void
zeta_series_em_choose_param(fmpr_t bound, ulong * N, ulong * M, const fmpcb_t s, const fmpcb_t a, long d, long target, long prec)
{
ulong A, B, C;
fmpr_t Abound, Bbound, Cbound, tol;
fmpr_init(Abound);
fmpr_init(Bbound);
fmpr_init(Cbound);
fmpr_init(tol);
fmpr_set_si_2exp_si(tol, 1, -target);
A = 1;
B = 2;
zeta_series_em_bound(Bbound, s, a, B, choose_M(B, target), d, prec);
if (fmpr_cmp(Bbound, tol) > 0)
{
while (fmpr_cmp(Bbound, tol) > 0)
{
fmpr_set(Abound, Bbound);
A *= 2;
B *= 2;
if (B == 0) abort();
zeta_series_em_bound(Bbound, s, a, B, choose_M(B, target), d, prec);
}
/* bisect (-A, B] */
while (B > A + 4)
{
C = A + (B - A) / 2;
zeta_series_em_bound(Cbound, s, a, C, choose_M(C, target), d, prec);
if (fmpr_cmp(Cbound, tol) < 0)
{
B = C;
fmpr_set(Bbound, Cbound);
}
else
{
A = C;
fmpr_set(Abound, Cbound);
}
}
}
fmpr_set(bound, Bbound);
*N = B;
*M = choose_M(B, target);
fmpr_clear(Abound);
fmpr_clear(Bbound);
fmpr_clear(Cbound);
fmpr_clear(tol);
}
static slong _fmpr_add_special(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
if (fmpr_is_zero(x))
{
if (fmpr_is_zero(y))
{
fmpr_zero(z);
return FMPR_RESULT_EXACT;
}
else
return fmpr_set_round(z, y, prec, rnd);
}
else if (fmpr_is_zero(y))
{
return fmpr_set_round(z, x, prec, rnd);
}
else if (fmpr_is_nan(x) || fmpr_is_nan(y)
|| (fmpr_is_pos_inf(x) && fmpr_is_neg_inf(y))
|| (fmpr_is_neg_inf(x) && fmpr_is_pos_inf(y)))
{
fmpr_nan(z);
return FMPR_RESULT_EXACT;
}
else if (fmpr_is_special(x))
{
fmpr_set(z, x);
return FMPR_RESULT_EXACT;
}
else
{
fmpr_set(z, y);
return FMPR_RESULT_EXACT;
}
}
void
fmpr_pow_sloppy_fmpz(fmpr_t y, const fmpr_t b, const fmpz_t e,
long prec, fmpr_rnd_t rnd)
{
long i, wp, bits;
if (fmpz_is_zero(e))
{
fmpr_set_ui(y, 1UL);
return;
}
if (fmpz_sgn(e) < 0)
{
fmpz_t f;
fmpz_init(f);
fmpz_neg(f, e);
fmpr_pow_sloppy_fmpz(y, b, f, prec + 2,
(rnd == FMPR_RND_FLOOR || rnd == FMPR_RND_DOWN)
? FMPR_RND_UP : FMPR_RND_DOWN);
fmpr_ui_div(y, 1UL, y, prec, rnd);
fmpz_clear(f);
}
if (y == b)
{
fmpr_t t;
fmpr_init(t);
fmpr_set(t, b);
fmpr_pow_sloppy_fmpz(y, t, e, prec, rnd);
fmpr_clear(t);
return;
}
fmpr_set(y, b);
bits = fmpz_bits(e);
wp = FMPR_PREC_ADD(prec, bits);
for (i = bits - 2; i >= 0; i--)
{
fmpr_mul(y, y, y, wp, rnd);
if (fmpz_tstbit(e, i))
fmpr_mul(y, y, b, wp, rnd);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("set_d....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
fmpr_t a, b, c;
mag_t m;
double x;
fmpr_init(a);
fmpr_init(b);
fmpr_init(c);
mag_init(m);
x = d_randtest2(state);
x = ldexp(x, 100 - n_randint(state, 200));
if (n_randint(state, 100) == 0)
x = 0.0;
fmpr_set_d(a, x);
mag_set_d(m, x);
mag_get_fmpr(b, m);
fmpr_set(c, a);
fmpr_mul_ui(c, c, 1025, MAG_BITS, FMPR_RND_UP);
fmpr_mul_2exp_si(c, c, -10);
MAG_CHECK_BITS(m)
if (!(fmpr_cmpabs(a, b) <= 0 && fmpr_cmpabs(b, c) <= 0))
{
flint_printf("FAIL\n\n");
