59d799dabc
* Moved the ExpressionParser class to shared. It's now built into its own static library. * Added hexadecimal number support to the expression parser as well as Evaluation*() methods to get a number instead of a string. git-svn-id: file:///srv/svn/repos/haiku/haiku/trunk@31298 a95241bf-73f2-0310-859d-f6bbb57e9c96
191 lines
5.1 KiB
C
191 lines
5.1 KiB
C
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/*
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* M_APM - mapmsqrt.c
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*
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* Copyright (C) 1999 - 2007 Michael C. Ring
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*
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* Permission to use, copy, and distribute this software and its
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* documentation for any purpose with or without fee is hereby granted,
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* provided that the above copyright notice appear in all copies and
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* that both that copyright notice and this permission notice appear
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* in supporting documentation.
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*
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* Permission to modify the software is granted. Permission to distribute
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* the modified code is granted. Modifications are to be distributed by
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* using the file 'license.txt' as a template to modify the file header.
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* 'license.txt' is available in the official MAPM distribution.
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*
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* This software is provided "as is" without express or implied warranty.
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*/
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/*
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* $Id: mapmsqrt.c,v 1.19 2007/12/03 01:57:31 mike Exp $
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*
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* This file contains the SQRT function.
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*
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* $Log: mapmsqrt.c,v $
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* Revision 1.19 2007/12/03 01:57:31 mike
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* Update license
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*
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* Revision 1.18 2003/07/21 20:39:00 mike
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* Modify error messages to be in a consistent format.
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*
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* Revision 1.17 2003/05/07 16:36:04 mike
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* simplify 'nexp' logic
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*
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* Revision 1.16 2003/03/31 21:50:14 mike
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* call generic error handling function
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*
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* Revision 1.15 2003/03/11 21:29:00 mike
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* round an intermediate result for faster runtime.
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*
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* Revision 1.14 2002/11/03 22:00:46 mike
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* Updated function parameters to use the modern style
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*
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* Revision 1.13 2001/07/10 22:50:31 mike
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* minor optimization
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*
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* Revision 1.12 2000/09/26 18:32:04 mike
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* use new algorithm which only uses multiply and subtract
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* (avoids the slower version which used division)
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*
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* Revision 1.11 2000/07/11 17:56:22 mike
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* make better estimate for initial precision
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*
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* Revision 1.10 1999/07/21 02:48:45 mike
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* added some comments
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*
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* Revision 1.9 1999/07/19 00:25:44 mike
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* adjust local precision again
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*
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* Revision 1.8 1999/07/19 00:09:41 mike
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* adjust local precision during loop
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*
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* Revision 1.7 1999/07/18 22:57:08 mike
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* change to dynamically changing local precision and
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* change tolerance checks using integers
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*
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* Revision 1.6 1999/06/19 21:18:00 mike
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* changed local static variables to MAPM stack variables
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*
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* Revision 1.5 1999/05/31 01:40:39 mike
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* minor update to normalizing the exponent
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*
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* Revision 1.4 1999/05/31 01:21:41 mike
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* optimize for large exponents
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*
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* Revision 1.3 1999/05/12 20:59:35 mike
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* use a better 'guess' function
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*
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* Revision 1.2 1999/05/10 21:15:26 mike
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* added some comments
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*
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* Revision 1.1 1999/05/10 20:56:31 mike
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* Initial revision
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*/
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#include "m_apm_lc.h"
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/****************************************************************************/
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void m_apm_sqrt(M_APM rr, int places, M_APM aa)
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{
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M_APM last_x, guess, tmpN, tmp7, tmp8, tmp9;
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int ii, bflag, nexp, tolerance, dplaces;
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if (aa->m_apm_sign <= 0)
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{
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if (aa->m_apm_sign == -1)
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{
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M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_sqrt\', Negative argument");
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}
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M_set_to_zero(rr);
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return;
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}
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last_x = M_get_stack_var();
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guess = M_get_stack_var();
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tmpN = M_get_stack_var();
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tmp7 = M_get_stack_var();
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tmp8 = M_get_stack_var();
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tmp9 = M_get_stack_var();
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m_apm_copy(tmpN, aa);
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/*
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normalize the input number (make the exponent near 0) so
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the 'guess' function will not over/under flow on large
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magnitude exponents.
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*/
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nexp = aa->m_apm_exponent / 2;
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tmpN->m_apm_exponent -= 2 * nexp;
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M_get_sqrt_guess(guess, tmpN); /* actually gets 1/sqrt guess */
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tolerance = places + 4;
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dplaces = places + 16;
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bflag = FALSE;
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m_apm_negate(last_x, MM_Ten);
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/* Use the following iteration to calculate 1 / sqrt(N) :
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X = 0.5 * X * [ 3 - N * X^2 ]
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n+1
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*/
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ii = 0;
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while (TRUE)
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{
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m_apm_multiply(tmp9, tmpN, guess);
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m_apm_multiply(tmp8, tmp9, guess);
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m_apm_round(tmp7, dplaces, tmp8);
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m_apm_subtract(tmp9, MM_Three, tmp7);
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m_apm_multiply(tmp8, tmp9, guess);
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m_apm_multiply(tmp9, tmp8, MM_0_5);
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if (bflag)
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break;
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m_apm_round(guess, dplaces, tmp9);
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/* force at least 2 iterations so 'last_x' has valid data */
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if (ii != 0)
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{
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m_apm_subtract(tmp7, guess, last_x);
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if (tmp7->m_apm_sign == 0)
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break;
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/*
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* if we are within a factor of 4 on the error term,
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* we will be accurate enough after the *next* iteration
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* is complete. (note that the sign of the exponent on
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* the error term will be a negative number).
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*/
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if ((-4 * tmp7->m_apm_exponent) > tolerance)
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bflag = TRUE;
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}
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m_apm_copy(last_x, guess);
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ii++;
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}
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/*
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* multiply by the starting number to get the final
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* sqrt and then adjust the exponent since we found
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* the sqrt of the normalized number.
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*/
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m_apm_multiply(tmp8, tmp9, tmpN);
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m_apm_round(rr, places, tmp8);
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rr->m_apm_exponent += nexp;
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M_restore_stack(6);
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}
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/****************************************************************************/
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