void
acb_lambertw_left(acb_t res, const acb_t z, const fmpz_t k, slong prec)
{
if (acb_contains_zero(z) && !(fmpz_equal_si(k, -1) && acb_is_real(z)))
{
acb_indeterminate(res);
return;
}
if (arb_is_positive(acb_imagref(z)))
{
acb_lambertw(res, z, k, 0, prec);
}
else if (arb_is_nonpositive(acb_imagref(z)))
{
fmpz_t kk;
fmpz_init(kk);
fmpz_add_ui(kk, k, 1);
fmpz_neg(kk, kk);
acb_conj(res, z);
acb_lambertw(res, res, kk, 0, prec);
acb_conj(res, res);
fmpz_clear(kk);
}
else
{
acb_t za, zb;
fmpz_t kk;
acb_init(za);
acb_init(zb);
fmpz_init(kk);
acb_set(za, z);
acb_conj(zb, z);
arb_nonnegative_part(acb_imagref(za), acb_imagref(za));
arb_nonnegative_part(acb_imagref(zb), acb_imagref(zb));
fmpz_add_ui(kk, k, 1);
fmpz_neg(kk, kk);
acb_lambertw(za, za, k, 0, prec);
acb_lambertw(zb, zb, kk, 0, prec);
acb_conj(zb, zb);
acb_union(res, za, zb, prec);
acb_clear(za);
acb_clear(zb);
fmpz_clear(kk);
}
}
void
_acb_poly_zeta_cpx_series(acb_ptr z, const acb_t s, const acb_t a, int deflate, slong d, slong prec)
{
ulong M, N;
slong i;
mag_t bound;
arb_ptr vb;
int is_real, const_is_real;
if (d < 1)
return;
if (!acb_is_finite(s) || !acb_is_finite(a))
{
_acb_vec_indeterminate(z, d);
return;
}
is_real = const_is_real = 0;
if (acb_is_real(s) && acb_is_real(a))
{
if (arb_is_positive(acb_realref(a)))
{
is_real = const_is_real = 1;
}
else if (arb_is_int(acb_realref(a)) &&
arb_is_int(acb_realref(s)) &&
arb_is_nonpositive(acb_realref(s)))
{
const_is_real = 1;
}
}
mag_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_mag(bound, vb + i);
arb_add_error_mag(acb_realref(z + i), bound);
if (!is_real && !(i == 0 && const_is_real))
arb_add_error_mag(acb_imagref(z + i), bound);
}
mag_clear(bound);
_arb_vec_clear(vb, d);
}
void
acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec)
{
if (arf_sgn(arb_midref(acb_realref(z))) >= 0
|| (acb_is_int(a) && arb_is_nonpositive(acb_realref(a))))
{
_acb_hypgeom_m_1f1(res, a, b, z, regularized, prec, prec, 0);
}
else
{
_acb_hypgeom_m_1f1(res, a, b, z, regularized, prec, prec, 1);
}
}
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);
}
}
int
acb_modular_is_in_fundamental_domain(const acb_t z, const arf_t tol, long prec)
{
arb_t t;
arb_init(t);
/* require re(w) + 1/2 >= 0 */
arb_set_ui(t, 1);
arb_mul_2exp_si(t, t, -1);
arb_add(t, t, acb_realref(z), prec);
arb_add_arf(t, t, tol, prec);
if (!arb_is_nonnegative(t))
{
arb_clear(t);
return 0;
}
/* require re(w) - 1/2 <= 0 */
arb_set_ui(t, 1);
arb_mul_2exp_si(t, t, -1);
arb_sub(t, acb_realref(z), t, prec);
arb_sub_arf(t, t, tol, prec);
if (!arb_is_nonpositive(t))
{
arb_clear(t);
return 0;
}
/* require |w| >= 1 - tol, i.e. |w| - 1 + tol >= 0 */
acb_abs(t, z, prec);
arb_sub_ui(t, t, 1, prec);
arb_add_arf(t, t, tol, prec);
if (!arb_is_nonnegative(t))
{
arb_clear(t);
return 0;
}
arb_clear(t);
return 1;
}
void
acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, long prec)
{
acb_t t;
if (regularized)
{
acb_init(t);
acb_rgamma(t, b, prec);
}
if (arf_sgn(arb_midref(acb_realref(z))) >= 0
|| (acb_is_int(a) && arb_is_nonpositive(acb_realref(a))))
