//===========================================================================
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//===========================================================================
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//
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//
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// e_asin.c
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// e_asin.c
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//
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//
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// Part of the standard mathematical function library
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// Part of the standard mathematical function library
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//
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//
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//===========================================================================
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//===========================================================================
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//####ECOSGPLCOPYRIGHTBEGIN####
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//####ECOSGPLCOPYRIGHTBEGIN####
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// -------------------------------------------
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// -------------------------------------------
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// This file is part of eCos, the Embedded Configurable Operating System.
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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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// Copyright (C) 1998, 1999, 2000, 2001, 2002 Red Hat, Inc.
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//
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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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// 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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// 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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// Software Foundation; either version 2 or (at your option) any later version.
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//
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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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// 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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// 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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// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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// for more details.
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// for more details.
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//
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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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// 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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// 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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// 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
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//
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//
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// As a special exception, if other files instantiate templates or use macros
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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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// 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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// 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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// 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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// 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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// in accordance with section (3) of the GNU General Public License.
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//
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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 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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// this file might be covered by the GNU General Public License.
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//
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//
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// Alternative licenses for eCos may be arranged by contacting Red Hat, Inc.
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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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// at http://sources.redhat.com/ecos/ecos-license/
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// -------------------------------------------
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// -------------------------------------------
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//####ECOSGPLCOPYRIGHTEND####
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//####ECOSGPLCOPYRIGHTEND####
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//===========================================================================
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//===========================================================================
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//#####DESCRIPTIONBEGIN####
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//#####DESCRIPTIONBEGIN####
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//
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//
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// Author(s): jlarmour
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// Author(s): jlarmour
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// Contributors: jlarmour
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// Contributors: jlarmour
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// Date: 1998-02-13
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// Date: 1998-02-13
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// Purpose:
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// Purpose:
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// Description:
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// Description:
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// Usage:
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// Usage:
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//
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//
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//####DESCRIPTIONEND####
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//####DESCRIPTIONEND####
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//
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//
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//===========================================================================
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//===========================================================================
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// CONFIGURATION
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// CONFIGURATION
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#include <pkgconf/libm.h> // Configuration header
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#include <pkgconf/libm.h> // Configuration header
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// Include the Math library?
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// Include the Math library?
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#ifdef CYGPKG_LIBM
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#ifdef CYGPKG_LIBM
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// Derived from code with the following copyright
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// Derived from code with the following copyright
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/* @(#)e_asin.c 1.3 95/01/18 */
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/* @(#)e_asin.c 1.3 95/01/18 */
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/*
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/*
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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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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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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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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*/
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*/
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/* __ieee754_asin(x)
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/* __ieee754_asin(x)
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* Method :
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* Method :
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* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
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* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
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* we approximate asin(x) on [0,0.5] by
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* we approximate asin(x) on [0,0.5] by
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* asin(x) = x + x*x^2*R(x^2)
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* asin(x) = x + x*x^2*R(x^2)
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* where
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* where
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* R(x^2) is a rational approximation of (asin(x)-x)/x^3
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* R(x^2) is a rational approximation of (asin(x)-x)/x^3
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* and its remez error is bounded by
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* and its remez error is bounded by
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* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
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* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
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*
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*
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* For x in [0.5,1]
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* For x in [0.5,1]
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* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
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* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
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* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
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* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
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* then for x>0.98
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* then for x>0.98
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
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* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
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* For x<=0.98, let pio4_hi = pio2_hi/2, then
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* For x<=0.98, let pio4_hi = pio2_hi/2, then
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* f = hi part of s;
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* f = hi part of s;
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* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
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* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
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* and
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* and
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
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* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
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* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
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* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
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*
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*
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* Special cases:
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* Special cases:
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* if x is NaN, return x itself;
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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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* if |x|>1, return NaN with invalid signal.
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*
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*
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*/
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*/
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#include "mathincl/fdlibm.h"
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#include "mathincl/fdlibm.h"
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static const double
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static const double
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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huge = 1.000e+300,
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huge = 1.000e+300,
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pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 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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pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
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pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
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pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
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/* coefficient for R(x^2) */
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/* coefficient for R(x^2) */
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pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
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pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
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pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
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pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
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pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
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pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
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pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
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pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
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pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
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pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
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pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
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pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
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qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
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qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
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qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
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qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
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qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
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qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
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qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
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qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
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double __ieee754_asin(double x)
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double __ieee754_asin(double x)
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{
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{
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double t,w,p,q,c,r,s;
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double t,w,p,q,c,r,s;
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int hx,ix;
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int hx,ix;
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hx = CYG_LIBM_HI(x);
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hx = CYG_LIBM_HI(x);
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ix = hx&0x7fffffff;
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ix = hx&0x7fffffff;
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if(ix>= 0x3ff00000) { /* |x|>= 1 */
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if(ix>= 0x3ff00000) { /* |x|>= 1 */
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if(((ix-0x3ff00000)|CYG_LIBM_LO(x))==0)
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if(((ix-0x3ff00000)|CYG_LIBM_LO(x))==0)
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/* asin(1)=+-pi/2 with inexact */
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/* asin(1)=+-pi/2 with inexact */
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return x*pio2_hi+x*pio2_lo;
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return x*pio2_hi+x*pio2_lo;
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return (x-x)/(x-x); /* asin(|x|>1) is NaN */
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return (x-x)/(x-x); /* asin(|x|>1) is NaN */
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} else if (ix<0x3fe00000) { /* |x|<0.5 */
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} else if (ix<0x3fe00000) { /* |x|<0.5 */
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if(ix<0x3e400000) { /* if |x| < 2**-27 */
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if(ix<0x3e400000) { /* if |x| < 2**-27 */
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if(huge+x>one) return x;/* return x with inexact if x!=0*/
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if(huge+x>one) return x;/* return x with inexact if x!=0*/
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} else {
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} else {
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t = x*x;
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t = x*x;
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p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
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p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
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q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
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q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
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w = p/q;
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w = p/q;
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return x+x*w;
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return x+x*w;
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}
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}
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}
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}
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/* 1> |x|>= 0.5 */
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/* 1> |x|>= 0.5 */
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w = one-fabs(x);
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w = one-fabs(x);
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t = w*0.5;
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t = w*0.5;
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p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
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p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
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q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
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q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
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s = sqrt(t);
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s = sqrt(t);
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if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
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if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
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w = p/q;
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w = p/q;
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t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
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t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
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} else {
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} else {
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w = s;
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w = s;
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CYG_LIBM_LO(w) = 0;
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CYG_LIBM_LO(w) = 0;
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c = (t-w*w)/(s+w);
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c = (t-w*w)/(s+w);
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r = p/q;
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r = p/q;
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p = 2.0*s*r-(pio2_lo-2.0*c);
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p = 2.0*s*r-(pio2_lo-2.0*c);
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q = pio4_hi-2.0*w;
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q = pio4_hi-2.0*w;
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t = pio4_hi-(p-q);
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t = pio4_hi-(p-q);
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}
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}
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if(hx>0) return t; else return -t;
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if(hx>0) return t; else return -t;
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}
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}
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#endif // ifdef CYGPKG_LIBM
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#endif // ifdef CYGPKG_LIBM
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// EOF e_asin.c
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// EOF e_asin.c
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