void _fmpq_poly_scalar_mul_fmpz(fmpz * rpoly, fmpz_t rden,
const fmpz * poly, const fmpz_t den, long len,
const fmpz_t c)
{
fmpz_t gcd; /* GCD( den, c ) */
if (fmpz_is_zero(c))
{
_fmpz_vec_zero(rpoly, len);
fmpz_one(rden);
return;
}
fmpz_init(gcd);
fmpz_one(gcd);
if (*c != 1L)
fmpz_gcd(gcd, c, den);
if (*gcd == 1L)
{
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, c);
fmpz_set(rden, den);
}
else
{
fmpz_t c2;
fmpz_init(c2);
fmpz_divexact(c2, c, gcd);
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, c2);
fmpz_divexact(rden, den, gcd);
fmpz_clear(c2);
}
fmpz_clear(gcd);
}
/* Assumes poly1 and poly2 are not length 0. */
void
_fmpz_poly_mul_classical(fmpz * res, const fmpz * poly1,
slong len1, const fmpz * poly2, slong len2)
{
if (len1 == 1 && len2 == 1) /* Special case if the length of both inputs is 1 */
{
fmpz_mul(res, poly1, poly2);
}
else /* Ordinary case */
{
slong i;
/* Set res[i] = poly1[i]*poly2[0] */
_fmpz_vec_scalar_mul_fmpz(res, poly1, len1, poly2);
/* Set res[i+len1-1] = in1[len1-1]*in2[i] */
_fmpz_vec_scalar_mul_fmpz(res + len1, poly2 + 1, len2 - 1,
poly1 + len1 - 1);
/* out[i+j] += in1[i]*in2[j] */
for (i = 0; i < len1 - 1; i++)
_fmpz_vec_scalar_addmul_fmpz(res + i + 1, poly2 + 1, len2 - 1,
poly1 + i);
}
}
/*
Assumes poly1 and poly2 are not length 0 and 0 < n <= len1 + len2 - 1.
*/
void
_fmpz_poly_mullow_classical(fmpz * res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2, long n)
{
if ((len1 == 1 && len2 == 1) || n == 1) /* Special case if the length of output is 1 */
{
fmpz_mul(res, poly1, poly2);
}
else /* Ordinary case */
{
long i;
/* Set res[i] = poly1[i]*poly2[0] */
_fmpz_vec_scalar_mul_fmpz(res, poly1, FLINT_MIN(len1, n), poly2);
/* Set res[i+len1-1] = in1[len1-1]*in2[i] */
if (n > len1)
_fmpz_vec_scalar_mul_fmpz(res + len1, poly2 + 1, n - len1,
poly1 + len1 - 1);
/* out[i+j] += in1[i]*in2[j] */
for (i = 0; i < FLINT_MIN(len1, n) - 1; i++)
_fmpz_vec_scalar_addmul_fmpz(res + i + 1, poly2 + 1,
FLINT_MIN(len2, n - i) - 1,
poly1 + i);
}
}
int padic_poly_get_fmpz_poly(fmpz_poly_t rop, const padic_poly_t op,
const padic_ctx_t ctx)
{
const slong len = op->length;
if (op->val < 0)
{
return 0;
}
if (padic_poly_is_zero(op))
{
fmpz_poly_zero(rop);
return 1;
}
fmpz_poly_fit_length(rop, len);
_fmpz_poly_set_length(rop, len);
if (op->val == 0)
{
_fmpz_vec_set(rop->coeffs, op->coeffs, len);
}
else /* op->val > 0 */
{
fmpz_t pow;
fmpz_init(pow);
fmpz_pow_ui(pow, ctx->p, op->val);
