1 2 /* 3 * M_APM - mapm_lg4.c 4 * 5 * Copyright (C) 2003 - 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: mapm_lg4.c,v 1.3 2007/12/03 01:43:32 mike Exp $ 23 * 24 * This file contains the LOG_NEAR_1 function. 25 * 26 * $Log: mapm_lg4.c,v $ 27 * Revision 1.3 2007/12/03 01:43:32 mike 28 * Update license 29 * 30 * Revision 1.2 2003/06/02 18:08:45 mike 31 * tweak decimal places and add comments 32 * 33 * Revision 1.1 2003/06/02 17:27:26 mike 34 * Initial revision 35 */ 36 37 #include "m_apm_lc.h" 38 39 /****************************************************************************/ 40 /* 41 calculate log (1 + x) with the following series: 42 43 x 44 y = ----- ( |y| < 1 ) 45 x + 2 46 47 48 [ 1 + y ] y^3 y^5 y^7 49 log [-------] = 2 * [ y + --- + --- + --- ... ] 50 [ 1 - y ] 3 5 7 51 52 */ 53 void M_log_near_1(M_APM rr, int places, M_APM xx) 54 { 55 M_APM tmp0, tmp1, tmp2, tmpS, term; 56 int tolerance, dplaces, local_precision; 57 long m1; 58 59 tmp0 = M_get_stack_var(); 60 tmp1 = M_get_stack_var(); 61 tmp2 = M_get_stack_var(); 62 tmpS = M_get_stack_var(); 63 term = M_get_stack_var(); 64 65 tolerance = xx->m_apm_exponent - (places + 6); 66 dplaces = (places + 12) - xx->m_apm_exponent; 67 68 m_apm_add(tmp0, xx, MM_Two); 69 m_apm_divide(tmpS, (dplaces + 6), xx, tmp0); 70 71 m_apm_copy(term, tmpS); 72 m_apm_multiply(tmp0, tmpS, tmpS); 73 m_apm_round(tmp2, (dplaces + 6), tmp0); 74 75 m1 = 3L; 76 77 while (TRUE) 78 { 79 m_apm_multiply(tmp0, term, tmp2); 80 81 if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0)) 82 break; 83 84 local_precision = dplaces + tmp0->m_apm_exponent; 85 86 if (local_precision < 20) 87 local_precision = 20; 88 89 m_apm_set_long(tmp1, m1); 90 m_apm_round(term, local_precision, tmp0); 91 m_apm_divide(tmp0, local_precision, term, tmp1); 92 m_apm_add(tmp1, tmpS, tmp0); 93 m_apm_copy(tmpS, tmp1); 94 m1 += 2; 95 } 96 97 m_apm_multiply(tmp0, MM_Two, tmpS); 98 m_apm_round(rr, places, tmp0); 99 100 M_restore_stack(5); /* restore the 5 locals we used here */ 101 } 102 /****************************************************************************/ 103