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