static void
_arb_poly_rising_ui_series_bsplit(arb_ptr res,
arb_srcptr f, slong flen, ulong a, ulong b,
slong trunc, slong prec)
{
flen = FLINT_MIN(flen, trunc);
if (b - a == 1)
{
arb_add_ui(res, f, a, prec);
_arb_vec_set(res + 1, f + 1, flen - 1);
}
else
{
arb_ptr L, R;
slong len1, len2;
slong m = a + (b - a) / 2;
len1 = poly_pow_length(flen, m - a, trunc);
len2 = poly_pow_length(flen, b - m, trunc);
L = _arb_vec_init(len1 + len2);
R = L + len1;
_arb_poly_rising_ui_series_bsplit(L, f, flen, a, m, trunc, prec);
_arb_poly_rising_ui_series_bsplit(R, f, flen, m, b, trunc, prec);
_arb_poly_mullow(res, L, len1, R, len2,
FLINT_MIN(trunc, len1 + len2 - 1), prec);
_arb_vec_clear(L, len1 + len2);
}
}
/* 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);
}
}
// truncated multiplication for fmpz
void fmpz_mul_trunc(fmpz_t res, fmpz_t a, fmpz_t b, unsigned long trunc)
{
unsigned long sizea = FLINT_MIN(fmpz_size(a), trunc);
unsigned long sizeb = FLINT_MIN(fmpz_size(b), trunc);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
if ((sizea == 0) || (sizeb == 0)) {
res[0] = 0;
return;
}
if (trunc >= sizea + sizeb) {
mp_limb_t mslimb;
if (sizea >= sizeb) mslimb = F_mpn_mul(res+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(res+1, b+1, sizeb, a+1, sizea);
res[0] = sizea + sizeb - (mslimb == 0);
} else {
mp_limb_t mslimb;
fmpz_t temp = flint_stack_alloc(sizea + sizeb + 1);
if (sizea >= sizeb) mslimb = F_mpn_mul_trunc(temp+1, a+1, sizea, b+1, sizeb, trunc);
else mslimb = F_mpn_mul_trunc(temp+1, b+1, sizeb, a+1, sizea, trunc);
temp[0] = trunc;
if (UNLIKELY(!mslimb))
__fmpz_normalise(temp); // normalise if most significant limb == 0
fmpz_set(res, temp);
flint_stack_release();
}
if ((long) (a[0] ^ b[0]) < 0L) res[0] = -res[0];
}
int
bessel(acb_ptr out, const acb_t inp, void * params, long order, long prec)
{
acb_ptr t;
acb_t z;
ulong n;
t = _acb_vec_init(order);
acb_init(z);
acb_set(t, inp);
if (order > 1)
acb_one(t + 1);
n = 10;
arb_set_si(acb_realref(z), 20);
arb_set_si(acb_imagref(z), 10);
/* z sin(t) */
_acb_poly_sin_series(out, t, FLINT_MIN(2, order), order, prec);
_acb_vec_scalar_mul(out, out, order, z, prec);
/* t n */
_acb_vec_scalar_mul_ui(t, t, FLINT_MIN(2, order), n, prec);
_acb_poly_sub(out, t, FLINT_MIN(2, order), out, order, prec);
_acb_poly_cos_series(out, out, order, order, prec);
_acb_vec_clear(t, order);
acb_clear(z);
return 0;
}
/*
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);
}
}
static __inline__ void
_arb_poly_addmullow_block(arb_ptr z, fmpz * zz,
const fmpz * xz, const fmpz * xexps, const slong * xblocks, slong xlen,
const fmpz * yz, const fmpz * yexps, const slong * yblocks, slong ylen,
slong n, slong prec, int squaring)
{
slong i, j, k, xp, yp, xl, yl, bn;
fmpz_t zexp;
fmpz_init(zexp);
if (squaring)
{
for (i = 0; (xp = xblocks[i]) != xlen; i++)
{
if (2 * xp >= n)
continue;
xl = xblocks[i + 1] - xp;
bn = FLINT_MIN(2 * xl - 1, n - 2 * xp);
xl = FLINT_MIN(xl, bn);
_fmpz_poly_sqrlow(zz, xz + xp, xl, bn);
_fmpz_add2_fast(zexp, xexps + i, xexps + i, 0);
for (k = 0; k < bn; k++)
arb_add_fmpz_2exp(z + 2 * xp + k, z + 2 * xp + k, zz + k, zexp, prec);
}
}
for (i = 0; (xp = xblocks[i]) != xlen; i++)
{
for (j = squaring ? i + 1 : 0; (yp = yblocks[j]) != ylen; j++)
{
if (xp + yp >= n)
continue;
xl = xblocks[i + 1] - xp;