_fmpz_vec_scalar_mul_fmpz(rop->coeffs, op->coeffs, len, pow);
fmpz_clear(pow);
}
return 1;
}
/* Assumes poly1 and poly2 are not length 0 and len1 >= len2. */
void
_fmpz_poly_mulmid_classical(fmpz * res, const fmpz * poly1,
slong len1, const fmpz * poly2, slong len2)
{
if ((len1 == 1) && (len2 == 1)) /* Special case if the length of both inputs is 1 */
{
fmpz_mul(res, poly1, poly2);
}
else /* Ordinary case */
{
slong i;
/* Set res[i] = poly1[i]*poly2[0] */
_fmpz_vec_scalar_mul_fmpz(res, poly1 + len2 - 1, len1 - len2 + 1,
poly2);
/* out[i+j] += in1[i]*in2[j] */
for (i = 0; i < len2 - 1; i++)
_fmpz_vec_scalar_addmul_fmpz(res, poly2 + len2 - i - 1,
FLINT_MIN(i + 1, len1 - len2 + 1),
poly1 + i);
for (; i < len1 - 1; i++)
_fmpz_vec_scalar_addmul_fmpz(res + i - len2 + 2, poly2 + 1,
FLINT_MIN(len2 - 1, len1 - i - 1),
poly1 + i);
}
}
void _qadic_exp_balanced(fmpz *rop, const fmpz *x, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N, const fmpz_t pN)
{
const slong d = j[lena - 1];
fmpz_t pw;
fmpz *r, *s, *t;
slong i, w;
r = _fmpz_vec_init(d);
s = _fmpz_vec_init(2*d - 1);
t = _fmpz_vec_init(d);
fmpz_init(pw);
fmpz_pow_ui(pw, p, v);
_fmpz_vec_scalar_mul_fmpz(t, x, len, pw);
_fmpz_vec_scalar_mod_fmpz(t, t, len, pN);
_fmpz_vec_zero(t + len, d - len);
fmpz_set(pw, p);
fmpz_one(rop + 0);
_fmpz_vec_zero(rop + 1, d - 1);
w = 1;
while (!_fmpz_vec_is_zero(t, d))
{
fmpz_mul(pw, pw, pw);
for (i = 0; i < d; i++)
{
fmpz_fdiv_r(r + i, t + i, pw);
fmpz_sub(t + i, t + i, r + i);
}
if (!_fmpz_vec_is_zero(r, d))
{
_qadic_exp_bsplit(r, r, w, d, a, j, lena, p, N);
_fmpz_poly_mul(s, rop, d, r, d);
_fmpz_poly_reduce(s, 2*d - 1, a, j, lena);
_fmpz_vec_scalar_mod_fmpz(rop, s, d, pN);
}
w *= 2;
}
_fmpz_vec_clear(r, d);
_fmpz_vec_clear(s, 2*d - 1);
_fmpz_vec_clear(t, d);
fmpz_clear(pw);
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("content....");
fflush(stdout);
/* Check that content(a f) = abs(a) content(f) */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_t a, c, d;
fmpz *f;
slong len = n_randint(state, 100);
fmpz_init(a);
fmpz_init(c);
fmpz_init(d);
f = _fmpz_vec_init(len);
_fmpz_vec_randtest(f, state, len, 200);
fmpz_randtest(a, state, 100);
_fmpz_vec_content(c, f, len);
_fmpz_vec_scalar_mul_fmpz(f, f, len, a);
fmpz_abs(a, a);
fmpz_mul(c, a, c);
_fmpz_vec_content(d, f, len);
result = (fmpz_equal(c, d));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_print(c), flint_printf("\n\n");
fmpz_print(d), flint_printf("\n\n");
abort();
}
fmpz_clear(a);
fmpz_clear(c);
