void
arb_rising_fmpq_ui(arb_t y, const fmpq_t x, ulong n, long prec)
{
if (n == 0)
{
arb_one(y);
}
else if (n == 1)
{
arb_set_fmpq(y, x, prec);
}
else
{
long wp;
wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n));
bsplit(y, fmpq_numref(x), fmpq_denref(x), 0, n, wp);
if (fmpz_is_one(fmpq_denref(x)))
{
arb_set_round(y, y, prec);
}
else
{
arb_t t;
arb_init(t);
arb_set_fmpz(t, fmpq_denref(x));
arb_pow_ui(t, t, n, wp);
arb_div(y, y, t, prec);
arb_clear(t);
}
}
}
void
custom_rate_mixture_get_prob(arb_t prob, const custom_rate_mixture_t x,
slong idx, slong prec)
{
if (x->mode == RATE_MIXTURE_UNDEFINED)
{
flint_fprintf(stderr, "internal error: undefined rate mixture\n");
abort();
}
else if (x->mode == RATE_MIXTURE_NONE)
{
arb_one(prob);
}
else if (x->mode == RATE_MIXTURE_UNIFORM)
{
/*
* This code branch involves a division that could
* unnecessarily lose exactness in some situations.
*/
arb_set_si(prob, x->n);
arb_inv(prob, prob, prec);
}
else if (x->mode == RATE_MIXTURE_CUSTOM)
{
arb_set_d(prob, x->prior[idx]);
}
else
{
flint_fprintf(stderr, "internal error: "
"unrecognized rate mixture mode\n");
abort();
}
}
int
f_pol(arb_t max, const arb_t t, params_t * p, slong prec)
{
slong k;
acb_t z;
arb_t tmp;
acb_init(z);
arb_init(tmp);
arb_one(max);
for (k = 0; k < p->len; k++)
{
acb_sub_arb(z, p->z + k, t, prec);
acb_abs(tmp, z, prec);
if (arb_contains_zero(tmp))
return 0;
arb_mul(max, max, tmp, prec);
}
arb_inv(max, max, prec);
arb_clear(tmp);
acb_clear(z);
return 1;
}
void
arb_pow(arb_t z, const arb_t x, const arb_t y, slong prec)
{
if (arb_is_zero(y))
{
arb_one(z);
return;
}
if (arb_is_zero(x))
{
if (arb_is_positive(y))
arb_zero(z);
else
arb_indeterminate(z);
return;
}
if (arb_is_exact(y) && !arf_is_special(arb_midref(x)))
{
const arf_struct * ymid = arb_midref(y);
/* small half-integer or integer */
if (arf_cmpabs_2exp_si(ymid, BINEXP_LIMIT) < 0 &&
arf_is_int_2exp_si(ymid, -1))
{
fmpz_t e;
fmpz_init(e);
if (arf_is_int(ymid))
{
arf_get_fmpz_fixed_si(e, ymid, 0);
arb_pow_fmpz_binexp(z, x, e, prec);
}
else
{
arf_get_fmpz_fixed_si(e, ymid, -1);
arb_sqrt(z, x, prec + fmpz_bits(e));
arb_pow_fmpz_binexp(z, z, e, prec);
}
fmpz_clear(e);
return;
}
else if (arf_is_int(ymid) && arf_sgn(arb_midref(x)) < 0)
{
/* use (-x)^n = (-1)^n * x^n to avoid NaNs
at least at high enough precision */
int odd = !arf_is_int_2exp_si(ymid, 1);
_arb_pow_exp(z, x, 1, y, prec);
if (odd)
arb_neg(z, z);
return;
}
}
_arb_pow_exp(z, x, 0, y, prec);
}
void
acb_dirichlet_vec_mellin_arb(acb_ptr res, const dirichlet_group_t G, const dirichlet_char_t chi, slong len, const arb_t t, slong n, slong prec)
