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
174 lines
4.2 KiB
C
174 lines
4.2 KiB
C
|
|
/*
|
|
* M_APM - mapm_cpi.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_cpi.c,v 1.4 2007/12/03 01:34:29 mike Exp $
|
|
*
|
|
* This file contains the PI related functions.
|
|
*
|
|
* $Log: mapm_cpi.c,v $
|
|
* Revision 1.4 2007/12/03 01:34:29 mike
|
|
* Update license
|
|
*
|
|
* Revision 1.3 2002/11/05 23:10:14 mike
|
|
* streamline the PI AGM algorithm
|
|
*
|
|
* Revision 1.2 2002/11/03 21:56:21 mike
|
|
* Updated function parameters to use the modern style
|
|
*
|
|
* Revision 1.1 2001/03/25 21:01:53 mike
|
|
* Initial revision
|
|
*/
|
|
|
|
#include "m_apm_lc.h"
|
|
|
|
/****************************************************************************/
|
|
/*
|
|
* check if our local copy of PI is precise enough
|
|
* for our purpose. if not, calculate PI so it's
|
|
* as precise as desired, accurate to 'places' decimal
|
|
* places.
|
|
*/
|
|
void M_check_PI_places(int places)
|
|
{
|
|
int dplaces;
|
|
|
|
dplaces = places + 2;
|
|
|
|
if (dplaces > MM_lc_PI_digits)
|
|
{
|
|
MM_lc_PI_digits = dplaces + 2;
|
|
|
|
/* compute PI using the AGM (see right below) */
|
|
|
|
M_calculate_PI_AGM(MM_lc_PI, (dplaces + 5));
|
|
|
|
m_apm_multiply(MM_lc_HALF_PI, MM_0_5, MM_lc_PI);
|
|
m_apm_multiply(MM_lc_2_PI, MM_Two, MM_lc_PI);
|
|
}
|
|
}
|
|
/****************************************************************************/
|
|
/*
|
|
* Calculate PI using the AGM (Arithmetic-Geometric Mean)
|
|
*
|
|
* Init : A0 = 1
|
|
* B0 = 1 / sqrt(2)
|
|
* Sum = 1
|
|
*
|
|
* Iterate: n = 1...
|
|
*
|
|
*
|
|
* A = 0.5 * [ A + B ]
|
|
* n n-1 n-1
|
|
*
|
|
*
|
|
* B = sqrt [ A * B ]
|
|
* n n-1 n-1
|
|
*
|
|
*
|
|
*
|
|
* C = 0.5 * [ A - B ]
|
|
* n n-1 n-1
|
|
*
|
|
*
|
|
* 2 n+1
|
|
* Sum = Sum - C * 2
|
|
* n
|
|
*
|
|
*
|
|
* At the end when C is 'small enough' :
|
|
* n
|
|
*
|
|
* 2
|
|
* PI = 4 * A / Sum
|
|
* n+1
|
|
*
|
|
* -OR-
|
|
*
|
|
* 2
|
|
* PI = ( A + B ) / Sum
|
|
* n n
|
|
*
|
|
*/
|
|
void M_calculate_PI_AGM(M_APM outv, int places)
|
|
{
|
|
M_APM tmp1, tmp2, a0, b0, c0, a1, b1, sum, pow_2;
|
|
int dplaces, nn;
|
|
|
|
tmp1 = M_get_stack_var();
|
|
tmp2 = M_get_stack_var();
|
|
a0 = M_get_stack_var();
|
|
b0 = M_get_stack_var();
|
|
c0 = M_get_stack_var();
|
|
a1 = M_get_stack_var();
|
|
b1 = M_get_stack_var();
|
|
sum = M_get_stack_var();
|
|
pow_2 = M_get_stack_var();
|
|
|
|
dplaces = places + 16;
|
|
|
|
m_apm_copy(a0, MM_One);
|
|
m_apm_copy(sum, MM_One);
|
|
m_apm_copy(pow_2, MM_Four);
|
|
m_apm_sqrt(b0, dplaces, MM_0_5); /* sqrt(0.5) */
|
|
|
|
while (TRUE)
|
|
{
|
|
m_apm_add(tmp1, a0, b0);
|
|
m_apm_multiply(a1, MM_0_5, tmp1);
|
|
|
|
m_apm_multiply(tmp1, a0, b0);
|
|
m_apm_sqrt(b1, dplaces, tmp1);
|
|
|
|
m_apm_subtract(tmp1, a0, b0);
|
|
m_apm_multiply(c0, MM_0_5, tmp1);
|
|
|
|
/*
|
|
* the net 'PI' calculated from this iteration will
|
|
* be accurate to ~4 X the value of (c0)'s exponent.
|
|
* this was determined experimentally.
|
|
*/
|
|
|
|
nn = -4 * c0->m_apm_exponent;
|
|
|
|
m_apm_multiply(tmp1, c0, c0);
|
|
m_apm_multiply(tmp2, tmp1, pow_2);
|
|
m_apm_subtract(tmp1, sum, tmp2);
|
|
m_apm_round(sum, dplaces, tmp1);
|
|
|
|
if (nn >= dplaces)
|
|
break;
|
|
|
|
m_apm_copy(a0, a1);
|
|
m_apm_copy(b0, b1);
|
|
|
|
m_apm_multiply(tmp1, pow_2, MM_Two);
|
|
m_apm_copy(pow_2, tmp1);
|
|
}
|
|
|
|
m_apm_add(tmp1, a1, b1);
|
|
m_apm_multiply(tmp2, tmp1, tmp1);
|
|
m_apm_divide(tmp1, dplaces, tmp2, sum);
|
|
m_apm_round(outv, places, tmp1);
|
|
|
|
M_restore_stack(9);
|
|
}
|
|
/****************************************************************************/
|