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 */ 58 void m_apm_arcsinh(M_APM rr, int places, M_APM aa) 59 { 60 M_APM tmp0, tmp1, tmp2; 61 62 /* result is 0 if input is 0 */ 63 64 if (aa->m_apm_sign == 0) 65 { 66 M_set_to_zero(rr); 67 return; 68 } 69 70 tmp0 = M_get_stack_var(); 71 tmp1 = M_get_stack_var(); 72 tmp2 = M_get_stack_var(); 73 74 m_apm_absolute_value(tmp0, aa); 75 m_apm_multiply(tmp1, tmp0, tmp0); 76 m_apm_add(tmp2, tmp1, MM_One); 77 m_apm_sqrt(tmp1, (places + 6), tmp2); 78 m_apm_add(tmp2, tmp0, tmp1); 79 m_apm_log(rr, places, tmp2); 80 81 rr->m_apm_sign = aa->m_apm_sign; /* fix final sign */ 82 83 M_restore_stack(3); 84 } 85 /****************************************************************************/ 86 /* 87 * arccosh(x) == log [ x + sqrt(x^2 - 1) ] 88 * 89 * x >= 1.0 90 */ 91 void m_apm_arccosh(M_APM rr, int places, M_APM aa) 92 { 93 M_APM tmp1, tmp2; 94 int ii; 95 96 ii = m_apm_compare(aa, MM_One); 97 98 if (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 } 104 105 tmp1 = M_get_stack_var(); 106 tmp2 = M_get_stack_var(); 107 108 m_apm_multiply(tmp1, aa, aa); 109 m_apm_subtract(tmp2, tmp1, MM_One); 110 m_apm_sqrt(tmp1, (places + 6), tmp2); 111 m_apm_add(tmp2, aa, tmp1); 112 m_apm_log(rr, places, tmp2); 113 114 M_restore_stack(2); 115 } 116 /****************************************************************************/ 117 /* 118 * arctanh(x) == 0.5 * log [ (1 + x) / (1 - x) ] 119 * 120 * |x| < 1.0 121 */ 122 void m_apm_arctanh(M_APM rr, int places, M_APM aa) 123 { 124 M_APM tmp1, tmp2, tmp3; 125 int ii, local_precision; 126 127 tmp1 = M_get_stack_var(); 128 129 m_apm_absolute_value(tmp1, aa); 130 131 ii = m_apm_compare(tmp1, MM_One); 132 133 if (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 } 140 141 tmp2 = M_get_stack_var(); 142 tmp3 = M_get_stack_var(); 143 144 local_precision = places + 8; 145 146 m_apm_add(tmp1, MM_One, aa); 147 m_apm_subtract(tmp2, MM_One, aa); 148 m_apm_divide(tmp3, local_precision, tmp1, tmp2); 149 m_apm_log(tmp2, local_precision, tmp3); 150 m_apm_multiply(tmp1, tmp2, MM_0_5); 151 m_apm_round(rr, places, tmp1); 152 153 M_restore_stack(3); 154 } 155 /****************************************************************************/ 156