void m_apm_sin_cos(M_APM sinv, M_APM cosv, int places, M_APM aa)
{
M_APM tmp5, tmp6, tmp7;
tmp5 = M_get_stack_var();
tmp6 = M_get_stack_var();
tmp7 = M_get_stack_var();
M_limit_angle_to_pi(tmp5, (places + 6), aa);
M_4x_cos(tmp7, (places + 6), tmp5);
/*
* compute sin(x) = sqrt(1 - cos(x) ^ 2).
*
* note that the sign of 'sin' will always be positive after the
* sqrt call. we need to adjust the sign based on what quadrant
* the original angle is in.
*/
M_cos_to_sin(tmp6, (places + 6), tmp7);
if (tmp6->m_apm_sign != 0)
tmp6->m_apm_sign = tmp5->m_apm_sign;
m_apm_round(sinv, places, tmp6);
m_apm_round(cosv, places, tmp7);
M_restore_stack(3);
}
/*
Calculate arcsin using the identity :
x
arcsin (x) == arctan [ --------------- ]
sqrt(1 - x^2)
*/
void M_arcsin_near_0(M_APM rr, int places, M_APM aa)
{
M_APM tmp5, tmp6;
tmp5 = M_get_stack_var();
tmp6 = M_get_stack_var();
M_cos_to_sin(tmp5, (places + 8), aa);
m_apm_divide(tmp6, (places + 8), aa, tmp5);
M_arctan_near_0(rr, places, tmp6);
M_restore_stack(2);
}
void m_apm_arccos(M_APM r, int places, M_APM x)
{
M_APM tmp0, tmp1, tmp2, tmp3, current_x;
int ii, maxiter, maxp, tolerance, local_precision;
current_x = M_get_stack_var();
tmp0 = M_get_stack_var();
tmp1 = M_get_stack_var();
tmp2 = M_get_stack_var();
tmp3 = M_get_stack_var();
m_apm_absolute_value(tmp0, x);
ii = m_apm_compare(tmp0, MM_One);
if (ii == 1) /* |x| > 1 */
{
M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arccos\', |Argument| > 1");
M_set_to_zero(r);
M_restore_stack(5);
return;
}
if (ii == 0) /* |x| == 1, arccos = 0, PI */
{
if (x->m_apm_sign == 1)
{
M_set_to_zero(r);
}
else
{
M_check_PI_places(places);
m_apm_round(r, places, MM_lc_PI);
}
M_restore_stack(5);
return;
}
if (m_apm_compare(tmp0, MM_0_85) == 1) /* check if > 0.85 */
{
M_cos_to_sin(tmp2, (places + 4), x);
if (x->m_apm_sign == 1)
{
m_apm_arcsin(r, places, tmp2);
}
else
{
M_check_PI_places(places);
m_apm_arcsin(tmp3, (places + 4), tmp2);
m_apm_subtract(tmp1, MM_lc_PI, tmp3);
m_apm_round(r, places, tmp1);
}
M_restore_stack(5);
return;
}
if (x->m_apm_sign == 0) /* input == 0 ?? */
{
M_check_PI_places(places);
m_apm_round(r, places, MM_lc_HALF_PI);
M_restore_stack(5);
return;
}
if (x->m_apm_exponent <= -4) /* input close to 0 ?? */
{
M_arccos_near_0(r, places, x);
M_restore_stack(5);
return;
}
tolerance = -(places + 4);
maxp = places + 8;
local_precision = 18;
/*
* compute the maximum number of iterations
* that should be needed to calculate to
* the desired accuracy. [ constant below ~= 1 / log(2) ]
*/
maxiter = (int)(log((double)(places + 2)) * 1.442695) + 3;
if (maxiter < 5)
maxiter = 5;
M_get_acos_guess(current_x, x);
/* Use the following iteration to solve for arc-cos :
cos(X) - N
X = X + ------------
n+1 sin(X)
*/
ii = 0;
while (TRUE)
{
M_4x_cos(tmp1, local_precision, current_x);
M_cos_to_sin(tmp2, local_precision, tmp1);
if (tmp2->m_apm_sign != 0)
tmp2->m_apm_sign = current_x->m_apm_sign;
m_apm_subtract(tmp3, tmp1, x);
m_apm_divide(tmp0, local_precision, tmp3, tmp2);
m_apm_add(tmp2, current_x, tmp0);
m_apm_copy(current_x, tmp2);
if (ii != 0)
{
if (((2 * tmp0->m_apm_exponent) < tolerance) || (tmp0->m_apm_sign == 0))
break;
}
if (++ii == maxiter)
{
M_apm_log_error_msg(M_APM_RETURN,
"\'m_apm_arccos\', max iteration count reached");
break;
}
local_precision *= 2;
if (local_precision > maxp)
local_precision = maxp;
}
m_apm_round(r, places, current_x);
M_restore_stack(5);
}