yl = yblocks[j + 1] - yp;
bn = FLINT_MIN(xl + yl - 1, n - xp - yp);
xl = FLINT_MIN(xl, bn);
yl = FLINT_MIN(yl, bn);
if (xl >= yl)
_fmpz_poly_mullow(zz, xz + xp, xl, yz + yp, yl, bn);
else
_fmpz_poly_mullow(zz, yz + yp, yl, xz + xp, xl, bn);
_fmpz_add2_fast(zexp, xexps + i, yexps + j, squaring);
for (k = 0; k < bn; k++)
arb_add_fmpz_2exp(z + xp + yp + k, z + xp + yp + k, zz + k, zexp, prec);
}
}
fmpz_clear(zexp);
}
void
acb_hypgeom_erf(acb_t res, const acb_t z, slong prec)
{
double x, y, absz2, logz;
slong prec2;
if (!acb_is_finite(z))
{
acb_indeterminate(res);
return;
}
if (acb_is_zero(z))
{
acb_zero(res);
return;
}
if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 0) < 0 &&
arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0))
{
acb_hypgeom_erf_1f1a(res, z, prec);
return;
}
if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 64) > 0 ||
arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 64) > 0))
{
acb_hypgeom_erf_asymp(res, z, prec, prec);
return;
}
x = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN);
y = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN);
absz2 = x * x + y * y;
logz = 0.5 * log(absz2);
if (logz - absz2 < -(prec + 8) * 0.69314718055994530942)
{
/* If the asymptotic term is small, we can
compute with reduced precision */
prec2 = FLINT_MIN(prec + 4 + (y*y - x*x - logz) * 1.4426950408889634074, (double) prec);
prec2 = FLINT_MAX(8, prec2);
prec2 = FLINT_MIN(prec2, prec);
acb_hypgeom_erf_asymp(res, z, prec, prec2);
}
else if (arf_cmpabs(arb_midref(acb_imagref(z)), arb_midref(acb_realref(z))) > 0)
{
acb_hypgeom_erf_1f1a(res, z, prec);
}
else
{
acb_hypgeom_erf_1f1b(res, z, prec);
}
}
void
nmod_poly_compose_series_horner(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, long n)
{
long len1 = poly1->length;
long len2 = poly2->length;
long lenr;
if (len2 != 0 && poly2->coeffs[0] != 0)
{
printf("exception: nmod_poly_compose_series_horner: inner polynomial "
"must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
nmod_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = poly1->coeffs[0];
res->length = 1;
_nmod_poly_normalise(res);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
nmod_poly_fit_length(res, lenr);
_nmod_poly_compose_series_horner(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, res->mod);
res->length = lenr;
_nmod_poly_normalise(res);
}
else
{
nmod_poly_t t;
nmod_poly_init2_preinv(t, res->mod.n, res->mod.ninv, lenr);
_nmod_poly_compose_series_horner(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, res->mod);
t->length = lenr;
_nmod_poly_normalise(t);
nmod_poly_swap(res, t);
nmod_poly_clear(t);
}
}
void
acb_poly_compose_series(acb_poly_t res,
const acb_poly_t poly1,
const acb_poly_t poly2, slong n, slong prec)
{
slong len1 = poly1->length;
slong len2 = poly2->length;
slong lenr;
if (len2 != 0 && !acb_is_zero(poly2->coeffs))
{
flint_printf("exception: compose_series: inner "
"polynomial must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
acb_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
acb_poly_set_acb(res, poly1->coeffs);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
acb_poly_fit_length(res, lenr);
_acb_poly_compose_series(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, prec);
_acb_poly_set_length(res, lenr);
_acb_poly_normalise(res);
}