{
_acb_hypgeom_m_1f1(res, a, b, z, prec);
}
else
{
/* Kummer's transformation */
acb_t u, v;
acb_init(u);
acb_init(v);
acb_sub(u, b, a, prec);
acb_neg(v, z);
_acb_hypgeom_m_1f1(u, u, b, v, prec);
acb_exp(v, z, prec);
acb_mul(res, u, v, prec);
acb_clear(u);
acb_clear(v);
}
if (regularized)
{
acb_mul(res, res, t, prec);
acb_clear(t);
}
}
void
acb_hypgeom_ci_asymp(acb_t res, const acb_t z, slong prec)
{
acb_t t, u, w, v, one;
acb_init(t);
acb_init(u);
acb_init(w);
acb_init(v);
acb_init(one);
acb_one(one);
acb_mul_onei(w, z);
/* u = U(1,1,iz) */
acb_hypgeom_u_asymp(u, one, one, w, -1, prec);
/* v = e^(-iz) */
acb_neg(v, w);
acb_exp(v, v, prec);
acb_mul(t, u, v, prec);
if (acb_is_real(z))
{
arb_div(acb_realref(t), acb_imagref(t), acb_realref(z), prec);
arb_zero(acb_imagref(t));
acb_neg(t, t);
}
else
{
/* u = U(1,1,-iz) */
acb_neg(w, w);
acb_hypgeom_u_asymp(u, one, one, w, -1, prec);
acb_inv(v, v, prec);
acb_submul(t, u, v, prec);
acb_div(t, t, w, prec);
acb_mul_2exp_si(t, t, -1);
}
if (arb_is_zero(acb_realref(z)))
{
if (arb_is_positive(acb_imagref(z)))
{
arb_const_pi(acb_imagref(t), prec);
arb_mul_2exp_si(acb_imagref(t), acb_imagref(t), -1);
}
else if (arb_is_negative(acb_imagref(z)))
{
arb_const_pi(acb_imagref(t), prec);
arb_mul_2exp_si(acb_imagref(t), acb_imagref(t), -1);
arb_neg(acb_imagref(t), acb_imagref(t));
}
else
{
acb_const_pi(u, prec);
acb_mul_2exp_si(u, u, -1);
arb_zero(acb_imagref(t));
arb_add_error(acb_imagref(t), acb_realref(u));
}
}
else
{
/* 0 if positive or positive imaginary
pi if upper left quadrant (including negative real axis)
-pi if lower left quadrant (including negative imaginary axis) */
if (arb_is_positive(acb_realref(z)))
{
/* do nothing */
}
else if (arb_is_negative(acb_realref(z)) && arb_is_nonnegative(acb_imagref(z)))
{
acb_const_pi(u, prec);
arb_add(acb_imagref(t), acb_imagref(t), acb_realref(u), prec);
}
else if (arb_is_nonpositive(acb_realref(z)) && arb_is_negative(acb_imagref(z)))
{
acb_const_pi(u, prec);
arb_sub(acb_imagref(t), acb_imagref(t), acb_realref(u), prec);
}
else
{
/* add [-pi,pi] */
acb_const_pi(u, prec);
arb_add_error(acb_imagref(t), acb_realref(u));
}
}
acb_swap(res, t);
acb_clear(t);
acb_clear(u);
acb_clear(w);
acb_clear(v);
acb_clear(one);
}
/* todo: use log(1-z) when this is better? would also need to
adjust strategy in the main function */
void
acb_hypgeom_dilog_bernoulli(acb_t res, const acb_t z, slong prec)
{
acb_t s, w, w2;
slong n, k;
fmpz_t c, d;
mag_t m, err;
double lm;
int real;
acb_init(s);
acb_init(w);
acb_init(w2);
fmpz_init(c);
fmpz_init(d);
mag_init(m);
mag_init(err);
real = 0;
if (acb_is_real(z))
{
arb_sub_ui(acb_realref(w), acb_realref(z), 1, 30);
real = arb_is_nonpositive(acb_realref(w));
}
acb_log(w, z, prec);
acb_get_mag(m, w);
/* for k >= 4, the terms are bounded by (|w| / (2 pi))^k */
mag_set_ui_2exp_si(err, 2670177, -24); /* upper bound for 1/(2pi) */
mag_mul(err, err, m);
lm = mag_get_d_log2_approx(err);
if (lm < -0.25)
{
n = prec / (-lm) + 1;
n = FLINT_MAX(n, 4);
