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/*
Copyright (C) 2020 Fredrik Johansson
This file is part of Calcium.
Calcium is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "ca.h"
void
ca_gamma_inert(ca_t res, const ca_t x, ca_ctx_t ctx)
{
if (CA_IS_SPECIAL(x))
{
flint_abort();
}
else
{
_ca_function_fx(res, CA_Gamma, x, ctx);
}
}
void
_ca_gamma_verbatim(ca_t res, const ca_t x, ca_ctx_t ctx)
{
ca_t y, tmp;
ca_init(y, ctx);
ca_init(tmp, ctx);
_ca_function_fx(y, CA_Gamma, x, ctx);
ca_merge_fields(tmp, res, x, y, ctx);
ca_clear(y, ctx);
ca_clear(tmp, ctx);
}
truth_t
ca_re_is_positive(const ca_t x, ca_ctx_t ctx)
{
ca_t t, u;
truth_t res;
ca_init(t, ctx);
ca_init(u, ctx);
ca_re(t, x, ctx);
res = ca_check_gt(t, u, ctx);
ca_clear(t, ctx);
ca_clear(u, ctx);
return res;
}
void
ca_gamma(ca_t res, const ca_t x, ca_ctx_t ctx)
{
if (CA_IS_SPECIAL(x))
{
/* todo: other signs */
if (ca_check_is_pos_inf(x, ctx))
{
ca_pos_inf(res, ctx);
}
else if (ca_check_is_neg_inf(x, ctx) || ca_check_is_undefined(x, ctx) || ca_check_is_uinf(x, ctx))
{
ca_undefined(res, ctx);
}
else if (ca_check_is_pos_i_inf(x, ctx) || ca_check_is_neg_i_inf(x, ctx))
{
ca_zero(res, ctx);
}
else
{
ca_unknown(res, ctx);
}
}
else
{
truth_t is_integer, is_positive;
slong expand_limit;
expand_limit = ctx->options[CA_OPT_PREC_LIMIT];
is_integer = ca_check_is_integer(x, ctx);
if (is_integer == T_TRUE)
{
is_positive = ca_re_is_positive(x, ctx);
if (is_positive == T_TRUE)
{
fmpz_t t;
fmpz_init(t);
if (ca_get_fmpz(t, x, ctx) && fmpz_cmp_ui(t, expand_limit) < 0)
{
fmpz_fac_ui(t, fmpz_get_ui(t) - 1);
ca_set_fmpz(res, t, ctx);
}
else
{
/* todo: may want to use the potentially simplified x (to an integer) here... */
_ca_gamma_verbatim(res, x, ctx);
}
fmpz_clear(t);
}
else if (is_positive == T_FALSE)
{
ca_uinf(res, ctx);
}
else
{
ca_unknown(res, ctx);
}
}
else if (is_integer == T_FALSE)
{
ca_t y;
fmpz_t t, u;
slong n;
ca_init(y, ctx);
fmpz_init(t);
fmpz_init(u);
ca_set_d(y, 0.5, ctx);
ca_sub(y, x, y, ctx);
if (ca_get_fmpz(t, y, ctx) && fmpz_cmp_si(t, expand_limit) < 0 &&
fmpz_cmp_si(t, -expand_limit) > 0)
{
n = fmpz_get_si(t);
ca_pi(res, ctx);
ca_sqrt(res, res, ctx);
if (n != 0)
{
if (n >= 0)
{
fmpz_fac_ui(t, 2 * n);
fmpz_fac_ui(u, n);
fmpz_mul_2exp(u, u, 2 * n);
}
else
{
fmpz_fac_ui(t, -n);
fmpz_mul_2exp(t, t, -2 * n);
fmpz_fac_ui(u, -2 * n);
if (n & 1)
fmpz_neg(t, t);
}
ca_mul_fmpz(res, res, t, ctx);
ca_div_fmpz(res, res, u, ctx);
}
}
else
{
_ca_gamma_verbatim(res, x, ctx);
}
ca_clear(y, ctx);
fmpz_clear(t);
fmpz_clear(u);
}
else
{
is_positive = ca_re_is_positive(x, ctx);
if (is_positive == T_TRUE)
{
_ca_gamma_verbatim(res, x, ctx);
}
else
{
ca_unknown(res, ctx);
}
}
}
}
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