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/*
Copyright (C) 2021 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_asin_special(ca_t res, const ca_t x, ca_ctx_t ctx)
{
if (ca_check_is_signed_inf(x, ctx) == T_TRUE)
{
ca_t s;
ca_init(s, ctx);
/* -i*csgn(i*z)*inf */
ca_i(s, ctx);
ca_mul(res, x, s, ctx);
ca_csgn(res, res, ctx);
ca_mul(res, res, s, ctx);
ca_neg(res, res, ctx);
ca_pos_inf(s, ctx);
ca_mul(res, res, s, ctx);
ca_clear(s, ctx);
return;
}
if (ca_check_is_uinf(x, ctx) == T_TRUE || ca_check_is_undefined(x, ctx) == T_TRUE)
{
ca_set(res, x, ctx);
return;
}
ca_unknown(res, ctx);
return;
}
static int
_ca_asin_rational(ca_t res, const ca_t x, ca_ctx_t ctx)
{
qqbar_t v;
slong p;
ulong q;
int success;
qqbar_init(v);
/* todo: rule out non-sines more quickly */
if (ca_get_qqbar(v, x, ctx) && qqbar_asin_pi(&p, &q, v))
{
ca_pi(res, ctx);
ca_mul_si(res, res, p, ctx);
ca_div_ui(res, res, q, ctx);
success = 1;
}
else
{
success = 0;
}
qqbar_clear(v);
return success;
}
void
ca_asin_logarithm(ca_t res, const ca_t x, ca_ctx_t ctx)
{
ca_t t, u;
if (CA_IS_SPECIAL(x))
{
ca_asin_special(res, x, ctx);
return;
}
if (_ca_asin_rational(res, x, ctx))
return;
/* asin(x) = -i log(ix + sqrt(1-x^2)) */
ca_init(t, ctx);
ca_init(u, ctx);
ca_sqr(t, x, ctx);
ca_ui_sub(t, 1, t, ctx);
ca_sqrt(t, t, ctx);
ca_i(u, ctx);
ca_mul(u, u, x, ctx);
ca_add(t, t, u, ctx);
ca_log(t, t, ctx);
ca_i(u, ctx);
ca_mul(res, t, u, ctx);
ca_neg(res, res, ctx);
ca_clear(t, ctx);
ca_clear(u, ctx);
}
void
ca_asin_direct(ca_t res, const ca_t x, ca_ctx_t ctx)
{
if (CA_IS_SPECIAL(x))
{
ca_asin_special(res, x, ctx);
return;
}
if (_ca_asin_rational(res, x, ctx))
return;
/* todo: csgn normalization, reflection...? */
_ca_function_fx(res, CA_Asin, x, ctx);
}
void
ca_asin(ca_t res, const ca_t x, ca_ctx_t ctx)
{
if (ctx->options[CA_OPT_TRIG_FORM] == CA_TRIG_EXPONENTIAL)
{
ca_asin_logarithm(res, x, ctx);
}
/* todo:
else if (ctx->options[CA_OPT_TRIG_FORM] == CA_TRIG_TANGENT)
{
ca_asin_arctangent(res, x, ctx);
}
*/
else
{
ca_asin_direct(res, x, ctx);
}
}
void
ca_acos_logarithm(ca_t res, const ca_t x, ca_ctx_t ctx)
{
ca_t t;
ca_init(t, ctx);
ca_pi(t, ctx);
ca_div_ui(t, t, 2, ctx);
ca_asin_logarithm(res, x, ctx);
ca_sub(res, t, res, ctx);
ca_clear(t, ctx);
}
void
ca_acos_direct(ca_t res, const ca_t x, ca_ctx_t ctx)
{
ca_t t;
ca_init(t, ctx);
ca_pi(t, ctx);
ca_div_ui(t, t, 2, ctx);
ca_asin_direct(res, x, ctx);
ca_sub(res, t, res, ctx);
ca_clear(t, ctx);
}
void
ca_acos(ca_t res, const ca_t x, ca_ctx_t ctx)
{
ca_t t;
ca_init(t, ctx);
ca_pi(t, ctx);
ca_div_ui(t, t, 2, ctx);
ca_asin(res, x, ctx);
ca_sub(res, t, res, ctx);
ca_clear(t, ctx);
}
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