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0d8733c4 | 1 | /* e_atan2l.c -- long double version of e_atan2.c. |
abfbdde1 | 2 | * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. |
0d8733c4 UD |
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 | ||
0d8733c4 UD |
16 | /* __ieee754_atan2l(y,x) |
17 | * Method : | |
abfbdde1 | 18 | * 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x). |
0d8733c4 | 19 | * 2. Reduce x to positive by (if x and y are unexceptional): |
0ac5ae23 | 20 | * ARG (x+iy) = arctan(y/x) ... if x > 0, |
0d8733c4 UD |
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 | ||
1ed0291c RH |
43 | #include <math.h> |
44 | #include <math_private.h> | |
0d8733c4 | 45 | |
15089e04 | 46 | static const _Float128 |
02bbfb41 | 47 | tiny = L(1.0e-4900), |
0d8733c4 | 48 | zero = 0.0, |
02bbfb41 PM |
49 | pi_o_4 = L(7.85398163397448309615660845819875699e-01), /* 3ffe921fb54442d18469898cc51701b8 */ |
50 | pi_o_2 = L(1.57079632679489661923132169163975140e+00), /* 3fff921fb54442d18469898cc51701b8 */ | |
51 | pi = L(3.14159265358979323846264338327950280e+00), /* 4000921fb54442d18469898cc51701b8 */ | |
52 | pi_lo = L(8.67181013012378102479704402604335225e-35); /* 3f8dcd129024e088a67cc74020bbea64 */ | |
0d8733c4 | 53 | |
15089e04 PM |
54 | _Float128 |
55 | __ieee754_atan2l(_Float128 y, _Float128 x) | |
0d8733c4 | 56 | { |
15089e04 | 57 | _Float128 z; |
abfbdde1 UD |
58 | int64_t k,m,hx,hy,ix,iy; |
59 | u_int64_t lx,ly; | |
0d8733c4 | 60 | |
abfbdde1 UD |
61 | GET_LDOUBLE_WORDS64(hx,lx,x); |
62 | ix = hx&0x7fffffffffffffffLL; | |
63 | GET_LDOUBLE_WORDS64(hy,ly,y); | |
64 | iy = hy&0x7fffffffffffffffLL; | |
65 | if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)|| | |
66 | ((iy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* x or y is NaN */ | |
0d8733c4 | 67 | return x+y; |
dbbbaf53 | 68 | if(((hx-0x3fff000000000000LL)|lx)==0) return __atanl(y); /* x=1.0L */ |
abfbdde1 | 69 | m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */ |
0d8733c4 UD |
70 | |
71 | /* when y = 0 */ | |
72 | if((iy|ly)==0) { | |
73 | switch(m) { | |
74 | case 0: | |
0ac5ae23 | 75 | case 1: return y; /* atan(+-0,+anything)=+-0 */ |
0d8733c4 UD |
76 | case 2: return pi+tiny;/* atan(+0,-anything) = pi */ |
77 | case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ | |
78 | } | |
79 | } | |
80 | /* when x = 0 */ | |
abfbdde1 | 81 | if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
0d8733c4 UD |
82 | |
83 | /* when x is INF */ | |
abfbdde1 UD |
84 | if(ix==0x7fff000000000000LL) { |
85 | if(iy==0x7fff000000000000LL) { | |
0d8733c4 UD |
86 | switch(m) { |
87 | case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ | |
88 | case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ | |
02bbfb41 PM |
89 | case 2: return 3*pi_o_4+tiny;/*atan(+INF,-INF)*/ |
90 | case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/ | |
0d8733c4 UD |
91 | } |
92 | } else { | |
93 | switch(m) { | |
94 | case 0: return zero ; /* atan(+...,+INF) */ | |
95 | case 1: return -zero ; /* atan(-...,+INF) */ | |
96 | case 2: return pi+tiny ; /* atan(+...,-INF) */ | |
97 | case 3: return -pi-tiny ; /* atan(-...,-INF) */ | |
98 | } | |
99 | } | |
100 | } | |
101 | /* when y is INF */ | |
abfbdde1 | 102 | if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
0d8733c4 UD |
103 | |
104 | /* compute y/x */ | |
abfbdde1 | 105 | k = (iy-ix)>>48; |
02bbfb41 PM |
106 | if(k > 120) z=pi_o_2+L(0.5)*pi_lo; /* |y/x| > 2**120 */ |
107 | else if(hx<0&&k<-120) z=0; /* |y|/x < -2**120 */ | |
abfbdde1 | 108 | else z=__atanl(fabsl(y/x)); /* safe to do y/x */ |
0d8733c4 UD |
109 | switch (m) { |
110 | case 0: return z ; /* atan(+,+) */ | |
111 | case 1: { | |
0ac5ae23 | 112 | u_int64_t zh; |
abfbdde1 UD |
113 | GET_LDOUBLE_MSW64(zh,z); |
114 | SET_LDOUBLE_MSW64(z,zh ^ 0x8000000000000000ULL); | |
0d8733c4 UD |
115 | } |
116 | return z ; /* atan(-,+) */ | |
117 | case 2: return pi-(z-pi_lo);/* atan(+,-) */ | |
118 | default: /* case 3 */ | |
0ac5ae23 | 119 | return (z-pi_lo)-pi;/* atan(-,-) */ |
0d8733c4 UD |
120 | } |
121 | } | |
0ac5ae23 | 122 | strong_alias (__ieee754_atan2l, __atan2l_finite) |