mag_geom_series(err, err, n);
BERNOULLI_ENSURE_CACHED(n)
acb_mul(w2, w, w, prec);
for (k = n - (n % 2 == 0); k >= 3; k -= 2)
{
fmpz_mul_ui(c, fmpq_denref(bernoulli_cache + k - 1), k - 1);
fmpz_mul_ui(d, c, (k + 1) * (k + 2));
acb_mul(s, s, w2, prec);
acb_mul_fmpz(s, s, c, prec);
fmpz_mul_ui(c, fmpq_numref(bernoulli_cache + k - 1), (k + 1) * (k + 2));
acb_sub_fmpz(s, s, c, prec);
acb_div_fmpz(s, s, d, prec);
}
acb_mul(s, s, w, prec);
acb_mul_2exp_si(s, s, 1);
acb_sub_ui(s, s, 3, prec);
acb_mul(s, s, w2, prec);
acb_mul_2exp_si(s, s, -1);
acb_const_pi(w2, prec);
acb_addmul(s, w2, w2, prec);
acb_div_ui(s, s, 6, prec);
acb_neg(w2, w);
acb_log(w2, w2, prec);
acb_submul(s, w2, w, prec);
acb_add(res, s, w, prec);
acb_add_error_mag(res, err);
if (real)
arb_zero(acb_imagref(res));
}
else
{
acb_indeterminate(res);
}
acb_clear(s);
acb_clear(w);
acb_clear(w2);
fmpz_clear(c);
fmpz_clear(d);
mag_clear(m);
mag_clear(err);
}
void
_acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z,
int regularized, slong prec, slong gamma_prec, int kummer)
{
if (regularized)
{
/* Remove singularity */
if (acb_is_int(b) && arb_is_nonpositive(acb_realref(b)) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(b)), 30) < 0)
{
acb_t c, d, t, u;
slong n;
n = arf_get_si(arb_midref(acb_realref(b)), ARF_RND_DOWN);
acb_init(c);
acb_init(d);
acb_init(t);
acb_init(u);
acb_sub(c, a, b, prec);
acb_add_ui(c, c, 1, prec);
acb_neg(d, b);
acb_add_ui(d, d, 2, prec);
_acb_hypgeom_m_1f1(t, c, d, z, 0, prec, gamma_prec, kummer);
acb_pow_ui(u, z, 1 - n, prec);
acb_mul(t, t, u, prec);
acb_rising_ui(u, a, 1 - n, prec);
acb_mul(t, t, u, prec);
arb_fac_ui(acb_realref(u), 1 - n, prec);
acb_div_arb(res, t, acb_realref(u), prec);
acb_clear(c);
acb_clear(d);
acb_clear(t);
acb_clear(u);
}
else
{
acb_t t;
acb_init(t);
acb_rgamma(t, b, gamma_prec);
_acb_hypgeom_m_1f1(res, a, b, z, 0, prec, gamma_prec, kummer);
acb_mul(res, res, t, prec);
acb_clear(t);
}
return;
}
/* Kummer's transformation */
if (kummer)
{
acb_t u, v;
acb_init(u);
acb_init(v);
acb_sub(u, b, a, prec);
acb_neg(v, z);
_acb_hypgeom_m_1f1(u, u, b, v, regularized, prec, gamma_prec, 0);
acb_exp(v, z, prec);
acb_mul(res, u, v, prec);
acb_clear(u);
acb_clear(v);
return;
}
if (acb_is_one(a))
{
acb_hypgeom_pfq_direct(res, NULL, 0, b, 1, z, -1, prec);
}
else
{
acb_struct c[3];
c[0] = *a;
c[1] = *b;
acb_init(c + 2);
acb_one(c + 2);
acb_hypgeom_pfq_direct(res, c, 1, c + 1, 2, z, -1, prec);
acb_clear(c + 2);
}
}
void
acb_hypgeom_2f1(acb_t res, const acb_t a, const acb_t b,
const acb_t c, const acb_t z, int flags, slong prec)
{
int algorithm, regularized;
regularized = flags & ACB_HYPGEOM_2F1_REGULARIZED;
if (!acb_is_finite(a) || !acb_is_finite(b) || !acb_is_finite(c) || !acb_is_finite(z))
{
acb_indeterminate(res);
return;
}
if (acb_is_zero(z))
{
if (regularized)
acb_rgamma(res, c, prec);
else
acb_one(res);
return;
}
if (regularized && acb_is_int(c) && arb_is_nonpositive(acb_realref(c)))
{
if ((acb_is_int(a) && arb_is_nonpositive(acb_realref(a)) &&
arf_cmp(arb_midref(acb_realref(a)), arb_midref(acb_realref(c))) >= 0) ||
