mapm_sin.c

任意精度的数学库

/* 
 *  M_APM  -  mapm_sin.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: mapm_sin.c,v 1.8 1999/09/21 21:03:06 mike Exp $
 *
 *      This file contains the top level (user callable) SIN / COS / TAN
 *	functions.
 *
 *      $Log: mapm_sin.c,v $
 *      Revision 1.8  1999/09/21 21:03:06  mike
 *      make sure the sign of 'sin' from M_cos_to_sin is non-zero
 *      before assigning it from the original angle.
 *
 *      Revision 1.7  1999/09/18 03:27:27  mike
 *      added m_apm_sin_cos
 *
 *      Revision 1.6  1999/07/09 22:50:33  mike
 *      skip limit to PI when not needed
 *
 *      Revision 1.5  1999/06/20 23:42:29  mike
 *      use new function for COS function
 *
 *      Revision 1.4  1999/06/20 19:27:12  mike
 *      changed local static variables to MAPM stack variables
 *
 *      Revision 1.3  1999/05/17 03:54:56  mike
 *      init globals in TAN function also
 *
 *      Revision 1.2  1999/05/15 02:18:31  mike
 *      add check for number of decimal places
 *
 *      Revision 1.1  1999/05/10 20:56:31  mike
 *      Initial revision
 */

#include "m_apm_lc.h"

/****************************************************************************/
void	m_apm_sin(r,places,a)
M_APM	r, a;
int	places;
{
M_APM	tmp3;

tmp3 = M_get_stack_var();
M_limit_angle_to_pi(tmp3, (places + 6), a);
M_5x_sin(r, places, tmp3);
M_restore_stack(1);
}
/****************************************************************************/
void	m_apm_cos(r,places,a)
M_APM	r, a;
int	places;
{
M_APM	tmp3;

tmp3 = M_get_stack_var();
M_limit_angle_to_pi(tmp3, (places + 6), a);
M_4x_cos(r, places, tmp3);
M_restore_stack(1);
}
/****************************************************************************/
void	m_apm_sin_cos(sinv,cosv,places,aa)
M_APM	sinv, cosv, aa;
int	places;
{
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);

MM_skip_limit_PI_check = TRUE;
m_apm_cos(tmp7, (places + 4), tmp5);
MM_skip_limit_PI_check = FALSE;

/*
 *   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 + 4), 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);
}
/****************************************************************************/
void	m_apm_tan(r,places,a)
M_APM	r, a;
int	places;
{
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), a);

MM_skip_limit_PI_check = TRUE;
m_apm_cos(tmp7, (places + 4), tmp5);
MM_skip_limit_PI_check = FALSE;

/*
 *   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 + 4), tmp7);
if (tmp6->m_apm_sign != 0)
  tmp6->m_apm_sign = tmp5->m_apm_sign;
 
/* tan(x) = sin(x) / cos(x) */

m_apm_divide(tmp5, (places + 4), tmp6, tmp7);
m_apm_round(r, places, tmp5);
M_restore_stack(3);
}
/****************************************************************************/
void	M_limit_angle_to_pi(rr, places, aa)
M_APM	rr, aa;
int	places;
{
M_APM	tmp7, tmp8, tmp9;

if (MM_skip_limit_PI_check)
  {
   m_apm_copy(rr, aa);
   return;
  }

tmp9 = M_get_stack_var();
m_apm_copy(tmp9, MM_PI);

if (m_apm_compare(aa, tmp9) == 1)       /*  > PI  */
  {
   tmp7 = M_get_stack_var();
   tmp8 = M_get_stack_var();

   M_check_dec_places(M_LIMIT, places);
   m_apm_add(tmp7, aa, tmp9);
   m_apm_integer_divide(tmp9, tmp7, MM_2_PI);
   m_apm_multiply(tmp8, tmp9, MM_2_PI);
   m_apm_subtract(tmp9, aa, tmp8);
   m_apm_round(rr, places, tmp9);

   M_restore_stack(3);
   return;
  }

tmp9->m_apm_sign = -1;
if (m_apm_compare(aa, tmp9) == -1)       /*  < -PI  */
  {
   tmp7 = M_get_stack_var();
   tmp8 = M_get_stack_var();

   M_check_dec_places(M_LIMIT, places);
   m_apm_add(tmp7, aa, tmp9);
   m_apm_integer_divide(tmp9, tmp7, MM_2_PI);
   m_apm_multiply(tmp8, tmp9, MM_2_PI);
   m_apm_subtract(tmp9, aa, tmp8);
   m_apm_round(rr, places, tmp9);

   M_restore_stack(3);
   return;
  }

m_apm_copy(rr, aa);
M_restore_stack(1);
}
/****************************************************************************/
/*
 *   compute  r = sqrt(1 - a ^ 2).
 */
void	M_cos_to_sin(r,places,a)
M_APM	r, a;
int	places;
{
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);
}
/****************************************************************************/