1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /* __ieee754_atan2(y,x)
13 * Method :
14 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
15 * 2. Reduce x to positive by (if x and y are unexceptional):
16 * ARG (x+iy) = arctan(y/x) ... if x > 0,
17 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
18 *
19 * Special cases:
20 *
21 * ATAN2((anything), NaN ) is NaN;
22 * ATAN2(NAN , (anything) ) is NaN;
23 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
24 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
25 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
26 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
27 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
28 * ATAN2(+-INF,+INF ) is +-pi/4 ;
29 * ATAN2(+-INF,-INF ) is +-3pi/4;
30 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
31 *
32 * Constants:
33 * The hexadecimal values are the intended ones for the following
34 * constants. The decimal values may be used, provided that the
35 * compiler will convert from decimal to binary accurately enough
36 * to produce the hexadecimal values shown.
37 */
38
39 #include "math.h"
40 #include "math_private.h"
41
42 static const double
43 tiny = 1.0e-300,
44 zero = 0.0,
45 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
46 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
47 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
48 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
49
__ieee754_atan2(double y,double x)50 double __ieee754_atan2(double y, double x)
51 {
52 double z;
53 int32_t k,m,hx,hy,ix,iy;
54 u_int32_t lx,ly;
55
56 EXTRACT_WORDS(hx,lx,x);
57 ix = hx&0x7fffffff;
58 EXTRACT_WORDS(hy,ly,y);
59 iy = hy&0x7fffffff;
60 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
61 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
62 return x+y;
63 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
64 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
65
66 /* when y = 0 */
67 if((iy|ly)==0) {
68 switch(m) {
69 case 0:
70 case 1: return y; /* atan(+-0,+anything)=+-0 */
71 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
72 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
73 }
74 }
75 /* when x = 0 */
76 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
77
78 /* when x is INF */
79 if(ix==0x7ff00000) {
80 if(iy==0x7ff00000) {
81 switch(m) {
82 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
83 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
84 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
85 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
86 }
87 } else {
88 switch(m) {
89 case 0: return zero ; /* atan(+...,+INF) */
90 case 1: return -zero ; /* atan(-...,+INF) */
91 case 2: return pi+tiny ; /* atan(+...,-INF) */
92 case 3: return -pi-tiny ; /* atan(-...,-INF) */
93 }
94 }
95 }
96 /* when y is INF */
97 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
98
99 /* compute y/x */
100 k = (iy-ix)>>20;
101 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
102 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
103 else z=atan(fabs(y/x)); /* safe to do y/x */
104 switch (m) {
105 case 0: return z ; /* atan(+,+) */
106 case 1: {
107 u_int32_t zh;
108 GET_HIGH_WORD(zh,z);
109 SET_HIGH_WORD(z,zh ^ 0x80000000);
110 }
111 return z ; /* atan(-,+) */
112 case 2: return pi-(z-pi_lo);/* atan(+,-) */
113 default: /* case 3 */
114 return (z-pi_lo)-pi;/* atan(-,-) */
115 }
116 }
117
118 /*
119 * wrapper atan2(y,x)
120 */
121 #ifndef _IEEE_LIBM
atan2(double y,double x)122 double atan2(double y, double x)
123 {
124 double z = __ieee754_atan2(y, x);
125 if (_LIB_VERSION == _IEEE_ || isnan(x) || isnan(y))
126 return z;
127 if (x == 0.0 && y == 0.0)
128 return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */
129 return z;
130 }
131 #else
132 strong_alias(__ieee754_atan2, atan2)
133 #endif
134 libm_hidden_def(atan2)
135