1 /* atan2q.c -- __float128 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 atan2q(y,x)=-atan2q(-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
atan2q(__float128 y,__float128 x)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=1.0Q */
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  3.0Q*pi_o_4+tiny;/*atan(+INF,-INF)*/
89 		    case 3: return -3.0Q*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=0.0Q; 		/* |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