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
__ieee754_atan2l(long double y,long double x)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(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(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 */
119 return (z-pi_lo)-pi;/* atan(-,-) */
120 }
121 }
122 libm_alias_finite (__ieee754_atan2l, __atan2l)
123