1 | /* e_atan2l.c -- long double version of e_atan2.c. |
2 | */ |
3 | |
4 | /* |
5 | * ==================================================== |
6 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
7 | * |
8 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
9 | * Permission to use, copy, modify, and distribute this |
10 | * software is freely granted, provided that this notice |
11 | * is preserved. |
12 | * ==================================================== |
13 | */ |
14 | |
15 | /* __ieee754_atan2l(y,x) |
16 | * Method : |
17 | * 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x). |
18 | * 2. Reduce x to positive by (if x and y are unexceptional): |
19 | * ARG (x+iy) = arctan(y/x) ... if x > 0, |
20 | * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, |
21 | * |
22 | * Special cases: |
23 | * |
24 | * ATAN2((anything), NaN ) is NaN; |
25 | * ATAN2(NAN , (anything) ) is NaN; |
26 | * ATAN2(+-0, +(anything but NaN)) is +-0 ; |
27 | * ATAN2(+-0, -(anything but NaN)) is +-pi ; |
28 | * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; |
29 | * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; |
30 | * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; |
31 | * ATAN2(+-INF,+INF ) is +-pi/4 ; |
32 | * ATAN2(+-INF,-INF ) is +-3pi/4; |
33 | * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; |
34 | * |
35 | * Constants: |
36 | * The hexadecimal values are the intended ones for the following |
37 | * constants. The decimal values may be used, provided that the |
38 | * compiler will convert from decimal to binary accurately enough |
39 | * to produce the hexadecimal values shown. |
40 | */ |
41 | |
42 | #include <math.h> |
43 | #include <math_private.h> |
44 | #include <libm-alias-finite.h> |
45 | |
46 | static const long double |
47 | tiny = 1.0e-300L, |
48 | zero = 0.0, |
49 | pi_o_4 = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */ |
50 | pi_o_2 = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */ |
51 | pi = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */ |
52 | pi_lo = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */ |
53 | |
54 | long double |
55 | __ieee754_atan2l(long double y, long double x) |
56 | { |
57 | long double z; |
58 | int64_t k,m,hx,hy,ix,iy; |
59 | uint64_t lx; |
60 | double xhi, xlo, yhi; |
61 | |
62 | ldbl_unpack (x, &xhi, &xlo); |
63 | EXTRACT_WORDS64 (hx, xhi); |
64 | EXTRACT_WORDS64 (lx, xlo); |
65 | ix = hx&0x7fffffffffffffffLL; |
66 | yhi = ldbl_high (y); |
67 | EXTRACT_WORDS64 (hy, yhi); |
68 | iy = hy&0x7fffffffffffffffLL; |
69 | if(((ix)>0x7ff0000000000000LL)|| |
70 | ((iy)>0x7ff0000000000000LL)) /* x or y is NaN */ |
71 | return x+y; |
72 | if(((hx-0x3ff0000000000000LL))==0 |
73 | && (lx&0x7fffffffffffffff)==0) return __atanl(x: y); /* x=1.0L */ |
74 | m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */ |
75 | |
76 | /* when y = 0 */ |
77 | if(iy==0) { |
78 | switch(m) { |
79 | case 0: |
80 | case 1: return y; /* atan(+-0,+anything)=+-0 */ |
81 | case 2: return pi+tiny;/* atan(+0,-anything) = pi */ |
82 | case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ |
83 | } |
84 | } |
85 | /* when x = 0 */ |
86 | if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
87 | |
88 | /* when x is INF */ |
89 | if(ix==0x7ff0000000000000LL) { |
90 | if(iy==0x7ff0000000000000LL) { |
91 | switch(m) { |
92 | case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ |
93 | case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ |
94 | case 2: return 3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/ |
95 | case 3: return -3.0L*pi_o_4-tiny;/*atan(-INF,-INF)*/ |
96 | } |
97 | } else { |
98 | switch(m) { |
99 | case 0: return zero ; /* atan(+...,+INF) */ |
100 | case 1: return -zero ; /* atan(-...,+INF) */ |
101 | case 2: return pi+tiny ; /* atan(+...,-INF) */ |
102 | case 3: return -pi-tiny ; /* atan(-...,-INF) */ |
103 | } |
104 | } |
105 | } |
106 | /* when y is INF */ |
107 | if(iy==0x7ff0000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
108 | |
109 | /* compute y/x */ |
110 | k = (iy-ix)>>52; |
111 | if(k > 120) z=pi_o_2+0.5L*pi_lo; /* |y/x| > 2**120 */ |
112 | else if(hx<0&&k<-120) z=0.0L; /* |y|/x < -2**120 */ |
113 | else z=__atanl(x: fabsl(x: y/x)); /* safe to do y/x */ |
114 | switch (m) { |
115 | case 0: return z ; /* atan(+,+) */ |
116 | case 1: return -z ; /* atan(-,+) */ |
117 | case 2: return pi-(z-pi_lo);/* atan(+,-) */ |
118 | default: /* case 3 */ |
119 | return (z-pi_lo)-pi;/* atan(-,-) */ |
120 | } |
121 | } |
122 | libm_alias_finite (__ieee754_atan2l, __atan2l) |
123 | |