else
{
acb_poly_t t;
acb_poly_init2(t, lenr);
_acb_poly_compose_series(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, prec);
_acb_poly_set_length(t, lenr);
_acb_poly_normalise(t);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
}
void
fmpz_poly_compose_series(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2, long n)
{
long len1 = poly1->length;
long len2 = poly2->length;
long lenr;
if (len2 != 0 && !fmpz_is_zero(poly2->coeffs))
{
printf("exception: fmpz_poly_compose_series: inner polynomial "
"must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
fmpz_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
fmpz_poly_set_fmpz(res, poly1->coeffs);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
fmpz_poly_fit_length(res, lenr);
_fmpz_poly_compose_series(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr);
_fmpz_poly_set_length(res, lenr);
_fmpz_poly_normalise(res);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, lenr);
_fmpz_poly_compose_series(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr);
_fmpz_poly_set_length(t, lenr);
_fmpz_poly_normalise(t);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
}
void
_arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sin_cos_pi(s, c, h, prec);
_arb_vec_zero(s + 1, n - 1);
_arb_vec_zero(c + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_const_pi(t, prec);
arb_mul(t, t, h + 1, prec);
arb_sin_cos_pi(s, c, h, prec);
arb_mul(s + 1, c, t, prec);
arb_neg(t, t);
arb_mul(c + 1, s, t, prec);
arb_clear(t);
}
else if (hlen < TANGENT_CUTOFF)
_arb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 1);
else
_arb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 1);
}
void fmpz_poly_sqrlow(fmpz_poly_t res, const fmpz_poly_t poly, long n)
{
const long len = poly->length;
if (len == 0 || n == 0)
{
fmpz_poly_zero(res);
return;
}
if (res == poly)
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
fmpz_poly_sqrlow(t, poly, n);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
return;
}
n = FLINT_MIN(2 * len - 1, n);
fmpz_poly_fit_length(res, n);
_fmpz_poly_sqrlow(res->coeffs, poly->coeffs, len, n);
_fmpz_poly_set_length(res, n);
_fmpz_poly_normalise(res);
}
void
_elem_poly_sub(elem_ptr res, elem_srcptr poly1, long len1,
elem_srcptr poly2, long len2, const ring_t ring)
{
long i, min;
long size = ring->size;
if (ring->type == TYPE_FMPZ && 0)
{
_fmpz_poly_sub(res, poly1, len1, poly2, len2);
return;
}
min = FLINT_MIN(len1, len2);
for (i = 0; i < min; i++)
elem_sub(INDEX(res, i, size), SRC_INDEX(poly1, i, size), SRC_INDEX(poly2, i, size), ring);
if (poly1 != res)
for (i = min; i < len1; i++)
elem_set(INDEX(res, i, size), SRC_INDEX(poly1, i, size), ring);
for (i = min; i < len2; i++)
elem_neg(INDEX(res, i, size), SRC_INDEX(poly2, i, size), ring);
}
void fmpq_poly_get_slice(fmpq_poly_t rop, const fmpq_poly_t op, long i, long j)
{
i = FLINT_MAX(i, 0);
j = FLINT_MIN(j, op->length);
if (i < j)
{
long k;
if (rop == op)
{
for (k = 0; k < i; k++)
fmpz_zero(rop->coeffs + k);
for (k = j; k < rop->length; k++)
fmpz_zero(rop->coeffs + k);
fmpq_poly_canonicalise(rop);
}
else
{
fmpq_poly_fit_length(rop, j);
_fmpq_poly_set_length(rop, j);
_fmpz_vec_set(rop->coeffs + i, op->coeffs + i, j - i);
fmpz_set(rop->den, op->den);
fmpq_poly_canonicalise(rop);
}
}
else
{
fmpq_poly_zero(rop);
