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 long double
      47  tiny  = 1.0e-300L,
      48  zero  = 0.0,
      49  pi_o_4  = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */
      50  pi_o_2  = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */
      51  pi      = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */
      52  pi_lo   = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */
      53  
      54  long double
      55  __ieee754_atan2l(long double y, long double x)
      56  {
      57  	long double z;
      58  	int64_t k,m,hx,hy,ix,iy;
      59  	uint64_t lx;
      60  	double xhi, xlo, yhi;
      61  
      62  	ldbl_unpack (x, &xhi, &xlo);
      63  	EXTRACT_WORDS64 (hx, xhi);
      64  	EXTRACT_WORDS64 (lx, xlo);
      65  	ix = hx&0x7fffffffffffffffLL;
      66  	yhi = ldbl_high (y);
      67  	EXTRACT_WORDS64 (hy, yhi);
      68  	iy = hy&0x7fffffffffffffffLL;
      69  	if(((ix)>0x7ff0000000000000LL)||
      70  	   ((iy)>0x7ff0000000000000LL))	/* x or y is NaN */
      71  	   return x+y;
      72  	if(((hx-0x3ff0000000000000LL))==0
      73  	   && (lx&0x7fffffffffffffff)==0) return __atanl(y);   /* x=1.0L */
      74  	m = ((hy>>63)&1)|((hx>>62)&2);	/* 2*sign(x)+sign(y) */
      75  
      76      /* when y = 0 */
      77  	if(iy==0) {
      78  	    switch(m) {
      79  		case 0:
      80  		case 1: return y;	/* atan(+-0,+anything)=+-0 */
      81  		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
      82  		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
      83  	    }
      84  	}
      85      /* when x = 0 */
      86  	if(ix==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
      87  
      88      /* when x is INF */
      89  	if(ix==0x7ff0000000000000LL) {
      90  	    if(iy==0x7ff0000000000000LL) {
      91  		switch(m) {
      92  		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
      93  		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
      94  		    case 2: return  3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/
      95  		    case 3: return -3.0L*pi_o_4-tiny;/*atan(-INF,-INF)*/
      96  		}
      97  	    } else {
      98  		switch(m) {
      99  		    case 0: return  zero  ;	/* atan(+...,+INF) */
     100  		    case 1: return -zero  ;	/* atan(-...,+INF) */
     101  		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
     102  		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
     103  		}
     104  	    }
     105  	}
     106      /* when y is INF */
     107  	if(iy==0x7ff0000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
     108  
     109      /* compute y/x */
     110  	k = (iy-ix)>>52;
     111  	if(k > 120) z=pi_o_2+0.5L*pi_lo;	/* |y/x| >  2**120 */
     112  	else if(hx<0&&k<-120) z=0.0L;		/* |y|/x < -2**120 */
     113  	else z=__atanl(fabsl(y/x));		/* safe to do y/x */
     114  	switch (m) {
     115  	    case 0: return       z  ;	/* atan(+,+) */
     116  	    case 1: 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)