1  /* e_atan2l.c -- long double version of e_atan2.c.
       2   */
       3  
       4  /*
       5   * ====================================================
       6   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       7   *
       8   * Developed at SunPro, a Sun Microsystems, Inc. business.
       9   * Permission to use, copy, modify, and distribute this
      10   * software is freely granted, provided that this notice
      11   * is preserved.
      12   * ====================================================
      13   */
      14  
      15  /* __ieee754_atan2l(y,x)
      16   * Method :
      17   *	1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x).
      18   *	2. Reduce x to positive by (if x and y are unexceptional):
      19   *		ARG (x+iy) = arctan(y/x)	   ... if x > 0,
      20   *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
      21   *
      22   * Special cases:
      23   *
      24   *	ATAN2((anything), NaN ) is NaN;
      25   *	ATAN2(NAN , (anything) ) is NaN;
      26   *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
      27   *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
      28   *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
      29   *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
      30   *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
      31   *	ATAN2(+-INF,+INF ) is +-pi/4 ;
      32   *	ATAN2(+-INF,-INF ) is +-3pi/4;
      33   *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
      34   *
      35   * Constants:
      36   * The hexadecimal values are the intended ones for the following
      37   * constants. The decimal values may be used, provided that the
      38   * compiler will convert from decimal to binary accurately enough
      39   * to produce the hexadecimal values shown.
      40   */
      41  
      42  #include <math.h>
      43  #include <math_private.h>
      44  #include <libm-alias-finite.h>
      45  
      46  static const _Float128
      47  tiny  = L(1.0e-4900),
      48  zero  = 0.0,
      49  pi_o_4  = L(7.85398163397448309615660845819875699e-01), /* 3ffe921fb54442d18469898cc51701b8 */
      50  pi_o_2  = L(1.57079632679489661923132169163975140e+00), /* 3fff921fb54442d18469898cc51701b8 */
      51  pi      = L(3.14159265358979323846264338327950280e+00), /* 4000921fb54442d18469898cc51701b8 */
      52  pi_lo   = L(8.67181013012378102479704402604335225e-35); /* 3f8dcd129024e088a67cc74020bbea64 */
      53  
      54  _Float128
      55  __ieee754_atan2l(_Float128 y, _Float128 x)
      56  {
      57  	_Float128 z;
      58  	int64_t k,m,hx,hy,ix,iy;
      59  	uint64_t lx,ly;
      60  
      61  	GET_LDOUBLE_WORDS64(hx,lx,x);
      62  	ix = hx&0x7fffffffffffffffLL;
      63  	GET_LDOUBLE_WORDS64(hy,ly,y);
      64  	iy = hy&0x7fffffffffffffffLL;
      65  	if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)||
      66  	   ((iy|((ly|-ly)>>63))>0x7fff000000000000LL))	/* x or y is NaN */
      67  	   return x+y;
      68  	if(((hx-0x3fff000000000000LL)|lx)==0) return __atanl(y);   /* x=1.0L */
      69  	m = ((hy>>63)&1)|((hx>>62)&2);	/* 2*sign(x)+sign(y) */
      70  
      71      /* when y = 0 */
      72  	if((iy|ly)==0) {
      73  	    switch(m) {
      74  		case 0:
      75  		case 1: return y;	/* atan(+-0,+anything)=+-0 */
      76  		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
      77  		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
      78  	    }
      79  	}
      80      /* when x = 0 */
      81  	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
      82  
      83      /* when x is INF */
      84  	if(ix==0x7fff000000000000LL) {
      85  	    if(iy==0x7fff000000000000LL) {
      86  		switch(m) {
      87  		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
      88  		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
      89  		    case 2: return  3*pi_o_4+tiny;/*atan(+INF,-INF)*/
      90  		    case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/
      91  		}
      92  	    } else {
      93  		switch(m) {
      94  		    case 0: return  zero  ;	/* atan(+...,+INF) */
      95  		    case 1: return -zero  ;	/* atan(-...,+INF) */
      96  		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
      97  		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
      98  		}
      99  	    }
     100  	}
     101      /* when y is INF */
     102  	if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
     103  
     104      /* compute y/x */
     105  	k = (iy-ix)>>48;
     106  	if(k > 120) z=pi_o_2+L(0.5)*pi_lo;	/* |y/x| >  2**120 */
     107  	else if(hx<0&&k<-120) z=0;		/* |y|/x < -2**120 */
     108  	else z=__atanl(fabsl(y/x));		/* safe to do y/x */
     109  	switch (m) {
     110  	    case 0: return       z  ;	/* atan(+,+) */
     111  	    case 1: {
     112  		      uint64_t zh;
     113  		      GET_LDOUBLE_MSW64(zh,z);
     114  		      SET_LDOUBLE_MSW64(z,zh ^ 0x8000000000000000ULL);
     115  		    }
     116  		    return       z  ;	/* atan(-,+) */
     117  	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
     118  	    default: /* case 3 */
     119  		    return  (z-pi_lo)-pi;/* atan(-,-) */
     120  	}
     121  }
     122  libm_alias_finite (__ieee754_atan2l, __atan2l)