text: /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
   *
   * ***** BEGIN LICENSE BLOCK *****
   * Version: MPL 1.1/GPL 2.0/LGPL 2.1
   *
   * The contents of this file are subject to the Mozilla Public License Version
   * 1.1 (the "License"); you may not use this file except in compliance with
   * the License. You may obtain a copy of the License at
   * http://www.mozilla.org/MPL/
   *
   * Software distributed under the License is distributed on an "AS IS" basis,
   * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
   * for the specific language governing rights and limitations under the
   * License.
   *
   * The Original Code is Mozilla Communicator client code, released
   * March 31, 1998.
   *
   * The Initial Developer of the Original Code is
   * Sun Microsystems, Inc.
   * Portions created by the Initial Developer are Copyright (C) 1998
   * the Initial Developer. All Rights Reserved.
   *
   * Contributor(s):
   *
   * Alternatively, the contents of this file may be used under the terms of
   * either of the GNU General Public License Version 2 or later (the "GPL"),
   * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
   * in which case the provisions of the GPL or the LGPL are applicable instead
   * of those above. If you wish to allow use of your version of this file only
   * under the terms of either the GPL or the LGPL, and not to allow others to
   * use your version of this file under the terms of the MPL, indicate your
   * decision by deleting the provisions above and replace them with the notice
   * and other provisions required by the GPL or the LGPL. If you do not delete
   * the provisions above, a recipient may use your version of this file under
   * the terms of any one of the MPL, the GPL or the LGPL.
   *
   * ***** END LICENSE BLOCK ***** */
  
  /* @(#)e_atan2.c 1.3 95/01/18 */
  /*
   * ====================================================
   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   *
   * Developed at SunSoft, a Sun Microsystems, Inc. business.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice 
   * is preserved.
   * ====================================================
   *
   */
  
  /* __ieee754_atan2(y,x)
   * Method :
   *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
   *	2. Reduce x to positive by (if x and y are unexceptional): 
   *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
   *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
   *
   * Special cases:
   *
   *	ATAN2((anything), NaN ) is NaN;
   *	ATAN2(NAN , (anything) ) is NaN;
   *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
   *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
   *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
   *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
   *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
   *	ATAN2(+-INF,+INF ) is +-pi/4 ;
   *	ATAN2(+-INF,-INF ) is +-3pi/4;
   *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
   *
   * Constants:
   * The hexadecimal values are the intended ones for the following 
   * constants. The decimal values may be used, provided that the 
   * compiler will convert from decimal to binary accurately enough 
   * to produce the hexadecimal values shown.
   */
  
  #include "fdlibm.h"
  
  #ifdef __STDC__
  static const double 
  #else
  static double 
  #endif
  tiny  = 1.0e-300,
  zero  = 0.0,
  pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  
  #ifdef __STDC__
  	double __ieee754_atan2(double y, double x)
  #else
  	double __ieee754_atan2(y,x)
  	double  y,x;
  #endif
  {  
          fd_twoints ux, uy, uz;
  	double z;
  	int k,m,hx,hy,ix,iy;
  	unsigned lx,ly;
  
          ux.d = x; uy.d = y;
  	hx = __HI(ux); ix = hx&0x7fffffff;
  	lx = __LO(ux);
  	hy = __HI(uy); iy = hy&0x7fffffff;
  	ly = __LO(uy);
  	if(((ix|((lx|-(int)lx)>>31))>0x7ff00000)||
  	   ((iy|((ly|-(int)ly)>>31))>0x7ff00000))	/* x or y is NaN */
  	   return x+y;
  	if(((hx-0x3ff00000)|lx)==0) return fd_atan(y);   /* x=1.0 */
  	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
  
      /* when y = 0 */
  	if((iy|ly)==0) {
  	    switch(m) {
  		case 0: 
  		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
  		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  	    }
  	}
      /* when x = 0 */
  	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  	    
      /* when x is INF */
  	if(ix==0x7ff00000) {
  	    if(iy==0x7ff00000) {
  		switch(m) {
  		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  		    case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
  		    case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
  		}
  	    } else {
  		switch(m) {
  		    case 0: return  zero  ;	/* atan(+...,+INF) */
  		    case 1: return -zero  ;	/* atan(-...,+INF) */
  		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
  		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
  		}
  	    }
  	}
      /* when y is INF */
  	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
  
      /* compute y/x */
  	k = (iy-ix)>>20;
  	if(k > 60) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**60 */
  	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
  	else z=fd_atan(fd_fabs(y/x));		/* safe to do y/x */
  	switch (m) {
  	    case 0: return       z  ;	/* atan(+,+) */
  	    case 1: uz.d = z;
                      __HI(uz) ^= 0x80000000;
                      z = uz.d;
  		    return       z  ;	/* atan(-,+) */
  	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
  	    default: /* case 3 */
  	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
  	}
  }
  