/* * M_APM - mapm_log.c * * Copyright (C) 1999 - 2003 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, but not the right to * distribute the modified code. Modifications are to be distributed * as patches to released version. * * This software is provided "as is" without express or implied warranty. */ /* * $Id: mapm_log.c,v 1.2 2003/05/01 12:46:55 alby Exp $ * * This file contains the LOG and LOG10 functions. * * $Log: mapm_log.c,v $ * Revision 1.2 2003/05/01 12:46:55 alby * - Updated MAPM to version 4.6.1 * - The MAPM class is now thread-safe * * 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" #include /****************************************************************************/ /* 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, "Warning! ... \'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 */ 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); mexp = a->m_apm_exponent; if (mexp >= -4 && mexp <= 4) { 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 */ } /****************************************************************************/ /* calculate log (1 + x) with the following series: x y = ----- ( |y| < 1 ) x + 2 [ 1 + y ] y^3 y^5 y^7 log [-------] = 2 * [ y + --- + --- + --- ... ] [ 1 - y ] 3 5 7 */ void M_log_near_1(M_APM rr, int places, M_APM xx) { M_APM tmp0, tmp1, tmp2, tmpS, term; int tolerance, local_precision; long m1; tmp0 = M_get_stack_var(); tmp1 = M_get_stack_var(); tmp2 = M_get_stack_var(); tmpS = M_get_stack_var(); term = M_get_stack_var(); tolerance = xx->m_apm_exponent - places - 4; local_precision = places + 8 - xx->m_apm_exponent; m_apm_add(tmp0, xx, MM_Two); m_apm_divide(tmpS, (local_precision + 6), xx, tmp0); m_apm_copy(term, tmpS); m_apm_multiply(tmp0, tmpS, tmpS); m_apm_round(tmp2, (local_precision + 6), tmp0); m1 = 3; while (TRUE) { m_apm_set_long(tmp1, m1); m_apm_multiply(tmp0, term, tmp2); m_apm_round(term, local_precision, tmp0); m_apm_divide(tmp0, local_precision, term, tmp1); m_apm_add(tmp1, tmpS, tmp0); if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0)) break; m_apm_copy(tmpS, tmp1); m1 += 2; } m_apm_multiply(tmp0, MM_Two, tmp1); m_apm_round(rr, places, tmp0); M_restore_stack(5); /* restore the 5 locals we used here */ } /****************************************************************************/