(acb_is_int(b) && arb_is_nonpositive(acb_realref(b)) &&
arf_cmp(arb_midref(acb_realref(b)), arb_midref(acb_realref(c))) >= 0))
{
acb_zero(res);
return;
}
}
if (regularized && acb_eq(a, c))
{
_acb_hypgeom_2f1r_reduced(res, b, c, z, prec);
return;
}
if (regularized && acb_eq(b, c))
{
_acb_hypgeom_2f1r_reduced(res, a, c, z, prec);
return;
}
/* polynomial */
if (acb_is_int(a) && arf_sgn(arb_midref(acb_realref(a))) <= 0 &&
arf_cmpabs_ui(arb_midref(acb_realref(a)), prec) < 0)
{
acb_hypgeom_2f1_direct(res, a, b, c, z, regularized, prec);
return;
}
/* polynomial */
if (acb_is_int(b) && arf_sgn(arb_midref(acb_realref(b))) <= 0 &&
arf_cmpabs_ui(arb_midref(acb_realref(b)), prec) < 0)
{
acb_hypgeom_2f1_direct(res, a, b, c, z, regularized, prec);
return;
}
/* Try to reduce to a polynomial case using the Pfaff transformation */
/* TODO: look at flags for integer c-b, c-a here, even when c is nonexact */
if (acb_is_exact(c))
{
acb_t t;
acb_init(t);
acb_sub(t, c, b, prec);
if (acb_is_int(t) && arb_is_nonpositive(acb_realref(t)))
{
acb_hypgeom_2f1_transform(res, a, b, c, z, flags, 1, prec);
acb_clear(t);
return;
}
acb_sub(t, c, a, prec);
if (acb_is_int(t) && arb_is_nonpositive(acb_realref(t)))
{
int f1, f2;
/* When swapping a, b, also swap the flags. */
f1 = flags & ACB_HYPGEOM_2F1_AC;
f2 = flags & ACB_HYPGEOM_2F1_BC;
flags &= ~ACB_HYPGEOM_2F1_AC;
flags &= ~ACB_HYPGEOM_2F1_BC;
if (f1) flags |= ACB_HYPGEOM_2F1_BC;
if (f2) flags |= ACB_HYPGEOM_2F1_AC;
acb_hypgeom_2f1_transform(res, b, a, c, z, flags, 1, prec);
acb_clear(t);
return;
}
acb_clear(t);
}
/* special value at z = 1 */
if (acb_is_one(z))
{
acb_t t, u, v;
acb_init(t);
acb_init(u);
acb_init(v);
acb_sub(t, c, a, prec);
acb_sub(u, c, b, prec);
acb_sub(v, t, b, prec);
if (arb_is_positive(acb_realref(v)))
{
acb_rgamma(t, t, prec);
acb_rgamma(u, u, prec);
acb_mul(t, t, u, prec);
acb_gamma(v, v, prec);
acb_mul(t, t, v, prec);
if (!regularized)
{
acb_gamma(v, c, prec);
acb_mul(t, t, v, prec);
}
acb_set(res, t);
}
else
{
acb_indeterminate(res);
}
acb_clear(t);
acb_clear(u);
acb_clear(v);
return;
}
algorithm = acb_hypgeom_2f1_choose(z);
if (algorithm == 0)
{
acb_hypgeom_2f1_direct(res, a, b, c, z, regularized, prec);
}
else if (algorithm >= 1 && algorithm <= 5)
{
acb_hypgeom_2f1_transform(res, a, b, c, z, flags, algorithm, prec);
}
else
{
acb_hypgeom_2f1_corner(res, a, b, c, z, regularized, prec);
}
}
void
acb_sqrt(acb_t y, const acb_t x, slong prec)
{
arb_t r, t, u;
slong wp;
#define a acb_realref(x)
#define b acb_imagref(x)
#define c acb_realref(y)
#define d acb_imagref(y)
if (arb_is_zero(b))
{
if (arb_is_nonnegative(a))
{
arb_sqrt(c, a, prec);
arb_zero(d);
return;
}
else if (arb_is_nonpositive(a))
{
arb_neg(d, a);
arb_sqrt(d, d, prec);
arb_zero(c);
return;
}
}
if (arb_is_zero(a))
{
if (arb_is_nonnegative(b))
{
arb_mul_2exp_si(c, b, -1);
arb_sqrt(c, c, prec);
arb_set(d, c);
return;
}
else if (arb_is_nonpositive(b))
{
arb_mul_2exp_si(c, b, -1);
arb_neg(c, c);
arb_sqrt(c, c, prec);
arb_neg(d, c);
return;