}
}
void
_arb_poly_sinh_cosh_series(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sinh_cosh(s, c, h, prec);
_arb_vec_zero(s + 1, n - 1);
_arb_vec_zero(c + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_set(t, h + 1);
arb_sinh_cosh(s, c, h, prec);
arb_mul(s + 1, c, t, prec);
arb_mul(c + 1, s, t, prec);
arb_clear(t);
}
else if (hlen < 60 || n < 120)
_arb_poly_sinh_cosh_series_basecase(s, c, h, hlen, n, prec);
else
_arb_poly_sinh_cosh_series_exponential(s, c, h, hlen, n, prec);
}
void
_fmprb_poly_sin_series(fmprb_ptr g, fmprb_srcptr h, long hlen, long n, long prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
fmprb_sin(g, h, prec);
_fmprb_vec_zero(g + 1, n - 1);
}
else if (n == 2)
{
fmprb_t t;
fmprb_init(t);
fmprb_sin_cos(g, t, h, prec);
fmprb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */
fmprb_clear(t);
}
else
{
fmprb_ptr t = _fmprb_vec_init(n);
_fmprb_poly_sin_cos_series(g, t, h, hlen, n, prec);
_fmprb_vec_clear(t, n);
}
}
void
_acb_poly_zeta_cpx_series(acb_ptr z, const acb_t s, const acb_t a, int deflate, long d, long prec)
{
ulong M, N;
long i;
arf_t bound;
arb_ptr vb;
if (d < 1)
return;
if (!acb_is_finite(s) || !acb_is_finite(a))
{
_acb_vec_indeterminate(z, d);
return;
}
arf_init(bound);
vb = _arb_vec_init(d);
_acb_poly_zeta_em_choose_param(bound, &N, &M, s, a, FLINT_MIN(d, 2), prec, MAG_BITS);
_acb_poly_zeta_em_bound(vb, s, a, N, M, d, MAG_BITS);
_acb_poly_zeta_em_sum(z, s, a, deflate, N, M, d, prec);
for (i = 0; i < d; i++)
{
arb_get_abs_ubound_arf(bound, vb + i, MAG_BITS);
arb_add_error_arf(acb_realref(z + i), bound);
arb_add_error_arf(acb_imagref(z + i), bound);
}
arf_clear(bound);
_arb_vec_clear(vb, d);
}
void
_acb_poly_binomial_transform_basecase(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec)
{
slong n, k;
fmpz_t t;
fmpz_init(t);
for (n = 0; n < len; n++)
{
acb_zero(b + n);
for (k = 0; k < FLINT_MIN(n + 1, alen); k++)
{
if (k == 0)
{
fmpz_one(t);
}
else
{
fmpz_mul_si(t, t, -(n - k + 1));
fmpz_divexact_ui(t, t, k);
}
acb_addmul_fmpz(b + n, a + k, t, prec);
}
}
fmpz_clear(t);
}
void
fmpr_divappr_abs_ubound(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec)
{
if (fmpr_is_special(x) || fmpr_is_special(y) || fmpz_is_pm1(fmpr_manref(y)))
{
fmpr_div(z, x, y, prec, FMPR_RND_UP);
fmpr_abs(z, z);
}
else
{
fmpz_t t, u;
slong xbits, ybits, tbits, ubits, shift;
xbits = fmpz_bits(fmpr_manref(x));
ybits = fmpz_bits(fmpr_manref(y));
fmpz_init(t);
fmpz_init(u);
ubits = FLINT_MIN(ybits, prec);
tbits = prec + ubits + 1;
/* upper bound for |x|, shifted */
if (xbits <= tbits)
{
fmpz_mul_2exp(t, fmpr_manref(x), tbits - xbits);
fmpz_abs(t, t);
}
else if (fmpz_sgn(fmpr_manref(x)) > 0)
{
fmpz_cdiv_q_2exp(t, fmpr_manref(x), xbits - tbits);
}
else
{
fmpz_fdiv_q_2exp(t, fmpr_manref(x), xbits - tbits);
fmpz_neg(t, t);
}
/* lower bound for |y|, shifted */
if (ybits <= ubits)
fmpz_mul_2exp(u, fmpr_manref(y), ubits - ybits);
else
fmpz_tdiv_q_2exp(u, fmpr_manref(y), ybits - ubits);
fmpz_abs(u, u);
fmpz_cdiv_q(fmpr_manref(z), t, u);
shift = (ubits - ybits) - (tbits - xbits);
fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y));
if (shift >= 0)
fmpz_add_ui(fmpr_expref(z), fmpr_expref(z), shift);
else
fmpz_sub_ui(fmpr_expref(z), fmpr_expref(z), -shift);
_fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, FMPR_RND_UP);