flint_printf("a = "); fmpr_print(a); flint_printf("\n\n");
flint_printf("b = "); fmpr_print(b); flint_printf("\n\n");
flint_printf("c = "); fmpr_print(c); flint_printf("\n\n");
abort();
}
fmpr_clear(a);
fmpr_clear(b);
fmpr_clear(c);
mag_clear(m);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
fmprb_sqrtpos(fmprb_t z, const fmprb_t x, slong prec)
{
if (!fmprb_is_finite(x))
{
if (fmpr_is_zero(fmprb_radref(x)) && fmpr_is_pos_inf(fmprb_midref(x)))
fmprb_pos_inf(z);
else
fmprb_zero_pm_inf(z);
}
else if (fmprb_contains_nonpositive(x))
{
fmpr_t t;
fmpr_init(t);
fmpr_add(t, fmprb_midref(x), fmprb_radref(x),
FMPRB_RAD_PREC, FMPR_RND_CEIL);
if (fmpr_sgn(t) <= 0)
{
fmprb_zero(z);
}
else
{
fmpr_sqrt(t, t, FMPRB_RAD_PREC, FMPR_RND_CEIL);
fmpr_mul_2exp_si(t, t, -1);
fmpr_set(fmprb_midref(z), t);
fmpr_set(fmprb_radref(z), t);
}
fmpr_clear(t);
}
else
{
fmprb_sqrt(z, x, prec);
}
fmprb_nonnegative_part(z, z, prec);
}
static __inline__ void
fmprb_nonnegative_part(fmprb_t z, const fmprb_t x, slong prec)
{
if (fmprb_contains_negative(x))
{
fmpr_add(fmprb_midref(z), fmprb_midref(x), fmprb_radref(x), prec, FMPR_RND_CEIL);
if (fmpr_sgn(fmprb_midref(z)) <= 0)
{
fmpr_zero(fmprb_radref(z));
}
else
{
fmpr_mul_2exp_si(fmprb_midref(z), fmprb_midref(z), -1);
fmpr_set(fmprb_midref(z), fmprb_radref(z));
}
}
else
{
fmprb_set(z, x);
}
}
/* convert to an fmpz poly with a common exponent and coefficients
at most prec bits, also bounding input error plus rounding error */
void _fmprb_poly_get_fmpz_poly_2exp(fmpr_t error, fmpz_t exp, fmpz * coeffs,
fmprb_srcptr A, long lenA, long prec)
{
fmpz_t top_exp, bot_exp;
long shift;
long i;
int rounding;
fmpz_init(top_exp);
fmpz_init(bot_exp);
if (!_fmprb_poly_mid_get_hull(bot_exp, top_exp, A, lenA))
{
fmpz_zero(exp);
_fmpz_vec_zero(coeffs, lenA);
fmpr_zero(error);
for (i = 0; i < lenA; i++)
{
if (fmpr_cmp(fmprb_radref(A + i), error) > 0)
fmpr_set(error, fmprb_radref(A + i));
}
return; /* no need to clear fmpzs */
}
/* only take as much precision as necessary */
shift = _fmpz_sub_small(top_exp, bot_exp);
prec = FLINT_MIN(prec, shift);
fmpz_sub_ui(exp, top_exp, prec);
/* extract integer polynomial */
rounding = 0;
for (i = 0; i < lenA; i++)
rounding |= fmpr_get_fmpz_fixed_fmpz(coeffs + i,
fmprb_midref(A + i), exp);
fmpr_zero(error);
/* compute maximum of input errors */
for (i = 0; i < lenA; i++)
{
if (fmpr_cmp(fmprb_radref(A + i), error) > 0)
fmpr_set(error, fmprb_radref(A + i));
}
/* add rounding error */
if (rounding)
{
fmpr_t t;
fmpr_init(t);
fmpz_set_ui(fmpr_manref(t), 1UL);
fmpz_set(fmpr_expref(t), exp);
fmpr_add(error, error, t, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_clear(t);
}
fmpz_clear(top_exp);
}
int main()
{
slong iter, iter2;
flint_rand_t state;
flint_printf("mul_si....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 3000; iter++)
{
fmpr_t x, z, v;
slong y;
slong prec, r1, r2;
