/* * M_APM - mapm_log.c * * Copyright (C) 1999 - 2007 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. Permission to distribute * the modified code is granted. Modifications are to be distributed by * using the file 'license.txt' as a template to modify the file header. * 'license.txt' is available in the official MAPM distribution. * * This software is provided "as is" without express or implied warranty. */ /* * $Id: mapm_log.c,v 1.29 2007/12/03 01:44:19 mike Exp $ * * This file contains the LOG and LOG10 functions. * * $Log: mapm_log.c,v $ * Revision 1.29 2007/12/03 01:44:19 mike * Update license * * Revision 1.28 2003/07/21 20:18:06 mike * Modify error messages to be in a consistent format. * * Revision 1.27 2003/06/02 17:22:46 mike * put 'log_near_1' into it's own separate module * * Revision 1.26 2003/05/12 17:42:46 mike * only check for 'near 1' if exponent is 0 or 1 * * Revision 1.25 2003/05/04 21:08:25 mike * *** empty log message *** * * Revision 1.24 2003/05/01 21:58:34 mike * remove math.h * * Revision 1.23 2003/05/01 21:39:09 mike * use 'abs' call * * Revision 1.22 2003/05/01 19:44:57 mike * optimize log_near_1 by calculating fewer digits * on subsequent iterations * * Revision 1.21 2003/03/31 22:00:56 mike * call generic error handling function * * Revision 1.20 2003/03/30 22:57:13 mike * call a new iterative log function which is cubically convergent * * Revision 1.19 2002/11/03 22:14:45 mike * Updated function parameters to use the modern style * * Revision 1.18 2001/07/16 19:21:16 mike * add function M_free_all_log * * Revision 1.17 2000/10/22 00:24:29 mike * minor optimization * * Revision 1.16 2000/10/21 16:22:50 mike * use an improved log_near_1 algorithm * * Revision 1.15 2000/10/20 16:49:33 mike * update algorithm for basic log function and add new * function when input is close to '1' * * Revision 1.14 2000/09/23 19:48:21 mike * change divide call to reciprocal * * Revision 1.13 2000/07/11 18:58:35 mike * do it right this time * * Revision 1.12 2000/07/11 18:19:27 mike * estimate a better initial precision * * Revision 1.11 2000/05/19 16:14:15 mike * update some comments * * Revision 1.10 2000/05/17 23:47:35 mike * recompute a local copy of log E base 10 on the fly * if more precision is needed. * * Revision 1.9 2000/03/27 21:44:12 mike * determine how many iterations should be required at * run time for log * * Revision 1.8 1999/07/21 02:56:18 mike * added some comments * * Revision 1.7 1999/07/19 00:28:51 mike * adjust local precision again * * Revision 1.6 1999/07/19 00:10:34 mike * adjust local precision during iterative loop * * Revision 1.5 1999/07/18 23:15:54 mike * change local precision dynamically and change * tolerance to integers for faster iterative routine. * * Revision 1.4 1999/06/19 21:08:32 mike * changed local static variables to MAPM stack variables * * Revision 1.3 1999/05/15 01:34:50 mike * add check for number of decimal places * * Revision 1.2 1999/05/10 21:42:32 mike * added some comments * * Revision 1.1 1999/05/10 20:56:31 mike * Initial revision */ #include "m_apm_lc.h" /****************************************************************************/ /* Calls the LOG function. The formula used is : log10(x) = A * log(x) where A = log (e) [0.43429448190325...] 10 */ void m_apm_log10(M_APM rr, int places, M_APM aa) { int dplaces; M_APM tmp8, tmp9; tmp8 = M_get_stack_var(); tmp9 = M_get_stack_var(); dplaces = places + 4; M_check_log_places(dplaces + 45); m_apm_log(tmp9, dplaces, aa); m_apm_multiply(tmp8, tmp9, MM_lc_log10R); m_apm_round(rr, places, tmp8); M_restore_stack(2); /* restore the 2 locals we used here */ } /****************************************************************************/ void m_apm_log(M_APM r, int places, M_APM a) { M_APM tmp0, tmp1, tmp2; int mexp, dplaces; if (a->m_apm_sign <= 0) { M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_log\', Negative argument"); M_set_to_zero(r); return; } tmp0 = M_get_stack_var(); tmp1 = M_get_stack_var(); tmp2 = M_get_stack_var(); dplaces = places + 8; /* * if the input is real close to 1, use the series expansion * to compute the log. * * 0.9999 < a < 1.0001 */ mexp = a->m_apm_exponent; if (mexp == 0 || mexp == 1) { m_apm_subtract(tmp0, a, MM_One); if (tmp0->m_apm_sign == 0) /* is input exactly 1 ?? */ { /* if so, result is 0 */ M_set_to_zero(r); M_restore_stack(3); return; } if (tmp0->m_apm_exponent <= -4) { M_log_near_1(r, places, tmp0); M_restore_stack(3); return; } } /* make sure our log(10) is accurate enough for this calculation */ /* (and log(2) which is called from M_log_basic_iteration) */ M_check_log_places(dplaces + 25); if (abs(mexp) <= 3) { M_log_basic_iteration(r, places, a); } else { /* * use log (x * y) = log(x) + log(y) * * here we use y = exponent of our base 10 number. * * let 'C' = log(10) = 2.3025850929940.... * * then log(x * y) = log(x) + ( C * base_10_exponent ) */ m_apm_copy(tmp2, a); mexp = tmp2->m_apm_exponent - 2; tmp2->m_apm_exponent = 2; /* force number between 10 & 100 */ M_log_basic_iteration(tmp0, dplaces, tmp2); m_apm_set_long(tmp1, (long)mexp); m_apm_multiply(tmp2, tmp1, MM_lc_log10); m_apm_add(tmp1, tmp2, tmp0); m_apm_round(r, places, tmp1); } M_restore_stack(3); /* restore the 3 locals we used here */ } /****************************************************************************/