mapmrsin.c

任意精度的数学库

/* 
 *  M_APM  -  mapmrsin.c
 *
 *  Copyright (C) 1999   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, but not the right to
 *  distribute the modified code.  Modifications are to be distributed 
 *  as patches to released version.
 *  
 *  This software is provided "as is" without express or implied warranty.
 */

/*
 *      $Id: mapmrsin.c,v 1.3 1999/06/20 16:23:10 mike Exp $
 *
 *      This file contains the basic series expansion functions for 
 *	the SIN / COS functions.
 *
 *      $Log: mapmrsin.c,v $
 *      Revision 1.3  1999/06/20 16:23:10  mike
 *      changed local static variables to MAPM stack variables
 *
 *      Revision 1.2  1999/05/12 21:06:36  mike
 *      changed global var names
 *
 *      Revision 1.1  1999/05/10 20:56:31  mike
 *      Initial revision
 */

#include "m_apm_lc.h"

/****************************************************************************/
/*
                                x^3     x^5     x^7    x^9
		 sin(x) == x -  ---  +  ---  -  ---  + ---  ...
                                 3!      5!      7!     9!
*/
void	M_raw_sin(rr,places,xx)
M_APM 	rr, xx;
int 	places;
{
M_APM	sum, term, tmp6, tmp7, tmp8, tmp9;
int     sign_flag, flag;
long	m1, m2;

sum  = M_get_stack_var();
term = M_get_stack_var();
tmp6 = M_get_stack_var();
tmp7 = M_get_stack_var();
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();

m_apm_copy(sum, xx);
m_apm_copy(term, xx);
m_apm_multiply(tmp8, xx, xx);
m_apm_round(tmp9, (places + 6), tmp8);

m_apm_copy(tmp6, MM_One);
tmp6->m_apm_exponent = -(places + 4);

m1   = 2L;
flag = 0;
sign_flag = xx->m_apm_sign;
tmp6->m_apm_sign = sign_flag;

while (TRUE)
  {
   m2 = m1 * (m1 + 1);
   m_apm_set_long(tmp7, m2);

   m_apm_multiply(tmp8, term, tmp9);
   m_apm_divide(term, (places + 6), tmp8, tmp7);

   if (flag == 0)
     {
      m_apm_subtract(tmp7, sum, term);
      m_apm_copy(sum, tmp7);
     }
   else
     {
      m_apm_add(tmp7, sum, term);
      m_apm_copy(sum, tmp7);
     }

   /*
    *    the SIN function only uses the odd powers of 'x',
    *    so the terms will always be positive OR negative
    *    during each call to this function.
    */

   if (sign_flag == -1)
     {
      if (m_apm_compare(term, tmp6) >= 0)
        break;
     }
   else
     {
      if (m_apm_compare(term, tmp6) <= 0)
        break;
     }

   m1 += 2;
   flag = 1 - flag;
  }

m_apm_round(rr, places, sum);
M_restore_stack(6);
}
/****************************************************************************/
/*
                                x^2     x^4     x^6    x^8
		 cos(x) == 1 -  ---  +  ---  -  ---  + ---  ...
                                 2!      4!      6!     8!
*/
void	M_raw_cos(rr,places,xx)
M_APM 	rr, xx;
int 	places;
{
M_APM	sum, term, tmp6, tmp7, tmp8, tmp9;
int     flag;
long	m1, m2;

sum  = M_get_stack_var();
term = M_get_stack_var();
tmp6 = M_get_stack_var();
tmp7 = M_get_stack_var();
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();

m_apm_copy(sum, MM_One);
m_apm_copy(term, MM_One);

m_apm_multiply(tmp8, xx, xx);
m_apm_round(tmp9, (places + 6), tmp8);

m_apm_copy(tmp6, MM_One);
tmp6->m_apm_exponent = -(places + 4);

m1   = 1L;
flag = 0;

while (TRUE)
  {
   m2 = m1 * (m1 + 1);
   m_apm_set_long(tmp7, m2);

   m_apm_multiply(tmp8, term, tmp9);
   m_apm_divide(term, (places + 6), tmp8, tmp7);

   if (flag == 0)
     {
      m_apm_subtract(tmp7, sum, term);
      m_apm_copy(sum, tmp7);
     }
   else
     {
      m_apm_add(tmp7, sum, term);
      m_apm_copy(sum, tmp7);
     }

   /*
    *  since the COS function only uses the even powers of 'x',
    *  the terms will always be positive.
    */

   if (m_apm_compare(term, tmp6) <= 0)
     break;

   m1 += 2;
   flag = 1 - flag;
  }

m_apm_round(rr, places, sum);
M_restore_stack(6);
}
/****************************************************************************/