fmpz_clear(d);
_fmpz_vec_clear(f, len);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
_fmpz_poly_pseudo_divrem_basecase(fmpz * Q, fmpz * R, ulong * d,
const fmpz * A, long lenA, const fmpz * B,
long lenB)
{
const fmpz * leadB = B + (lenB - 1);
long iQ = lenA - lenB, iR = lenA - 1;
fmpz_t rem;
fmpz_init(rem);
*d = 0;
_fmpz_vec_zero(Q, lenA - lenB + 1);
if (R != A)
_fmpz_vec_set(R, A, lenA);
while (iR >= lenB - 1)
{
fmpz_fdiv_qr(Q + iQ, rem, R + iR, leadB);
if (!fmpz_is_zero(rem))
{
_fmpz_vec_scalar_mul_fmpz(Q, Q, lenA - lenB + 1, leadB);
fmpz_set(Q + iQ, R + iR);
_fmpz_vec_scalar_mul_fmpz(R, R, lenA, leadB);
(*d)++;
}
if (lenB > 1)
_fmpz_vec_scalar_submul_fmpz(R + (iR - lenB + 1), B, lenB - 1, Q + iQ);
fmpz_zero(R + iR);
iR--;
iQ--;
}
fmpz_clear(rem);
}
void
fmpz_poly_scalar_mul_fmpz(fmpz_poly_t poly1, const fmpz_poly_t poly2,
const fmpz_t x)
{
/* Either scalar or input poly is zero */
if ((*x == 0) || (poly2->length == 0))
{
fmpz_poly_zero(poly1);
return;
}
fmpz_poly_fit_length(poly1, poly2->length);
_fmpz_vec_scalar_mul_fmpz(poly1->coeffs, poly2->coeffs, poly2->length, x);
_fmpz_poly_set_length(poly1, poly2->length);
}
/* Assumes len > 0. */
void _fmpz_poly_sqr_classical(fmpz *rop, const fmpz *op, long len)
{
if (len == 1) /* Special case */
{
fmpz_mul(rop, op, op);
}
else /* Ordinary case */
{
long i;
_fmpz_vec_scalar_mul_fmpz(rop, op, len, op);
_fmpz_vec_scalar_mul_fmpz(rop + len, op + 1, len - 1, op + len - 1);
for (i = 1; i < len - 1; i++)
_fmpz_vec_scalar_addmul_fmpz(rop + i + 1, op + 1, i - 1, op + i);
for (i = 1; i < 2 * len - 2; i++)
fmpz_mul_ui(rop + i, rop + i, 2);
for (i = 1; i < len - 1; i++)
fmpz_addmul(rop + 2 * i, op + i, op + i);
}
}
void
_fmpz_poly_pseudo_divrem_cohen(fmpz * Q, fmpz * R, const fmpz * A,
long lenA, const fmpz * B, long lenB)
{
const fmpz * leadB = B + (lenB - 1);
long e, lenQ;
fmpz_t pow;
if (lenB == 1)
{
fmpz_init(pow);
fmpz_pow_ui(pow, leadB, lenA - 1);
_fmpz_vec_scalar_mul_fmpz(Q, A, lenA, pow);
_fmpz_vec_zero(R, lenA);
fmpz_clear(pow);
return;
}
lenQ = lenA - lenB + 1;
_fmpz_vec_zero(Q, lenQ);
if (R != A)
_fmpz_vec_set(R, A, lenA);
e = lenA - lenB;
/* Unroll the first run of the while loop */
{
fmpz_set(Q + (lenQ - 1), R + (lenA - 1));
_fmpz_vec_scalar_mul_fmpz(R, R, lenA - 1, leadB);
_fmpz_vec_scalar_submul_fmpz(R + (lenA - lenB), B, lenB - 1, R + (lenA - 1));
fmpz_zero(R + (lenA - 1));
for (lenA -= 2; (lenA >= 0) && (R[lenA] == 0L); lenA--) ;
lenA++;
}
while (lenA >= lenB)
{
