1 2 /* 3 * M_APM - mapmasn0.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: mapmasn0.c,v 1.8 2007/12/03 01:49:49 mike Exp $ 23 * 24 * This file contains the 'ARC' family of functions; ARC-SIN, 25 * ARC-COS, ARC-TAN when the input arg is very close to 0 (zero). 26 * 27 * $Log: mapmasn0.c,v $ 28 * Revision 1.8 2007/12/03 01:49:49 mike 29 * Update license 30 * 31 * Revision 1.7 2003/06/02 16:51:13 mike 32 * *** empty log message *** 33 * 34 * Revision 1.6 2003/06/02 16:49:48 mike 35 * tweak the decimal places 36 * 37 * Revision 1.5 2003/06/02 16:47:39 mike 38 * tweak arctan algorithm some more 39 * 40 * Revision 1.4 2003/05/31 22:38:07 mike 41 * optimize arctan by using fewer digits as subsequent 42 * terms get smaller 43 * 44 * Revision 1.3 2002/11/03 21:36:43 mike 45 * Updated function parameters to use the modern style 46 * 47 * Revision 1.2 2000/12/02 20:11:37 mike 48 * add comments 49 * 50 * Revision 1.1 2000/12/02 20:08:27 mike 51 * Initial revision 52 */ 53 54 #include "m_apm_lc.h" 55 56 /****************************************************************************/ 57 /* 58 Calculate arcsin using the identity : 59 60 x 61 arcsin (x) == arctan [ --------------- ] 62 sqrt(1 - x^2) 63 64 */ 65 void M_arcsin_near_0(M_APM rr, int places, M_APM aa) 66 { 67 M_APM tmp5, tmp6; 68 69 tmp5 = M_get_stack_var(); 70 tmp6 = M_get_stack_var(); 71 72 M_cos_to_sin(tmp5, (places + 8), aa); 73 m_apm_divide(tmp6, (places + 8), aa, tmp5); 74 M_arctan_near_0(rr, places, tmp6); 75 76 M_restore_stack(2); 77 } 78 /****************************************************************************/ 79 /* 80 Calculate arccos using the identity : 81 82 arccos (x) == PI / 2 - arcsin (x) 83 84 */ 85 void M_arccos_near_0(M_APM rr, int places, M_APM aa) 86 { 87 M_APM tmp1, tmp2; 88 89 tmp1 = M_get_stack_var(); 90 tmp2 = M_get_stack_var(); 91 92 M_check_PI_places(places); 93 M_arcsin_near_0(tmp1, (places + 4), aa); 94 m_apm_subtract(tmp2, MM_lc_HALF_PI, tmp1); 95 m_apm_round(rr, places, tmp2); 96 97 M_restore_stack(2); 98 } 99 /****************************************************************************/ 100 /* 101 calculate arctan (x) with the following series: 102 103 x^3 x^5 x^7 x^9 104 arctan (x) = x - --- + --- - --- + --- ... 105 3 5 7 9 106 107 */ 108 void M_arctan_near_0(M_APM rr, int places, M_APM aa) 109 { 110 M_APM tmp0, tmp2, tmpR, tmpS, digit, term; 111 int tolerance, dplaces, local_precision; 112 long m1; 113 114 tmp0 = M_get_stack_var(); 115 tmp2 = M_get_stack_var(); 116 tmpR = M_get_stack_var(); 117 tmpS = M_get_stack_var(); 118 term = M_get_stack_var(); 119 digit = M_get_stack_var(); 120 121 tolerance = aa->m_apm_exponent - (places + 4); 122 dplaces = (places + 8) - aa->m_apm_exponent; 123 124 m_apm_copy(term, aa); 125 m_apm_copy(tmpS, aa); 126 m_apm_multiply(tmp0, aa, aa); 127 m_apm_round(tmp2, (dplaces + 8), tmp0); 128 129 m1 = 1L; 130 131 while (TRUE) 132 { 133 /* 134 * do the subtraction term 135 */ 136 137 m_apm_multiply(tmp0, term, tmp2); 138 139 if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0)) 140 { 141 m_apm_round(rr, places, tmpS); 142 break; 143 } 144 145 local_precision = dplaces + tmp0->m_apm_exponent; 146 147 if (local_precision < 20) 148 local_precision = 20; 149 150 m1 += 2; 151 m_apm_set_long(digit, m1); 152 m_apm_round(term, local_precision, tmp0); 153 m_apm_divide(tmp0, local_precision, term, digit); 154 m_apm_subtract(tmpR, tmpS, tmp0); 155 156 /* 157 * do the addition term 158 */ 159 160 m_apm_multiply(tmp0, term, tmp2); 161 162 if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0)) 163 { 164 m_apm_round(rr, places, tmpR); 165 break; 166 } 167 168 local_precision = dplaces + tmp0->m_apm_exponent; 169 170 if (local_precision < 20) 171 local_precision = 20; 172 173 m1 += 2; 174 m_apm_set_long(digit, m1); 175 m_apm_round(term, local_precision, tmp0); 176 m_apm_divide(tmp0, local_precision, term, digit); 177 m_apm_add(tmpS, tmpR, tmp0); 178 } 179 180 M_restore_stack(6); /* restore the 6 locals we used here */ 181 } 182 /****************************************************************************/ 183