* M_APM - mapmasn0.c
*
* Copyright (C) 2000 - 2007 Michael C. Ring
*
* Permission to use, copy, and distribute this software and its
* documentation for any purpose with or without fee is hereby granted,
* provided that the above copyright notice appear in all copies and
* that both that copyright notice and this permission notice appear
* in supporting documentation.
*
* Permission to modify the software is granted. Permission to distribute
* the modified code is granted. Modifications are to be distributed by
* using the file 'license.txt' as a template to modify the file header.
* 'license.txt' is available in the official MAPM distribution.
*
* This software is provided "as is" without express or implied warranty.
*/
* $Id: mapmasn0.c,v 1.8 2007/12/03 01:49:49 mike Exp $
*
* This file contains the 'ARC' family of functions; ARC-SIN,
* ARC-COS, ARC-TAN when the input arg is very close to 0 (zero).
*
* $Log: mapmasn0.c,v $
* Revision 1.8 2007/12/03 01:49:49 mike
* Update license
*
* Revision 1.7 2003/06/02 16:51:13 mike
* *** empty log message ***
*
* Revision 1.6 2003/06/02 16:49:48 mike
* tweak the decimal places
*
* Revision 1.5 2003/06/02 16:47:39 mike
* tweak arctan algorithm some more
*
* Revision 1.4 2003/05/31 22:38:07 mike
* optimize arctan by using fewer digits as subsequent
* terms get smaller
*
* Revision 1.3 2002/11/03 21:36:43 mike
* Updated function parameters to use the modern style
*
* Revision 1.2 2000/12/02 20:11:37 mike
* add comments
*
* Revision 1.1 2000/12/02 20:08:27 mike
* Initial revision
*/
#include "m_apm_lc.h"
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);
}
Calculate arccos using the identity :
arccos (x) == PI / 2 - arcsin (x)
*/
void M_arccos_near_0(M_APM rr, int places, M_APM aa)
{
M_APM tmp1, tmp2;
tmp1 = M_get_stack_var();
tmp2 = M_get_stack_var();
M_check_PI_places(places);
M_arcsin_near_0(tmp1, (places + 4), aa);
m_apm_subtract(tmp2, MM_lc_HALF_PI, tmp1);
m_apm_round(rr, places, tmp2);
M_restore_stack(2);
}
calculate arctan (x) with the following series:
x^3 x^5 x^7 x^9
arctan (x) = x - --- + --- - --- + --- ...
3 5 7 9
*/
void M_arctan_near_0(M_APM rr, int places, M_APM aa)
{
M_APM tmp0, tmp2, tmpR, tmpS, digit, term;
int tolerance, dplaces, local_precision;
long m1;
tmp0 = M_get_stack_var();
tmp2 = M_get_stack_var();
tmpR = M_get_stack_var();
tmpS = M_get_stack_var();
term = M_get_stack_var();
digit = M_get_stack_var();
tolerance = aa->m_apm_exponent - (places + 4);
dplaces = (places + 8) - aa->m_apm_exponent;
m_apm_copy(term, aa);
m_apm_copy(tmpS, aa);
m_apm_multiply(tmp0, aa, aa);
m_apm_round(tmp2, (dplaces + 8), tmp0);
m1 = 1L;
while (TRUE)
{
* do the subtraction term
*/
m_apm_multiply(tmp0, term, tmp2);
if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0))
{
m_apm_round(rr, places, tmpS);
break;
}
local_precision = dplaces + tmp0->m_apm_exponent;
if (local_precision < 20)
local_precision = 20;
m1 += 2;
m_apm_set_long(digit, m1);
m_apm_round(term, local_precision, tmp0);
m_apm_divide(tmp0, local_precision, term, digit);
m_apm_subtract(tmpR, tmpS, tmp0);
* do the addition term
*/
m_apm_multiply(tmp0, term, tmp2);
if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0))
{
m_apm_round(rr, places, tmpR);
break;
}
local_precision = dplaces + tmp0->m_apm_exponent;
if (local_precision < 20)
local_precision = 20;
m1 += 2;
m_apm_set_long(digit, m1);
m_apm_round(term, local_precision, tmp0);
m_apm_divide(tmp0, local_precision, term, digit);
m_apm_add(tmpS, tmpR, tmp0);
}
M_restore_stack(6);
}