}
}
wp = prec + 4;
arb_init(r);
arb_init(t);
arb_init(u);
acb_abs(r, x, wp);
arb_add(t, r, a, wp);
if (arb_rel_accuracy_bits(t) > 8)
{
/* sqrt(a+bi) = sqrt((r+a)/2) + b/sqrt(2*(r+a))*i, r = |a+bi| */
arb_mul_2exp_si(u, t, 1);
arb_sqrt(u, u, wp);
arb_div(d, b, u, prec);
arb_set_round(c, u, prec);
arb_mul_2exp_si(c, c, -1);
}
else
{
/*
sqrt(a+bi) = sqrt((r+a)/2) + (b/|b|)*sqrt((r-a)/2)*i
(sign)
*/
arb_mul_2exp_si(t, t, -1);
arb_sub(u, r, a, wp);
arb_mul_2exp_si(u, u, -1);
arb_sqrtpos(c, t, prec);
if (arb_is_nonnegative(b))
{
arb_sqrtpos(d, u, prec);
}
else if (arb_is_nonpositive(b))
{
arb_sqrtpos(d, u, prec);
arb_neg(d, d);
}
else
{
arb_sqrtpos(t, u, wp);
arb_neg(u, t);
arb_union(d, t, u, prec);
}
}
arb_clear(r);
arb_clear(t);
arb_clear(u);
#undef a
#undef b
#undef c
#undef d
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("2f1_continuation....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t a, b, c, z1, z2, f1, f2, g1, g2, h1, h2, aa, bb, cc;
mag_t d0, d1, dt;
slong prec;
int regularized, ebits;
acb_init(a); acb_init(b); acb_init(c);
acb_init(aa); acb_init(bb); acb_init(cc);
acb_init(z1); acb_init(z2);
acb_init(f1); acb_init(f2);
acb_init(g1); acb_init(g2);
acb_init(h1); acb_init(h2);
mag_init(d0); mag_init(d1); mag_init(dt);
prec = 2 + n_randint(state, 300);
ebits = 10;
regularized = n_randint(state, 2);
acb_randtest_param(a, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits / 2));
acb_randtest_param(b, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits / 2));
acb_randtest_param(c, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits / 2));
acb_randtest(h1, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
acb_randtest(h2, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
do {
int left, upper, lower;
acb_randtest_param(z1, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
acb_randtest_param(z2, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits));
/* we test both convergent and non-convergent cases, but
try to be more efficient by generating more convergent cases */
if (n_randint(state, 2))
{
acb_sub_ui(aa, z1, 1, prec);
acb_get_mag(d0, z1);
acb_get_mag(d1, aa);
acb_get_mag(dt, z2);
if (mag_cmp(dt, d0) >= 0 || mag_cmp(dt, d1) >= 0)
continue;
}
acb_add(z2, z1, z2, prec);
/* for the test, don't cross the branch cut */
acb_sub_ui(aa, z1, 1, prec);
acb_sub_ui(bb, z2, 1, prec);
left = arb_is_negative(acb_realref(aa)) && arb_is_negative(acb_realref(bb));
upper = arb_is_positive(acb_imagref(aa)) && arb_is_positive(acb_imagref(bb));
lower = arb_is_nonpositive(acb_imagref(aa)) && arb_is_nonpositive(acb_imagref(bb));
if (left || upper || lower)
break;
} while (1);
acb_add_ui(aa, a, 1, prec);
acb_add_ui(bb, b, 1, prec);
acb_add_ui(cc, c, 1, prec);
acb_hypgeom_2f1(f1, a, b, c, z1, regularized, prec);
acb_hypgeom_2f1(f2, aa, bb, cc, z1, regularized, prec);
acb_mul(f2, f2, a, prec);
acb_mul(f2, f2, b, prec);
if (!regularized)
acb_div(f2, f2, c, prec);
acb_hypgeom_2f1_continuation(h1, h2, a, b, c, z1, z2, f1, f2, prec);
