void
arb_mat_set_round_fmpz_mat(arb_mat_t dest, const fmpz_mat_t src, slong prec)
{
slong i, j;
if (arb_mat_ncols(dest) != 0)
{
for (i = 0; i < arb_mat_nrows(dest); i++)
for (j = 0; j < arb_mat_ncols(dest); j++)
arb_set_round_fmpz(arb_mat_entry(dest, i, j),
fmpz_mat_entry(src, i, j), prec);
}
}
static void
bsplit(arb_t y, const fmpz_t p, const fmpz_t q, ulong a, ulong b, long prec)
{
if (b - a <= 8)
{
fmpz_t t, u;
ulong c;
fmpz_init(t);
fmpz_init(u);
fmpz_mul_ui(t, q, a);
fmpz_add(t, t, p);
fmpz_set(u, t);
for (c = a + 1; c < b; c++)
{
fmpz_add(u, u, q);
fmpz_mul(t, t, u);
}
arb_set_round_fmpz(y, t, prec);
fmpz_clear(t);
fmpz_clear(u);
}
else
{
arb_t w;
ulong m = a + (b - a) / 2;
arb_init(w);
bsplit(y, p, q, a, m, prec);
bsplit(w, p, q, m, b, prec);
arb_mul(y, y, w, prec);
arb_clear(w);
}
}
void
_acb_poly_zeta_em_tail_naive(acb_ptr sum, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong d, slong prec)
{
acb_ptr u, term;
acb_t Na2, splus, rec;
arb_t x;
fmpz_t c;
int aint;
slong r;
BERNOULLI_ENSURE_CACHED(2 * M);
u = _acb_vec_init(d);
term = _acb_vec_init(d);
acb_init(splus);
acb_init(rec);
acb_init(Na2);
arb_init(x);
fmpz_init(c);
_acb_vec_zero(sum, d);
/* u = 1/2 * Nasx */
_acb_vec_scalar_mul_2exp_si(u, Nasx, d, -WORD(1));
/* term = u * (s+x) / (N+a) */
_acb_poly_mullow_cpx(u, u, d, s, d, prec);
_acb_vec_scalar_div(term, u, d, Na, prec);
/* (N+a)^2 or 1/(N+a)^2 */
acb_mul(Na2, Na, Na, prec);
aint = acb_is_int(Na2);
if (!aint)
acb_inv(Na2, Na2, prec);
for (r = 1; r <= M; r++)
{
/* flint_printf("sum 2: %wd %wd\n", r, M); */
/* sum += bernoulli number * term */
arb_set_round_fmpz(x, fmpq_numref(bernoulli_cache + 2 * r), prec);
arb_div_fmpz(x, x, fmpq_denref(bernoulli_cache + 2 * r), prec);
_acb_vec_scalar_mul_arb(u, term, d, x, prec);
_acb_vec_add(sum, sum, u, d, prec);
/* multiply term by ((s+x)+2r-1)((s+x)+2r) / ((N+a)^2 * (2*r+1)*(2*r+2)) */
acb_set(splus, s);
arb_add_ui(acb_realref(splus), acb_realref(splus), 2*r-1, prec);
_acb_poly_mullow_cpx(term, term, d, splus, d, prec);
arb_add_ui(acb_realref(splus), acb_realref(splus), 1, prec);
_acb_poly_mullow_cpx(term, term, d, splus, d, prec);
/* TODO: combine with previous multiplication? */
if (aint)
{
arb_mul_ui(x, acb_realref(Na2), 2*r+1, prec);
arb_mul_ui(x, x, 2*r+2, prec);
_acb_vec_scalar_div_arb(term, term, d, x, prec);
}
else
{
fmpz_set_ui(c, 2*r+1);
fmpz_mul_ui(c, c, 2*r+2);
acb_div_fmpz(rec, Na2, c, prec);
_acb_vec_scalar_mul(term, term, d, rec, prec);
}
}
_acb_vec_clear(u, d);
_acb_vec_clear(term, d);
acb_clear(splus);
acb_clear(rec);
acb_clear(Na2);
arb_clear(x);
fmpz_clear(c);
}
static int
arb_set_float_str(arb_t res, const char * inp, slong prec)
{
char * emarker;
char * buf;
int error;
slong i;
fmpz_t exp;
fmpz_t man;
slong num_int, num_frac;
int after_radix;
if (inp[0] == '+')
{
return arb_set_float_str(res, inp + 1, prec);
}
if (inp[0] == '-')
{
error = arb_set_float_str(res, inp + 1, prec);
arb_neg(res, res);
return error;
}
if (strcmp(inp, "inf") == 0)
{
arb_pos_inf(res);
return 0;
}
if (strcmp(inp, "nan") == 0)
{
arb_indeterminate(res);
return 0;
}
error = 0;
fmpz_init(exp);
fmpz_init(man);
buf = flint_malloc(strlen(inp) + 1);
emarker = strchr(inp, 'e');
/* parse exponent (0 by default) */
if (emarker != NULL)
{
/* allow e+42 as well as e42 */
if (emarker[1] == '+')
{
if (!(emarker[2] >= '0' && emarker[2] <= '9'))
error = 1;
else
error = fmpz_set_str(exp, emarker + 2, 10);
}
else
error = fmpz_set_str(exp, emarker + 1, 10);
if (error)
goto cleanup;
}
/* parse floating-point part */
{
num_int = 0;
num_frac = 0;
after_radix = 0;
for (i = 0; inp + i != emarker && inp[i] != '\0'; i++)
{
if (inp[i] == '.' && !after_radix)
{
after_radix = 1;
}
else if (inp[i] >= '0' && inp[i] <= '9')
{
buf[num_int + num_frac] = inp[i];
num_frac += after_radix;
num_int += !after_radix;
}
else
{
error = 1;
goto cleanup;
}
}
buf[num_int + num_frac] = '\0';
/* put trailing zeros into the exponent */
while (num_int + num_frac > 1 && buf[num_int + num_frac - 1] == '0')
{
buf[num_int + num_frac - 1] = '\0';
num_frac--;
}
fmpz_sub_si(exp, exp, num_frac);
error = fmpz_set_str(man, buf, 10);
if (error)
goto cleanup;
}
if (fmpz_is_zero(man))
{
arb_zero(res);
}
else if (fmpz_is_zero(exp))
{
arb_set_round_fmpz(res, man, prec);
}
else
{
arb_t t;
arb_init(t);
arb_set_ui(t, 10);
arb_set_fmpz(res, man);
if (fmpz_sgn(exp) > 0)
{
arb_pow_fmpz_binexp(t, t, exp, prec + 4);
arb_mul(res, res, t, prec);
}
else
{
fmpz_neg(exp, exp);
arb_pow_fmpz_binexp(t, t, exp, prec + 4);
arb_div(res, res, t, prec);
}
arb_clear(t);
}
cleanup:
fmpz_clear(exp);
fmpz_clear(man);
flint_free(buf);
if (error)
arb_indeterminate(res);
return error;
}