fmpr_rnd_t rnd;
fmpr_init(x);
fmpr_init(z);
fmpr_init(v);
for (iter2 = 0; iter2 < 30; iter2++)
{
fmpr_randtest_special(x, state, 2000, 200);
y = z_randtest(state);
prec = 2 + n_randint(state, 2000);
switch (n_randint(state, 4))
{
case 0: rnd = FMPR_RND_DOWN; break;
case 1: rnd = FMPR_RND_UP; break;
case 2: rnd = FMPR_RND_FLOOR; break;
default: rnd = FMPR_RND_CEIL; break;
}
switch (n_randint(state, 2))
{
case 0:
r1 = fmpr_mul_si(z, x, y, prec, rnd);
r2 = fmpr_mul_si_naive(v, x, y, prec, rnd);
if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec))
{
flint_printf("FAIL!\n");
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = %wd\n\n", y);
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("v = "); fmpr_print(v); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
default:
fmpr_set(v, x);
fmpr_set(z, x);
r1 = fmpr_mul_si(z, z, y, prec, rnd);
r2 = fmpr_mul_si_naive(v, v, y, prec, rnd);
if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec))
{
flint_printf("FAIL (aliasing 1)!\n");
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = %wd\n\n", y);
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("v = "); fmpr_print(v); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
}
}
fmpr_clear(x);
fmpr_clear(z);
fmpr_clear(v);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
fmprb_contains(const fmprb_t x, const fmprb_t y)
{
fmpr_t t;
fmpr_t u;
fmpr_struct tmp[4];
int left_ok, right_ok;
if (fmprb_is_exact(y))
return fmprb_contains_fmpr(x, fmprb_midref(y));
if (fmpr_is_nan(fmprb_midref(y)))
return fmpr_is_nan(fmprb_midref(x));
fmpr_init(t);
fmpr_init(u);
/* fast check */
fmpr_sub(t, fmprb_midref(x), fmprb_radref(x), 30, FMPR_RND_CEIL);
fmpr_sub(u, fmprb_midref(y), fmprb_radref(y), 30, FMPR_RND_FLOOR);
left_ok = fmpr_cmp(t, u) <= 0;
/* exact check */
if (!left_ok)
{
fmpr_init(tmp + 0);
fmpr_init(tmp + 1);
fmpr_init(tmp + 2);
fmpr_init(tmp + 3);
fmpr_set(tmp + 0, fmprb_midref(x));
fmpr_neg(tmp + 1, fmprb_radref(x));
fmpr_neg(tmp + 2, fmprb_midref(y));
fmpr_set(tmp + 3, fmprb_radref(y));
fmpr_sum(t, tmp, 4, 30, FMPR_RND_DOWN);
left_ok = fmpr_sgn(t) <= 0;
fmpr_clear(tmp + 0);
fmpr_clear(tmp + 1);
fmpr_clear(tmp + 2);
fmpr_clear(tmp + 3);
}
/* fast check */
fmpr_add(t, fmprb_midref(x), fmprb_radref(x), 30, FMPR_RND_FLOOR);
fmpr_add(u, fmprb_midref(y), fmprb_radref(y), 30, FMPR_RND_CEIL);
right_ok = (fmpr_cmp(t, u) >= 0);
/* exact check */
if (!right_ok)
{
fmpr_init(tmp + 0);
fmpr_init(tmp + 1);
fmpr_init(tmp + 2);
fmpr_init(tmp + 3);
fmpr_set(tmp + 0, fmprb_midref(x));
fmpr_set(tmp + 1, fmprb_radref(x));
fmpr_neg(tmp + 2, fmprb_midref(y));
fmpr_neg(tmp + 3, fmprb_radref(y));
fmpr_sum(t, tmp, 4, 30, FMPR_RND_DOWN);
right_ok = fmpr_sgn(t) >= 0;
fmpr_clear(tmp + 0);
fmpr_clear(tmp + 1);
fmpr_clear(tmp + 2);
fmpr_clear(tmp + 3);
}
fmpr_clear(t);
fmpr_clear(u);
return left_ok && right_ok;
}