if (acb_is_finite(h1) || acb_is_finite(h2))
{
acb_hypgeom_2f1(g1, a, b, c, z2, regularized, prec);
acb_hypgeom_2f1(g2, aa, bb, cc, z2, regularized, prec);
acb_mul(g2, g2, a, prec);
acb_mul(g2, g2, b, prec);
if (!regularized)
acb_div(g2, g2, c, prec);
if (!acb_overlaps(g1, h1) || !acb_overlaps(g2, h2))
{
flint_printf("FAIL: consistency\n\n");
flint_printf("regularized = %d, prec = %wd\n\n", regularized, prec);
flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n");
flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n");
flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n");
flint_printf("z2 = "); acb_printd(z2, 30); flint_printf("\n\n");
flint_printf("F(a,b,c,z1) and F'(a,b,c,z1):\n");
flint_printf("f1 = "); acb_printd(f1, 30); flint_printf("\n\n");
flint_printf("f2 = "); acb_printd(f2, 30); flint_printf("\n\n");
flint_printf("F(a,b,c,z2) and F'(a,b,c,z2):\n");
flint_printf("g1 = "); acb_printd(g1, 30); flint_printf("\n\n");
flint_printf("g2 = "); acb_printd(g2, 30); flint_printf("\n\n");
flint_printf("Computed F and F':\n");
flint_printf("h1 = "); acb_printd(h1, 30); flint_printf("\n\n");
flint_printf("h2 = "); acb_printd(h2, 30); flint_printf("\n\n");
flint_abort();
}
}
acb_clear(a); acb_clear(b); acb_clear(c);
acb_clear(aa); acb_clear(bb); acb_clear(cc);
acb_clear(z1); acb_clear(z2);
acb_clear(f1); acb_clear(f2);
acb_clear(g1); acb_clear(g2);
acb_clear(h1); acb_clear(h2);
mag_clear(d0); mag_clear(d1); mag_clear(dt);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
acb_lambertw_middle(acb_t res, const acb_t z, slong prec)
{
fmpz_t k;
if (acb_contains_zero(z))
{
acb_indeterminate(res);
return;
}
fmpz_init(k);
fmpz_set_si(k, -1);
if (arb_is_positive(acb_imagref(z)))
{
acb_lambertw(res, z, k, 0, prec);
}
else if (arb_is_negative(acb_imagref(z)))
{
acb_conj(res, z);
acb_lambertw(res, res, k, 0, prec);
acb_conj(res, res);
}
else if (arb_is_negative(acb_realref(z)))
{
if (arb_is_nonnegative(acb_imagref(z)))
{
acb_lambertw(res, z, k, 0, prec);
}
else if (arb_is_negative(acb_imagref(z)))
{
acb_conj(res, z);
acb_lambertw(res, res, k, 0, prec);
acb_conj(res, res);
}
else
{
acb_t za, zb;
acb_init(za);
acb_init(zb);
acb_set(za, z);
acb_conj(zb, z);
arb_nonnegative_part(acb_imagref(za), acb_imagref(za));
arb_nonnegative_part(acb_imagref(zb), acb_imagref(zb));
acb_lambertw(za, za, k, 0, prec);
acb_lambertw(zb, zb, k, 0, prec);
acb_conj(zb, zb);
acb_union(res, za, zb, prec);
acb_clear(za);
acb_clear(zb);
}
}
else /* re is positive */
{
if (arb_is_positive(acb_imagref(z)))
{
acb_lambertw(res, z, k, 0, prec);
}
else if (arb_is_nonpositive(acb_imagref(z)))
{
acb_conj(res, z);
acb_lambertw(res, res, k, 0, prec);
acb_conj(res, res);
}
else
{
acb_t za, zb;
acb_init(za);
acb_init(zb);
acb_set(za, z);
acb_conj(zb, z);
arb_nonnegative_part(acb_imagref(za), acb_imagref(za));
arb_nonnegative_part(acb_imagref(zb), acb_imagref(zb));
acb_lambertw(za, za, k, 0, prec);
acb_lambertw(zb, zb, k, 0, prec);
acb_conj(zb, zb);
acb_union(res, za, zb, prec);
acb_clear(za);
acb_clear(zb);
}
}
fmpz_clear(k);
}
