - 1) > 0) ? 0 : -1;
if (n > len1 + len2 - 1)
{
_fmpz_vec_zero(res + len1 + len2 - 1, n - (len1 + len2 - 1));
n = len1 + len2 - 1;
}
bits1 = _fmpz_vec_max_bits(poly1, len1);
if (bits1 < 0)
{
sign = 1;
bits1 = -bits1;
}
if (poly1 != poly2)
{
bits2 = _fmpz_vec_max_bits(poly2, len2);
if (bits2 < 0)
{
sign = 1;
bits2 = -bits2;
}
}
else
bits2 = bits1;
loglen = FLINT_BIT_COUNT(FLINT_MIN(len1, len2));
bits = bits1 + bits2 + loglen + sign;
limbs1 = (bits * len1 - 1) / FLINT_BITS + 1;
limbs2 = (bits * len2 - 1) / FLINT_BITS + 1;
if (poly1 == poly2)
{
arr1 = (mp_ptr) flint_calloc(limbs1, sizeof(mp_limb_t));
arr2 = arr1;
_fmpz_poly_bit_pack(arr1, poly1, len1, bits, neg1);
}
else
{
arr1 = (mp_ptr) flint_calloc(limbs1 + limbs2, sizeof(mp_limb_t));
arr2 = arr1 + limbs1;
_fmpz_poly_bit_pack(arr1, poly1, len1, bits, neg1);
_fmpz_poly_bit_pack(arr2, poly2, len2, bits, neg2);
}
arr3 = (mp_ptr) flint_malloc((limbs1 + limbs2) * sizeof(mp_limb_t));
if (limbs1 == limbs2)
mpn_mul_n(arr3, arr1, arr2, limbs1);
else if (limbs1 > limbs2)
mpn_mul(arr3, arr1, limbs1, arr2, limbs2);
else
mpn_mul(arr3, arr2, limbs2, arr1, limbs1);
if (sign)
_fmpz_poly_bit_unpack(res, n, arr3, bits, neg1 ^ neg2);
else
_fmpz_poly_bit_unpack_unsigned(res, n, arr3, bits);
flint_free(arr1);
flint_free(arr3);
}
/* 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;
}