{
slong k;
arb_t tk, xt, stk, st;
acb_ptr a;
mag_t e;
a = _acb_vec_init(len);
acb_dirichlet_chi_vec(a, G, chi, len, prec);
if (dirichlet_parity_char(G, chi))
{
for (k = 2; k < len; k++)
acb_mul_si(a + k, a + k, k, prec);
}
arb_init(tk);
arb_init(xt);
arb_init(st);
arb_init(stk);
mag_init(e);
arb_sqrt(st, t, prec);
arb_one(tk);
arb_one(stk);
for (k = 0; k < n; k++)
{
_acb_dirichlet_theta_argument_at_arb(xt, G->q, tk, prec);
mag_tail_kexpk2_arb(e, xt, len);
arb_neg(xt, xt);
arb_exp(xt, xt, prec);
/* TODO: reduce len */
acb_dirichlet_qseries_arb(res + k, a, xt, len, prec);
acb_add_error_mag(res + k, e);
acb_mul_arb(res + k, res + k, stk, prec);
arb_mul(tk, tk, t, prec);
arb_mul(stk, stk, st, prec);
}
mag_clear(e);
arb_clear(xt);
arb_clear(tk);
arb_clear(stk);
arb_clear(st);
_acb_vec_clear(a, len);
}
static void
bound_K(arb_t C, const arb_t AN, const arb_t B, const arb_t T, slong wp)
{
if (arb_is_zero(B) || arb_is_zero(T))
{
arb_one(C);
}
else
{
arb_div(C, B, AN, wp);
/* TODO: atan is dumb, should also bound by pi/2 */
arb_atan(C, C, wp);
arb_mul(C, C, T, wp);
if (arb_is_nonpositive(C))
arb_one(C);
else
arb_exp(C, C, wp);
}
}
void
arb_div_2expm1_ui(arb_t y, const arb_t x, ulong n, long prec)
{
if (n < FLINT_BITS)
{
arb_div_ui(y, x, (1UL << n) - 1, prec);
}
else if (n < 1024 + prec / 32 || n > LONG_MAX / 4)
{
arb_t t;
fmpz_t e;
arb_init(t);
fmpz_init_set_ui(e, n);
arb_one(t);
arb_mul_2exp_fmpz(t, t, e);
arb_sub_ui(t, t, 1, prec);
arb_div(y, x, t, prec);
arb_clear(t);
fmpz_clear(e);
}
else
{
arb_t s, t;
long i, b;
arb_init(s);
arb_init(t);
/* x / (2^n - 1) = sum_{k>=1} x * 2^(-k*n)*/
arb_mul_2exp_si(s, x, -n);
arb_set(t, s);
b = 1;
for (i = 2; i <= prec / n + 1; i++)
{
arb_mul_2exp_si(t, t, -n);
arb_add(s, s, t, prec);
b = i;
}
/* error bound: sum_{k>b} x * 2^(-k*n) <= x * 2^(-b*n - (n-1)) */
arb_mul_2exp_si(t, x, -b*n - (n-1));
arb_abs(t, t);
arb_add_error(s, t);
arb_set(y, s);
arb_clear(s);
arb_clear(t);
}
}
void
arb_mat_ones(arb_mat_t mat)
{
slong R, C, i, j;
R = arb_mat_nrows(mat);
C = arb_mat_ncols(mat);
for (i = 0; i < R; i++)
for (j = 0; j < C; j++)
arb_one(arb_mat_entry(mat, i, j));
}
void
scaled_bessel_select_N(arb_t N, ulong k, slong prec)
{
slong e;
double f = log(k/3.14159265358979)/log(2);
e = 1;
while ((k / 2.0) * (e - f) - e < prec + 5)
e++;
arb_one(N);
arb_mul_2exp_si(N, N, e);
}
void
arb_sinc(arb_t z, const arb_t x, slong prec)
{
mag_t c, r;
mag_init(c);
mag_init(r);
mag_set_ui_2exp_si(c, 5, -1);
arb_get_mag_lower(r, x);
if (mag_cmp(c, r) < 0)
{
/* x is not near the origin */