_fmpz_vec_scalar_mul_fmpz(Q, Q, lenQ, leadB);
fmpz_add(Q + (lenA - lenB), Q + (lenA - lenB), R + (lenA - 1));
_fmpz_vec_scalar_mul_fmpz(R, R, lenA - 1, leadB);
_fmpz_vec_scalar_submul_fmpz(R + lenA - lenB, B, lenB - 1, R + (lenA - 1));
fmpz_zero(R + (lenA - 1));
for (lenA -= 2; (lenA >= 0) && (R[lenA] == 0L); lenA--) ;
lenA++;
e--;
}
fmpz_init(pow);
fmpz_pow_ui(pow, leadB, e);
_fmpz_vec_scalar_mul_fmpz(Q, Q, lenQ, pow);
_fmpz_vec_scalar_mul_fmpz(R, R, lenA, pow);
fmpz_clear(pow);
}
/* Assumes poly1 and poly2 are not length 0. */
void
_fmpz_poly_mulhigh_classical(fmpz * res, const fmpz * poly1,
long len1, const fmpz * poly2, long len2,
long start)
{
_fmpz_vec_zero(res, start);
if (len1 == 1 && len2 == 1) /* Special case if the length of both inputs is 1 */
{
if (start == 0)
fmpz_mul(res, poly1, poly2);
}
else /* Ordinary case */
{
long i, m, n;
/* Set res[i] = poly1[i]*poly2[0] */
if (start < len1)
_fmpz_vec_scalar_mul_fmpz(res + start, poly1 + start, len1 - start,
poly2);
/* Set res[i+len1-1] = in1[len1-1]*in2[i] */
m = FLINT_MAX(len1 - 1, start);
_fmpz_vec_scalar_mul_fmpz(res + m, poly2 + m - len1 + 1,
len2 - 1 + len1 - m, poly1 + len1 - 1);
/* out[i+j] += in1[i]*in2[j] */
m = FLINT_MAX(start, len2 - 1);
for (i = m - len2 + 1; i < len1 - 1; i++)
{
n = FLINT_MAX(i + 1, start);
_fmpz_vec_scalar_addmul_fmpz(res + n, poly2 + n - i, len2 + i - n,
poly1 + i);
}
}
}
static void
_qadic_exp_bsplit(fmpz *y, const fmpz *x, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
const slong n = _padic_exp_bound(v, N, p);
if (n == 1)
{
fmpz_one(y + 0);
_fmpz_vec_zero(y + 1, d - 1);
}
else
{
fmpz *P, *T;
fmpz_t Q, R;
slong f;
P = _fmpz_vec_init(2*d - 1);
T = _fmpz_vec_init(2*d - 1);
fmpz_init(Q);
fmpz_init(R);
_qadic_exp_bsplit_series(P, Q, T, x, len, 1, n, a, j, lena);
fmpz_add(T + 0, T + 0, Q); /* (T,Q) := (T,Q) + 1 */
/* Note exp(x) is a unit so val(T) == val(Q). */
f = fmpz_remove(Q, Q, p);
fmpz_pow_ui(R, p, f);
_fmpz_vec_scalar_divexact_fmpz(T, T, d, R);
_padic_inv(Q, Q, p, N);
_fmpz_vec_scalar_mul_fmpz(y, T, d, Q);
_fmpz_vec_clear(P, 2*d - 1);
_fmpz_vec_clear(T, 2*d - 1);
fmpz_clear(Q);
fmpz_clear(R);
}
}
void fmpq_poly_randtest_unsigned(fmpq_poly_t poly, flint_rand_t state,
long len, mp_bitcnt_t bits)
{
ulong m;
m = n_randlimb(NULL);
fmpq_poly_fit_length(poly, len);
_fmpq_poly_set_length(poly, len);
if (m & 1UL)
{
_fmpz_vec_randtest_unsigned(poly->coeffs, state, len, bits);
}
else
{
fmpz_t x;
fmpz_init(x);
fmpz_randtest_unsigned(x, state, bits / 2);