fmpz_clear(t);
fmpz_clear(u);
}
}
void
_nmod_poly_div_basecase_2(mp_ptr Q, mp_ptr W,
mp_srcptr A, long A_len, mp_srcptr B, long B_len,
nmod_t mod)
{
long coeff, i, len;
mp_limb_t lead_inv = n_invmod(B[B_len - 1], mod.n);
mp_ptr B2, R2;
mp_srcptr Btop;
B2 = W;
for (i = 0; i < B_len - 1; i++)
{
B2[2 * i] = B[i];
B2[2 * i + 1] = 0;
}
Btop = B2 + 2*(B_len - 1);
R2 = W + 2*(B_len - 1);
for (i = 0; i < A_len - B_len + 1; i++)
{
R2[2 * i] = A[B_len + i - 1];
R2[2 * i + 1] = 0;
}
coeff = A_len - B_len;
while (coeff >= 0)
{
mp_limb_t r_coeff;
r_coeff =
n_ll_mod_preinv(R2[2 * coeff + 1], R2[2 * coeff], mod.n, mod.ninv);
while (coeff >= 0 && r_coeff == 0L)
{
Q[coeff--] = 0L;
if (coeff >= 0)
r_coeff =
n_ll_mod_preinv(R2[2 * coeff + 1], R2[2 * coeff], mod.n,
mod.ninv);
}
if (coeff >= 0)
{
mp_limb_t c, * R_sub;
Q[coeff] =
n_mulmod2_preinv(r_coeff, lead_inv, mod.n, mod.ninv);
c = n_negmod(Q[coeff], mod.n);
len = FLINT_MIN(B_len - 1, coeff);
R_sub = R2 + 2 * (coeff - len);
if (len > 0)
mpn_addmul_1(R_sub, Btop - 2*len, 2 * len, c);
coeff--;
}
}
}
void padic_poly_sub(padic_poly_t f,
const padic_poly_t g, const padic_poly_t h,
const padic_ctx_t ctx)
{
const slong lenG = g->length;
const slong lenH = h->length;
const slong lenF = FLINT_MAX(lenG, lenH);
if (lenG == 0)
{
padic_poly_neg(f, h, ctx);
return;
}
if (lenH == 0)
{
padic_poly_set(f, g, ctx);
return;
}
if ((lenG == 0 && lenH == 0) || (FLINT_MIN(g->val, h->val) >= f->N))
{
padic_poly_zero(f);
return;
}
padic_poly_fit_length(f, lenF);
_padic_poly_sub(f->coeffs, &(f->val), f->N,
g->coeffs, g->val, lenG, g->N,
h->coeffs, h->val, lenH, h->N, ctx);
_padic_poly_set_length(f, lenF);
_padic_poly_normalise(f);
}
void
_arb_poly_log1p_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec)
{
arb_t a;
flen = FLINT_MIN(flen, n);
arb_init(a);
arb_log1p(a, f, prec);
if (flen == 1)
{
_arb_vec_zero(res + 1, n - 1);
}
else if (n == 2)
{
arb_add_ui(res, f + 0, 1, prec);
arb_div(res + 1, f + 1, res + 0, prec);
}
else if (_arb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
{
slong i, j, d = flen - 1;
arb_add_ui(res, f + 0, 1, prec);
for (i = 1, j = d; j < n; j += d, i++)
{
if (i == 1)
arb_div(res + j, f + d, res, prec);
else
arb_mul(res + j, res + j - d, res + d, prec);
_arb_vec_zero(res + j - d + 1, flen - 2);
}
_arb_vec_zero(res + j - d + 1, n - (j - d + 1));
for (i = 2, j = 2 * d; j < n; j += d, i++)
arb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
}
else
{
arb_ptr f_diff, f_inv;
slong alloc;
alloc = n + flen;
f_inv = _arb_vec_init(alloc);
f_diff = f_inv + n;
arb_add_ui(f_diff, f, 1, prec);
_arb_vec_set(f_diff + 1, f + 1, flen - 1);
_arb_poly_inv_series(f_inv, f_diff, flen, n, prec);
_arb_poly_derivative(f_diff, f, flen, prec);
_arb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_arb_poly_integral(res, res, n, prec);
_arb_vec_clear(f_inv, alloc);
}
arb_swap(res, a);
arb_clear(a);
}
void _nmod_poly_reverse(mp_ptr output, mp_srcptr input, long len, long m)
{
long i, min;
mp_limb_t temp;
if (input != output)
{
min = FLINT_MIN(m, len);
for (i = 0; i < min; i++)
output[m - i - 1] = input[i];
for ( ; i < m; i++)
output[m - i - 1] = 0L;
} else
{
for (i = 0; i < m/2; i++)
{
temp = i < len ? input[i] : 0;
output[i] = m - i - 1 < len ? input[m - i - 1] : 0;
output[m - i - 1] = temp;
}
