1  /* e_atan2l.c -- long double version of e_atan2.c.
       2   * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
       3   */
       4  
       5  /*
       6   * ====================================================
       7   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       8   *
       9   * Developed at SunPro, a Sun Microsystems, Inc. business.
      10   * Permission to use, copy, modify, and distribute this
      11   * software is freely granted, provided that this notice
      12   * is preserved.
      13   * ====================================================
      14   */
      15  
      16  /* atan2q(y,x)
      17   * Method :
      18   *	1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x).
      19   *	2. Reduce x to positive by (if x and y are unexceptional):
      20   *		ARG (x+iy) = arctan(y/x)	   ... if x > 0,
      21   *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
      22   *
      23   * Special cases:
      24   *
      25   *	ATAN2((anything), NaN ) is NaN;
      26   *	ATAN2(NAN , (anything) ) is NaN;
      27   *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
      28   *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
      29   *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
      30   *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
      31   *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
      32   *	ATAN2(+-INF,+INF ) is +-pi/4 ;
      33   *	ATAN2(+-INF,-INF ) is +-3pi/4;
      34   *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
      35   *
      36   * Constants:
      37   * The hexadecimal values are the intended ones for the following
      38   * constants. The decimal values may be used, provided that the
      39   * compiler will convert from decimal to binary accurately enough
      40   * to produce the hexadecimal values shown.
      41   */
      42  
      43  #include "quadmath-imp.h"
      44  
      45  static const __float128
      46  tiny  = 1.0e-4900Q,
      47  zero  = 0.0,
      48  pi_o_4  = 7.85398163397448309615660845819875699e-01Q, /* 3ffe921fb54442d18469898cc51701b8 */
      49  pi_o_2  = 1.57079632679489661923132169163975140e+00Q, /* 3fff921fb54442d18469898cc51701b8 */
      50  pi      = 3.14159265358979323846264338327950280e+00Q, /* 4000921fb54442d18469898cc51701b8 */
      51  pi_lo   = 8.67181013012378102479704402604335225e-35Q; /* 3f8dcd129024e088a67cc74020bbea64 */
      52  
      53  __float128
      54  atan2q(__float128 y, __float128 x)
      55  {
      56  	__float128 z;
      57  	int64_t k,m,hx,hy,ix,iy;
      58  	uint64_t lx,ly;
      59  
      60  	GET_FLT128_WORDS64(hx,lx,x);
      61  	ix = hx&0x7fffffffffffffffLL;
      62  	GET_FLT128_WORDS64(hy,ly,y);
      63  	iy = hy&0x7fffffffffffffffLL;
      64  	if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)||
      65  	   ((iy|((ly|-ly)>>63))>0x7fff000000000000LL))	/* x or y is NaN */
      66  	   return x+y;
      67  	if(((hx-0x3fff000000000000LL)|lx)==0) return atanq(y);   /* x=1.0L */
      68  	m = ((hy>>63)&1)|((hx>>62)&2);	/* 2*sign(x)+sign(y) */
      69  
      70      /* when y = 0 */
      71  	if((iy|ly)==0) {
      72  	    switch(m) {
      73  		case 0:
      74  		case 1: return y;	/* atan(+-0,+anything)=+-0 */
      75  		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
      76  		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
      77  	    }
      78  	}
      79      /* when x = 0 */
      80  	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
      81  
      82      /* when x is INF */
      83  	if(ix==0x7fff000000000000LL) {
      84  	    if(iy==0x7fff000000000000LL) {
      85  		switch(m) {
      86  		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
      87  		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
      88  		    case 2: return  3*pi_o_4+tiny;/*atan(+INF,-INF)*/
      89  		    case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/
      90  		}
      91  	    } else {
      92  		switch(m) {
      93  		    case 0: return  zero  ;	/* atan(+...,+INF) */
      94  		    case 1: return -zero  ;	/* atan(-...,+INF) */
      95  		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
      96  		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
      97  		}
      98  	    }
      99  	}
     100      /* when y is INF */
     101  	if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
     102  
     103      /* compute y/x */
     104  	k = (iy-ix)>>48;
     105  	if(k > 120) z=pi_o_2+0.5Q*pi_lo;	/* |y/x| >  2**120 */
     106  	else if(hx<0&&k<-120) z=0;		/* |y|/x < -2**120 */
     107  	else z=atanq(fabsq(y/x));		/* safe to do y/x */
     108  	switch (m) {
     109  	    case 0: return       z  ;	/* atan(+,+) */
     110  	    case 1: {
     111  		      uint64_t zh;
     112  		      GET_FLT128_MSW64(zh,z);
     113  		      SET_FLT128_MSW64(z,zh ^ 0x8000000000000000ULL);
     114  		    }
     115  		    return       z  ;	/* atan(-,+) */
     116  	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
     117  	    default: /* case 3 */
     118  		    return  (z-pi_lo)-pi;/* atan(-,-) */
     119  	}
     120  }