_fmpz_vec_randtest_unsigned(poly->coeffs, state, len, (bits + 1) / 2);
_fmpz_vec_scalar_mul_fmpz(poly->coeffs, poly->coeffs, len, x);
fmpz_clear(x);
}
if (m & 2UL)
{
fmpz_randtest_not_zero(poly->den, state, FLINT_MAX(bits, 1));
fmpz_abs(poly->den, poly->den);
fmpq_poly_canonicalise(poly);
}
else
{
fmpz_set_ui(poly->den, 1);
_fmpq_poly_normalise(poly);
}
}
/* 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;
}
static void
_qadic_exp_bsplit_series(fmpz *P, fmpz_t Q, fmpz *T,
const fmpz *x, slong len, slong lo, slong hi,
const fmpz *a, const slong *j, slong lena)
{
const slong d = j[lena - 1];
if (hi - lo == 1)
{
_fmpz_vec_set(P, x, len);
_fmpz_vec_zero(P + len, 2*d - 1 - len);
fmpz_set_si(Q, lo);
_fmpz_vec_set(T, P, 2*d - 1);
}
else if (hi - lo == 2)
{
_fmpz_poly_sqr(P, x, len);
_fmpz_vec_zero(P + (2*len - 1), d - (2*len - 1));
_fmpz_poly_reduce(P, 2*len - 1, a, j, lena);
fmpz_set_si(Q, lo);
fmpz_mul_si(Q, Q, lo + 1);
_fmpz_vec_scalar_mul_si(T, x, len, lo + 1);
_fmpz_vec_zero(T + len, d - len);
_fmpz_vec_add(T, T, P, d);
}
else
{
const slong m = (lo + hi) / 2;
fmpz *PR, *TR, *W;
fmpz_t QR;
PR = _fmpz_vec_init(2*d - 1);
TR = _fmpz_vec_init(2*d - 1);
W = _fmpz_vec_init(2*d - 1);
fmpz_init(QR);
_qadic_exp_bsplit_series(P, Q, T, x, len, lo, m, a, j, lena);
_qadic_exp_bsplit_series(PR, QR, TR, x, len, m, hi, a, j, lena);
_fmpz_poly_mul(W, TR, d, P, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_scalar_mul_fmpz(T, T, d, QR);
_fmpz_vec_add(T, T, W, d);
_fmpz_poly_mul(W, P, d, PR, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_swap(P, W, d);
fmpz_mul(Q, Q, QR);
_fmpz_vec_clear(PR, 2*d - 1);
_fmpz_vec_clear(TR, 2*d - 1);
_fmpz_vec_clear(W, 2*d - 1);
fmpz_clear(QR);
}
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("scalar_submul_fmpz....");
fflush(stdout);
flint_randinit(state);
/* Compare with fmpz_vec_scalar_submul_si */
for (i = 0; i < 10000; i++)
{
fmpz *a, *b, *c;
long len, n;
fmpz_t n1;
len = n_randint(state, 100);
n = (long) n_randbits(state, FLINT_BITS - 1);
if (n_randint(state, 2))
n = -n;
fmpz_init(n1);
fmpz_set_si(n1, n);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
c = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_randtest(b, state, len, 200);
_fmpz_vec_set(c, b, len);
_fmpz_vec_scalar_submul_fmpz(b, a, len, n1);
_fmpz_vec_scalar_submul_si(c, a, len, n);
result = (_fmpz_vec_equal(c, b, len));
if (!result)
{
printf("FAIL:\n");
_fmpz_vec_print(c, len), printf("\n\n");