if (m & 1 && i >= len) output[i] = 0;
}
}
void
_arb_poly_sqrt_series(arb_ptr g,
arb_srcptr h, long hlen, long len, long prec)
{
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_sqrt(g, h, prec);
_arb_vec_zero(g + 1, len - 1);
}
else if (len == 2)
{
arb_sqrt(g, h, prec);
arb_div(g + 1, h + 1, h, prec);
arb_mul(g + 1, g + 1, g, prec);
arb_mul_2exp_si(g + 1, g + 1, -1);
}
else
{
arb_ptr t;
t = _arb_vec_init(len);
_arb_poly_rsqrt_series(t, h, hlen, len, prec);
_arb_poly_mullow(g, t, len, h, hlen, len, prec);
_arb_vec_clear(t, len);
}
}
void
_arb_poly_sinh_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sinh(g, h, prec);
_arb_vec_zero(g + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_sinh_cosh(g, t, h, prec);
arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */
arb_clear(t);
}
else
{
arb_ptr t = _arb_vec_init(n);
_arb_poly_sinh_cosh_series(g, t, h, hlen, n, prec);
_arb_vec_clear(t, n);
}
}
void
_acb_dirichlet_hardy_z_series(acb_ptr res, acb_srcptr s, slong slen,
const dirichlet_group_t G, const dirichlet_char_t chi,
slong len, slong prec)
{
slen = FLINT_MIN(slen, len);
if (len == 0)
return;
if (slen == 1)
{
acb_dirichlet_hardy_z(res, s, G, chi, 1, prec);
_acb_vec_zero(res + 1, len - 1);
}
else
{
acb_ptr t, u;
t = _acb_vec_init(len);
u = _acb_vec_init(slen);
acb_dirichlet_hardy_z(t, s, G, chi, len, prec);
/* compose with nonconstant part */
acb_zero(u);
_acb_vec_set(u + 1, s + 1, slen - 1);
_acb_poly_compose_series(res, t, len, u, slen, len, prec);
_acb_vec_clear(t, len);
_acb_vec_clear(u, slen);
}
}
void
_acb_poly_revert_series_lagrange_fast(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec)
{
slong i, j, k, m;
acb_ptr R, S, T, tmp;
acb_t t;
if (n <= 2)
{
if (n >= 1)
acb_zero(Qinv);
if (n == 2)
acb_inv(Qinv + 1, Q + 1, prec);
return;
}
m = n_sqrt(n);
acb_init(t);
R = _acb_vec_init((n - 1) * m);
S = _acb_vec_init(n - 1);
T = _acb_vec_init(n - 1);
acb_zero(Qinv);
acb_inv(Qinv + 1, Q + 1, prec);
_acb_poly_inv_series(Ri(1), Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec);
for (i = 2; i <= m; i++)
_acb_poly_mullow(Ri(i), Ri((i + 1) / 2), n - 1, Ri(i / 2), n - 1, n - 1, prec);
for (i = 2; i < m; i++)
acb_div_ui(Qinv + i, Ri(i) + i - 1, i, prec);
_acb_vec_set(S, Ri(m), n - 1);
for (i = m; i < n; i += m)
{
acb_div_ui(Qinv + i, S + i - 1, i, prec);
for (j = 1; j < m && i + j < n; j++)
{
acb_mul(t, S + 0, Ri(j) + i + j - 1, prec);
for (k = 1; k <= i + j - 1; k++)
acb_addmul(t, S + k, Ri(j) + i + j - 1 - k, prec);
acb_div_ui(Qinv + i + j, t, i + j, prec);
}
if (i + 1 < n)
{
_acb_poly_mullow(T, S, n - 1, Ri(m), n - 1, n - 1, prec);
tmp = S; S = T; T = tmp;
}
}
acb_clear(t);
_acb_vec_clear(R, (n - 1) * m);
_acb_vec_clear(S, n - 1);
_acb_vec_clear(T, n - 1);
}
void fmpz_multi_mod_ui(unsigned long * out, fmpz_t in, fmpz_comb_t comb, fmpz_t ** temp)
{
ulong i, j, k;
ulong n = comb->n;
long log_comb;
ulong size;
mp_limb_t * ptr;
ulong num;
unsigned long num_primes = comb->num_primes;
if (num_primes == 1) // we are reducing modulo a single prime which is assumed to be big enough
{
if ((long)in[0] > 0L) out[0] = in[1];
else if ((long)in[0] < 0L) out[0] = comb->primes[0] - in[1];
else out[0] = 0L;
return;
}
log_comb = n - 1;
// find level in comb with entries bigger than the input integer
log_comb = 0;
if ((long) in[0] < 0L)