_arb_sinc_direct(z, x, prec);
}
else if (mag_cmp_2exp_si(arb_radref(x), 1) < 0)
{
/* determine error magnitude using the derivative bound */
if (arb_is_exact(x))
{
mag_zero(c);
}
else
{
_arb_sinc_derivative_bound(r, x);
mag_mul(c, arb_radref(x), r);
}
/* evaluate sinc at the midpoint of x */
if (arf_is_zero(arb_midref(x)))
{
arb_one(z);
}
else
{
arb_get_mid_arb(z, x);
_arb_sinc_direct(z, z, prec);
}
/* add the error */
mag_add(arb_radref(z), arb_radref(z), c);
}
else
{
/* x has a large radius and includes points near the origin */
arf_zero(arb_midref(z));
mag_one(arb_radref(z));
}
mag_clear(c);
mag_clear(r);
}
int
sin_x(arb_ptr out, const arb_t inp, void * params, long order, long prec)
{
int xlen = FLINT_MIN(2, order);
arb_set(out, inp);
if (xlen > 1)
arb_one(out + 1);
_arb_poly_sin_series(out, out, xlen, order, prec);
eval_count++;
return 0;
}
static void
bound_I(arb_ptr I, const arb_t A, const arb_t B, const arb_t C, slong len, slong wp)
{
slong k;
arb_t D, Dk, L, T, Bm1;
arb_init(D);
arb_init(Dk);
arb_init(Bm1);
arb_init(T);
arb_init(L);
arb_sub_ui(Bm1, B, 1, wp);
arb_one(L);
/* T = 1 / (A^Bm1 * Bm1) */
arb_inv(T, A, wp);
arb_pow(T, T, Bm1, wp);
arb_div(T, T, Bm1, wp);
if (len > 1)
{
arb_log(D, A, wp);
arb_add(D, D, C, wp);
arb_mul(D, D, Bm1, wp);
arb_set(Dk, D);
}
for (k = 0; k < len; k++)
{
if (k > 0)
{
arb_mul_ui(L, L, k, wp);
arb_add(L, L, Dk, wp);
arb_mul(Dk, Dk, D, wp);
}
arb_mul(I + k, L, T, wp);
arb_div(T, T, Bm1, wp);
}
arb_clear(D);
arb_clear(Dk);
arb_clear(Bm1);
arb_clear(T);
arb_clear(L);
}
void
custom_rate_mixture_expectation(arb_t rate, const custom_rate_mixture_t x, slong prec)
{
if (x->mode == RATE_MIXTURE_UNDEFINED)
{
flint_fprintf(stderr, "internal error: undefined rate mixture\n");
abort();
}
else if (x->mode == RATE_MIXTURE_NONE)
{
arb_one(rate);
}
else if (x->mode == RATE_MIXTURE_UNIFORM || x->mode == RATE_MIXTURE_CUSTOM)
{
slong i;
arb_t tmp, tmpb;
arb_init(tmp);
arb_init(tmpb);
arb_zero(rate);
if (x->mode == RATE_MIXTURE_UNIFORM)
{
for (i = 0; i < x->n; i++)
{
arb_set_d(tmp, x->rates[i]);
arb_add(rate, rate, tmp, prec);
}
arb_div_si(rate, rate, x->n, prec);
}
else if (x->mode == RATE_MIXTURE_CUSTOM)
{
for (i = 0; i < x->n; i++)
{
arb_set_d(tmp, x->rates[i]);
arb_set_d(tmpb, x->prior[i]);
arb_addmul(rate, tmp, tmpb, prec);
}
}
arb_clear(tmp);
arb_clear(tmpb);
}
else
{
flint_fprintf(stderr, "internal error: "
"unrecognized rate mixture mode\n");
abort();
}
}
static void _stirling_number_2_vec_next(arb_ptr row,
arb_srcptr prev, slong n, slong klen, slong prec)
{
slong k;
if (klen > n) arb_one(row + n);
