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