while ((fmpz_bits(in) >= fmpz_bits(comb->comb[log_comb][0]) - 1) && (log_comb < comb->n - 1)) log_comb++;
else
while (fmpz_cmpabs(in, comb->comb[log_comb][0]) >= 0) log_comb++;
num = (1L<<(n - log_comb - 1));
// set each entry of this level of temp to the input integer
for (i = 0; i < num; i++)
{
fmpz_set(temp[log_comb][i], in);
}
log_comb--;
num *= 2;
// fill in other entries of temp by taking entries of temp at higher level mod pairs from comb
while (log_comb > FLINT_LOG_MULTI_MOD_CUTOFF) // keep going until we reach the basecase
{
for (i = 0, j = 0; i < num; i += 2, j++)
{
fmpz_mod(temp[log_comb][i], temp[log_comb + 1][j], comb->comb[log_comb][i]);
fmpz_mod(temp[log_comb][i+1], temp[log_comb + 1][j], comb->comb[log_comb][i+1]);
}
num *= 2;
log_comb--;
}
// do basecase
num /= 2;
log_comb++;
ulong stride = (1L << (log_comb + 1));
for (i = 0, j = 0; j < num_primes; i++, j += stride)
{
fmpz_multi_mod_ui_basecase(out + j, temp[log_comb][i], comb->primes + j, FLINT_MIN(stride, num_primes - j));
}
}
int
main(void)
{
int i, result = 1;
flint_rand_t state;
flint_randinit(state);
printf("log_series_monomial_ui....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
nmod_poly_t A, logA, res;
long n;
mp_limb_t mod;
ulong power;
mp_limb_t coeff;
mod = n_randtest_prime(state, 0);
n = n_randtest(state) % 100;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(logA, mod);
nmod_poly_init(res, mod);
coeff = n_randlimb(state) % mod;
power = 1 + n_randint(state, 2*n + 1);
nmod_poly_set_coeff_ui(A, 0, 1UL);
nmod_poly_set_coeff_ui(A, power, coeff);
nmod_poly_log_series(logA, A, n);
nmod_poly_log_series_monomial_ui(res, coeff, power, n);
result = nmod_poly_equal(logA, res);
if (!result)
{
printf("FAIL:\n");
printf("n = %ld, mod = %lu\n", n, mod);
printf("power = %lu, coeff = %lu\n", power, coeff);
printf("A: "); nmod_poly_print(A), printf("\n\n");
printf("log(A): "); nmod_poly_print(logA), printf("\n\n");
printf("res: "); nmod_poly_print(res), printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(logA);
nmod_poly_clear(res);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
void
_acb_hypgeom_coulomb_series(acb_ptr F, acb_ptr G,
acb_ptr Hpos, acb_ptr Hneg, const acb_t l, const acb_t eta,
acb_srcptr z, slong zlen, slong len, slong prec)
{
acb_ptr t, v;
if (len == 0)
return;
zlen = FLINT_MIN(zlen, len);
if (zlen == 1)
{
acb_hypgeom_coulomb(F, G, Hpos, Hneg, l, eta, z, prec);
if (F != NULL) _acb_vec_zero(F + 1, len - 1);
if (G != NULL) _acb_vec_zero(G + 1, len - 1);
if (Hpos != NULL) _acb_vec_zero(Hpos + 1, len - 1);
if (Hneg != NULL) _acb_vec_zero(Hneg + 1, len - 1);
return;
}
t = _acb_vec_init(len);
v = _acb_vec_init(zlen);
/* copy nonconstant part first to allow aliasing */
acb_zero(v);
_acb_vec_set(v + 1, z + 1, zlen - 1);
acb_hypgeom_coulomb_jet(F, G, Hpos, Hneg, l, eta, z, len, prec);
if (F != NULL)
{
_acb_vec_set(t, F, len);
_acb_poly_compose_series(F, t, len, v, zlen, len, prec);
}
if (G != NULL)
{
_acb_vec_set(t, G, len);
_acb_poly_compose_series(G, t, len, v, zlen, len, prec);
}
if (Hpos != NULL)
{
_acb_vec_set(t, Hpos, len);
_acb_poly_compose_series(Hpos, t, len, v, zlen, len, prec);
}
if (Hneg != NULL)
{
_acb_vec_set(t, Hneg, len);
_acb_poly_compose_series(Hneg, t, len, v, zlen, len, prec);
}
_acb_vec_clear(t, len);
_acb_vec_clear(v, zlen);
}