if (n != 0 && klen != 0) arb_zero(row);
for (k = FLINT_MIN(n, klen) - 1; k >= 1; k--)
{
arb_mul_ui(row + k, prev + k, k, prec);
arb_add(row + k, prev + k - 1, row + k, prec);
}
for (k = n + 1; k < klen; k++)
arb_zero(row + k);
}
static __inline__ void
_log_rising_ui_series(arb_ptr t, const arb_t x, slong r, slong len, slong prec)
{
arb_struct f[2];
slong rflen;
arb_init(f);
arb_init(f + 1);
arb_set(f, x);
arb_one(f + 1);
rflen = FLINT_MIN(len, r + 1);
_arb_poly_rising_ui_series(t, f, FLINT_MIN(2, len), r, rflen, prec);
_arb_poly_log_series(t, t, rflen, len, prec);
arb_clear(f);
arb_clear(f + 1);
}
int
f_aj(arb_t m, const arb_t t, params_t * p, slong prec)
{
slong k;
acb_t z, zu;
arb_t abs;
arb_init(abs);
acb_init(z);
acb_init(zu);
arb_const_pi(abs, prec);
arb_mul_2exp_si(abs, abs, -2); /* Pi/4 */
arb_set(acb_realref(z), t);
arb_set(acb_imagref(z), abs);
acb_sinh(z, z, prec);
arb_mul_2exp_si(abs, abs, 1); /* Pi/2 */
acb_mul_arb(z, z, abs, prec);
acb_tanh(z, z, prec);
arb_one(m);
for (k = 0; k < p->len; k++)
{
acb_sub(zu, z, p->z + k, prec);
if (acb_contains_zero(zu))
{
arb_clear(abs);
acb_clear(zu);
acb_clear(z);
return 0;
}
acb_abs(abs, zu, prec);
arb_mul(m, m, abs, prec);
}
arb_inv(m, m, prec);
arb_clear(abs);
acb_clear(zu);
acb_clear(z);
return 1;
}
/* invalid in (-1,0) */
int
_acb_hypgeom_legendre_q_single_valid(const acb_t z)
{
arb_t t;
int ok;
if (!arb_contains_zero(acb_imagref(z)))
return 1;
if (arb_is_positive(acb_imagref(z)))
return 1;
arb_init(t);
arb_one(t);
arb_neg(t, t);
ok = arb_lt(acb_realref(z), t);
arb_clear(t);
return ok;
}
int
z_function(arb_ptr out, const arb_t inp, void * params, long order, long prec)
{
arb_struct x[2];
arb_init(x);
arb_init(x + 1);
arb_set(x, inp);
arb_one(x + 1);
_arb_poly_riemann_siegel_z_series(out, x, FLINT_MIN(2, order), order, prec);
arb_clear(x);
arb_clear(x + 1);
eval_count++;
return 0;
}
/* sin((pi/2)x) */
static int
sin_pi2_x(arb_ptr out, const arb_t inp, void * params, slong order, slong prec)
{
arb_ptr x;
x = _arb_vec_init(2);
arb_set(x, inp);
arb_one(x + 1);
arb_const_pi(out, prec);
arb_mul_2exp_si(out, out, -1);
_arb_vec_scalar_mul(x, x, 2, out, prec);
_arb_poly_sin_series(out, x, order, order, prec);
_arb_vec_clear(x, 2);
return 0;
}
int
sin_1x(arb_ptr out, const arb_t inp, void * params, long order, long prec)
{
arb_ptr x;
int xlen = FLINT_MIN(2, order);
x = _arb_vec_init(xlen);
arb_set(x, inp);
if (xlen > 1)
arb_one(x + 1);
_arb_poly_inv_series(out, x, xlen, order, prec);
_arb_poly_sin_series(out, out, order, order, prec);
_arb_vec_clear(x, xlen);
eval_count++;
return 0;
}
void
