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      1 /* e_atan2l.c -- long double version of e_atan2.c.
      2  * Conversion to long double by Jakub Jelinek, jj (at) 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 }
    121