mirror of
https://github.com/levinsv/pgadmin3.git
synced 2026-05-15 14:15:49 -06:00
430 lines
9.2 KiB
C++
430 lines
9.2 KiB
C++
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/*
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* M_APM - mapmasin.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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*
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* This file contains the 'ARC' family of functions; ARC-SIN, ARC-COS,
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* ARC-TAN, and ARC-TAN2.
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*
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*/
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#include "pgAdmin3.h"
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#include "pgscript/utilities/mapm-lib/m_apm_lc.h"
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/****************************************************************************/
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void m_apm_arctan2(M_APM rr, int places, M_APM yy, M_APM xx)
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{
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M_APM tmp5, tmp6, tmp7;
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int ix, iy;
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iy = yy->m_apm_sign;
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ix = xx->m_apm_sign;
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if (ix == 0) /* x == 0 */
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{
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if (iy == 0) /* y == 0 */
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{
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M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arctan2\', Both Inputs = 0");
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M_set_to_zero(rr);
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return;
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}
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M_check_PI_places(places);
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m_apm_round(rr, places, MM_lc_HALF_PI);
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rr->m_apm_sign = iy;
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return;
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}
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if (iy == 0)
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{
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if (ix == 1)
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{
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M_set_to_zero(rr);
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}
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else
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{
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M_check_PI_places(places);
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m_apm_round(rr, places, MM_lc_PI);
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}
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return;
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}
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/*
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* the special cases have been handled, now do the real work
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*/
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tmp5 = M_get_stack_var();
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tmp6 = M_get_stack_var();
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tmp7 = M_get_stack_var();
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m_apm_divide(tmp6, (places + 6), yy, xx);
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m_apm_arctan(tmp5, (places + 6), tmp6);
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if (ix == 1) /* 'x' is positive */
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{
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m_apm_round(rr, places, tmp5);
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}
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else /* 'x' is negative */
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{
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M_check_PI_places(places);
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if (iy == 1) /* 'y' is positive */
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{
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m_apm_add(tmp7, tmp5, MM_lc_PI);
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m_apm_round(rr, places, tmp7);
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}
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else /* 'y' is negative */
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{
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m_apm_subtract(tmp7, tmp5, MM_lc_PI);
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m_apm_round(rr, places, tmp7);
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}
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}
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M_restore_stack(3);
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}
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/****************************************************************************/
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/*
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Calculate arctan using the identity :
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x
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arctan (x) == arcsin [ --------------- ]
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sqrt(1 + x^2)
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*/
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void m_apm_arctan(M_APM rr, int places, M_APM xx)
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{
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M_APM tmp8, tmp9;
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if (xx->m_apm_sign == 0) /* input == 0 ?? */
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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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if (xx->m_apm_exponent <= -4) /* input close to 0 ?? */
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{
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M_arctan_near_0(rr, places, xx);
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return;
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}
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if (xx->m_apm_exponent >= 4) /* large input */
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{
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M_arctan_large_input(rr, places, xx);
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return;
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}
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tmp8 = M_get_stack_var();
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tmp9 = M_get_stack_var();
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m_apm_multiply(tmp9, xx, xx);
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m_apm_add(tmp8, tmp9, MM_One);
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m_apm_sqrt(tmp9, (places + 6), tmp8);
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m_apm_divide(tmp8, (places + 6), xx, tmp9);
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m_apm_arcsin(rr, places, tmp8);
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M_restore_stack(2);
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}
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/****************************************************************************/
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/*
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for large input values use :
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arctan(x) = (PI / 2) - arctan(1 / |x|)
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and sign of result = sign of original input
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*/
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void M_arctan_large_input(M_APM rr, int places, M_APM xx)
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{
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M_APM tmp1, tmp2;
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tmp1 = M_get_stack_var();
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tmp2 = M_get_stack_var();
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M_check_PI_places(places);
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m_apm_divide(tmp1, (places + 6), MM_One, xx); /* 1 / xx */
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tmp1->m_apm_sign = 1; /* make positive */
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m_apm_arctan(tmp2, (places + 6), tmp1);
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m_apm_subtract(tmp1, MM_lc_HALF_PI, tmp2);
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m_apm_round(rr, places, tmp1);
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rr->m_apm_sign = xx->m_apm_sign; /* fix final sign */
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M_restore_stack(2);
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}
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/****************************************************************************/
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void m_apm_arcsin(M_APM r, int places, M_APM x)
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{
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M_APM tmp0, tmp1, tmp2, tmp3, current_x;
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int ii, maxiter, maxp, tolerance, local_precision;
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current_x = M_get_stack_var();
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tmp0 = M_get_stack_var();
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tmp1 = M_get_stack_var();
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tmp2 = M_get_stack_var();
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tmp3 = M_get_stack_var();
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m_apm_absolute_value(tmp0, x);
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ii = m_apm_compare(tmp0, MM_One);
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if (ii == 1) /* |x| > 1 */
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{
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M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arcsin\', |Argument| > 1");
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M_set_to_zero(r);
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M_restore_stack(5);
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return;
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}
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if (ii == 0) /* |x| == 1, arcsin = +/- PI / 2 */
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{
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M_check_PI_places(places);
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m_apm_round(r, places, MM_lc_HALF_PI);
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r->m_apm_sign = x->m_apm_sign;
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M_restore_stack(5);
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return;
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}
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if (m_apm_compare(tmp0, MM_0_85) == 1) /* check if > 0.85 */
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{
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M_cos_to_sin(tmp2, (places + 4), x);
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m_apm_arccos(r, places, tmp2);
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r->m_apm_sign = x->m_apm_sign;
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M_restore_stack(5);
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return;
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}
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if (x->m_apm_sign == 0) /* input == 0 ?? */