_fmpz_vec_print(b, len), printf("\n\n");
abort();
}
fmpz_clear(n1);
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
_fmpz_vec_clear(c, len);
}
/* Compute a different way */
for (i = 0; i < 10000; i++)
{
fmpz *a, *b, *c, *d;
long len = n_randint(state, 100);
fmpz_t n1;
fmpz_init(n1);
fmpz_randtest(n1, state, 200);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
c = _fmpz_vec_init(len);
d = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_randtest(b, state, len, 200);
_fmpz_vec_set(c, b, len);
_fmpz_vec_scalar_submul_fmpz(b, a, len, n1);
_fmpz_vec_scalar_mul_fmpz(d, a, len, n1);
_fmpz_vec_sub(c, c, d, len);
result = (_fmpz_vec_equal(c, b, len));
if (!result)
{
printf("FAIL:\n");
_fmpz_vec_print(c, len), printf("\n\n");
_fmpz_vec_print(b, len), printf("\n\n");
abort();
}
fmpz_clear(n1);
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
_fmpz_vec_clear(c, len);
_fmpz_vec_clear(d, len);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
void _padic_poly_sub(fmpz *rop, slong *val, slong N,
const fmpz *op1, slong val1, slong len1, slong N1,
const fmpz *op2, slong val2, slong len2, slong N2,
const padic_ctx_t ctx)
{
const slong len = FLINT_MAX(len1, len2);
*val = FLINT_MIN(val1, val2);
if (val1 == val2)
{
_fmpz_poly_sub(rop, op1, len1, op2, len2);
_padic_poly_canonicalise(rop, val, len, ctx->p);
}
else
{
fmpz_t x;
fmpz_init(x);
if (val1 < val2) /* F := p^g (G - p^{h-g} H) */
{
fmpz_pow_ui(x, ctx->p, val2 - val1);
if (rop == op1)
{
_fmpz_vec_zero(rop + len1, len2 - len1);
_fmpz_vec_scalar_submul_fmpz(rop, op2, len2, x);
}
else
{
_fmpz_vec_scalar_mul_fmpz(rop, op2, len2, x);
_fmpz_vec_neg(rop, rop, len2);
_fmpz_poly_add(rop, op1, len1, rop, len2);
}
}
else /* F := p^h (p^(g-h) G - H) */
{
fmpz_pow_ui(x, ctx->p, val1 - val2);
if (rop == op2)
{
_fmpz_vec_neg(rop, op2, len2);
_fmpz_vec_zero(rop + len2, len1 - len2);
_fmpz_vec_scalar_addmul_fmpz(rop, op1, len1, x);
}
else
{
_fmpz_vec_scalar_mul_fmpz(rop, op1, len1, x);
_fmpz_poly_sub(rop, rop, len1, op2, len2);
}
}
fmpz_clear(x);
}
/* Reduce */
if (N - *val > 0)
{
fmpz_t pow;
int alloc;
alloc = _padic_ctx_pow_ui(pow, N - *val, ctx);
if (N >= N1 && N >= N2)
{
slong i;
for (i = 0; i < len; i++)
if (fmpz_sgn(rop + i) < 0)
fmpz_add(rop + i, rop + i, pow);
}
else
{
_fmpz_vec_scalar_mod_fmpz(rop, rop, len, pow);
}
if (alloc)
fmpz_clear(pow);
}
else
{
_fmpz_vec_zero(rop, len);
*val = 0;
}
}
void _fmpq_poly_scalar_div_mpq(fmpz * rpoly, fmpz_t rden,
const fmpz * poly, const fmpz_t den, long len,