_arb_poly_inv_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec)
{
slong i;
arb_t t;
arb_init(t);
arb_one(t);
for (i = 0; i < len; i++)
{
if (i > 1)
arb_mul_ui(t, t, i, prec);
arb_mul(res + i, poly + i, t, prec);
}
arb_clear(t);
}
void
arb_hypgeom_sum(arb_t P, arb_t Q, const hypgeom_t hyp, long n, long prec)
{
if (n < 1)
{
arb_zero(P);
arb_one(Q);
}
else
{
arb_t B, T;
arb_init(B);
arb_init(T);
bsplit_recursive_arb(P, Q, B, T, hyp, 0, n, 0, prec);
if (!arb_is_one(B))
arb_mul(Q, Q, B, prec);
arb_swap(P, T);
arb_clear(B);
arb_clear(T);
}
}
static void
bound_rfac(arb_ptr F, const acb_t s, ulong n, slong len, slong wp)
{
if (len == 1)
{
acb_rising_ui_get_mag(arb_radref(F), s, n);
arf_set_mag(arb_midref(F), arb_radref(F));
mag_zero(arb_radref(F + 0));
}
else
{
arb_struct sx[2];
arb_init(sx + 0);
arb_init(sx + 1);
acb_abs(sx + 0, s, wp);
arb_one(sx + 1);
_arb_vec_zero(F, len);
_arb_poly_rising_ui_series(F, sx, 2, n, len, wp);
arb_clear(sx + 0);
arb_clear(sx + 1);
}
}
void
acb_acosh(acb_t res, const acb_t z, slong prec)
{
if (acb_is_one(z))
{
acb_zero(res);
}
else
{
acb_t t, u;
acb_init(t);
acb_init(u);
acb_add_ui(t, z, 1, prec);
acb_sub_ui(u, z, 1, prec);
acb_sqrt(t, t, prec);
acb_sqrt(u, u, prec);
acb_mul(t, t, u, prec);
acb_add(t, t, z, prec);
if (!arb_is_zero(acb_imagref(z)))
{
acb_log(res, t, prec);
}
else
{
/* pure imaginary on (-1,1) */
arb_abs(acb_realref(u), acb_realref(z));
arb_one(acb_imagref(u));
acb_log(res, t, prec);
if (arb_lt(acb_realref(u), acb_imagref(u)))
arb_zero(acb_realref(res));
}
acb_clear(t);
acb_clear(u);
}
}
void
custom_rate_mixture_get_rate(arb_t rate, const custom_rate_mixture_t x, slong idx)
{
if (x->mode == RATE_MIXTURE_UNDEFINED)
{
flint_fprintf(stderr, "internal error: undefined rate mixture\n");
abort();
}
else if (x->mode == RATE_MIXTURE_NONE)
{
arb_one(rate);
}
else if (x->mode == RATE_MIXTURE_UNIFORM || x->mode == RATE_MIXTURE_CUSTOM)
{
arb_set_d(rate, x->rates[idx]);
}
else
{
flint_fprintf(stderr, "internal error: "
"unrecognized rate mixture mode\n");
abort();
}
}
/* TODO: BSGS can reduce to nv mul */
void
acb_dirichlet_arb_quadratic_powers(arb_ptr v, slong nv, const arb_t x, slong prec)
{
slong i;
arb_t dx, x2;
arb_init(dx);
arb_init(x2);
arb_set(dx, x);
arb_mul(x2, x, x, prec);
for (i = 0; i < nv; i++)
{
if (i == 0)
arb_one(v + i);
else if (i == 1)
arb_set_round(v + i, x, prec);
else
{
arb_mul(dx, dx, x2, prec);
arb_mul(v + i, v + i - 1, dx, prec);
}
}
arb_clear(dx);
arb_clear(x2);
}
static __inline__ void
zeta_coeff_k(zeta_bsplit_t S, slong k, slong n, slong s)
{
arb_set_si(S->D, 2 * (n + k));