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{
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M_set_to_zero(r);
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M_restore_stack(5);
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return;
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}
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if (x->m_apm_exponent <= -4) /* input close to 0 ?? */
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{
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M_arcsin_near_0(r, places, x);
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M_restore_stack(5);
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return;
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}
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tolerance = -(places + 4);
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maxp = places + 8 - x->m_apm_exponent;
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local_precision = 20 - x->m_apm_exponent;
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/*
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* compute the maximum number of iterations
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* that should be needed to calculate to
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* the desired accuracy. [ constant below ~= 1 / log(2) ]
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*/
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maxiter = (int)(log((double)(places + 2)) * 1.442695) + 3;
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if (maxiter < 5)
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maxiter = 5;
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M_get_asin_guess(current_x, x);
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/* Use the following iteration to solve for arc-sin :
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sin(X) - N
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X = X - ------------
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n+1 cos(X)
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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_4x_cos(tmp1, local_precision, current_x);
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M_cos_to_sin(tmp2, local_precision, tmp1);
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if (tmp2->m_apm_sign != 0)
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tmp2->m_apm_sign = current_x->m_apm_sign;
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m_apm_subtract(tmp3, tmp2, x);
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m_apm_divide(tmp0, local_precision, tmp3, tmp1);
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m_apm_subtract(tmp2, current_x, tmp0);
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m_apm_copy(current_x, tmp2);
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if (ii != 0)
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{
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if (((2 * tmp0->m_apm_exponent) < tolerance) || (tmp0->m_apm_sign == 0))
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break;
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}
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if (++ii == maxiter)
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{
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M_apm_log_error_msg(M_APM_RETURN,
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"\'m_apm_arcsin\', max iteration count reached");
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break;
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}
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local_precision *= 2;
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if (local_precision > maxp)
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local_precision = maxp;
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}
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m_apm_round(r, places, current_x);
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M_restore_stack(5);
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}
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/****************************************************************************/
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void m_apm_arccos(M_APM r, int places, M_APM x)
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{
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M_APM tmp0, tmp1, tmp2, tmp3, current_x;
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int ii, maxiter, maxp, tolerance, local_precision;
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current_x = M_get_stack_var();
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tmp0 = M_get_stack_var();
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tmp1 = M_get_stack_var();
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tmp2 = M_get_stack_var();
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tmp3 = M_get_stack_var();
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m_apm_absolute_value(tmp0, x);
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ii = m_apm_compare(tmp0, MM_One);
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if (ii == 1) /* |x| > 1 */
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{
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M_apm_log_error_msg(M_APM_RETURN, "\'m_apm_arccos\', |Argument| > 1");
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M_set_to_zero(r);
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M_restore_stack(5);
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return;
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}
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if (ii == 0) /* |x| == 1, arccos = 0, PI */
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{
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if (x->m_apm_sign == 1)
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{
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M_set_to_zero(r);
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}
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else
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{
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M_check_PI_places(places);
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m_apm_round(r, places, MM_lc_PI);
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}
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M_restore_stack(5);
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return;
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}
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if (m_apm_compare(tmp0, MM_0_85) == 1) /* check if > 0.85 */
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{
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M_cos_to_sin(tmp2, (places + 4), x);
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if (x->m_apm_sign == 1)
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{
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m_apm_arcsin(r, places, tmp2);
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}
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else
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{
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M_check_PI_places(places);
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m_apm_arcsin(tmp3, (places + 4), tmp2);
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m_apm_subtract(tmp1, MM_lc_PI, tmp3);
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m_apm_round(r, places, tmp1);
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}
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M_restore_stack(5);
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return;
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}
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if (x->m_apm_sign == 0) /* input == 0 ?? */
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{
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M_check_PI_places(places);
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m_apm_round(r, places, MM_lc_HALF_PI);
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M_restore_stack(5);
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return;
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}
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if (x->m_apm_exponent <= -4) /* input close to 0 ?? */
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{
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M_arccos_near_0(r, places, x);
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M_restore_stack(5);
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return;
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}
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tolerance = -(places + 4);
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maxp = places + 8;
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local_precision = 18;
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/*
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* compute the maximum number of iterations
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* that should be needed to calculate to
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* the desired accuracy. [ constant below ~= 1 / log(2) ]
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*/
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maxiter = (int)(log((double)(places + 2)) * 1.442695) + 3;
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if (maxiter < 5)
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maxiter = 5;
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M_get_acos_guess(current_x, x);
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/* Use the following iteration to solve for arc-cos :
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cos(X) - N
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X = X + ------------
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n+1 sin(X)
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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_4x_cos(tmp1, local_precision, current_x);
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M_cos_to_sin(tmp2, local_precision, tmp1);
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if (tmp2->m_apm_sign != 0)
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tmp2->m_apm_sign = current_x->m_apm_sign;
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m_apm_subtract(tmp3, tmp1, x);
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m_apm_divide(tmp0, local_precision, tmp3, tmp2);
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m_apm_add(tmp2, current_x, tmp0);
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m_apm_copy(current_x, tmp2);
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if (ii != 0)
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{
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if (((2 * tmp0->m_apm_exponent) < tolerance) || (tmp0->m_apm_sign == 0))
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break;
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}
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if (++ii == maxiter)
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{
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M_apm_log_error_msg(M_APM_RETURN,
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"\'m_apm_arccos\', max iteration count reached");
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break;
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}
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local_precision *= 2;
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if (local_precision > maxp)
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local_precision = maxp;
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}
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m_apm_round(r, places, current_x);
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M_restore_stack(5);
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}
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/****************************************************************************/
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