const fmpz_t r, const fmpz_t s)
{
fmpz_t gcd1; /* GCD( poly, r ) */
fmpz_t gcd2; /* GCD( s, den ) */
fmpz_init(gcd1);
fmpz_init(gcd2);
fmpz_set_ui(gcd1, 1);
fmpz_set_ui(gcd2, 1);
if (*r != 1L)
{
_fmpz_vec_content(gcd1, poly, len);
if (*gcd1 != 1L)
fmpz_gcd(gcd1, gcd1, r);
}
if (*den != 1L && *s != 1L)
fmpz_gcd(gcd2, s, den);
if (*gcd1 == 1L)
{
if (*gcd2 == 1L)
{
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, s);
fmpz_mul(rden, den, r);
}
else
{
fmpz_t s2;
fmpz_init(s2);
fmpz_divexact(s2, s, gcd2);
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, s2);
fmpz_divexact(rden, den, gcd2);
fmpz_mul(rden, rden, r);
fmpz_clear(s2);
}
}
else
{
fmpz_t r2;
fmpz_init(r2);
fmpz_divexact(r2, r, gcd1);
if (*gcd2 == 1L)
{
_fmpz_vec_scalar_divexact_fmpz(rpoly, poly, len, gcd1);
_fmpz_vec_scalar_mul_fmpz(rpoly, rpoly, len, s);
fmpz_mul(rden, den, r2);
}
else
{
fmpz_t s2;
fmpz_init(s2);
fmpz_divexact(s2, s, gcd2);
_fmpz_vec_scalar_divexact_fmpz(rpoly, poly, len, gcd1);
_fmpz_vec_scalar_mul_fmpz(rpoly, rpoly, len, s2);
fmpz_divexact(rden, den, gcd2);
fmpz_mul(rden, rden, r2);
fmpz_clear(s2);
}
fmpz_clear(r2);
}
if (_fmpz_vec_is_zero(rpoly, len))
fmpz_set_ui(rden, 1);
if (fmpz_sgn(rden) < 0)
{
_fmpz_vec_neg(rpoly, rpoly, len);
fmpz_neg(rden, rden);
}
fmpz_clear(gcd1);
fmpz_clear(gcd2);
}
void
_fmpz_poly_compose_divconquer(fmpz * res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2)
{
long i, j, k, n;
long *hlen, alloc, powlen;
fmpz *v, **h, *pow, *temp;
if (len1 == 1)
{
fmpz_set(res, poly1);
return;
}
if (len2 == 1)
{
_fmpz_poly_evaluate_fmpz(res, poly1, len1, poly2);
return;
}
if (len1 == 2)
{
_fmpz_poly_compose_horner(res, poly1, len1, poly2, len2);
return;
}
/* Initialisation */
hlen = (long *) malloc(((len1 + 1) / 2) * sizeof(long));
for (k = 1; (2 << k) < len1; k++) ;
hlen[0] = hlen[1] = ((1 << k) - 1) * (len2 - 1) + 1;
for (i = k - 1; i > 0; i--)
{
long hi = (len1 + (1 << i) - 1) / (1 << i);
for (n = (hi + 1) / 2; n < hi; n++)
hlen[n] = ((1 << i) - 1) * (len2 - 1) + 1;
}
powlen = (1 << k) * (len2 - 1) + 1;
alloc = 0;
for (i = 0; i < (len1 + 1) / 2; i++)
alloc += hlen[i];
v = _fmpz_vec_init(alloc + 2 * powlen);
h = (fmpz **) malloc(((len1 + 1) / 2) * sizeof(fmpz *));
h[0] = v;
for (i = 0; i < (len1 - 1) / 2; i++)
{
h[i + 1] = h[i] + hlen[i];
hlen[i] = 0;
}
hlen[(len1 - 1) / 2] = 0;
pow = v + alloc;
temp = pow + powlen;
/* Let's start the actual work */
for (i = 0, j = 0; i < len1 / 2; i++, j += 2)
{
if (poly1[j + 1] != 0L)
{
