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
45static const __float128
46tiny  = 1.0e-4900Q,
47zero  = 0.0,
48pi_o_4  = 7.85398163397448309615660845819875699e-01Q, /* 3ffe921fb54442d18469898cc51701b8 */
49pi_o_2  = 1.57079632679489661923132169163975140e+00Q, /* 3fff921fb54442d18469898cc51701b8 */
50pi      = 3.14159265358979323846264338327950280e+00Q, /* 4000921fb54442d18469898cc51701b8 */
51pi_lo   = 8.67181013012378102479704402604335225e-35Q; /* 3f8dcd129024e088a67cc74020bbea64 */
52
53__float128
54atan2q (__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