mirror of
https://github.com/levinsv/pgadmin3.git
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154 lines
4.2 KiB
C++
154 lines
4.2 KiB
C++
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/*
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* M_APM - mapm5sin.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 functions that implement the sin (5x)
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* and cos (4x) multiple angle relations
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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_5x_sin(M_APM r, int places, M_APM x)
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{
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M_APM tmp8, tmp9;
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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, x, MM_5x_125R); /* 1 / (5*5*5) */
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M_raw_sin(tmp8, (places + 6), tmp9);
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M_5x_do_it(tmp9, (places + 4), tmp8);
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M_5x_do_it(tmp8, (places + 4), tmp9);
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M_5x_do_it(r, places, tmp8);
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M_restore_stack(2);
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}
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/****************************************************************************/
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void M_4x_cos(M_APM r, int places, M_APM x)
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{
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M_APM tmp8, tmp9;
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tmp8 = M_get_stack_var();
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tmp9 = M_get_stack_var();
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/*
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* if |x| >= 1.0 use multiple angle identity 4 times
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* if |x| < 1.0 use multiple angle identity 3 times
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*/
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if (x->m_apm_exponent > 0)
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{
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m_apm_multiply(tmp9, x, MM_5x_256R); /* 1 / (4*4*4*4) */
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M_raw_cos(tmp8, (places + 8), tmp9);
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M_4x_do_it(tmp9, (places + 8), tmp8);
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M_4x_do_it(tmp8, (places + 6), tmp9);
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M_4x_do_it(tmp9, (places + 4), tmp8);
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M_4x_do_it(r, places, tmp9);
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}
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else
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{
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m_apm_multiply(tmp9, x, MM_5x_64R); /* 1 / (4*4*4) */
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M_raw_cos(tmp8, (places + 6), tmp9);
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M_4x_do_it(tmp9, (places + 4), tmp8);
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M_4x_do_it(tmp8, (places + 4), tmp9);
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M_4x_do_it(r, places, tmp8);
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}
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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 the multiple angle identity for sin (5x)
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*
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* sin (5x) == 16 * sin^5 (x) - 20 * sin^3 (x) + 5 * sin(x)
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*/
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void M_5x_do_it(M_APM rr, int places, M_APM xx)
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{
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M_APM tmp0, tmp1, t2, t3, t5;
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tmp0 = M_get_stack_var();
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tmp1 = M_get_stack_var();
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t2 = M_get_stack_var();
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t3 = M_get_stack_var();
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t5 = M_get_stack_var();
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m_apm_multiply(tmp1, xx, xx);
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m_apm_round(t2, (places + 4), tmp1); /* x ^ 2 */
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m_apm_multiply(tmp1, t2, xx);
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m_apm_round(t3, (places + 4), tmp1); /* x ^ 3 */
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m_apm_multiply(t5, t2, t3); /* x ^ 5 */
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m_apm_multiply(tmp0, xx, MM_Five);
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m_apm_multiply(tmp1, t5, MM_5x_Sixteen);
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m_apm_add(t2, tmp0, tmp1);
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m_apm_multiply(tmp1, t3, MM_5x_Twenty);
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m_apm_subtract(tmp0, t2, tmp1);
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m_apm_round(rr, places, tmp0);
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M_restore_stack(5);
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}
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/****************************************************************************/
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/*
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* calculate the multiple angle identity for cos (4x)
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*
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* cos (4x) == 8 * [ cos^4 (x) - cos^2 (x) ] + 1
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*/
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void M_4x_do_it(M_APM rr, int places, M_APM xx)
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{
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M_APM tmp0, tmp1, t2, t4;
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tmp0 = M_get_stack_var();
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tmp1 = M_get_stack_var();
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t2 = M_get_stack_var();
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t4 = M_get_stack_var();
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m_apm_multiply(tmp1, xx, xx);
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m_apm_round(t2, (places + 4), tmp1); /* x ^ 2 */
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m_apm_multiply(t4, t2, t2); /* x ^ 4 */
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m_apm_subtract(tmp0, t4, t2);
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m_apm_multiply(tmp1, tmp0, MM_5x_Eight);
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m_apm_add(tmp0, MM_One, tmp1);
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m_apm_round(rr, places, tmp0);
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M_restore_stack(4);
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}
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/****************************************************************************/
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/*
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* compute r = sqrt(1 - a ^ 2).
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*/
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void M_cos_to_sin(M_APM r, int places, M_APM a)
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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_apm_multiply(tmp1, a, a);
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m_apm_subtract(tmp2, MM_One, tmp1);
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m_apm_sqrt(r, places, tmp2);
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M_restore_stack(2);
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}
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/****************************************************************************/
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