_fmpz_vec_scalar_mul_fmpz(h[i], poly2, len2, poly1 + j + 1);
fmpz_add(h[i], h[i], poly1 + j);
hlen[i] = len2;
}
else if (poly1[j] != 0L)
{
fmpz_set(h[i], poly1 + j);
hlen[i] = 1;
}
}
if ((len1 & 1L))
{
if (poly1[j] != 0L)
{
fmpz_set(h[i], poly1 + j);
hlen[i] = 1;
}
}
_fmpz_poly_mul(pow, poly2, len2, poly2, len2);
powlen = 2 * len2 - 1;
for (n = (len1 + 1) / 2; n > 2; n = (n + 1) / 2)
{
if (hlen[1] > 0)
{
long templen = powlen + hlen[1] - 1;
_fmpz_poly_mul(temp, pow, powlen, h[1], hlen[1]);
_fmpz_poly_add(h[0], temp, templen, h[0], hlen[0]);
hlen[0] = FLINT_MAX(hlen[0], templen);
}
for (i = 1; i < n / 2; i++)
{
if (hlen[2*i + 1] > 0)
{
_fmpz_poly_mul(h[i], pow, powlen, h[2*i + 1], hlen[2*i + 1]);
hlen[i] = hlen[2*i + 1] + powlen - 1;
} else
hlen[i] = 0;
_fmpz_poly_add(h[i], h[i], hlen[i], h[2*i], hlen[2*i]);
hlen[i] = FLINT_MAX(hlen[i], hlen[2*i]);
}
if ((n & 1L))
{
_fmpz_vec_set(h[i], h[2*i], hlen[2*i]);
hlen[i] = hlen[2*i];
}
_fmpz_poly_mul(temp, pow, powlen, pow, powlen);
powlen += powlen - 1;
{
fmpz * t = pow;
pow = temp;
temp = t;
}
}
_fmpz_poly_mul(res, pow, powlen, h[1], hlen[1]);
_fmpz_vec_add(res, res, h[0], hlen[0]);
_fmpz_vec_clear(v, alloc + 2 * powlen);
free(h);
free(hlen);
}
void
_fmpq_poly_inv_series_newton(fmpz * Qinv, fmpz_t Qinvden,
const fmpz * Q, const fmpz_t Qden, long n)
{
if (n == 1)
{
if (fmpz_sgn(Q) > 0)
{
fmpz_set(Qinv, Qden);
fmpz_set(Qinvden, Q);
}
else
{
fmpz_neg(Qinv, Qden);
fmpz_neg(Qinvden, Q);
}
}
else
{
const long alloc = FLINT_MAX(n, 3 * FMPQ_POLY_INV_NEWTON_CUTOFF);
long *a, i, m;
fmpz *W, *Wden;
W = _fmpz_vec_init(alloc + 1);
Wden = W + alloc;
for (i = 1; (1L << i) < n; i++) ;
a = (long *) flint_malloc(i * sizeof(long));
a[i = 0] = n;
while (n >= FMPQ_POLY_INV_NEWTON_CUTOFF)
a[++i] = (n = (n + 1) / 2);
/* Base case */
{
fmpz *rev = W + 2 * FMPQ_POLY_INV_NEWTON_CUTOFF;
_fmpz_poly_reverse(rev, Q, n, n);
_fmpz_vec_zero(W, 2*n - 2);
fmpz_one(W + (2*n - 2));
fmpz_one(Wden);
_fmpq_poly_div(Qinv, Qinvden, W, Wden, 2*n - 1, rev, Qden, n);
_fmpq_poly_canonicalise(Qinv, Qinvden, n);
_fmpz_poly_reverse(Qinv, Qinv, n, n);
}
for (i--; i >= 0; i--)
{
m = n;
n = a[i];
_fmpz_poly_mullow(W, Q, n, Qinv, m, n);
fmpz_mul(Wden, Qden, Qinvden);
_fmpz_poly_mullow(Qinv + m, Qinv, m, W + m, n - m, n - m);
fmpz_mul(Qinvden, Qinvden, Wden);
_fmpz_vec_scalar_mul_fmpz(Qinv, Qinv, m, Wden);
_fmpz_vec_neg(Qinv + m, Qinv + m, n - m);
_fmpq_poly_canonicalise(Qinv, Qinvden, n);
}
_fmpz_vec_clear(W, alloc + 1);
flint_free(a);
}
}
