1
2/*
3 *  M_APM  -  mapmhasn.c
4 *
5 *  Copyright (C) 2000 - 2007   Michael C. Ring
6 *
7 *  Permission to use, copy, and distribute this software and its
8 *  documentation for any purpose with or without fee is hereby granted,
9 *  provided that the above copyright notice appear in all copies and
10 *  that both that copyright notice and this permission notice appear
11 *  in supporting documentation.
12 *
13 *  Permission to modify the software is granted. Permission to distribute
14 *  the modified code is granted. Modifications are to be distributed by
15 *  using the file 'license.txt' as a template to modify the file header.
16 *  'license.txt' is available in the official MAPM distribution.
17 *
18 *  This software is provided "as is" without express or implied warranty.
19 */
20
21/*
22 *      $Id: mapmhasn.c,v 1.7 2007/12/03 01:53:33 mike Exp $
23 *
24 *      This file contains the Inverse Hyperbolic SIN, COS, & TAN functions.
25 *
26 *      $Log: mapmhasn.c,v $
27 *      Revision 1.7  2007/12/03 01:53:33  mike
28 *      Update license
29 *
30 *      Revision 1.6  2003/07/24 16:28:50  mike
31 *      update arcsinh
32 *
33 *      Revision 1.5  2003/07/23 23:08:27  mike
34 *      fix problem with arcsinh when input is a very large
35 *      negative number.
36 *
37 *      Revision 1.4  2003/07/21 20:36:33  mike
38 *      Modify error messages to be in a consistent format.
39 *
40 *      Revision 1.3  2003/03/31 21:53:21  mike
41 *      call generic error handling function
42 *
43 *      Revision 1.2  2002/11/03 21:25:03  mike
44 *      Updated function parameters to use the modern style
45 *
46 *      Revision 1.1  2000/04/03 18:16:29  mike
47 *      Initial revision
48 */
49
50#include "m_apm_lc.h"
51
52/****************************************************************************/
53/*
54 *      arcsinh(x) == log [ x + sqrt(x^2 + 1) ]
55 *
56 *      also, use arcsinh(-x) == -arcsinh(x)
57 */
58void	m_apm_arcsinh(M_APM rr, int places, M_APM aa)
59{
60M_APM	tmp0, tmp1, tmp2;
61
62/* result is 0 if input is 0 */
63
64if (aa->m_apm_sign == 0)
65  {
66   M_set_to_zero(rr);
67   return;
68  }
69
70tmp0 = M_get_stack_var();
71tmp1 = M_get_stack_var();
72tmp2 = M_get_stack_var();
73
74m_apm_absolute_value(tmp0, aa);
75m_apm_multiply(tmp1, tmp0, tmp0);
76m_apm_add(tmp2, tmp1, MM_One);
77m_apm_sqrt(tmp1, (places + 6), tmp2);
78m_apm_add(tmp2, tmp0, tmp1);
79m_apm_log(rr, places, tmp2);
80
81rr->m_apm_sign = aa->m_apm_sign; 			  /* fix final sign */
82
83M_restore_stack(3);
84}
85/****************************************************************************/
86/*
87 *      arccosh(x) == log [ x + sqrt(x^2 - 1) ]
88 *
89 *      x >= 1.0
90 */
91void	m_apm_arccosh(M_APM rr, int places, M_APM aa)
92{
93M_APM	tmp1, tmp2;
94int     ii;
95
96ii = m_apm_compare(aa, MM_One);
97
98if (ii == -1)       /* x < 1 */
99  {
100   M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arccosh\', Argument < 1");
101   M_set_to_zero(rr);
102   return;
103  }
104
105tmp1 = M_get_stack_var();
106tmp2 = M_get_stack_var();
107
108m_apm_multiply(tmp1, aa, aa);
109m_apm_subtract(tmp2, tmp1, MM_One);
110m_apm_sqrt(tmp1, (places + 6), tmp2);
111m_apm_add(tmp2, aa, tmp1);
112m_apm_log(rr, places, tmp2);
113
114M_restore_stack(2);
115}
116/****************************************************************************/
117/*
118 *      arctanh(x) == 0.5 * log [ (1 + x) / (1 - x) ]
119 *
120 *      |x| < 1.0
121 */
122void	m_apm_arctanh(M_APM rr, int places, M_APM aa)
123{
124M_APM	tmp1, tmp2, tmp3;
125int     ii, local_precision;
126
127tmp1 = M_get_stack_var();
128
129m_apm_absolute_value(tmp1, aa);
130
131ii = m_apm_compare(tmp1, MM_One);
132
133if (ii >= 0)       /* |x| >= 1.0 */
134  {
135   M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arctanh\', |Argument| >= 1");
136   M_set_to_zero(rr);
137   M_restore_stack(1);
138   return;
139  }
140
141tmp2 = M_get_stack_var();
142tmp3 = M_get_stack_var();
143
144local_precision = places + 8;
145
146m_apm_add(tmp1, MM_One, aa);
147m_apm_subtract(tmp2, MM_One, aa);
148m_apm_divide(tmp3, local_precision, tmp1, tmp2);
149m_apm_log(tmp2, local_precision, tmp3);
150m_apm_multiply(tmp1, tmp2, MM_0_5);
151m_apm_round(rr, places, tmp1);
152
153M_restore_stack(3);
154}
155/****************************************************************************/
156