mirror of
https://github.com/levinsv/pgadmin3.git
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157 lines
3.9 KiB
C++
157 lines
3.9 KiB
C++
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/*
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* M_APM - mapmasn0.c
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*
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* Copyright (C) 2000 - 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,
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* ARC-COS, ARC-TAN when the input arg is very close to 0 (zero).
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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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/*
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Calculate arcsin using the identity :
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x
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arcsin (x) == arctan [ --------------- ]
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sqrt(1 - x^2)
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*/
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void M_arcsin_near_0(M_APM rr, int places, M_APM aa)
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{
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M_APM tmp5, tmp6;
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tmp5 = M_get_stack_var();
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tmp6 = M_get_stack_var();
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M_cos_to_sin(tmp5, (places + 8), aa);
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m_apm_divide(tmp6, (places + 8), aa, tmp5);
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M_arctan_near_0(rr, places, tmp6);
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M_restore_stack(2);
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}
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/****************************************************************************/
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/*
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Calculate arccos using the identity :
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arccos (x) == PI / 2 - arcsin (x)
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*/
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void M_arccos_near_0(M_APM rr, int places, M_APM aa)
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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_arcsin_near_0(tmp1, (places + 4), aa);
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m_apm_subtract(tmp2, MM_lc_HALF_PI, tmp1);
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m_apm_round(rr, places, tmp2);
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M_restore_stack(2);
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}
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/****************************************************************************/
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/*
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calculate arctan (x) with the following series:
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x^3 x^5 x^7 x^9
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arctan (x) = x - --- + --- - --- + --- ...
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3 5 7 9
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*/
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void M_arctan_near_0(M_APM rr, int places, M_APM aa)
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{
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M_APM tmp0, tmp2, tmpR, tmpS, digit, term;
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int tolerance, dplaces, local_precision;
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long m1;
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tmp0 = M_get_stack_var();
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tmp2 = M_get_stack_var();
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tmpR = M_get_stack_var();
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tmpS = M_get_stack_var();
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term = M_get_stack_var();
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digit = M_get_stack_var();
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tolerance = aa->m_apm_exponent - (places + 4);
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dplaces = (places + 8) - aa->m_apm_exponent;
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m_apm_copy(term, aa);
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m_apm_copy(tmpS, aa);
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m_apm_multiply(tmp0, aa, aa);
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m_apm_round(tmp2, (dplaces + 8), tmp0);
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m1 = 1L;
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while (TRUE)
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{
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/*
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* do the subtraction term
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*/
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m_apm_multiply(tmp0, term, tmp2);
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if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0))
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{
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m_apm_round(rr, places, tmpS);
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break;
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}
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local_precision = dplaces + tmp0->m_apm_exponent;
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if (local_precision < 20)
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local_precision = 20;
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m1 += 2;
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m_apm_set_long(digit, m1);
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m_apm_round(term, local_precision, tmp0);
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m_apm_divide(tmp0, local_precision, term, digit);
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m_apm_subtract(tmpR, tmpS, tmp0);
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/*
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* do the addition term
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*/
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m_apm_multiply(tmp0, term, tmp2);
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if ((tmp0->m_apm_exponent < tolerance) || (tmp0->m_apm_sign == 0))
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{
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m_apm_round(rr, places, tmpR);
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break;
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}
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local_precision = dplaces + tmp0->m_apm_exponent;
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if (local_precision < 20)
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local_precision = 20;
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m1 += 2;
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m_apm_set_long(digit, m1);
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m_apm_round(term, local_precision, tmp0);
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m_apm_divide(tmp0, local_precision, term, digit);
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m_apm_add(tmpS, tmpR, tmp0);
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}
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M_restore_stack(6); /* restore the 6 locals we used here */
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}
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/****************************************************************************/
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