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//===========================================================================
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//
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// e_acos.c
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//
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// Part of the standard mathematical function library
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//
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//===========================================================================
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//####ECOSGPLCOPYRIGHTBEGIN####
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// -------------------------------------------
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// This file is part of eCos, the Embedded Configurable Operating System.
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// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc.
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//
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// eCos is free software; you can redistribute it and/or modify it under
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// the terms of the GNU General Public License as published by the Free
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// Software Foundation; either version 2 or (at your option) any later version.
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//
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// eCos is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or
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// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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// for more details.
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//
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// You should have received a copy of the GNU General Public License along
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// with eCos; if not, write to the Free Software Foundation, Inc.,
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// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
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//
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// As a special exception, if other files instantiate templates or use macros
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// or inline functions from this file, or you compile this file and link it
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// with other works to produce a work based on this file, this file does not
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// by itself cause the resulting work to be covered by the GNU General Public
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// License. However the source code for this file must still be made available
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// in accordance with section (3) of the GNU General Public License.
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//
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// This exception does not invalidate any other reasons why a work based on
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// this file might be covered by the GNU General Public License.
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//
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// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc.
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// at http://sources.redhat.com/ecos/ecos-license/
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// -------------------------------------------
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//####ECOSGPLCOPYRIGHTEND####
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//===========================================================================
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//#####DESCRIPTIONBEGIN####
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//
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// Author(s): jlarmour
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// Contributors: jlarmour
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// Date: 1998-02-13
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// Purpose:
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// Description:
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// Usage:
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//
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//####DESCRIPTIONEND####
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//
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//===========================================================================
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// CONFIGURATION
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#include <pkgconf/libm.h> // Configuration header
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// Include the Math library?
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#ifdef CYGPKG_LIBM
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// Derived from code with the following copyright
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/* @(#)e_acos.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* __ieee754_acos(x)
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* Method :
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* acos(x) = pi/2 - asin(x)
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* acos(-x) = pi/2 + asin(x)
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* For |x|<=0.5
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* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
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* For x>0.5
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* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
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* = 2asin(sqrt((1-x)/2))
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* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
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* = 2f + (2c + 2s*z*R(z))
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* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
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* for f so that f+c ~ sqrt(z).
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* For x<-0.5
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* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
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* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
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*
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* Special cases:
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* if x is NaN, return x itself;
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* if |x|>1, return NaN with invalid signal.
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*
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* Function needed: sqrt
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*/
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#include "mathincl/fdlibm.h"
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static const double
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one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
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pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
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pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
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pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
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pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
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pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
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pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
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pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
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pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
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qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
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qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
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qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
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qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
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double __ieee754_acos(double x)
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{
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double z,p,q,r,w,s,c,df;
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int hx,ix;
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hx = CYG_LIBM_HI(x);
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ix = hx&0x7fffffff;
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if(ix>=0x3ff00000) { /* |x| >= 1 */
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if(((ix-0x3ff00000)|CYG_LIBM_LO(x))==0) { /* |x|==1 */
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if(hx>0) return 0.0; /* acos(1) = 0 */
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else return pi+2.0*pio2_lo; /* acos(-1)= pi */
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}
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return (x-x)/(x-x); /* acos(|x|>1) is NaN */
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}
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if(ix<0x3fe00000) { /* |x| < 0.5 */
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if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
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z = x*x;
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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r = p/q;
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return pio2_hi - (x - (pio2_lo-x*r));
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} else if (hx<0) { /* x < -0.5 */
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z = (one+x)*0.5;
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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s = sqrt(z);
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r = p/q;
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w = r*s-pio2_lo;
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return pi - 2.0*(s+w);
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} else { /* x > 0.5 */
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z = (one-x)*0.5;
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s = sqrt(z);
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df = s;
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CYG_LIBM_LO(df) = 0;
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c = (z-df*df)/(s+df);
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
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r = p/q;
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w = r*s+c;
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return 2.0*(df+w);
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}
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}
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#endif // ifdef CYGPKG_LIBM
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// EOF e_acos.c
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