* M_APM - mapm5sin.c
*
* Copyright (C) 1999 - 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: mapm5sin.c,v 1.10 2007/12/03 01:26:16 mike Exp $
*
* This file contains the functions that implement the sin (5x)
* and cos (4x) multiple angle relations
*
* $Log: mapm5sin.c,v $
* Revision 1.10 2007/12/03 01:26:16 mike
* Update license
*
* Revision 1.9 2002/11/03 21:50:36 mike
* Updated function parameters to use the modern style
*
* Revision 1.8 2001/03/25 20:57:03 mike
* move cos_to_sin func in here
*
* Revision 1.7 2000/05/04 23:50:21 mike
* use multiple angle identity 4 times of larger COS angles
*
* Revision 1.6 1999/06/30 00:08:53 mike
* pass more decimal places to raw functions
*
* Revision 1.5 1999/06/20 23:41:32 mike
* changed COS to use 4x multiple angle identity instead of 5x
*
* Revision 1.4 1999/06/20 19:42:26 mike
* tweak number of dec places passed to sub-functions
*
* Revision 1.3 1999/06/20 19:03:56 mike
* changed local static variables to MAPM stack variables
*
* Revision 1.2 1999/05/12 21:30:09 mike
* replace local 5.0 with global
*
* Revision 1.1 1999/05/10 20:56:31 mike
* Initial revision
*/
#include "m_apm_lc.h"
void M_5x_sin(M_APM r, int places, M_APM x)
{
M_APM tmp8, tmp9;
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();
m_apm_multiply(tmp9, x, MM_5x_125R);
M_raw_sin(tmp8, (places + 6), tmp9);
M_5x_do_it(tmp9, (places + 4), tmp8);
M_5x_do_it(tmp8, (places + 4), tmp9);
M_5x_do_it(r, places, tmp8);
M_restore_stack(2);
}
void M_4x_cos(M_APM r, int places, M_APM x)
{
M_APM tmp8, tmp9;
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();
* if |x| >= 1.0 use multiple angle identity 4 times
* if |x| < 1.0 use multiple angle identity 3 times
*/
if (x->m_apm_exponent > 0)
{
m_apm_multiply(tmp9, x, MM_5x_256R);
M_raw_cos(tmp8, (places + 8), tmp9);
M_4x_do_it(tmp9, (places + 8), tmp8);
M_4x_do_it(tmp8, (places + 6), tmp9);
M_4x_do_it(tmp9, (places + 4), tmp8);
M_4x_do_it(r, places, tmp9);
}
else
{
m_apm_multiply(tmp9, x, MM_5x_64R);
M_raw_cos(tmp8, (places + 6), tmp9);
M_4x_do_it(tmp9, (places + 4), tmp8);
M_4x_do_it(tmp8, (places + 4), tmp9);
M_4x_do_it(r, places, tmp8);
}
M_restore_stack(2);
}
* calculate the multiple angle identity for sin (5x)
*
* sin (5x) == 16 * sin^5 (x) - 20 * sin^3 (x) + 5 * sin(x)
*/
void M_5x_do_it(M_APM rr, int places, M_APM xx)
{
M_APM tmp0, tmp1, t2, t3, t5;
tmp0 = M_get_stack_var();
tmp1 = M_get_stack_var();
t2 = M_get_stack_var();
t3 = M_get_stack_var();
t5 = M_get_stack_var();
m_apm_multiply(tmp1, xx, xx);
m_apm_round(t2, (places + 4), tmp1);
m_apm_multiply(tmp1, t2, xx);
m_apm_round(t3, (places + 4), tmp1);
m_apm_multiply(t5, t2, t3);
m_apm_multiply(tmp0, xx, MM_Five);
m_apm_multiply(tmp1, t5, MM_5x_Sixteen);
m_apm_add(t2, tmp0, tmp1);
m_apm_multiply(tmp1, t3, MM_5x_Twenty);
m_apm_subtract(tmp0, t2, tmp1);
m_apm_round(rr, places, tmp0);
M_restore_stack(5);
}
* calculate the multiple angle identity for cos (4x)
*
* cos (4x) == 8 * [ cos^4 (x) - cos^2 (x) ] + 1
*/
void M_4x_do_it(M_APM rr, int places, M_APM xx)
{
M_APM tmp0, tmp1, t2, t4;
tmp0 = M_get_stack_var();
tmp1 = M_get_stack_var();
t2 = M_get_stack_var();
t4 = M_get_stack_var();
m_apm_multiply(tmp1, xx, xx);
m_apm_round(t2, (places + 4), tmp1);
m_apm_multiply(t4, t2, t2);
m_apm_subtract(tmp0, t4, t2);
m_apm_multiply(tmp1, tmp0, MM_5x_Eight);
m_apm_add(tmp0, MM_One, tmp1);
m_apm_round(rr, places, tmp0);
M_restore_stack(4);
}
* compute r = sqrt(1 - a ^ 2).
*/
void M_cos_to_sin(M_APM r, int places, M_APM a)
{
M_APM tmp1, tmp2;
tmp1 = M_get_stack_var();
tmp2 = M_get_stack_var();
m_apm_multiply(tmp1, a, a);
m_apm_subtract(tmp2, MM_One, tmp1);
m_apm_sqrt(r, places, tmp2);
M_restore_stack(2);
}
