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f964490f | 1 | /* e_atan2l.c -- long double version of e_atan2.c. |
f964490f RM |
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): | |
0ac5ae23 | 19 | * ARG (x+iy) = arctan(y/x) ... if x > 0, |
f964490f RM |
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 | ||
1ed0291c RH |
42 | #include <math.h> |
43 | #include <math_private.h> | |
220622dd | 44 | #include <libm-alias-finite.h> |
f964490f | 45 | |
f964490f | 46 | static const long double |
f964490f RM |
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 | ||
0ac5ae23 UD |
54 | long double |
55 | __ieee754_atan2l(long double y, long double x) | |
f964490f RM |
56 | { |
57 | long double z; | |
58 | int64_t k,m,hx,hy,ix,iy; | |
765714ca AM |
59 | uint64_t lx; |
60 | double xhi, xlo, yhi; | |
f964490f | 61 | |
765714ca AM |
62 | ldbl_unpack (x, &xhi, &xlo); |
63 | EXTRACT_WORDS64 (hx, xhi); | |
64 | EXTRACT_WORDS64 (lx, xlo); | |
f964490f | 65 | ix = hx&0x7fffffffffffffffLL; |
765714ca AM |
66 | yhi = ldbl_high (y); |
67 | EXTRACT_WORDS64 (hy, yhi); | |
f964490f RM |
68 | iy = hy&0x7fffffffffffffffLL; |
69 | if(((ix)>0x7ff0000000000000LL)|| | |
70 | ((iy)>0x7ff0000000000000LL)) /* x or y is NaN */ | |
71 | return x+y; | |
16a0e2ec JM |
72 | if(((hx-0x3ff0000000000000LL))==0 |
73 | && (lx&0x7fffffffffffffff)==0) return __atanl(y); /* x=1.0L */ | |
f964490f RM |
74 | m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */ |
75 | ||
76 | /* when y = 0 */ | |
765714ca | 77 | if(iy==0) { |
f964490f RM |
78 | switch(m) { |
79 | case 0: | |
0ac5ae23 | 80 | case 1: return y; /* atan(+-0,+anything)=+-0 */ |
f964490f RM |
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 */ | |
765714ca | 86 | if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
f964490f RM |
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; | |
0ac5ae23 UD |
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 */ | |
f964490f RM |
113 | else z=__atanl(fabsl(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 */ | |
0ac5ae23 | 119 | return (z-pi_lo)-pi;/* atan(-,-) */ |
f964490f RM |
120 | } |
121 | } | |
220622dd | 122 | libm_alias_finite (__ieee754_atan2l, __atan2l) |