arb_mul_si(S->D, S->D, n - k, ARF_PREC_EXACT);
arb_set_si(S->Q1, k + 1);
arb_mul_si(S->Q1, S->Q1, 2*k + 1, ARF_PREC_EXACT);
if (k == 0)
{
arb_zero(S->A);
arb_one(S->Q2);
}
else
{
arb_set_si(S->A, k % 2 ? 1 : -1);
arb_mul(S->A, S->A, S->Q1, ARF_PREC_EXACT);
arb_ui_pow_ui(S->Q2, k, s, ARF_PREC_EXACT);
}
arb_mul(S->Q3, S->Q1, S->Q2, ARF_PREC_EXACT);
arb_zero(S->B);
arb_set(S->C, S->Q1);
}
int main()
{
long iter;
flint_rand_t state;
printf("div_2expm1_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
arb_t a, b, c;
ulong n;
long prec, acc1, acc2;
fmpz_t t;
arb_init(a);
arb_init(b);
arb_init(c);
fmpz_init(t);
prec = 2 + n_randint(state, 10000);
arb_randtest(a, state, 1 + n_randint(state, 10000), 10);
if (n_randint(state, 2))
n = 1 + (n_randtest(state) % (10 * prec));
else
n = n_randtest(state);
arb_div_2expm1_ui(b, a, n, prec);
arb_one(c);
if (n >= (1UL << (FLINT_BITS-1)))
{
arb_mul_2exp_si(c, c, (1UL << (FLINT_BITS-2)));
arb_mul_2exp_si(c, c, (1UL << (FLINT_BITS-2)));
arb_mul_2exp_si(c, c, n - (1UL << (FLINT_BITS-1)));
}
else
{
arb_mul_2exp_si(c, c, n);
}
arb_sub_ui(c, c, 1, prec);
arb_div(c, a, c, prec);
acc1 = arb_rel_accuracy_bits(a);
acc2 = arb_rel_accuracy_bits(b);
if (!arb_overlaps(b, c))
{
printf("FAIL: containment\n\n");
printf("n = %lu\n", n);
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
if (n > 0 && (acc2 < FLINT_MIN(prec, acc1) - 10) &&
!(acc1 == -ARF_PREC_EXACT && acc2 == -ARF_PREC_EXACT))
{
printf("FAIL: poor accuracy\n\n");
printf("prec=%ld, acc1=%ld, acc2=%ld\n\n", prec, acc1, acc2);
printf("n = %lu\n\n", n);
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
fmpz_clear(t);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("zeta_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 500; iter++)
{
long m, n1, n2, bits1, bits2, bits3;
int deflate;
arb_poly_t S, A, B, C, D, E, F;
arb_t a, a1;
bits1 = 2 + n_randint(state, 300);
bits2 = 2 + n_randint(state, 300);
bits3 = 2 + n_randint(state, 300);
m = 1 + n_randint(state, 30);
n1 = 1 + n_randint(state, 30);
n2 = 1 + n_randint(state, 30);
arb_poly_init(S);
arb_poly_init(A);
arb_poly_init(B);
arb_poly_init(C);
arb_poly_init(D);
arb_poly_init(E);
arb_poly_init(F);
arb_init(a);
arb_init(a1);
deflate = n_randint(state, 2);
arb_poly_randtest(S, state, m, bits1, 3);
arb_randtest_precise(a, state, bits1, 3);
arb_poly_set_coeff_arb(S, 0, a);
if (n_randint(state, 2))
arb_randtest(a, state, bits1, 3);
else
arb_one(a);
arb_poly_zeta_series(A, S, a, deflate, n1, bits2);
arb_poly_zeta_series(B, S, a, deflate, n2, bits3);
arb_poly_set(C, A);
arb_poly_truncate(C, FLINT_MIN(n1, n2));
arb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!arb_poly_overlaps(B, C))
{
printf("FAIL\n\n");
printf("S = "); arb_poly_printd(S, 15); printf("\n\n");
printf("a = "); arb_printd(a, 15); printf("\n\n");
printf("A = "); arb_poly_printd(A, 15); printf("\n\n");
printf("B = "); arb_poly_printd(B, 15); printf("\n\n");
abort();
}
/* check zeta(s,a) = zeta(s,a+1) + a^(-s) */
arb_poly_set_arb(D, a);
arb_poly_log_series(D, D, n1, bits2);
arb_poly_mullow(D, D, S, n1, bits2);
arb_poly_neg(D, D);
arb_poly_exp_series(D, D, n1, bits2);
arb_add_ui(a1, a, 1, bits2);
arb_poly_zeta_series(E, S, a1, deflate, n1, bits2);
arb_poly_add(E, E, D, bits2);
if (!arb_poly_overlaps(A, E))
{
printf("FAIL (functional equation)\n\n");
printf("S = "); arb_poly_printd(S, 15); printf("\n\n");
printf("a = "); arb_printd(a, 15); printf("\n\n");
printf("A = "); arb_poly_printd(A, 15); printf("\n\n");
printf("E = "); arb_poly_printd(A, 15); printf("\n\n");
abort();
}
arb_poly_zeta_series(S, S, a, deflate, n1, bits2);
if (!arb_poly_overlaps(A, S))
{
printf("FAIL (aliasing)\n\n");
abort();
}
arb_poly_clear(S);
arb_poly_clear(A);
arb_poly_clear(B);
arb_poly_clear(C);
arb_poly_clear(D);
arb_poly_clear(E);
arb_poly_clear(F);
arb_clear(a);
arb_clear(a1);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
keiper_li_series(arb_ptr z, slong len, slong prec)
{
arb_ptr t, u, v;
t = _arb_vec_init(len);
u = _arb_vec_init(len);
v = _arb_vec_init(len);
/* -zeta(s) */
flint_printf("zeta: ");
TIMEIT_ONCE_START
arb_zero(t + 0);
arb_one(t + 1);
arb_one(u);
_arb_poly_zeta_series(v, t, 2, u, 0, len, prec);
_arb_vec_neg(v, v, len);
TIMEIT_ONCE_STOP
SHOW_MEMORY_USAGE
/* logarithm */
flint_printf("log: ");
TIMEIT_ONCE_START
_arb_poly_log_series(t, v, len, len, prec);
TIMEIT_ONCE_STOP
/* add log(gamma(1+s/2)) */
flint_printf("gamma: ");
TIMEIT_ONCE_START
arb_one(u);
arb_one(u + 1);
arb_mul_2exp_si(u + 1, u + 1, -1);
_arb_poly_lgamma_series(v, u, 2, len, prec);
_arb_vec_add(t, t, v, len, prec);
TIMEIT_ONCE_STOP
/* subtract 0.5 s log(pi) */
arb_const_pi(u, prec);
arb_log(u, u, prec);
arb_mul_2exp_si(u, u, -1);
arb_sub(t + 1, t + 1, u, prec);
/* add log(1-s) */
arb_one(u);
arb_set_si(u + 1, -1);
_arb_poly_log_series(v, u, 2, len, prec);
_arb_vec_add(t, t, v, len, prec);
/* binomial transform */
flint_printf("binomial transform: ");
TIMEIT_ONCE_START
arb_set(z, t);
_arb_vec_neg(t + 1, t + 1, len - 1);
_arb_poly_binomial_transform(z + 1, t + 1, len - 1, len - 1, prec);
TIMEIT_ONCE_STOP
_arb_vec_clear(t, len);
_arb_vec_clear(u, len);
_arb_vec_clear(v, len);
}
